Note: Descriptions are shown in the official language in which they were submitted.
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FIELD CURVATURE CONTROL
CROSS REFERENCE TO RELATED APPLICATIONS
Reference should be made to our copending Canadian patent applications
Serial No. 388,788 entitled "Compact Optical System" and Serial No. 388,788 en-
titled 'IOptical System Having A Dual Field of View", which are filed on even
date herewith and which are assigned to the same assignee as the present appli-
cation.
BACKGROUND OF THE INVENTION
The present invention relates to control of field curvature in optical
systems. The invention has application in optical systems generally and is par-
ticularly advantageous in compact cassegrainian arrangements.
It is particularly important in gimbal-mounted infrared sensor systems
typical of, for example, missile born sensors that the system be extremely com-
pact. In addition, it is important in such infrared systems to avoid field
flatteners or separate lenses placed near the image for controlling field curva-
ture; the infrared detector sees itself in any such lens and causes a cold spot
in the system output because the detector area is cold. In addition, it is im-
portant that the system have a weight distribution providing a relatively small
moment of inertia to minimize power requirements for rotating the system by the
gimbals.
These requirements have been found to be particularly well satisfied
by a concave primary mirror and a convex secondary
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mirror comprising a config~ration often referred to as a
cassegrainian arrangement. (The precise definition of a
Cassegrain system is one where the primary mirror is specifical]y
a parabola and the secondary mirror a hyperbola. However r
~ystems comprising a concave primary mirror and a convex
secondary mirror are no~ often referred to as cassegrainlar,
systems without particular reference to the particular geometry
of the mirrors.) Two-mirror arrangements of this kind offer the
maximum ratio of focal length to system length.
~ he compactness of Euch a configuration is improved ~s
the primary mirror focal length is shortened requiring, as a
consequence, a related decrease in the focal length of the
secondary mirror. As this design feature is extended, such a
system normally shows an increasing amount of field curvature
arising from the disparity in the magnitude of radii of the
primary and secondary mirrors.
In prior art systems, control ~of field curvature has
typically been handled through use of field flatteners or
additional lenses located within the system. See, for example,
U.S. Patent No. 3,515,461, Casas èt al, June 2, 1970, column 2,
lines 44-46. ~s previously mentioned, if such a field flattener
or corrector is located near the image in an infrared system, it
has a distinct disadvantage since the detector can see itself as
a reflection in the correcting lens. In addition, systems having
such additional lenses are heavier and more complex.
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In systems where these factors are a problem, 8
particular feature of the present invention is the us~ of a
mangin mirror having its surfaces shaped for providing control of
field curvature without the use of special additional lenses~
Mangin mirrors have classically been used w-th
spherical mirrors to correct spherical aberrations. See, for
example, the indicated disclosures within the following U.S
Patents:
2,730,013, Mandler, Jan. 10, 1956, Col. 1, lines 19 and 46.
2,817,270, Mandler, Dec. 24, 1957, Col. 1, lines Sl - 56
and 60 - 61.
3,064,526, Lindsay, Nov. 20, 1962, Col. 5, lines 20 - 23
and 66 - 67.
3,296,443, Argyle, Jan. 3, 1967, Col. 2, lines 33 - 36.
3,632,190, Shimizu, Jan. 4, 1972, Col. 2, lines 34 - 39.
See also Rogers, "A Comparison Between Optimized
Spheric and ~spheric Optical Systems for the Thermal Infrared",
SPIE Vol. 147, Computer-~ided OPtical Design, 1978, pp. 141-14
(text at bottom of page 145).
tIn addition, see U.S. Patent No. 3,527,526,
Silvertooth, Sept. 8, 1970, Col. 4, lines 64-67 which discloses
use of a mangin in a cassegrainian arrangement for unspecified
reasons).
While some of the above patents indicate use of a
mangin mirror for correcting other aberrations, it is believed
unique to configure mangin mirror surfaces for providing control
.
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of field curvature. As previously indicated, the field curvature problem be-
comes more severe as the optical system is made more compact. However, inasmuch
as a mangin mirror may also be defined as a lens having its back surface coated
with reflective material, it can be uniquely applied to correct the amount of
field curvature by controlling the particular shape or radii of mangin mirror
surfaces. Thus, for any given objective system or subsystem, the particular
field curvature correction may be established by a unique set of values for the
two radii of the mangin mirror surfaces. Further, this can be accomplished as
an integral part of one of the two mirrors in a two mirror system and, therefore,
does not require supplementing such systems with additional corrector lenses.
SUMMARY_OF THE INVF_TION
The present invention is an optical element for providing control of
field curvature. The element consists of a lens having a first and a second
surface. The second surface is coated with reflective material. The radiation
received by the lens is refracted at the first surface, reflected back from the
second surface, and then refracted once again by the first surface. The first
and second surfaces have a shape for providing control of field curvature.
In accordance with the present invention there is provided an optical
element for providing control of field curvature, the optical element consist-
ing of a mangin mirror comprising a lens having a first and a second surface,the second surface being coated with reflective material, the radiation received
by the lens being refracted at the first surface, reflected back from the
second surface, and then refracted once again by the first surface, the first
and second surfaces having a shape for providing control of field curvature.
In accordance with another aspect of the invention~ there is provided
an optical element for providing control of field curvature, the optical element
consisting of a mangin mirror comprising a lens having a first and a second sur-
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face, the second surface being coated with reflective material, the radiationreceived by the lens being refracted at the first surface, reflected back from
the second surface, and then refracted once again by the first surface, the
first and second surfaces each having a radius defined by the equation
l/R = 2/n[(n+l)/rl * 1/r2] where R is the radius of the field curvature, n is
the index of refraction of the lens, rl is the radius of the first surface, and
r2 is the radius of the second surface.
In accordance with a further aspect of the invention, there is pro-
vided an optical arrangement for providing control of field curvature, the
arrangement comprising a lens having a first and a second surface, the second
surface being coated with reflective ma*erial, the radiation received by the
lens being refracted at the first surface, reflected back from the second sur-
face, and then refracted once again by the first surface, the first and second
surfaces having a shape for providing control of field curvature.
In accordance with yet another aspect of the invention, there is pro-
vided an optical arrangement for providing control of field curvature, the
arrangement comprising a lens having a first and a second surface, the second
surface being coated with reflective material, the radiation received by the
lens being refracted at the first surface, reflected back from the second sur-
face, and then refracted once again by the first surface, the first and secondsurfaces each having radii which determine the field curvature by the equation
l/R = 2[~n-1)/rl-~ 1/r2]/n where R is the radius of the field curvature, n is
the index of refraction of the lens, rl is the radius of the first surface, and
r2 is the radius of the second surface.
BRIEF DESCRIPTI~N OF TH_ DRAWING
The single Figure illustrates the present invention embodied in a
compact optical system.
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DESCRIPTION OF THE PREFERRED EMBODIMENT
_
There are described in ~his application various
~eatures and functions of a disclosed system which are not the
subject of the present invention, but rather are the subject of
an invention claimed in the previously mentioned copenâing
application entitled "Compact Optical System." The descriptions
of these features and functions are included in the present
application in order to demonstrate utility of the present
invention within an optical system.
Reference is made to the accompanying Figure in which
the present invention is illustrated as mirror or lens 12 within
a compact optical system. Collimated radiation from a point in
the scene is tr`ansmitted through a concentric dome window 10 with
appropriate refractions at each surface. The beam is slightly
divergent as it impinges upon a concave primary front s~rface
mirror 11. It is then converged to mangin secondary mirror 12 at
which the radiation is refracted at a first surface of incidence
13, reflected from a back surface 14, and then refracted once
again by the first surface.
As previously indicated, a particular feature of the
present invention is providing surfaces 13 and 14 with a shape
for controlling field curvature. Mangin secondary mirror 12 also
reduces convergence of the beam while reflecting it backward, the
radiation being focused at a field stop 17. The radiation may
then be transmi~ted through collimator 15 comprising lenses 16
and 20 having appropriate refractions at each surface. Lenses 16
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and 20 collimate the radiation and direct it through exit pupil 21.
In the optical system disclosed, mangin secondary mirror 12 only par-
tially corrects field curvature, the field curvature being completely corrected
following collimator 15 (lenses 16 and 20). However, in alternate embodiments,
surfaces 13 and 14 of mirror 12 may be shaped to completely correct field curva-
ture at field stop 17. Thus, mangin secondary mirror 12 may be employed to con-
tribute whatever degree of field curvature is necessary to flatten the field or
to control the field curvature to the desired flatness.
The field curvature contribution of mangin secondary mirror 12 is l/R
and may be defined by an equation l/R = 2[(n-1)/rl + 1/r2]/n. In this equation,
R is the radius of the field curvature, n is the index of refraction of the man-
gin mirror lens, rl is the radius of the first surface (surface 13 in the dis-
closed embodiment), and r2 is the radius of the second or back surface (surface
14 in the disclosed embodiment). Thus, once the material for the mangin mirror
lens is selected, n is known from available references, and the radii of sur-
faces 13 and 14 can be calculated to provide any desired degree of field curva-
ture control.
The first and second surfaces of mangin mirror 12 also allow one to
select any combination of focusing power and field curvature contribution. For
the normal situation in which the mangin mirror is thin, power of the mangin
mirror is l/f and may be defined by the equation l/f = 2[n/r2 - (n-l)/rl]. In
this equation, f is the focal length of the mangin mirror, n is the index of re-
fraction of the mangin mirror lens, rl is the radius of the first surface (sur-
face 13 in the disclosed embodiment), and r2 is the radius of the second or rear
surface (surface 14 in the disclosed embodiment).
Tables 1 and 2 set forth below give the dimensions and parameters of
one preferred embodiment of an optical system comprising the present invention.
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TABLE 1
SPECIFICATION-SYSTEM EXAMPLE
Element Radius Thickness Material Conic Constant
(inches) (inches)
Dome 10 6.0 .30 Zinc Sulfide
5.7 4.8
Primary Mirror 11 -7.166 -2.555 Aluminum -.75102
Secondary Mirror 12 -6.758 -.10 Germanium
-5.475* .10 -4.7
Field Stop 17 2.555
.501
Collimator Lens 16 -.818 .401 Germanium
-1.047 .01
Collimator Lens 20 1.544 .20 Germanium -.3565
2.340
Exit Pupil 21 1.04
* Surface is Aspheric:
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Sag r ~ dy4 ~ ey6 ~ fy
_
1 + V 1 - ~K + 1)
wnere
d = 2.213 x 10-3 y = ~perture height
e = -1.459 x 10-3 r = Radius of the surace
f = 4.591 x 10-4 k = Conic constant
TABLE 2
EXA~PLE SYSTE~ PhR~METERS
Telescope Magnification 11.9
External Field of View 2.38 x 3.22
Entrance Pupil Diameter 4.4 in.
Objective F-Number 2.0
Objective Focal Length 8.85 in.
Collimator Focal Length .744 in.
Table 1 is laid out in a manner common in the art; if
more than one dimension is given for an element, the dimensions
appear in the order that light travels from the scene through the
system. For example, for dome 10, the first radius listed of 6.0
inches corresponds to the first surface of dome 10, and the
radius of 5.7 inches corresponds to the second surface of dome
10.
In the thickness column of Table 1, the numbers include
on-axis air space thicknesses listed in the order in which light
travels through the system. Accordingly, the firs~ number of .30
r
incn is the thickness of dome 10. ~ The second number of 4.~
inches corresponds to the~ on-axis distance be~ween the second
surface of dome 10 and a point that would intersect the radius of
the reflective front surface of primary mirror 11. The minus
sign associated with the first dimension of 2.555 inches
indicates light traveling in a backward direction. The .10 inch
number listed in association with mangin secondary mirror 12
indicates the thickness of the mirror, the first number being
negative since light is traveling in the reverse direction in its
first transit to the reflective back surface 14 of that mirror.
The positive 2.555 inch dimension is the air space distance
between first surface 13 of mirror 12 and field stop 17, which is
the first focal p~ane. The dimension of .501 inch is the
distance between field stop 17 and the first surface of lens 16
within collimator 15. The .401 inch dimension listed in
association with collimator lens 16 is the thickness of that
lens, the .01 inch dimension being the air space thickness
between the second surface of lens 16 and the first surface of
lens 20. The .20 inch dimension listed in association with lens
20 is the thickness of that lens, the 1.04 inch dimension being
the distance between the second surface of lens 20 and exit pupil
21.
It should be noted/ of course, that the dimensions and
parameters listed in Tables 1 and 2 do not represent the present
invention, but rather the dimensions and parameters of a system
comprising the present invention.
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It should also be noted that, while the mangin mirror
has been shown as a secondary mirror in the disclosed embodiment,
the secondary mirror could be a front surface mirror, and the
primary mirror could be a mangin mirror with first and second
surfaces shaped for providing control of field curvature.
Alternately, both mirrors could be mangin mirrors with one or
both having surfaces so shaped.
Further, although mirror 12 comprising the present
invention is disclosed as aspheric see Table 1), a mangin mirror
comprising the present invention may also be spherical.
In addition, while a mangin mirror in accordance with
the present invention is shown implemented in a cassegrainian
arrangement, such an implementation is illustrative only since a
mangin mirror in accordance with the present invention may be
applied in any optical system wherein radiation may
be suitably received, refracted, and reflected by the mirror in
order to control field curvature.
Finally, it should be noted that the present invention
provides field curvature control. Such control may be desiyned
to include only partial correction of field curvature, either
without further correction provided by additional system optics
or, as in the disclosed example, with further correction by
additional system optics (collimator 15 in the disclosed system).
Alternately, the field curvature control provided by the present
invention may be designed to completely correct field curvature
introduced by other optics within a system.
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The present invention is to be limited only in
accordance with the scope of the appended claims, since persons
skilled in the art may devise o~her embodiments still within the
limits of ~he claims.
.
