Note: Descriptions are shown in the official language in which they were submitted.
~7~ ~7~7
This is a division of copending Canadian Patent Application
~erial Number 379,198~ filed June 8, l9al.
.
. . : . .
MET~OD AND AP _ TUS FOR ANALYSIS O~ CORNEAL SHAPE
.. This invention relates to a method and apparatus
for analy~ing corneal shape. ~ore particularly, a method and
apparatus is disclosed in which the central "k" readings in
eguivalent sphere a~d astigmatism and axis are disclosed, the
corneal shape parameterized, the apex of ~he cornea located
both as to temporal up and down spacing and uncertainty of
location, the cap size specified, the ~ault height predicted,
. the coxrected central k computed, and a goodness of fit
parameter ~enerated which indicates the fit of the model to
the particular eye being measured. Utilization of these
components relative to the fitting of contact lenses is
disclosed~ .
SUMMARY OF THE PRIOR ART
- Corneal shape measurement finds its origi~ in ear~y
woxk by two bxilliant ophthalmic xesearchers~ I~ the year .
1619, Christopher Scheiner ~irst measured the curvature of
the anterior surfa~e of the cornea by comparing th~ size of
the corneal reflex with the ~ize of.the reflex from a series
of glass balls o different size.
The next major step forward in corneAt shape deter-
minations was made by ~ermann von Helmholtz in the X~ lB~6.
Using an image-doubling technique ~imilar to ~ha~ Qf modern
day instruments, Helmholtz devised a specific ~e~s~i~g
. . -- 1 --
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instrument for the study of corneal curvatures. As a practi-
cal matter, extensive use over many years has been made of
instruments similar to the Helmholt2 device with the emphasis
on a determination of the corneal shape at the center of the
S cornea - the so-called "central k reading." Those few aca-
demic studies which have ventured into the area of peripheral
corneal measurements have, for the most paxt~ also been
reliant on the same optical principles of measuring the size
of reflected images from the anterior surface of the cornea.
There are a few exceptions. Some studies have been
carried out using a technique akin to aerial mapping. A
powdery substance is scattered on the surface of the cornea
and stereographic photographs of the cornea are taken. These
particles on the surface of the cornea can then be brought
into coincidence using aerial mapmaking technigues to produce
height contours which represent the corneal shape. Natural-
ly, such measurements have to be carried out with an anesthe-
tized eye because of the irritation of the particle matter
disposed across the cornea (soot or talc, for example). A
related method employing fluorescein dye eliminates the need
for anesthetic. Other studies have been carried out by
taking silouette photographs of the cornea with the camera
arranged 90 to the line of sight. And still further studies
have been carried out by actually pouring moIding material
onto the cornea and then examining a positive cast of the
corneal shape using calipers. These and numerous techniques
including ultrasonic and mechanical tracing devices have
found utility only in the laboratory. The only two currently
used clinical methods are the traditional keratometer similar
to that developed by ~elmholtz and the more recent photo-
graphic methods referred tv as photokeratometers. Each of
these devices has its strengths and weaknesses. For example,
the keratometer (as it is commonly used) provides only infor-
mation near the center of the cornea. Photokeratometers such
as the corneascope, on the other hand, do provide peripheral
information, but apparently at the expense of considerable
difficulty in the analysis or a loss of precision in the
measurement. (Descriptions of such photokeratometers can be
~7~77
found in Townsley, 1967; Clark, 1971i Mandell and St. Helen,
1971; and Knoll, 1961.)
From this brief sketch of the history and the
currently available equipment, it is apparent that the need
for better information regarding corneal shape has been
recognized but that no practical instrument system has yet
been made available to provide the benefits of peripheral
measurements at the clinical level.
The prior art has attempted to measure the curva-
ture of the human cornea by providing fixation targets. Withsuch targets, the eye is aligned at varying angles while the
curvature of the cornea is measured. Through actual experi-
mentation, we have found that prior art keratometers are not
sufficiently accurate to generate useful information about
the corneal shape. Thus, the keratometer disclosed herein
makes possible for the first time the practical utilization
of peripheral targets.
Several method of parameterizing corneal shape have
been suggested in the literature. These methods can be
divided into two classes~
1) those which present lists or graphs of the
size of numerous departures from a reference
surface for various locations on the cornea;
2) those which attempt to distill general shape
in the form of a few shape parameters.
Among schemes of the first type, deviation in
corneal depth from a best fit to the central cornea (either a
sphere or parabola) has been suggested (Clark, 1973, 1974~.
This method is subject to problems in regard to the best fit
procedure for a central region as well as yielding an enor-
mous number of depth deviations that can only be comprehended
in the whole in graphical form. It seems unlikely that such
undistilled, detailed knowledge of the cornea can be easily
used to arrive at a formalized fitting philosophy or to
specify some improved class of contact lens shape, except on
a unigue or custom basis.
Elliptical models of corneal cross section have
been shown to be effective in fitting actual populations of
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corneas (Townsley, 1970). Although many authors parameterize
corneal shape in terms of the eccentricity (e) of an ellipse,
it can be shown that eZ is a far more effective and intuitive
measure of corneal shape. In the "lnl' model developed here,
the shape parameter corresponds very much to e2 in an
ellipsoidal model and should be an equally acceptable parame-
terization of corneal shape.
Several experimental studies which have appeared in
the literature on the subject of corneal shape are worth
mentioning. Examples of the measurement of curvatures of
individual corneas appear in Mandell's book on contact lens
fitting (Mandell, 1976). These curves were developed through
the use of a special small mire keratometer combined with
fixation targets arranged at angular intervals from the
central line of sight.
Five other investigators have published works
employing the photokeratoscope technique. The first study to
appear (Henry A. Knoll, 1961) divided the sample of corneas
into two groups -one having notable asymmetries and the other
bein~ essentially symmetrical. Combining all the results for
the symmetrical corneas, a very acceptable corneal shape fit
is achieved for a value of = . 248.
The second paper (Townsley, 1970) provides an
interesting example of the choice of shape factor and its
influence on the appearance of corneal data. This paper is a
published study of 350 eyes (Townsley, 1970), but this sample
includes 259 patients having a "high content of difficult
cases". The published data of this paper display a format in
which eccentricity (e) was chosen as the shape factor. There
appear to be two populations of people peaked at eccentrici-
ties on either side of zero (spherical corneas) neglecting
- the question of propriety of plotting negative
eccentricities.
The third paper (Robert E. Mandell and Roger
St. Helen, 1971) found a range of eccentricity values of .2
to .85 with an average of .48.
The fourth contribution (Barry A. J. Clark, 1974)
reveals many typical cornea properties based on an analysis
77
of 164 keratograms. The data are fairly complete out ts 2 or
3 mm and indicate a shape factor ~ = .10 i .05, .54 ~ .35
diopter cylinder at 180, .4 mm decentration of the corneal
apex temporal of the visual axis and a cap radius of curva-
ture of 7.759 ~ .260 mm. The data show differing corneal
height at the visual axis for different meridians indicating
these values are by interpolation. The subjects were chosen
to have refractive error less than 1.5 dopter in any meridian
and less than .5 diopter astig~atism.
Additional information on corneal apex position is
provided in the fifth paper (Tomlinson & Schwartz, 1979)
which shows a temporal displacement of the corneal axis from
the visual axis by about .5 mm. About 82% of the corneas had
their axes 1 mm or less from the visual axis. Taking an axis
.5 mm temporal of the visual axis would cause about 87% of
the corneas to fall within 1 mm of the displaced axis. The
"shape factor" for the sample ranged from .26 to .60. The
shape factor employed was established to be eccentricity
squared. This would seem to be a sample based toward large
shape factors. Corneal displacement and radial flattening
were found to be inversely correlated in the temporal
meridian.
Two of the papers (Mandell and St. Helen, 1971;
Clark, ~arch, 1974) provide data illustrating the extent to
which individual "normal" corneas may depart from the ideal-
ized ellipsoidal model usually considered in connection with
the cornea.
Taking the "parameterization" approach to describ-
ing corneal shape, it appears from the literature as a whole
that the typical normal cornea can be characterized as being
roughly ellipsoidal in shape with a shape factor = e2/2 =
- .12 i .06 and with the apex of the ellipsoid decentered
temporal of the visual axis by .4 mm but with 90% Df the
apices falling in a 1 mm reading circle. The central "cap"
of the typical normal cornea has an average radius of curva-
ture of 7.8 ~ .26 mm and .55 i .35 diopters of "with-the-
rule" astigmatism. Individual corneas may depart radically
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from the idealized "typical" cornea, both qualitatively and
guantitatively.
Lens metexs measure the power of the lens in at
least sphere, cylinder and axis. Automated lens meters are
known For example, see my U.S. Patent 4,1~0,325, issued
December 25, 1979, entitled "Lens Meter with Automated Read-
out" and see my U.S. Patent 4,182,572, entitled "Lens Meter
Utilizing Non-Parallel Light", issued January 8, l9B0. In
both these patents, the lens meter manufactured by Humphrey
Instruments, Inc. of San Leandro, California, now a wholly-
~wned subsidiary of SmithKline, Inc., of Philadelphia,
Pennsylvania, is illustrated. In this apparatus, a light
source appears over a broad area. A moving boundary locus is
provided with a conjugate image typically focused to a detec-
tor aperture. Light from four discrete light paths is passedto a pupil or stop at the position of the lens to be sampled.
The lens, in accordance with its power in sphere, cylinder
and axis, causes deflection at the pupil or stop of the image
of the moving boundary locus at the detector aperture. By
timing successive occultations of the area light source at
the detector aperture, one can determine the deflection of
the boundary locus image when passing through the lens and
thus determine the desired measurements in sphere, cylinder
and axis.
Keratometxy involves the measurement of the curva-
ture of the cornea of the eye in at least sphere, cylinder
and axis. However, applying automated lens meter technology
to keratometry has proved to be surprisingly difficult.
First, in a lens meter the measured lens is always positioned
at the same place. In keratometry, positioning of the eye is
not nearly as easy. For example, the eye cannot simply be
rested upon a surface. Requiring the operator to continually
position and reobserve ~he eye to determine that it is and
that it remains in position is not acceptable for an auto-
3~ mated keratometer. This type of positioning is used in myU.S. Patent entitled "Method and Apparatus for the Corneal
Positioning of a Patient's Eye", U.S. Patent 4,189,215,
issued ~ebruary 19, 1980).
. /
It is important to recogni~e that after the eye is
properly positioned, it is a constantly moving target.
Assuming that the patient maintains adequate fixation on the
target, there is at a minimum the underlying saccadic move-
ment of the eye. Complicating factors ~uch as eye blinkingand the like make the measurement of the surface of the eye a
vastly more complicated problem than is suggested by any
remote lens meter.
It has been found that keratometers are particular-
ly sensitive to movement of the human eye towards and awayfrom the instrument. A means of detecting the exact axial
position of the eye with respect to a keratometer is not
suggested or disclosed in the known prior art.
Standard keratometers typically employ a target
mire. In the use of a mire, a large image from known outside
angles is focused onto the surface of the eye. The virtual
image in the cornea of the eye is observed by the eye examin-
er first focusing (to obtain towards and away distance) and
thereafter measuring image size on the eye By determining
along diameters a maximum mire diameter and a minimum mire
diameter, the principal axis, power of sphere and power of
cylinder can all be located, measured and guantified. Diffi-
culties determining axis at low power cylinder are present.
The difficulty of applying the aforementioned prior
art to automated keratometry was in the course of my inven-
tion further complicated by a surprising factor. Specifical-
ly, in actually'testing automated keratometric devices on a
population of humans, I found that eyelashes of some individ-
uals presented surprising interference with the desired
measurements. These eyelash problems came from all se~ments
of the population and were not readily identifiable prior to
- measurement.
It should be understood that holding or bracing of
the eye lashes out of positions of interference with auto-
mated keratometric measurement is unacceptable. First, ifrelatively unskilled instrument operators are used, it is
pxeferable that such operators refrain from all contact with
the human eye. Second, contact with the eye can produce
various accomodative movements, involuntary or otherwise,
which can produce non-representative corneal deformations.
Finally, holding or bracing of the lashes if improperly done
can result in "temporary" corneal deformation. This unex-
pected problem once understood and recognized had to besurmounted.
Some means of measurement around the eyelash there-
fore had to be devised to allow relatively unskilled opera-
tors to make accurate keratometric measurements with the pro-
posed instrument. It will be understood that I -claim both
the recognition of this problem as well as its solution to be
part of my invention hereinafter set forth.
SUMMARY OF THE INVENTION
The curvature and standard dimensions of the con-
tact lens are relatively well known. The lens in its activeportion is 6.3-8.5 mm wide. Overall the lens can be
7-9.5 mm~ The lens includes a base curve, a secondary curve
and a peripheral curve or bevel. It is typically rounded at
~he edges. The typical corneal diameter is on the order of
12 mm.
The ordering and fitting of contact lenses is
typically iterative. Typically, a keratometric method of
sphere, cylinder and axis on the center ~ is taken. Kerato-
metric reading is given, thereafter the refraction is added.
Pupil size is sometimes added and the lens can be ordered.
In a more complete and diagnostic fitting procedure
for contact lens fitting, the above procedure is first uti-
lized. Thereafter, a diagnostic lens is applied. Once the
diagnostic lens is applied, one observes the centration,
movement, subjective comfort, subjective vision and tear
layer, possibly with the conventional fluorozene test for
- determining tear layer thickness. Over-refraction of the
patient is then done to see what additions to prescription
are made due to the present tear layer.
To date, physicians prescribe contact lenses with~
out an accurate corneal map of the patient's eye. Lenses are
commonly fitted for the first time in the presence of artifi-
cial and excessive tearing. This is due to the new and/or
changed addition of the contact lens to the human eye.
Naturally, without a long period of measurement, accurate
measurement of the eye during the first fitting of a contact
lens is not possible.
~ ollow-ups should be routinely done. Typically, a
follow-up measurement of the patient may be done in as little
a time interval as four hours. Thereafter, one week, three
weeks, eight weeks, sixteen weeks checks may be used. Pro-
gress checks should be re~uired every six months.
One of the problems that one has with contact lens
fitting is the penetration of life-giving oxygen to the
cornea. The cornea is typically supplied with oxygen from
the tear surface over the top of it. What one wants to be
careful to prevent is any kind of damage to the cornea. When
a patient comes in for a follow-up, checks on central corneal
clouding are performed. Additionally keratometry changes or
changes in refraction, as well as corneal staining should all
be observed.
The vault height for the clearance between the
contact lens on one hand and the cornea on the other hand is
crucial for soft lenses. In the case of some hard lenses,
where large components of astigmatism originated at the
"toric" cornea, by placement of a hard contact lens over the
eye having a spherical surface, the tear layer filled in what
would otherwise be a gap. By filling in what otherwise would
be a gap, the tear layer applies a lens power.
Fitting of contact lenses thus becomes an extremely
complex problem. Calling the role of the refractive sur-
faces, we have the eye and tear layer. Thereafter we have
the tear layer and the contact lens. Finally, we have the -
contact lens and the atmosphere.
- When we fit a patient with contact lenses, the
three ~asic things we are after are: ~
a. Comfort;
b. Vision improvement,
c. Corneal physiology unchanged.
All these factors can be vastly improved by using
the method and apparatus of corneal modeling that follows.
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An analysis of the corneal shape through the com-
bination of several keratometer measurements is disclosed.
The eye is preferably scanned to a nasal angular position, a
central angular position and a temporal angular position.
The central position is straight ahead along the patient's
line of sight. The temporal and nasal positions are in the
broad range of up to 5 to 22; th~o intermediate range of 10
to 15~; and the narrow range of 12 to 14~ on either side.
Measurements in sphere, cylinder and axes are taken. Astig-
matism is in the more preferable format of 0-90 astigmatism
and 45-135 astigmatism. When each individual point is
measured with its respective estimate for sphere and cylinder
components, these measurements are fitted to an idealized
parameter. Then the three sets of curvature measurements
taken at the specified locations are reduced to a set of
adjusted, idealized curvatures all fitted to an elliptical
model. Thereafter, these fitted values create final corneal
shape parameters, the particular process here including the
creation of intermediate parameters. Finally, readings of
central "k", corneal shape, apex position, cap size, vault
height, corrected central "kl' and goodness of fit are all set
forth.
A keratometer is disclosed for remotely measuring
corneal curvature in at least sphere, cylinder and axis.
Assuming the eye is precisely positioned for measurement,
light sources are overlapped and imaged to a virtual image
position behind the human cornea. These sources of light-
preferably three in number (although more than three can be
used)- each have their own discrete path from the source to
the eye and thence to their own discrete detector. Between
e light source and the eye, the light traveling along each
light path is interrupted by a moving boundary locus having a
transparent portion, an opaque portion and a boundary there-
between. The moving boundary locus is in turn imaged by
reflection from the cornea being measured to a real image
position superimposed to and upon a light detectox. The
detector for each eyepath is aligned to and towards the
virtual image produced by the light source in the precisely
~L3L7~ 7~
11
positioned eye. Stray light emanating from positions other
than the vicinity of a virtual image position of the light
source in the cornea cannot be received by the detector. By
measuring the displacement on the eye of the virtual images
of each moving boundary of the locus with its associated
discrete light path, a keratometric measurement can be made
with as few as three light sources, three detectors and three
separate and discrete paths therebetween. A preferred geome-
try of the eye interrogation pattern is disclosed in which
two horizontally spaced points and a third medial and lower
point are simultaneously interrogated. Omission from use of
the upper portion of the pattern avoids interference which
can be caused by the upper eyelash. These points are angu-
larly spaced by 90~ intervals from the optical axis of the
instrument, thereby permitting similar measurement of the
concave surface of contact lenses with the preferable addi-
tion of a single extra light source (or detector). For
automated eye acquisition, each light source -- preferably in
the infrared -- is provided with two discrete diodes t which
diodes, when the eye is optimally positioned in distance
towards and away from the instrument along the optical axis,
are simultaneously occulted by the moving boundary locus.
Where the eye is axially out of position telltale shifting of
the optical center of the dual light sources alone or in
combination with accompanying shifting of other dual light
sources signals axial misalignment. Improper axial eye
position can be detected by shift of the dual light source
optical center alone. Preferably the produced shift can be
analyzed by a microprocessor for both position and presence
of non-toric surfaces (the latter being an indication of
coxneal irregularity). This analysis is not interrupted by
natural eye movement, such as saccadic eye movement. An
~ embodiment of the moving boundary locus which has opa~ue
transmissive boundaries sweeping each of the light paths
substantially ~imultaneously minimizes the ever-present
movement of the human eye by producing an effective high
shutter speed for measurement. The dual light sources are
given a coded oscillation, to be detected and identified, the
12
identity used to move the instrument transversely of the eye
from a gross instrument alignment to and towards the preci-
sion alignment required for corneal measurement. A-wholly
automated apparatus and process for keratometry results.
Ol~IER OBJECTS, FEATURES AND ADVANTAOES
An object of this invention is to provide a kerato-
meter with an automatic eye acquisition feature. According
to this aspect of ~he invention, at least three light sources
are imaged to three discrete areas of the human eye. Each of
the light sources is coded by intensity modulation. Each of
the detector areas is capable of looking at and detecting
which light source is incident upon that particular area.
Once the instrument is grossly aligned so that any of the
three light sources hit any of the three detector areas, the
light source is recognized and the instrument translates to
effect full acquisition.
An advantage of this aspect of the invention is
that the instrument can first be grossly aligned using the
operator viewing along a direct line of sight and registering
a virtual image to the eye being observed. Thereafter,
automated eye ac~uisition as above described can be used with
minimum amount of instrument movement to precisely align on
the eye.
A further objëct of this invention is to disclose a
system of detecting towards and away eye movement for proper
distance calibration of the eye axially towards and away from
the instrument. According to this aspect of the invention,
each light path includes an area for light emission which
includes two sources of light, these sources typically having
a discrete area of light emission. Each of the paired light
sources for each optical path is in effect oscillated or
- timed in its emission, such that the detector for that path
~ may recognize the particular light source emitting-photons.
When the instrument is properly positioned, occultation by
the boundary of the moving boundary locus causes both light
sources in each light path to have an essentially constant
optical center of occultation. Where the light sources are
out of position, the paired light sources undergo movement
~ ~ 7r~P~7
13
with respect to the time of occultation of their detected
optical center. This movement gives a telltale indication
which can be remotely monitored that the monitored eye is out
of position and that the instrument requires movement in
distance positioning together with the required direction and
amount of movement necessary to result in optimal
positioning.
An advantage of the paired light sources is that a
single optical path having two light sources can be suffi-
cient for distance calibration. Assuming the eye to be anessentially stationary object, merely telltale movement of
the detected optical center of the light sources will be
sufficient to indicate errors in distance positioning~
Yet another object is to disclose the utility of
lS employing paired light sources for each of three optical
paths. According to this aspect of the invention, each
optical path is provided with paired light sources. Two of
the light sources are typically aligned along axes at 90~ one
to another. A medial light source is aligned substantially
obliquely to the axes of both light paths and typically
displaced from an axis extending centrally between the two
light sources. The optical center shift for a first group of
light sources -- one from each light path -- is measured.
Thereafter, the optical shift of another group of light
sources -- the remaining source from each path -- is mea-
sured. These measurements are then used to determine towards
and away distance position.
A further object of this invention is to use the
immediately above-described paired light sources for each
optical path to examine for possible non-toric surfaces.
Where non-toric surfaces are encountered, a measurement can
- be rejected and the eye examiner warned by the rejection that
~ a patient with a possible non-toric cornea is being examined.
In the foregoing, it will be appreciated that only
three light sources are used. Those having skill in the art
will appreciate that more than three can be used. For exam-
ple, a system of four detectors can be utilized.
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14
An advantage of the above-described aspect of this
invention is that the problem of positioning the patient
towards and away from the keratometer by focus is avoided.
Moreover, optically compensated paths are no longer required.
S Instead the disclosed keratometer can be remotely positioned
towards and away from the eye to a precisely determined
distance. Intimate operator attention to keratometer posi-
tioning to obtain the measurement and during the duration of
the instrument measurement is no longer required.
A further advantage of the automated eye position-
ing mechanism is that the resultant measurement is more
accurate; errors due to unfavorable instrument positioning
are not present.
A further object of this invention is to disclose a
pattern for point source keratometric measurement of the eye.
According to this aspect of the invention, three points on
the cornea are measured about an optical axis. Two points
are substantially horizontally aligned and on opposite sides
of the optical axis. The third point is below a line through
the optical axis and on the corneal surface of the eye.
Preferably all three measurement points are separated by 90
intervals. That 90 interval which is vertically above the
optic axis is omitted and not used.
It has been found that the above eye measurement
pattern, that of not having a point at the upper portions of
the eye, avoids a surprisingly difficult problem of inter-
ference of human eyelashes with keratometric measurement.
That substantial rcmdom portion of the population which have
inherently interfering eyelids can be measured utilizing the
above pattern because the upper eyelash will not interfere
with the light impinging upon the eye.
An advantage of the avoidance of interference of
human eyelashes with the disclosed keratometric measurement
is that the eyelashes do not have to be manipulated. Having
an eye examiner reach close to the delicate surface of the
eye is avoided. Touching of sensitive areas of the eye, such
as the sclera, is avoided.
``` '` ~L~7~ 7 J
A further advantage of avoiding manipulation of the
eye is that physical and autonomic deformations of the cornea
are avoided or at least minimized. It is known that the
cornea deforms for finite lengths of time.
A further object of this invention is to disclose
the utility of the three point source of measurement used.
According to this aspest of the invention, the analyses of
the three points to determine the desired keratometric mea-
surement is disclosed.
A further object of this invention is to use the
same light impingent pattern on the eye as for the comple~
mentary measurement of the equal and opposite surface which
constitutes the inside portion of contact lenses. According
to this aspect, the same light pattern is generated for
measuring contact lenses. A second vertical source is added
to project the light source in a new position. By the simple
addition of a single source, complementary curving surfaces
of contact lenses can be measured.
An advantage of this aspect of the invention is
that the same instrument can be used for the remote measuring
of contact lenses as well as the remote measuring of the
human eye. Consistency of matching contacts to the eye by
using the same measurement standard is possible.
A further advantage of this invention is that the
light sources and detectors are essentially interchangeable.
While such interchcmge may provide varying trade-off with
respect to the disclosed optical design, it will be under-
stood that reversing of the light paths is feasible.
A further advantage is that the light sources can
be point sources of high intensity infrared light. These
sources are chosen to be below the threshold that could
possibly have physiological effect on the eye but small
~ enough in area so that eyelash interference is minimized.
The advantage of point sources of light becomes even more
pronounced where viewing through the eyelashes is required.
A further object of this invention is to disclose a
light path. According to this aspect of the invention, dual
117`1,~
16
light source detectors are located behind the moving boundary
locus. Single infrared emitters emit light onto the cornea.
An advantage of this aspect of the invention is
that the light sources can essentially be point light
sources. The use of high intensity point light sources
minimizes any interference which eyelashes may cause to the
disclosed keratometric measurement.
A further object of this invention using three
psint sources herein disclosed is that screening for non-
toric functions can result. Consequently, measurements whichexceed a given threshold can be rejected. With such rejec-
tion, cases of instrument measurement with highly erroneous
readings are avoided. Moreover, abberations of the eye from
the norm can be detected. For example, cases of kerataconus,
along with other corneal deformations, can be looked for upon
instrument rejection of a candidate for keratometric
measurement.
A further object of this invention is to disclose a
system of automated measurement of spaced points of the eye
on substantially a simultaneous basis. According to this
aspect of the invention, the three chosen point sources of
light are imaged to the eye. A moving boundary locus is
chosen having at least three similarly spaced boundaries.
The boundaries are such that the eye is swept at all three
points at substantially the same time interval by the locus.
There results simultaneity of image sweep at the eye points.
An advantage of this aspect of the invention is
that greater accuracy can be achieved even though the eye is
moving constantly during the measurement. By applying a very
high "shutter speed," the resultant movement of the eye can
be neutralized. Thus, the natural movement of the eye is in
- effect neutralized by the disclosed instrumentation.
An object of this invention is to disclose a pro-
cess and apparatus for mapping the contour of the human eye.
According to this aspect of the invention, a keratometer is
provided with central, temporal and nasal fixation points.
The central fixation point corresponds to a straight ahead
eye view. The nasal and temporal points depart from the
~ ~L7l~r~7~
17
central view by angles in the range of between 5 and 22~, in
the intermediate range of 15-10 and in the narrow range of
12-14. Discrete measurements of sphere, cylinder and axes
are taken at each fixation. These fixation measurements are
thereafter idealized to fit an elliptical model. From the
elliptical model, at least one of the following measurements
is generated:
Central i'k" readings in eguivalent sphere, axis and
cylinder;
A corneal shape factor;
An apex position, including horizontal and vertical
displacement as well as an uncertainty factor in locating the
apex;
Cap size;
Vault height (in millimeters over a 25mm diameter
sclera); and
Corrected central "k" and a "goodness of fit"
factor indicating the performance of the model to the mea-
sured eye.
An advantage of the disclosure of this invention is
that for the first time commercialization of fixation points
in measuring the human cornea can be made. The accuracy of
the disclosed keratometer now permits corneal modeling in the
disclosed elliptical format.
A further advantage of the disclosed method of
mapping is that the provided shape parameters do include some
intuitive inputs that may be utilized by the practitioner to
visualize the surface being mapped.
A further object of this invention is to disclose a
process apparatus for fitting contact lenses. According to
this aspect of the invention, measurements of the contact
lens and the provided corneal map are taken for fitted con-
tact lenses having high degrees of comfort. A data bank of
stored information is created, which data bank includes at
least one or more of the following parameters from a measured
human eye:
Central "k";
Corneal shape;
11'7;13~7~
Apex position;
Cap size;
Vault height;
Corrected central "k"; and/or goodness of fit.
Measurement of the contact lens is conventionally made and the
data likewise stored with the data of the map corresponded to the data of
the fitted lens. Maps of eyes measured are compared against the stored data
in the table. There can result vastly improved fitting of contact lenses.
It will be apparent as of this writing that I have now created
the apparatus and method capable of making the measurement, but I have not
been able to accumulate the data indicating a correlation between the map
of the eye and the dimensions of contact lenses needed to fit the various
individual eyes from the total population of eyes capable of being mapped.
It will be noted that I expect generation of the data required will at least
in some part involve only ordinary skill in the art.
The reader should be aware that I claim utility in the
measurements generated. Specifically, the claimed utility can be derived
into two broad classes of benefits.
m e benefits of additional corneal information can probably
be divided into two types. me first benefit is associated with the itting
of contact lenses. Additional corneal information can be used in the
fitting of oontact lenses in several ways. For example, at the prelim mary
fitting stage, an analysis of corneal shape can result ~1 the judgment of
the optical suitability of contact lenses to individual patients. The shape
of the cornea can have many implications in the anaylsis of a patient's
potential for good vision. m e degree of departure of the cornea from a
sphere, as well as misalignment of the cornea's axis of symmetry, are all
potential sources of optical aberrations --including astigmatism and even
more complex forms of aberratiorn One has often heard the story of
patients whose vision
- 18 -
19
is degraded somewhat through the use of contact lenses.
However, the converse may occasionally also be true, i.e.,
contact lenses may actually increase the visual acuity of
some patients. The source of these optical trade-offs has
been analyzed in the literature (Ludlan and Wittenberg,
1966). It is a simple extrapolation of these results to say
that by knowing the departure of the cornea from a spherical
shape, it might also be possible to choose the lens type most
likely to result in high ~isual acuity, for example, by
minimizing the effects of spherical aberration (Campbell).
Corneal shape information may also lead to better estimates
as to the dynamic performance of a contact lens as it will
perform in place on the patient's eye. ~or example, esti-
mates of contact lens motion during blink or the choice
regarding hard contact lenses vs soft contact lenses may all
be somewhat dependent upon knowledge of the corneal shape.
Going on to the second phase of contact lens fit-
ting, after the suitability of contact lenses has been deter-
mined or the selection of type has taken place, corneal shape
information can be expected to be a benefit in the actual
contact lens fitting procedure. Traditionally, a "central k
value" is taken to pick a trial contact lens, and, at least
in the case of hard contact lenses, there is a strong reli-
ance on the use of fluorescein patterns to modify the choice
of trial lenses in order to take into account the peripheral
effects of the corneal shape. A better first try could be
possible with a greater knowledge of the corneal shape in the
peripheral as well as the central regions. The benefit to
the patient is the perception of increased professionalism
and reduced discomfort from repeated trials; the benefit to
the doctor is a more comfortable patient and a reduced
- examination time.
Now, going on to the second general use of corneal
shape information, there is the matter of monitoring changes
of corneal shape over intervals of time. Generally speaking,
there are two common situations in which this is of interest.
One of them is in the case of a pathology, for example,
developing keratoconus. Routine examinations can help the
doctor establish the state of progress of the disease and
determine the effectiveness of treatment. Another common
reason to monitor corneal changes over time has again to do
with contact fitting. It is generally accepted that a
patient's routine use of contact lenses should not have the
effect of producing substantial changes in corneal shape.
Periodic central as well as peripheral measurements of the
corneal shape during the first months of patient use can help
the doctor satisfy himself that the contact lenses are indeed
having minimal effect upon corneal shape.
Now we will consider some detailed mathematical
models for the corneal shape. This is accomplished by scal-
ing all dimensions in terms of the radius of curvature at the
apex of the cornea. By taking the sagittal depth of the
cornea in units of the central radius of curvature and repre-
senting that as a function of the radial distance from the
corneal axis of symmetry, again in terms of units of central
radius of curvature, it is possible to characterize entire
families of corneas having entirely different scales of size
but having similar shape through the use of a single shape
parameter. In this way, dimensionless analysis of the
corneal shape simplifies the manifold of possible corneal
shapes that has to be dealt with as an entire family of
shapes can be derived from a single set of tables or a single
set of relationships simply by multipl~ing appropriate varia-
bles by a scaling factor, which is the central xadius of
curvature.
There is a second advantage to the dimensionless
analysis. A dimensionless representation of the cornea
ignores the linear scale of size but preserves the angular
scale of cornea shapes. When fixation sources at specified
angular intervals from the central fixation are employed, the
corneal sampling areas occur at fixed values of the dimension-
less radius for any given shape factor. This contributes to
simplifying the mathematical analysis.
In the analysis which follows, the symbol ~ will
represent the sagittal cornal depth in dimensionless form and
~ will represent the corneal radial distance in dimensionless
7~7
21
form; these two terms will be related by functional relation-
ships involving only one other parameter, specifically the
corneal shape factor which is also dimensionless.
A shape model fox the cornea has been developed
based on a combination of known anatomical features of the
corneal structure as well as upon various assumptions having
to do with the physics of the fluid statics and of the dis-
tribution of stresses at the corneal surface. It is assumed
that the corneal shape is maintained by layers of strap-like
tissue members called lamellae. It is further assumed that
the lamellae of the eye are distributed in such a way that
they all sustain approximately the same tension per fiber.
The lamellae are assumed to pass as uninterrupted bands
entirely across the cornea. Thexe is an observed thickening
of the cornea toward the periphery amounting to something
like a 20% thickening at 6 mm fxom the center of ~he cornea.
(This result is reported by Mandell and Polse, 1969, although
there are differing results reported elsewhere, such as
Smith, 1977.) The assumption is made that this thickening is
a result of additional density of lamellae. (One interest-
ing, semi-quantitative result of these assumptions dictated
by fluid statics as well as the equality of the radial and
tangential fiber tension leads to the conclusion that toward
the periphery of the cornea the growth in the density of
radial fibers will be only 1/3 as great as the growth of
tangential fibers because the hoop tensions must grow more
rapidly than the radial tensions. Hence, this accounts for a
larger portion of the corneal thickening toward the edge of
the cornea.)
Based on this meager input of assumptions and data,
it is possible to develop a mathematical model capable of
predicting several known properties of the cornea. Aside
from having the correct corneal thickening, which ~s input
information, the model would predict approximately 3 diopters
curvature reduction at 3 mm from the center of the typical
cornea which is in reasonable agreement with measured varia-
tions. (The model predicts somewhat greater departures from
a spherical corneal than most studies in the literature.)
77
22
The model would also predict a sagittal height for a cornea
of average diameter of 2.58 mm while the measured value is
2.59 ~ .22, again in excellent agreement; and the slope sf
the cornea at its periphery is nearly tàngent to the opening
5 in a 25 mm sphere representing the scleral shell, again in
good agreement with observations and consistent with the
hydrostatic requirements for this model of the eye. It is a
very encouraging result to have a corneal model with only one
free parameter which is reasonably consistent with so many
known physical measurements of the cornea.
~ owever, a word of caution is in order. Although
the corneal model may be in excellent agreement with the
average values for a large ensemble of corneal measurements,
~he very process of averaging measurements tends to have a
smoothing effect on the possible variations that any particu-
lar individual cornea may have. The success of this mathe-
matical model of the cornea, then, depends upon the shape
parameter and corneal apex location being the dominant effect
in describing the shape of the cornea over and above the
individual corneal variations.
There is almost certainly going to be some small
fraction of the subjects for whom this condition does not
holdO Perhaps the first important point to bring out is that
I have discovered what might be termed a three-to-one rule.
This rule states that for any reasonably smooth corneal shape
model, the variation of the curvature of the cornea measured
from the axis of symmetry will show three times as large a '
variation for the curvature in the meridional (radial) cross
section as it does in the sagittal (tangential) cross sec-
tion. Since the difference in the curvatures in these twocross sections can be interpreted as a component of corneal
- astigmatism, it becomes apparent that changes of corneal
astigmatism are a direct measure of the corneal shape factor
as are the more commonly used variations of curvature along
the radial cross section. This valuable information in
regard to corneal shape which resides in the change in
corneal astigmatism has been neglected possibly as a result
of ignorance of its importance and possibly because of the
~ ti~7~
difficulty in the mathematical analysis of changes in the astigmatism. It
will be immediately apparent that both the ln model and the ellopsoidal
approximation obey the three-to-one rule.
In the following description and especially in the claims, it
will be understood that I refer generically to eyes and contact lenses as
optical surfaces with curvature or words of like effect.
The foregoing and objects and advantages may be summarized
according to the present invention as a keratometer for measuring by
reflection curvature of an optical surface including at least a plurality
of li~ht sources, a corresponding plurality of detectors; means for modulating
each light source in a distinctly different manner; means for synchronizing
each of the detectors with each distinct modulation to enable each detector to
identify each light source; means for focusing each of the detector areas to
an area of the optical surface with curvature to receive light from the optical
surface with curvature; means for positioning the optical surface with
curvature to reflect path to one of the detectors; and means for relatively
moving the optical surface with curvature responsive to detection of the light
sources at the detecting areas along axes of movement that include components
of movement transverse to the optical axis of the instrument whereby movement
of the instrument can register the keratometer to a medial position along the
optical axis to register the corresponding light sources and corresponding
detectors for measurement of the curvature of the optical surface.
Cther objects, features and advanta~es of this invention will
become more apparent after referring to the following specification and
attached drawings in which:
~ - 23 -
csm/~
i~7~ 7
Fig. LA is a perspective view of the instrument illustrating the
various degrees of motion of the instrument about the patient for automated
acquisition;
Fig. lB is a partial section of Fig. lA illustrating the
placement of a oontact lens;
Fig. 2A is a perspective view of the inner-wDrking elements
of the instrument, illustrating the eyepath for gross alignment and the three
detector eyepaths for both fine alignment as well as actual keratometric
measurements;
Fig. 2B is a schematic illustration of the principal light paths
for vement of the human eye showing infrared light source adjacent the locus
and detectors adjacent the eye;
Fig. 2C is an illustration of light paths similar to those
illustrated with respect to Fig. 2B with measurement of a contact lens
illustrated and the detector and light sources being reversed with the light
sources adjacent the contact lens and the detectors adjacent the moving
boundary locus (this particular configuration being preferred?;
Fig. 2D is an expanded image of the light sources superimposed
on the corresponding measuring areas of a human eye used for this invention;
Flg. 2E is an enlarged cross-sectional view of an emitter or
detector;
Fig. 3A is a view of a patient's eye illustrating the
interrogating detectors with the sources of light being used in the
acquisition mode;
- 23a - I
csm/r~d
7Ub~7 7
24
Fig. 3B is a view of the same eye illustrating
~weeping of the three sources substantially simultaneously to
generate the measurement of this invenion, liberty being
taken with the actual placement of the image of the moving
boundary locus for ease of understandingi
Fig. 3C i5 a schematic illustrating the detector
circuitry for identifying from each detector the particular
light source being imaged;
Fig. 3D is a schematic of the analog to digital
converter used in ~ig. 3C;
Fig. 3E is a schematic of a filter utilized for
signal recognition at the photosensors;
Fig. 4~ is a side view detailed optical schematic
illustrating the light paths used herein;
Fig. 4B is a patient's view of the instrument
illustrating detector positioning as well as certain fixation
targets which can be used;
Fig. 4C is a perspective view of the preferred
detector;
Fig. 5 is an illustration of the moving boundary
locus utilized with this invention, which moving boundary
locus is typically registered to the detector by means of a
real image relayed by reflection from the cornea or contact
lens being measured;
Fig. 6 is a diagram of micro-processor logic that
can be used with the light measurement system of this
invention;
Fig. 7 is an illustration of a digital detector for
detecting occultations in the presence of diffusely reflected
light from the human iris;
Fig. 8 is a front view illustrating in a format
similar to that shown on Fig. 2C with photodiscrete sensing
~ elements being shown analyzing the sphere, cylinder and axis
at three discxete points on the human cornea;
Fig. g is a section of the human eye illustrating
the cornea without a lens placed thereon;
Fig. 10 is a view of the human cornea with a con-
tact lens placed thereon for the purposes of illustrating the
various refractive interfaces created thereby; and
~L~ 7ir'i~77
Fig. 11 is a block diagram illustrating the method
of this invention for the fitting of contact lenses.
The following description is lengthy. ~irst, the
physical configuration of the unit is described. Then the
moving boundary locus -which essentially is a rotating disk
having light and dark areas of special, known shapes used to
interrupt the light passing between the eye and a detector-
is described. The measurement of the position of the beam
using the moving boundary locus is described. Then computa-
tions exemplary of those which can be used to demonstrate theutility of the invention are set forth in the next two
sections.
An electrical circuit schematic is discussed fol-
lowed by a section on the disclosed computer flowchart and
timing diagram.
Following the description of the keratometer, its
use in obtaining a corneal map is set forth. Specifically,
measurement of the eye in sphere, cylinder and axis at three
spaced apart points is set forth. Thereafter, the parameter-
ization of my invention resulting in the generation of an eyemap is disclosed. Finally, the use of the eye map in fitting
at least contact lenses is illustrated.
PhYsical Confiqurat on
Referring to Figure 2A, the optical portions of
this keratometer are placed within a housing H. Housing H is
mounted to a table T and given the degrees of movement gener-
ally illustrated in Fig. lA. Generally, housing H is mounted
on a pivotal mount 14 movable in azimuth indicated by arrow
15. Mount 14 in turn is movable on ball screws, belts or
similar devices 16 for towards and away movement 17 relative
to the patient P. Rack 16 on its own mount is movable in a
side-to-side movement 19 on ball screws, belts or similar
~ mechanisms 18.
Patient P registers his head and chin to a headrest
20 and chin rest 22. The forehead is registered to a head-
rest crossbar 25. In this position the eye E of the patient
is registered for keratometric measurement. Degrees of
movement are responsive to the outputs which will hereinafter
7~tl~ 7
26
be discussed. Since methods and apparatuses of effecting the
illustrated degrees of movement of Fig. lA are well-known to
those having ordinary skill in the art, they will not further
be discussed here.
Headrest 20 is typically rigidly mounted to the
table T at a bar mount 28. It will thus be seen that the
housing H is free to move with respect to the headrest 20.
In such movement the housing will move about so that the eye
E of the patient is properly addressed for keratometric
measurement.
The present invention is also capable of measuring
the curvature of a contact lens C. The mounting of such a
contact lens C for reflective measurement of the inside
radius of curvature is illustrated in Fig. lB.
Bar 28 mounted to table T (not shown in the view of
~ig. lB~ has the headrest removably mounted to a hole 30 in
the upward portion of the bar. As here illustrated, the bar
28 includes a flat portion mounted to the table, an angularly
and upwardly extending medial portion and a flat upper por-
tion. The flat upper portion contains hole 30 and is the
point to which b~th the headrest 20 and the removable contact
lens mount 35 mounts.
The contact lens mount consists of a vertical rod
36 having an upper bar 37. Bar 37 has a V-shaped groove
containing a rod 38. Rod 38 has a cylinder 39 on the end
thereof, which cylinder is provided with a curved surface to
which the contact lens C is mounted, typically on a fluid
layer.
In operation, contact lens C is mounted to the
surface 3S on the end of rod 38. Thereafter, rod 38 is
placed within the V-shaped groove of bar 37 Bar 37 at
- attached rod 36 is mounted to the removable mount 35. Upon
insertion of bar 37 into removable mount 35, reed ~witch 32
closes. As will hereinafter be made clear in the following
description, reed switch 32 functions to reorder the logic
within the apparatus. This reordering is re~uired because
the concave surface of the contact lens alters the optical
path from light source to detector. It will be noted here-
27
after that the 90 spatial interval which has been chosen
about the optic axis of the instrument allows this switching
to occur by the addition of either an additional light source
or additional detector.
It will be appreciated that the disclosed
keratometer measures curvatures only within a preselected
range. These curvatures (positive for the convex surface of
eyes; negative for the concave surface of contact lenses)
must be in a preselected range or measurement will be
rejected.
Before proceeding further, and with reference toFig. 2A, the major operative parts of the keratometer will be
discussed. Thereafter, and with reference to ~ig. ZB, the
optical path utilized in examining an eye will be set forth.
In ~ig. 2B, this path will be described having the light
sources adjacent the moving boundary locus and the detectors
adjacent the eye.
~ ollowing this description, reference will be made
to ~ig. 2C. In Fig. 2C, the optical path generated for
monitoring a contact lens will be discussed. Moreover, and
with reference to Fig. 2C, the preferred embodiment having
the light source adjacent the optical surface being examined
(here the contact lens) and the detectors adjacent the moving
boundary locus will be set forth.
25 - In order that these matters may be easily under-
stood, the contents of the keratometer within opa~ue housing
H will first be discussed.
Referring to Fig. 2A, the opa~ue housing ~ is
illustrated in schematic section. A brief explanation~of the
optics contained therein with respect to the eye E of the
patient is illustrated.
- Housing H includes four light sources 41, 42, 43
and 44. These light sources are typically infrared, have
paired emitting sources and will be more fully set forth
3S hereinafter. For the present, one of the light sources 43
will be explained in its full optical path. Such explanation
will refer both to the side view of Fig. 4A and the perspec-
tive view of Figs. 2A and 2B.
~7~b~'7~7
Light source 43 typically consists of two inner and paired point
sources of light. These lights are focused through a lens in source 43 to
a mirror 45. Mirror 45 merely serves to fold the light path and shorten the
overall length of housing H The invention will likewise work with the
positions of the detectors and sources reversed as in Fig. 2C. The paired
light receiving areas 41a, 41b are shown in Fig. 2E.
From mirror 45 the light from source 43 passes through
focusing optics 46. From focusing optics 46 the light path is folded, first
to a pyramid mirror 47 and thence to a convex mirror 48 where the light
sources come to a focus at an aperture stop 50.
From a real image of the sources at aperture stop 50 light passes
through fo~lsing optics 52.
Eye E of a properly positioned patient intercepts the light. With
this interception, a virtual image of the light source is formed interior of
the eye at a position dependent upon the radius of curvature of the cornea
to be measured.
Moving Bounda~y L cus
Referring to Fig. 5, the configuration of the moving boundary
locus is set forth. m is moving boundary locus is described in my U.S.
Patent 4,182,572, issued January 8, 1980, at Fig. 3A thereof. me disclosure
of the patent may be summarized as follows:
A unitary light source is imaged through a prism array to
generate a plurality of, preferably four, apparent light sources forming a
point of origi~l for a discrete lens sampling light path. From each apparent
light source, each discrete sampling path diverges to a relay lens system.
This relay lens system relays and registers to a lens sampling interval
discrete images of each apparent light source. The images may be registered
to a correspondingly apertur~d ]ens sampling diaphragm agains-t which suspect
optics are placed for measurement. A moving boundary locus sweeps ~he light
between each apparent source and the sampling interval with
- 28 -
,~
~t7~ 7
~9
paired boundaries of differing slopes which produce non-
ambiguous points of intersection with respect to time. After
passage through the suspect optics at the sampling interval,
light is passed to a photodetector having an overlying set of
apertures, each aperture corresponding to one of the four
apparent light sources. A le~s pair functions as relay
optics to focus a conjugate image of the light at the suspect
optics to the overlying apertures at the detector. Light
other than that passing through the suspect optics at the
point of the images of the apparent ight source is excluded.
Moreover, a sampling aperture in combination with one of the
len6es of the relay pair passes only that light with limited
angularity substantially parallel to a selected optic path
for each discrete light source. Light having an angularity
other than the selected angularity is excluded from the
~onjugate image. Provision is made to fold the light paths
to a C-shaped configuration to shield both extraneous light
and electro-mechanical interferences from sensitive photo-
- detector elements.
An e~emplary claim of this patent is as follows:
1. In combination, means for emanating light from
a discrete light emikting area; a moving boundary locus
including at least one boundary for occulting said discrete
light emitting area; a sampling interval to which suspect
optics may ~e placed for deflecting light passing through
~aid ~ampling interval; means for converging light from said
light emitting area to a bundle of non-parallel light rays
having a pupil located coincident with said 6uspect optics
located in said sampling interval to which suspect optics may
be placed for deflecting ~aid light, ~aid light diverging as
deflected in a diverging bundle from 6aid 6uspect optics at
6aid sampling interval; a light path downstream from ~aid
sampling interval to receive at least a portion of said light
from said suspect optics; and a photodetector fixed in space
with respect to said downstream light path located within an
area of expected excursion of ~aid light from said ~ampling
inter~al to detect changes of occultation of 6aid light path
by 6aid moving boundary locus.
In the present invention, the moving boundary locus
L used can be identical in configuration to that illustrated
in my U.S. Patent 4,182,572. Referring to ~ig. 5 herein,
moving boundary locus L is made of a disc of material such as
glass or even metal. The disc is provided with two broad
information areas. The first area is a border area 120 which
defines disc rotation. The second area comprises an internal
area 124 of the disc which occults the view of the light
detectors to the virtual image of the light sources in the
eye of the patient E. Border area 120 consists of a group of
discrete notches for bar patterns 122 placed in a preselected
angular spatial relationship around the periphery of the
disc. In this case, they are placed at spatial intervals of
256 notches to the revolution. The function of the notches
122 is for precise rotational location of the disc. When
this precise rotational location of the disc is identified in
combination with the occultations of light to a detector from
a light source, precise angular measurement of the position
of the disc can occur.
Gross overall rotational reference is made to a
missing notch at interval 121. By electronic recognition of
this interval through time-sensing circuitry, precise rota-
tional positioning of the locus L at the time of occultation
can be determined.
It shoulcl be understood that border area 120 can
consist of a number of embodiments. For example, a Baldwin
type digitizer disc can be used to determine the pxecise
rotational location of the moving boundary locus L. Such
discs are manufactured by Baldwin Electronics, Inc. of Little
Rock, Arkansas as a commercial item of manufacture.
It will be appreciated that the light path from
each of the light sources 41-44 intersect the moving boundary
locus L at respective areas 70-73. These areas are shown in
broken lines on the disc as it is illustrated in Fig. 5.
Using the corneal surface of the eye E (see Fig.
2B), a real image of the moving boundary locus is registered
to the detectors. Taking the case of detector D3, a real
image of the locus passes in front of the detector D3 to
t77
31
effect occultation of any virtual image of the light source
within the eye E. In other words, locus L is placed along
the optical paths between the detectors and the light
sources. As the moving boundary locus rotates, the light
traveling along the various paths at areas 70-73 is sequen-
tially interrupted by the opaque portions 140, 142.
Keeping in mind the projection of the real image of
the moving boundary locus to the aperture of the detector D3,
it will be realized that the position o~ the virtual image of
the light source 43 within the eye E can readily be deter-
mined with occultation. In explaining how such occultation
theoretically works, attention will first be given to the
parameters of the disc and a discussion of the boundaries
between the opaque and transparent areas. Second, the func-
tion of how these areas work will be set forth. ~inally, thegeneral case for such a moving boundary locus will be
explained.
Broadly, the rotating boundary locus includes two
transparent areas and two opaque areas. Turning attention to
the transparent areas 132, 133, each area includes a boundary
which can be described by the equation R-ke (for boundaries
134a and 134b) and R=-ke (for boundaries 135a and 135b)
where:
R is radial distance of a point on the boundary
from center of boundary locus (in inches);
4 is angular distance of a point on the boundary
from a reference a~is ~in degrees);
k is a constant, .017453.
In the subject specification, very precise values
are given for constants. These values come from actual
experiment. The reader will understand that different units
- can yield different constants.
Each of the boundaries 134a and 134b on one hand,
and 135a and 135b on the other hand, are separated by a
precise angular interval of 90~ at any given radius. Thus,
it can be seen that the transparent portions of the moving
disk as they pass any one spot within area 124, pass light
for one half of the time and do not pass light for the re-
'7~17732
maining one-half of the time, all this over one complete
turn.
Referring to opaque portion 140, it will be seen
that the opaque area gradually increases in occupied angular
interval with movement away from the axis 141 of the rotating
boundary locus. This is because the respective boundaries
134a and 135a occupy an increasing angular interval of the
disk as tne distance radially outward from axis 141
increases.
Portion 142 is of the opposite construction.
Specifically, the angular interval between the curves 134b
and 135b decreases with outwardly moving radial distance from
the axis of rotation 141.
Measurement of Position of Beam
Usinq the Movin~ Boundary Locus
Assuming that a beam passes through the disk at a
distance r and an angle e, the passage of the beam can be
intuitively understood before considering the more general
case. Specifically, for changes of the distance r towards
and away from axis 141, it will be seen that the time during
which the beam is obscured by the respective opaque surfaces
140 and 142 can be determined. In the case of opaque surface
140, the longer the obscuration of the beam by the surface
140, the further away from the axis 141 will be the location
of the beam. In the case of opaque surface 142, the shorter
the obscuration of the beam, the further away from the axis
141 will be the beam. Thus, the opaque surfaces each provide
discrete timed intervals which indicate the polar coordinates
r of the beam away from the rotational axis 141.
Referring to the angle 4 of the beam from axis 145,
the average integrated time interval between the reference
position of the disk and two opaque to transparent boundaries
- can be used to determine angularity. For example,-by observ-
ing the boundaries 134a and 135a as they respectively occult
a beam it will be observed that the angle subtended between
detection of marker 121 and these obscurations will average
to a value representing the azimuthal position of the beam
about the axis 141. This azimuthal position can be measured
~ ~ 7 IP ~ ~7
33
with'extreme accuracy. By relating this rotation interval to
the precise rotational interval of the tracks 120, migration
of the beam in angle 4 can readily be determined.
It will be apparent that more than the preferred
four boundaries here shown can be utilized. For example, six
boundaries could be used. Likewise, the opague and transpar-
ent portion~ of the boundaries could be reversed.
Having set forth the migration of the beam, the
more general case can now be explained.
It should be apparent to the reader that'the moving
path of a boundary locus according to this invention can vary
widely. For example, the moving path could be linear and
comprise a series of boundaries all sequentially passing the
area of expected beam excursion. Likewise, the boundary
locus could be painted on the exterior of a transparent
revolving cylinder. Light could be deflected through the
sidewalls of the cylinder with occultation of a beam occur-
ring with boundaries painted on the cylinder sidewalls. It
is to be understood that the rotational disk embodiment here
shown is a preferred example.
The boundary here illustrated comprises successive
opague and transparent areas on the surface of the disk. It
should be understood that absolutely transparent or absolute-
ly opaque areas are not required for the practice of this
invention. Varyiny surfaces can be used so long as the
relatively transparent areas are capable of passing there-
through a beam of light which can be intercepted without
appreciable degradation by a detector. Likewise, lights of
various colors could be used in combination with color'dis-
criminatory filters. For example, a combination of lightsand narrow band pass filters could be used to successively
- pass various beams. These beams, when passed, could be
measured in timed sequence at a single detector plane.
The boundaries cannot be parallel to the intended
path of movement of the boundary locus. In such a case,
there would be no sweeping of the area of excursion and no
detection of the beam.
~ ~7 ~
34
It is required that the two boundaries be boundar-
ies of distinctly different shape. This differinq in angu-
larity requires that each boundary sweep the area of intended
beam excursion and that the two boundaries, when occultation
occurs, form a common point of intersection. This common
point of intersection can define the point of excursion of
the beam.
Regarding the moving boundary locus, it is prefer-
red that the boundary move at a known and constant speed.
When moving at a known and reasonably constant speedF the
equation for determination of the location of the beam can be
reduced to one of time combined with knowledge of position
from the marks 121 and 122. That is to say, by observing the
time of respective occultations, precise location of the beam
excursion can be measured. Once excursion is known, the
resultant prescription can be obtained.
The particular configuration of the moving boundary
locus illustrated in Fig. 5 is preferred. In actual prac-
tice, the boundary can have other configurations.
As a practical matter, it is important that at
least two boundary contours be employed. The slope of one of
these boundary contours must be algebraically larger ~han the
other with respect to the direction of translation of the
boundary across the light path. Such a slope gives the
boundaries a non-ambiguous point of intersection, which
non-ambiguous point of intersection insures accurate location
of the beam within a suspected area of excursion, for examp~e
the area 70.
It has been found convenient that the slope not
change its sign. If the slope is chosen so that a sign
change occurs, it will be found that the resultant function
- is non-monotonic. That is to say, the value of one component
producing the slope decreases instead of increases-over the
area of excursion. This produces difficulty of ~olution of
the resultant equations.
Naturally, the boundary can be described with
respect to polar coordinates~-where the boundary is rotated
as shown in the preferred en~odiment; or Cartesian coordin-
7~)~77
ates - where the boundary is merely translated by the light
beams with the respective opaque and transparent areas defin-
ing boundaries described by the conventional X,Y description.
Where the boundary is one that rotates, the slope
de/dr of one boundary must be algebraically larger than the
other. Obviously, this is where translation occurs in the
direction ~. -
Where the boundary is translated in the X directionin a ~artesian system, the slope dx/dy of one boundary must
be algebraically larger than the corresponding slope for the
other boundary.
It is an important limitation that each boundary
sweep over the expected area of excursion. Naturally, where
the boundary does not completely sweep the expected area of
excursion, the limitations of this general condition would
not be met.
Referring to ~igs. 2A and 4A, it will be remembered
that the light from each of the light sources impinges on the
pyramid type mirror 47. In actual fact, pyramid mirror 47 is
provided with a central hole or aperture 49. The mirror
includes sloped surfaces, each sloped surface forming a
surface from which the light forming image of the moving
boundary locus near the detectors is reflected.
It will be remembered that the moving boundary
locus L has its real image relayed by the cornea being mea-
sured to a position at or near the aperture of the detector
D3. Looking back through the detector D3 onto the surface of
the eye E, the virtual image of the light source 43 will be
occulted. If one were to draw a diagram on the eye illus-
trating the projected photosensitive area of each detectorand illustrate the occultation of all of the virtual images
- of the light sources by the real image of the moving boundary
locus, one can generate a diagram that looks like Figure 3B.
The reader should understand however that Figure 3B is a
diagrammatic and schematic representation of the occultation
of the virtual images of the light sources taking place and
does not represent with complete accuracy images occurring at
these points.
3~77
36
Specifically, in Fig. 3B a human eye E is illus-
trated. Eye E includes the optical axis 57 of this instru-
ment impinging upon the eye. The pyramid mirror 47 creates
quadrants of the eye onto which the light paths are project-
ed. In the view of 3B, we see the locus superimposed upon aview of the eye. Thus, we see boundary 135b sweeping guad-
rant III at 135b'. Similarly, the boundary 135a sweeping
quadrant II at 135a' and boundary 134a sweeping quadrant I at
boundary 134a'~
Referring briefly to Fig. 5 and then ~ig. 3B, it
will be noted that another feature appears. Referring to
Eig. 5, it will be seen that areas 70, 71 and 72 are formed
about the locus L with spatial intervals therebetween.
Specifically, a spatial interval sufficient to accommodate
the drive shaft 143, of the moving boundary locus ~ is
illustrated.
However, referring to Fig. 3B, it can be seen that
the spatial interval between the respective imaging areas 70,
71 and 72 has been removed and now areas 70-72 essentially
correspond to sectors I, II and III. This is a function of
the pyramid mirror 47. This mirror acts to bring the respec-
tive images of areas 70, 71 and 72 into an overlapping real
image area at the eye of the viewer. Thus, the real image of
the spatial areas swept by the locus at the eye in fact
overlap a small amount along the boundaries of the quadrants
I, II and III.
As will hereinafter more completely appear, once
each of the light sources is in registry with its own seg-
ment, further movement can and must occur to even more finely
align the instrument. This movement includes more precise
angular positioning as well as axial distance calibration.
- This movement occurs with respect to a mathematical parameter
which is in effect nulled by further controlled mo~ement of
the instrument. In order that this parameter may be under~
stood, the instrument measurement will now be discussed using
the view of Eig. 3B; optical axis 57 will be assumed to be
adequately centered upon the cornea of the eye E.
' ~jL 3~7~! ~77
37
Referring to ~ig. 3B, it will be remembered that
the image of the locus L is focused to the eye E. At the
same time, each of the detectors Dl, D2 and D3 is capable of
viewing the eye. Some attention can be given to the light
gathering properties of these detectors. A typical detector
is illustrated in Fig. 4C.
Typically, the detector includes a lens 150 and an
infrared detecting element 151. The lens and detecting
element are spaced apart along an opaque housing 152.
The detector has a discrete solid angle of accep-
tance. This is defined by the detector 151 and the lens 150.
The conjugate image of each detector element 151 is formed to
and on the virtual image of the light source as it appears in
the cornea of the eye E. This is shown as areas A, B and C
on Fig. 3B.
With further reference to ~ig. 3B, it will be
remembered that an image of a moving boundary locus L is
projected to the detectors. Further, it will be understood
that the timing markings 120 ~see ~ig. 5) on the periphery of
the disk enable the precise angular positioning of the disk
with respect to an occultation to be determined. Knowing the
shape of the boundaries of the locus L, one can therefore
determine the R and e position of each of the vixtual images
A', B' and C' with precision. This is set forth in equations
which follow.
Ex~pIary~Computations for
Measurement of Curvature of Eye
The following mathematical equations are different
in scope and extent to that material set forth in my U.S.
Patent 4,180,325, issued December 25, 1979, entitled "Lens
Meter with Automated Read-Out." It will be observed that
- with the following equations, only three points are used to
determine readings in sphere, cylinder and axis.
It will be appreciated in reading the following
e~uations that they are only suited for the keratometric
exercise herein set forth. They are unsuitable and do not
work with a lens meter.
~ ~. 71~ ~7 7
38
Once the mathematical eguations are understood, it
is believed that pxogramming can be arrived at by those
having skill in ~he art by following the format of the exemp-
lary program set forth in the above-referenced patent and
adapting the programming to the equations set forth.
Although only three detectors Dl-D3 are illustrat-
ed, it should be remembered that the location of the detec-
tors and light sources can be reversed as in ~igs. 2B and 2C.
Therefore, in Fig. 2B, elements Dl-D3 are detectors while in
Fig. 2C elements Dl-D3 are light sources and elements 41-44
are detectors.
It should be noted that no image is projected onto
the upper guadrant of the eye, although that quadrant may be
used when measuring contact lenses, to minimize upper eyelash
interference. The use of relatively small, paired light
sources or detectors for each path further reduces eyelash
interference.
In the equation format given below, let Ri ei be
the position on Fig. 3B of a virtual image A', B', C' cor-
responding to the particular detector Dl-D3. Let dj be the
number of counts between two edge crossings for a given
detector. In noting the moving boundary locus of ~ig; 5, the
reader will observe that there are four edges 90 apart at
any crossing and thus each expression has four terms whereas
we are only determining the position of three images.
In the solution of eguations, we first need to
determine the radius of the virtual image of the spots A', B'
and C' at the physical plane of the boundary locus. This is
given by the equations:
Rl = 4 (d3 -d4 +d2 dl)
R2 4 (d2 -d3 +dl -d4) + 2.5708
R3 4 (dl -d2 +d4 -d3) + 1.0000
Where: R1 is radial distance (in inches) of
point A' from optical axis 57;
R2 is radial distance (in inches) of
point B' from optical axis 57;
7`L3~
39
R3 is radial distance (in inches) of
point C' from optical axis 57;
k is a constant, .017453;
dl-d4 are angular distance (in degrees)
between reference mark 121 and consecutive edge crossings for
a particular spot, A', B', or C'.
Similarly, we need to determine the angle from the
axis 57" of each of the Yirtual images A'-C'. This is given
by the equations:
el = 45 + 4 ~dj - 180D
42 = 225 + 4l ~dj - 180
~3 = 315 ~ 4 ~dj - 180
Where: ~1' 42' e3 are angular distances clock-
wise (in degrees) between reference axis 57" and points A',
B', and C' respectively.
In the above eguations, the constants naturally
depend upon the particular shape of the boundary loci.
As is set forth in my above-referenced U.S. Patent
4,180,325, locus L is equipped with 256 timing markers about
its periphery (one of the markers being omitted to determine
angular reference)O Moreover, approximately 256 timing
counts are made between the passage of each timing mark.
This being the case, it is possible to establish the accuracy
of a particular timing measurement by determining the devia-
tion from æero of the checksums Tl, T2, T3:
Tl d3 -d2 -dl +d4 - 360
T2 = d2 ~dl ~d3 d4
T3 = -d3 ~d2 -d4 ~dl
Where: T1 is checksum for measurement of point A';
T2 is checksum for measurement of point B';
- T3 is checksum for measurement of point C';
and,
dl-d4 are defined above.
A measurement is to be rejected if Tl, T2, or T3 is
greater than some predetermined value.
Thereafter, each of the angular determined ~ values
is corrected by predetermined constants. As an example, the
~L7~ 77
following constants for each of the determined e values, ~1'
e2 ~ e3 have been used:
~1 ~ 41 ~ 4.97
e2 ~ 43 - 4.62
e3 ~ e4 - 4.58n
It will be remembered that a pyramid mirror 47 is
present in the optical train. Mirror 47 adds a distortion to
the determined radius along radial components which are along
the slope of the mirrors. Accordingly, the determined radius
must be corrected for that component added by the slope of
the mirror as follows:
Rill = ri cos (ei ~oi)
Ril = ri sin (4i ~oi)
Where: i = 1,2,3
Rill is component of R; along a line
bisecting the particular ~uadrant;
Ril is component of R; perpendicular to
Rill;
Ri is radial distance of a spot from
optical center 57;
~i is defined above;
401 = 45
~02 = 31
~03 = 225
Once these corrections have been made, the real
radii and angles must be determined as follows:
R'ill = Rill [1--021 (Rill )]
R i ~(R'~ (Ril~
i ~oi + sin 1 ( il )
Where: R'ill is the corrected Rill component;
R'i is the corrected distance Ri;
~'i is the corrected angular position ~i.
41
Further, correction must be made for any magnifica-
tion factor present in the disclosed optics as well as any
distortions. The reader will understand that these are
empirically determined terms so that the numerical values
given here are actual constants used in practice which will
have to be re-evaluated should the apparatus be practiced
using another or alternate embodiments .
R'i as determined above is the spot distance as
measured at the plane of the physical locus. As measured at
the corneal plane, the corresponding distance ri is given by:
ri = ~O99lR'i-.00142R'i3
Thereafter, conversion of polar to Cartesian co-
ordinates can be made. This conversion is as follows:
convert to (Xi, Yi):
i Ri cos 4i
Yi = Ri sin ~i
Correct for mirror angle and
displacement resulting therefrom:
X'l = Xl - k Y'l = Yl - k
2 X2 k Y'2 = Y2 + k
X'3 = X3 ~ k Y'3 = Y4 + k
Where k = .0235
Once this has been done, computation of equivalent
sphere (Sl), 0-90 astigmatic component (S2), 45-135
cylindrical component (S3), and error function x2 (S4) can
then be generated. These equations take the form:
~orm the sums:
1 X2-X3 + Yl-Y2 (Seq)
- S2 Xl_X t X lX + y 1 + 1 ( Cx/2 )
S3 X3-X2 Xl-X2 Yl-Y3 Y2 Yl (C+/2)
S4 Xl-X3 ~ X3-X2 + Y3-Yl + Yl-Y (x23
71~i~377
42
Where: seq is equivalent sphere;
(C+/2) is half the 0-90 astigmatic
component;
(Cx/2) is half the 45-135 astigmatic
component;
(x2) is an error function.
Regarding equation S4, two important points can be
made. First, S4 is typically analyzed to determine the
desired distance calibration. This analysis involves a
comparison of S4 using first one set of light sources and
then the other set of light sources utilized in point sources
41-43. Instrument movement occurs to change the values.
When both determinations of S4 agree, the instrument is
axially positioned at the proper distance from eye E of the
patient.
Second, if equation S4 produces similar, and sub-
stantial non-zero values for each set of light sources,
non-toric surfaces can be indicated. This value will vary
with the particular construction. This value acts as a check
for non-toric functions. That is to say, that where S4
exceeds a certain empirically determined value, the measure-
ment may be "flagged," indicating to the operator of ~he
instrument that he has an eye E which is a candidate to be
examined for non-toric surfaces.
The determined values Sl through S3 are scaled to
produce readings of sphere and astigmatism (in diopters) by
the following:
S = K Sl
C+/2 = -K S3
Cx/2 = +K S2
Where: S is equivalent sphere in diopters;
- K = 1.8698 and is an empirical constant;
C+/2 and Cx/2 are the astigmatic compo-
nents in diopters.
Thereafter, these determined values of sphere and
astigmatism can be corrected for incipient error by the
following curve fit relations wherein the constants aO~ a
7~ 177
43
and a2 are determined according to standard curve fitting
procedures.
Y ~ Y- [aO ~ al (S -SO) + a2 (S -SO) ]
Where: Y represents either S, C~/2, or Cx/2;
aO, al, a2 are constants particular to S,
C~/2, and Cx/2;
S0 is a preselected reference value of
eguivalent sphere.
Cylinder may then be found using simultaneous
solutions of the following eguations:
C+/2 - (C/2) cos 2~
Cx/2 = (C/2) sin 2e
Where: C is total cylinder power;
~ is cylinder axis.
Finally, the result can be presented in conven-
tional form giving the powers in two perpendicular axes:
SR~l, the power along a direction normal to the cylinder
axis, and SRx2, the power along the cylinder axis.
S~xl = S + C/2
SRx2 = S - C/2
Where: S is equivalent sphere;
C/2 is half the total cylinder power.
Having set forth with reference to Fig. 3B the
actual measurement of an eye, the acquistion of an eye will
now be discussed.
ExemPlary Com~tations for
Ali~nment of Keratometer with E~
Referring to Fig. 2A, the optics by which gross
acquisition of the eye E of the patient are acquired can now
be set forth.
The keratometer housing H is provided with a direct
- eyepath by which an operator O (schematically shown) can view
along a direct line of sight to the eye of a patient E. A
light source 80 interior of housing H impinges upon a beam
splitter 81. At beam splitter 81, the light source B0 has a
virtual image which appears to be at or near the vicinity of
eye E.
77
44
To aid alignment, especially in subdued light,
light sources 83, 84 in the face of the instrument, shown in
~ig. 4B, are turned on. These light sources are in turn
visible as virtual images in the cornea of the patient's eye.
The keratometer operator o registers the imaginary image of
light source 80 to and typically between the virtual images
of the light sources 83, 84 of the instrument face light
sources in the eye of the patient E. When this registration
occurs, gross alignment of the instrument is effected.
i0 Once gross alignment of the instrument is effected,
the optics of the instrument must then be used to effect fine
alignment. Such fine alignment will be discussed once the
light paths illustrated in Figs. 2B and 2D and the circuitry
of Fig. 3C is understood.
Referring to ~ig. 2B, light emanating from the
housing H is illustrated impinging upon an eye E. The eye E
displays to such light a convex surface. Consequently,
respective detectors Dl-D3 receive light from sources 41-43.
(See Fig. 2A).
The point has previously been made in Fig. lA that
the disclosed invention can just as well be used for measur-
ing contact lenses C. Such measurement i5 illustrated in the
schematic light train of ~ig. 2C. In Fig. 2C, however, it
will be remembered that the contact lens C is a concave
surface. This being the case, light source 41 is imaged at
detector D3 and light source 43 is imaged at detector Dl.
Light source 42 is not used. Source 44 is substituted for
this light source and images at detector D2.
It will be recalled that with respect to Fig. lB, a
microswitch 32 was attached. Microswitch 32 is switched upon
the insertion of contact lens holder 35. This microswitch
functions to switch the detector ali~nment to the circuit
~ logic as hereinafter set forth when a contact lens-C is
substituted for the eye E. It will be realized this is
optional (a simplification) as the correspondence between
sources and detectors also identifies contacts, and which
contact lens surface is exposed.
:lS ~ 77
It will be appreciated that light sources 41-44 and
detectors Dl-D3 are interchangeable. As of the moment of
filing of this patent application, I have not yet identified
the preferred location of light sources and detectors insofar
as their interchangeability is concerned.
Additionally, it may be desired to measure optical
curvature of the convex portion of a contact lens. It will
be appreciated that the instrument herein could be so used
and so adapted.
Having set forth the light paths and the respective
switching of detectors, attention can now be directed to the
light sources.
Referring to Figs. 2C and 2D and describing the
disclosed invention whexein high intensity light sources are
placed at positions D1, D2, and D3 adjacent the contact lens
C, the detectors placed at positions 41-44 can be described.
Each of these detectors and their alignment is schematically
illustrated in Fig. 2D. The following explanation occurs
with the image of the detectors being schematically relayed
to the eye E schematically shown in Fig. 2D.
With reference to Fig. 2D and the detectors sche-
matically there illustrated, detector 41 comprises two light
receiving areas 41a, 41b. These photosensitive elements are
sensitive in the infrared and aligned in side-by-side rela-
tion along a first obligue axis 90.
Detector 42 includes two side-by-side light photo~
sensitive areas 42a, 42b. These respective infrared light
receiving areas are aligned along a horizontal axis 91.
Detector 43 includes two spaced apart light receiving areas
43a, 43b. These respective light receiving areas are sensi-
tive in the infrared and aligned an oblique axis 92. The use
of infrared light to measure the corneal surface of the eye
avoids complications of instrument measurement whi~h could
occur where the eye -which is sensitive to visible light ~has
visible light suddenly impinging upon it resulting in squint-
ing, blinking or other movement.
Referring to Figs. 2B-2D, it will be understood
that the paired light sources shown in Fig. 2B or the paired
~:~!t~ 77
,
46
light detectors shown in Fig. 2C at Fig. 2B can be used alone
or in combination to determine the axial or Z spacing of the
instrument from the human eye. This spacing can be deter-
mined in two different ways.
First, and using for example paired photosensitive
areas 41a, 41b, these respective paired surfaces act in a
manner not unliXe split-image range finder in a 35 mm camera.
Specifically, by having the moving boundary locus L measure
the optical center of each of the sections of the paired
photosensitive areas 41a, 41b, a rather precise distance
spacing of the eye E from the housing H can be determined.
The same principles used in split-image range finders by
using optically active and differing portions of a camera
lens, the axial distance to the eye can be measured. Assum-
ing that the eye does not move appreciably between the mea-
surement occurring on surface 41a and the measurement occur-
ring on surface 41b, by detecting the optical center and
~bserving for shifts, one may determine proper distance
spacing.
As a practical matter, the eye is always undergoing
movement. At a minimum there is the rapid saccadic panning
movement of the eye which panning saccadic movement makes
desirable a quantification of any shifting of the optical
centers detected by the instrument. Accordingly, and in
order to maximize utility to the optical paths which I have
disclosed, I have cleveloped a mathematical relationship for
determining distance, S~, defined ab~ve.
It is emphasized that the mathematical relationship
that I have hereto set forth for the quantity S4 reguires
that each light path have two photo-distinct portions. For
purposes of the analysis here it does not matter whether
- these surfaces are photo-emitters or photo-detectors. Hence,
~ I will refer to these side-by-side areas as "photo-distinct"
to cover both emitters and detectors.
-Each of the two side-by-side photo-distinct areas
must be set in spaced apart relation. Moreover, the axes 90,
91 and 92 must all be at differing angles with respect to one
another. Preferably, the alignment is such that axis 9Q is
s~
47
obligue, axis 91 horizontal and axis 92 oblique. Oblique
axes 90, 92 intersect normally, one to the other. The
sources 42a and 42b can optimally be somewhat further spaced
apart as shown in Fig. 2D although this is not required.
This is preferably done by a factor of about ~. In the
event that four ~4) channels are used, variable separation is
not preferred.
As will hereinafter be set forth, the occultation
of the paired photo-distinct areas 41a, 41b 42a, 42b and 43a,
43b occurs so as not to shift the observed optical center
when the eye is optimally positioned. When the eye is out of
position, a shift of the observed optical center occurs.
Before this can be set out to the reader, a schematic of the
circuitry for this invention must be set forth.
Referring to Fig. 3C, respective photo-distinct
areas 41a, 41b, 42a, 42b, 43a, 43b, 44a and 44b are illus-
trated here as light emitting sources or areas. Each of
these light sources is infrared and includes a first light
emitting diode and a second light emitting diode. The par-
ticular alignment necessary for the practice of the invention
and set forth in Fig. 2B.
Circuit Schematics
Referring to the schematic of of the circuit dia-
gram at Fig. 3C, it can be seen that an oscillator A, through
a driver can drive through switch matrix 101 either a light
source 41a, or a light source 41b dependent upon the polarity
of LED control switch 102. Likewise, oscillator B can drive
light source 42a or 42b and oscillator C can drive light
source 43a or 43b. It will be appreciated that the disclosed
oscillators will operate at distinct and separate modes.
Oscillators A, B and C have three discrete frequencies of
oscillation.
~~ Referring to the embodiment shown in Fig. 2B, it
will be remembered that light sources 41a and 41b are inci-
dent upon detector Dl. Likewise, light sources 42a and 42bare incident upon detector D2. Similarly, light sources 43a
and 43b are incident upon detector D3.
It is necessary that each of the detectors Dl
through D3 be sensitive to determine which light source is
incident upon them. Switching network 101 is provided with a
switching pulse 100. Pulse 100 causes the output from oscil-
lators A-C to step from light source to light source. Simi-
larly, LED control switch 102 is provided with a switching
pulse 104a for switching between the dual light sources 41a,
42a and 43a to 41b, 42b and 43b.
Detectors Dl-D3 are connected to preamplifiers
104-106 respectively. Detectors Dl-D3 put their respective
outputs through amplifiers 104-106 to frequency selective
phase detectors 111, 112, 114, respectively. Oscillators A-C
also provide their output to detectors 111, 112, 114, respec-
tively.
As noted above, switch pulse 100 causes matrix
stepping between the respective signals from the respective
oscillators to drive the respective light sources with dif-
fering frequences. The particular light source signals
incident to detectors Dl, D2 and D3 can be identified by
comparing the freguency of the signal received by the par-
ticular detector at a particular time with the frequencies of
the oscillators. Note that these signals could come from any
of the light sources 41a, 41b, 42a, 42b, 43a, 43b (or 44a and
44b as set forth hereafter) on any single detector. Once the
light sources are identified at the comparator, digital logic
can cause the keratometer to move from a position of gross
alignment to exact positions for keratometric measurement.
This is possible based upon the R-e relationship discussed
with reference to Fig. 5. Thereafter, and as set forth with
respect to the logic illustrated in Fig. 6, actual measure-
ment of the eye can occur.
Having set forth the circuitry for recognition at
each sensitive quadrant of the discrete point sources of
light, and having described how gross registration of the
housing ~ occurs, the actual acquisition of the eye E of a
patient can be described by first referring to Fig. 2~ and
thereafter to Fig. 3A.
$~ 7
49
In Fig. 2B, it will be seen that the three active
detectors Dl, D~ and D3 address the eye at an angle in the
order of 20. The light sources 41a-43b impinge upon the eye
along the optical axis 57 of the instrument. It will be
remembered that the cornea of the eye E is a convex surface
and we in effect want the mire foxmed between the images of
the light sources A', C' and B' to impinge about a pole of
the eye coincident with the optical axis 57 (see Fig. 2).
Referring to Fig. 3A, a gross alignment is assumed that has
left the housing H with the optical axis 57' below and to the
right. Consequently, the center of the illuminating areas of
the light sources A', B' and C' will have moved below and to
the right.
Where gross alignment has occurred, areas of detec-
tor sensitivity of detectors Dl, D2 and D3 will remain sub-
stantially unchanged. These detector areas A, B and C will
remain substantially on the same quadrants of the eye.
Referring specifically to the view of Fig. 3A, it
can be seen that light source C' is incident upon detector
area B in this type of misalignment. With appropriate
switching of the circuitry of Fig. 3C, detector D2 in moni-
toring segment B of the eye will soon detect that sources
43a, 43b are being seen. Comparator 112 will output a signal
that it has recognized image C' from light sources 41a in its
quadrant. Translation of the overall instrument can then
remotely occur by moving the keratometer illustrated in Fig.
lA in the direction of arrows 15, 19.
The reader will appreciate at this point, that two
methods of instrument alignment have been set forth. ~irst,
and with respect to logic of Fig. 3C and the diagram of Fig.
3A, alignment of the instxument along the X and Y axes have
- been demonstrated. Secondly, and with respect to Fi~. 2D, a
system of detecting optical shifts in the disclosed optical
centers of faced sources or detectors has enabled positioning
of the instrument towards and away from the patient or along
"the axis". Thus, there has been described thus ~ar an
automated positioning of the instrument.
D&'7~
.
It will be apparent to the reader that in moving
from the alignment shown in Fig. 3A to that shown in Fig. 3B,
instrument panning will occur to register the light sources
A'-C' in quadrants I-III. However, registration may move so
that the light sources are within the proper quadrant but not
~roperly registered. Such a registration of light sources is
illustrated with the optical axis being shown at 57 " and
light source A ", B " and C " in their respective quadrants
I, II, III. In this case, it will be rernembered that by
using the eguations for R and e previously set forth, mea-
surement of this lack of alignment may be easily made.
Further instrument movement can occur until the alignment to
the optical position shown at Fig. 3B occurs.
Com~uter
Figure 6 sets forth the logic and computer hardware
which the preferred embodiment herein contains.
The electronic circuitry of this invention includes
four logical steps. First, monitoring of the rotational
position of the rotating boundary locus L occurs. Secondly,
recordation of occultations (typically by inference from a
digitally produced intensity curve) as they occur at the
photodiode D occurs. Thixd, the circuitry computes the
angular interval of the inferred occultation. This is typi-
cally done to an accuracy of about 1 part in 50,000 of the
total rotation, or 2/lOO,OOOths of the total rotation.
Finally, these angular values are computed to spherical
power, cylindrical power and axis and position. These com-
puted values are presented to the operator by either a light
emitting diode (LED) display or printout~
Referring to Fig. 6, the standard parts of an
electronic computer are shown. Particularly, a central
- processing unit (or CPU) 200, designated as Chip 8086, manu-
factured by Intel Corporation of Santa Clara, California
(hereinafter Intel) includes a system clock 201 (Intel 8224).
The clock 201 is used for driving a position counter 202
(National Semiconductor chip 163 of Sunnyvale, California).
The CPU 200 inputs and outputs through a bus con-
trol 208 (Intel 8228). Bus control 208 functions to align
~7~Pi~77
51
the various inputs and outputs for circuit interrogation,
computation and output.
A read only memory (ROM) 202 (Intel 2708) contains
the program for the central processing unit 200. Read write
memory (RAM) 204 (Intel 8111) stores for retrieval various
quantities read partially computed and fully computed by the
detectors D.
An address bus 207 and a data bus 208a function to
move data throughout the system. Standard computer compo-
nents such as printer interface and printer 212 and a displaykeyboard interface 211, including a display and keyboard, are
connected. Since these are standard state-of-the-art items,
they will not be further discussed herein.
Referring to the moving boundary locus L as sche-
matically shown on ~ig. 6, it will be appreciated that threepaired and separate outputs are received. As set forth
herein, photodiode and amplifier-buffer assembly 210 monitors
the counts of each of the notches 121 as they pass. This
photodiode gives a rotational reading of the moving boundary
locus L. Similarly, each of the areas of the photodiode Dl,
D2 and D3 has a discrete output from the central area 125 of
locus L.
Each of these optical outputs from t~he respective
photodiodes included in 210 are buffered. This is accom-
plished by a double amplifier which includes a current to
voltage amplifier and then one or more simple voltage ampli-
fiers connected in series. The output signal is convention-
ally provided with reduced impedence which is less subject to
noise interference.
It is necessary to note when one complete rotation
of the boundary locus L occurs. This can be accomplished by
- either omitting a mark (as shown in Fig. 5) or alternately
having a mark a double thickness. In the illustration shown
in Fig. 5, omission of a mark occurs.
Regarding the inference of the light intensity
curve and over that logic which I have previously disclosed,
one problem peculiar to corneal measurements is present.
Specifically, where a light such as the infrared lights of my
~b~i77
52
invention are utilized, corneal reflection necessary for
keratometric measurement and diffuse reflected iris illu-
mination may simultaneously occur. In the case of the latter
iris illumination, it will be appreciated that the light
produced thereby is extraneous. This being the case, provi-
sion must be taken to screen out the iris illumination.
It will be appreciated that this iris illumination
will vary. For example, in the case of brown eyes, the
background illumination may differ from that of bluer eyes.
Referring to Fig. 7, a plot of illumination versus
time is illustrated. Specifically, background iris illumina-
tion is illustrated by the line 300. It is noted that it has
a variable magnitude and is present whether or not occulta-
tions occur.
The broken line 301 illustrates the infrared re-
flection from the eye which is a product of the occultations
of the moving boundary locus. This produces a bell-shaped
curve which gives a tell-tale indication of illumination.
Adding these two curves together, we get a compos-
ite curve, such as 302. The reguirements for accurate mea-
surement include pinpointing those portions of the curve
having a rapid change in slope, such as point 303, 304, 305,
and 306.
Although optical means, such as reduced sampling
sectors in the moving boundary, may be used to reduce iris
effects, I propose to locate these points by digital filters.
Specifically, the development o~ light intensity is continu-
ously monitored by the disclosed logic. In this monitoring
(schematically shown along composite curve 302 as mark points
"X"), the logic examines the intensity with respect to time.
Where points of curvatures are located, indications are made.
- By appropriate and subtractive logic, the crossing of the
curves of the composite curve 302 with a medial line 310, can
be observed. The eguations previously set forth can then be
solved, using the data o~ equation 310.
Remembering the logic previously illustrated with
respect to Fig. 3C and referring specifically to Fig. 3D, a
phase detector useful with this invention is illustrated.
;~ ;77 J
53
Specifically, the input signal to a typical phase detector
(111, 112, 114) is received and routed to a comparator 301A.
Comparator 301A receives a second signal. This signal comes
from a 12-bit up-down counter 302A through a digital-to-
analog converter 303A. The comparator 301A compares a signal304A to a photosensitive element. The output of the compara-
tor is fed back to the up~down control. From the feedback to
the up-down control, the output of the 12-bit up-down counter
302A passes to appropriate gating 305A with output at 306A to
the CPU-data buss as indicated at 306 on the schematic dia-
gram of ~ig. 6.
The signal into this circuit has the intensity of
the solid line 310A at the lower righthand corner of Fig. 3D.
Output 306A at the gate 305A follows the illustrated sguare
wave form which by interaction of the comparator and feedhack
to the 12-bit up-down counter tracks digitally the bell-
shaped curve 310A.
It is important that the filters reject signals out
of phase with the respective oscillators. Specifically, a
simultaneous rectifying filter is illustrated in the view of
~ig. 3E. Broadly, a double-pole double-throw switch 320 is
thrown at the freguency of the oscillator at input 321. The
switched output of double-pole double-throw switch 320 passes
through a different:ial amplifier 322 with output 324.
Where the signal in line 323 is in phase with the
reference freguency, the system in conjunction with ~le
differential amplifier 322 reverses the phase of the signal
for each half cycle of reference freguency. A signal at the
same freguency and in phase with the oscillation will appear
at the output as a positive DC level. This positive DC level
will pass the low pass filter 325 and go on for further
- processing.
Where the signal is out of phase with the oscil-
lator, the switch, in conjunction with the differential
amplifier, again reverses the phase for each half cycle of
the reference frequency. Here however the signal will not be
in phase. The result will be that those portions of the
signal out of phase will be reversed and cancel those por-
~ '7C~77
54
tions of the signal which are in phase. There will result ablocking of out of phase signals.
I will not further discuss switching of the logic
upon the insertion of a contact lens. Such logic switching
is believed to be well within the skill of those having skill
in this art.
Detecting the Corneal ShaPe
~ eferring to Fig. 4B, it will be observed that
fixation lights 500, 501 and 502 are in the face of the
instrument. Typically, these lights will assign fixation to
the patient. The patient will be told to view an illuminated
light while the keratometric measurement is being taken.
Naturally, lights 500-502 will only be illuminated one at a
time.
Preferably, the lights have angularity assigned to
them. The angularity can be in the broad range of 5~ to 22,
the intermediate range of 10 to 15 or the narrow range of 12
to 1~.
In accordance with the foregoing description, there
will occur at the respective points 500', ~01', 502' the
measurements specifically described. Comparing the view of
the eye in Fig. 8 to the view of the eye in Fig. 2B, it will
be immediately seen that the photodiscrete elements in ~ig. 8
are vastly reduced in size. These photodiscrete elements are
more nearly the size actually used in my keratometer. Speci-
fically, the typical corneal diameter of the human eye is on
the order of 12 mm. My photodiscrete elements cover an area
of approximately 3 mm in diameter. Thus and with the fixa-
tion that I set forth, discrete measurements along the eye
can occur.
It should be further noted that my measurements
- occur typically along a horizontal axis 503'. Preferably, I
do not measure along other than a horizontal axis so that
interference with the eyelashes may not occur.
It will also be observed that my method of computa-
tion has a surprising result. By use of measurement along a
straight line, I am able to predict with some accuracy the
corneal shape above and below the axis 503'. That is to say
by scanning along such an axis, I get a determination of the
overall shape and slope of the human eye well outside the
line of scan.
Referring to ~ig. 9, a ~ectional view of a human
eye at the vicinity of a cornea 510 is shown. Specifically,
and with reference to ~ig. 9 it will be noticed that there is
one air cornea interface 511 at which refraction occurs.
Interiorly of the cornea and at lens 512, conventional refrac-
tion occurs for focus on the retinal plane of the eye in the
vicinity of fovea 514 and the retinal plane 515.
Having set forth this much, an eye E similar to
that shown in Fig. 9 is shown at Fig. 10. Here, however, the
eye E has fitted thereon a contact lens 520.
It is instructive to consider the num'oer of addi-
tional refractive interfaces that a contact lens can intro-
duce. ~irst, there is the conventional corneal interface
511. It will be appreciated that the mere presence of the
contact lens 520 can have an effect at altering and/or chang-
ing the shape of the interface 511.
Secondly, and trapped between the contact lens 520
on one hand and the corneal surface 511 on the other hand
there exists a tear layer 518. Tear layer 518 can have
dimension and furthermore can have the requisite rate of
change of dimension so that it becomes a very effective
refractive interface. ~or example, as is known in the con-
tact lens art and when a hard lens is present, this interface
can be relied upon to produce astigmatism opposite it in
typical effect to astigmatism afflicting the eye. It may be
realized that this sort of correction of astigmlatism at the
cornea will not affect other astigmatism present in the eye
such as that which may be resident in the lens 512 or on the
- retinal plane 515. Accordingly, the accurate determination
of the depth of the tear layer and its optical effect may
have importance.
Given that increased information in regard to
corneal shape is a desira~le goal, consider the possible ways
in which corneal shape might be characterized. Two types of
parameters come to mind - those that are primarily of theoreti-
7~
56
cal interest in providing an improved description of the
corneal shape and those which might be considered to have
primarily a practical or clinical value in that they are an
aid in contact lens fitting procedures. Naturally, some
corneal parameters will be important on both counts. The
list below represents in general terms the kind of additional
information that can be expected.
1. Central "k" readings;
2. A measure of departure from circular cross
sections;
3. A measure of alignment or positioning of the
axis of symmetry of the cornea;
4. Detection of corneal irregularities;
5. Corneal diameter;
6. Vault height of the cornea ~over the scleral
extension);
7. "Cap size"; and
8. Corrected apex "k" readings.
These classes of corneal information have been
characterized in a very general form. In actually arriving
at a specific means of describing these corneal shape fac-
tors, it is necessary to arrive at some kind of compromise
between the extent and detail of corneal information and the
burden on both the patient and the doctor (or the technician,
if the measurements are by a technician).
An overly complex examination places a burden upon
a patient which can detract from the examination in two ways.
First of all, the attention ~pan varies greatly from one
patient to another. The ability to successfully carry'out a
complex corneal measurement is enhanced as the measuring
process becomes shorter and simpler. And, of course, the
patient tires less. For instrumentation designed to make
corneal measurements by a technician, it is probably prefer-
able to maintain as simple and as objective a measuring
procedure as possible. This implies a minimum of technician
skill in arriving at the measurements. Such operations as
retracting the upper or lower eye lid for any substantial
fraction of the patients should be avoided. This type of
1~ 77
57
manipulation is not only an inconvenience to the technician
and the patient, but also has the potential of inducing
si~nificant changes Df corneal shape. And finally, the
matter of too much information vs. too little information is
a factor of importance for the doctor. Overly detailed
information on the corneal shape may confuse the basic charac-
terization of the corneal shape through an over abundance of
parameters which are unintuitive and difficult for the doctor
to interpret. Inasmuch as it is probably impossible to
devise any comprehensive, numeric description of every pos
sible corneal shape, it becomes a question of finding the
most effective and intuitive means of abstracting the avail-
able data to make the data more manageable and more easily
interpreted by the doctor.
This balance between complexity of characteriza-
tions of ~he corneal shape and difficulty of measurement and
interpretation has resulted in the following specific list of
suggested corneal shape parameters.
1. Central "k" readings, mm. or diopters;
2G 2. Corneal shape factor (~);
3. Corneal decentration ~istances (~s~ Qt' ap);
4. Chi-square values for individual corneal
measurements and for fits of corneal measurements to an
overall corneal shapei
5. Estimated vault height, mm.;
6. Cap size, mm.; and
7. "k" readings, transposed to the corneal apex
and corrected, mm. or diopters.
Of these parameters, the last three are derivable
from the first three but will be included as a matter of
convenience.
- The analysis of corneal shàpe through the combina-
tion of several keratometer measurements could be divided
into two parts. Part I is each individual corneal measure-
ment complete with its estimate for sphere and cylindercomponents, plus goodness of fit chec~.s in the form of an X 2 .
For a 4-point keratometer measurement using full information
in each of the four sample areas, the y~ c2n be a "3c" X 2 .
~ . 17~&'7~
58
For keratometer measurement employing full information from
three sampling areas the x2 is a "lc" fit (this latter method
is preferred). Attention will be directed now toward combin-
ing individual measurements with the measurement values at
each individual fixation angle assumed to be given.
The mathematical analysis of the ~ornea shape takes
nlace as a sequence of analysis processes. ~irst, the reflec-
tive deflections for one small area of cornea are distilled
into a set of curvature measurements along with a goodness of
fit parameter. Thén, several such sets of curvature measure-
ments taken at several corneal locations are reduced to a set
of adjusted, idealized curvatures, i.e. fitted curvatures.
Then, these fitted values are used to create intermediate
parameters, and these parameters are then combined to produce
the final corneal shape parameters.
Subject to several assumptions, it is conceivable
that corneal shape factors could be estimated based on just a
central "k" reading and one peripheral reading. However, the
mathematical treatment of this abbreviated corneal measure-
ment will be skipped over in favor of what will be termed thethree-point corneal measurement. The reason for the prefer-
ence of the three-point corneal measurement lies in the fact
that not only the corneal shape factor can be determined, but
also the corneal decentration distances ~s and ~t can also be
determined.
The more detailed mathematical treatment of the
three-point method which follows will reguire establishing a
few mathematical conventions. The observed curvature measure-
ments will be designated by xi, as defined in the chart
below:
xO central, perpendicular to sampling line
- xl central, parallel to 6ampling line
- X2 nasal, perpendicular to sampling line-
X3 nasal, parallel to sampling line
X4 temporal, perpendicular to sampling line
X5 temporal, parallel to sampling line
7~7
59
X6 central, oblique to sampling line, astigmatism
component
X7 nasal, oblique to sampling line, astigmatism
component
x~ temporal, oblique to sampling line, astigmatism
component.
Optimized estimates for x0 through x~ are desig-
nated by f0 through f8 (fitted values~. The fitting proce-
dure deals with the data as two sets. The first set consist-
ing of x0 through X5, is dealt with in the following manner.
A chi squared estimate is employed, subject to the
following constraints:
3(fo ~ f2) ~ (fl ~ f ) =
3(fo ~ f4) ~ (fl - ~5) = 0
These constraints are simply a mathematical state-
ment of the "three-to-one" xule mentioned earlier.
~7~7~
The rule is applied separately for nasal and tem-
poral measurements to allow for the effects of moderate
corneal angular decentration. This is only approximately
justified, as is the "three-to-one" rule itself.
S Subject to the above mentioned constraints, the
form of the chi-square function is as follows:
X2=a2~ (xo-fo)2+(xl-fl)2+(x2-f2)2+(x3-fl)2+(x4-f4)2+(x5-f5)2}
The fitted values are determined by the following relations:
fO = 1/30 (l2~o+6xl+9(x2+x4)-3(x3+x5))
fl = 1/30 (6Xo+28l-3(x2+x4)+(x3 X5))
f2 = 1/30 (9xo-3xl+l2x2+9x4+6x3-3x5)
f3 = 1/30 t-3xo+xl+6x2-3x4+28X3+x5)
f4 = 1/30 (9xo-3xl+l2x4+9x2+6x5-3x3)
f5 = 1/30 (-3xo+xl+6x4-3x2+28x5+x3 )
1S x2 two degxees = 1/1OF2 ( 2/3)(a2+b2-ab)
freedom
a = 3xo-xl-~x2+x3~ b = 3xo xl 3x4 5
The corneal shape factor information as well as
part of the corneal orientation information is contained in
the measurements xO through X5, while the obli~ue asigmatism
measurements x6 through x8 contain the remaining information
regarding corneal orientation. In fitting this data, it is
beneficial to all~w for corneal decentration perpendicular to
the sampling line. This accomplished through the use of the
following constraint relation:
2 f6 f7 ~ f8 =
A chi-sguare is then defined as:
- x2 = 1/~2[(X6-f6)2 + (x7-f7) + (x8-f8) ]
~ with fitted values determined by the following relations:
f6 = 1/3(X6 + x7 + x8)
f7 = (1/3)x6 + (5/6)x7 - (1/6)x8
f8 = (1/3)x6 - (1/6)x7 + (5/6)x8
7'7
61
X one degree _ (2X6 ~ x7 - x8)2
freedom 6~2
After having arrived at this set of fitted curva-
ture values, these "f" values may be manipulated to arrive at
the corneal shape parameters defined earlier. The chart
below is a comprehensive collection of relations for inter-
mediate values and final shape parameter estimates based on
these "f" values:
i0 ~, ~
m3~ ~ m5~ ~ T2~ ~ ~T4~ defined by
1 - m3~ 2(fl - f3)
(1 + m3~ ) fo + fl
1 ~ ~m5~2 2 = 1 _ 2(fl _ f5)
(1 + m5~ ) fo + fl
~ 2 = 1 _ ~fo ~ f2)
1 + T2~ fo + fl
2(fo f4)
= 1 -- - _ ....
1 ~ T4~ fo + fl
Nrl = . 9m311 + . 1T2rl
T m5~.lT4~
11 = ~(NI~2 + Trl2)
t~2 is a shape factor. This factor combines the
- overall shape of the eye with the magnitude of the offaxis dis-
placement from the "summit" or "peak" of the cornea.
~2 defined by
~ 7~7
62
d~ f ~ )2~ ~ = geometric constant), or
rl2/( 1 + 1~2 ) = Kl
( fo + fl ~
K = ~ ~ ~ (mm 1)
.3375 x 103
Part II: Corneal Parameters
1. Central "k"
Eguivalent Sphere = 2 1 = Seq.
0-90 Astigmatism = 2 1 = Ao 9O
(+ cyl. at 0 ~ Ao 9O > 0)
45-135 Astigmatism = f6 = A45_
(+ cyl. at 45 ~ A4s 135 ~ )
The central k readings thus give the power in
sphere, cylinder and axis of the "peak" and/or "summit" of
20 the cornea.
2. Corneal shape factor;
- E: = ~L _
The corneal shape factor gives a measure of the
departure from a true sphere of the corneal surface. For
example, if the corneal surface were spherical, the value
would be 0. In actual fact, a flattening of the eye occurs
r~377
63
which gives a value of .2 as a typical result found
for this parameter.
-
- 3. Apex position; ~s' ~T~ ~P
--Nr~2 + Tr~Z
S ~T = 4~K ~ t+ if visual axis is
_ l _ temporal of apex)
~s = 1/4~ ~ 1 +( _K ) 1 1(+ if visual axis
1~ 1 fo + f I is superior of
L , 2 l J apex, right eye)
~P = K2/4Fr~k - (43 ) 4~r~k
(expected precision
T' s' K2 is an
empircally determined
precision constant)
These figures are a measure of the displacement of
the peak with respect to a line of sight. QT is horizontal,
20 ~S vertical with ~p a measure of the uncertainty of locating
this summit value.
4. Cap size - 1 diopter level, diameter in mm
cap k [e s2eq(s (g(Seq,)2 _ 3 Seq ) ~ 2
S. Vault height (mm over a 25 mm sclera)
V - H( ) l/k - ~ - [(22J ( k )
H(~) = .3596 - .1902 + .1115~2
.~'7~377
~4
6. Corrected central llkll
r 2
Se~. = Seg. ~l + 'm )
m2
~here ~m is the surface tangent at the corneal measuring
areas, and k3 is the resulting computational constant,
typically .036.
7. Goodness of fit X2D and XlD (2 degrees of freedom
and 1 degree of freedom)
These corneal parameters may be altered or expanded
upon in various ways. ~or example, goodness of fit may be
extended to include fit information from each local measure-
ment. Or, eccentricity and decentration information may be
used to produce a more sophisticated correction for the
central "k" measurement.
A few general comments are in order. First of 211,
it should again be stressed that the mathematical analysis is
based on the assumption that the corneal axis is closer to
the visual axis than are the peripheral sampling areas. This
requixement is adequately satisfied for corneal axes within
1 mm of the visual axis, and the literature indicates the
vast majority of corneas will satisfy this condition. ~or
those corneas which have excessive decentration, there are
several possible courses of action. One possibility is to
merely indicate the excessive decentration as a factor of
interest in itself and omit those computations which are most
sensitive to the decentration. However, it should be noted
that only statistically significant decentrations need be
dealt with in this way. ~or example, a near spherical cornea
has a very poorly defined corneal axis which can easily
appear to be excessively decentered, but many of the calcula-
tions remain valid because the corrections implied for near
spherical corneas are so small that the amount of corneal
decentxation is not very material.
Another possibility is to reformulate the mathe-
matics based on the best estimate of the corneal apex posi-
.
b~ ~ 7
tion and recompute the corneal paramet~r, iterating until a
consistent set of parameters is achieved. This iteration
process may involve corrections to the local corneal measure-
ment data (xi), particularly for unsymmetric corneal sampling
arrays. This approach to the problem is manageable but
computationally time-consuming and will not be dealt with
here.
Referring to Fig. 11, the use of my invention in
the fitting of contact lenses is schematically illustrated.
First, and as to eye E, successive measurements of ~he tem-
poral, central and nasal portions of the cornea are taken.
Once these successive measurements are taken, they are indi-
vidually determined in accordance with the previous disclo-
sure as represented by block 400. Thereafter, the results
are typically processed for fitting as indicated at block 402
and forwarded to a map of the eye in the form of the parame-
ters illustrated, the map being shown at block 403. Results
of the map of the eye are passed to a data bank 404 where the
map is retained.
Simultaneously with this measure, a contact lens
empirically fitted to the eye E is removed and conventionally
measured. These parameters of the contact lens are there-
after placed to the data bank. Measurement of the contact
lens could of course occux by use of the individual
keratometer.
It is important to note that the eye map and the
contact lens dimensions constitute paired and corresponding
data entries. These paired and corresponding data entries
can be indexed in any convenient pattern desired so that upon
location of similar and like eye maps, the appropriate con-
tact lens can be called for.
Use of my eye measurement techni~ue should at this
--- point be apparent. Specifically, by mapping an eye, and
making reference to a loaded data bank, a good estimate of
those parameters necessary for a proper eye fit can be made.
I have previously noted that on the filing of this
application, the mapping of eyes and the entry of a fitted
contact lens into the data bank is simultaneous. Therefore,
77
..~. ,~ ,.
66
it may be expected that for similar maps, similar lens appli-
cations may result. At a minimum, I expect to be able to
prescribe with much greater accuracy contact lenses.
It will be understood that there can be expected
other parameters developed for the fitting of contact lenses
as a result of the vastly more detailed corneal map which I
have created. This will have to be recognized in the data as
it develops. I file this application in advance of the
accumulation of any such data.
I also contemplate as part of my invention the very
important concept of taking corneal measurements over time
spans. Specifically, it is ~nown that the shape of the
cornea can be effected by the presence of a contact lens upon
it. Where the cornea undergoes shape alteration over a
period of time because of the presence of a contact lens, it
returns to a shape upon removal of the contact lens. It is
important to remember that both the rate of return of the
cornea to a shape upon removal of the contact lens as well as
the shape to which the cornea returns can vary. For example,
in orthokeratometry, the shape of the eye can conceivably be
either permanently altered or temporarily altered dependent
upon the characteristics of the contact lens used. With the
measurements I disclosed taken over a time base, I clearly
contemplate making measurements of the disclosed rates of
return as well as the final state to which return occurs.
Referring to Fig. 11, it can be seen that the
sphere, cylinder and axis results are plotted at specific
time spans. For example, a first measurement is taken at
4:00. A second measurement is taken at 4:30. Likewise it
will be apparent that additional time base measurements can
be taken and the rates of change of corneal shape determined.
By way of illustration, I have shown a preferred
map of the eye patterned after an elliptical model~ It will
be realized by those having skill in the art that other
models exist by which the map I set forth may be predicted.
What I have done is to ~et forth an apparatus and method
whereby for the first time the enumerated factors of the eye
may be rapidly obtained and practically used, not only to
determine or monitor eye physiology but to insure enhanced
fitting of contact lenses.
Regarding the time-base measurement which I have
set forth wherein the cornea changes shape after removal of a
contact lens, the time-base should be fully understood.
Specifically, I contemplate beginning the counting of any
time rate from the instant a contact lens is removed. It is
at that time that the cornea is relieved of forces that might
hold it out of shape and placed under its own natural
dynamics to change to a new shape.
It will be appreciated that the foregoing specification
and disclosed apparatus and method can be modified. For example,
infrared diodes and detectors do not necessarily have to be
used. Likewise, other modifications may be made without departing
from the spirit of the invention.
Certain features disclosed hereinbefore are also
disclosed and claimed in copending Canadian application
379,198 filed June 8, 1981.
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