Note: Descriptions are shown in the official language in which they were submitted.
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WO 99/49280 1 PCT/EP99/02041
Method for determining the position and rotational
position of an object
Field of the Invention
The invention relates to a method for
determining the position and rotational position of an
object in three-dimensional space.
The objects suitable for the invention are
varied and are very different in their function and
application. Examples of such objects are surgical
microscopes and surgical tools in the medical sector,
levelling staffs in geodetic surveying, gun barrelsw in
the military sector or aerials, in particular
directional aerials and radar aerials. In the case of
such objects, their position in space l plays an
important role. This is determined in a specified
coordinate system completely by six real position
parameters which are composed of three parameters for
the position (translation group) and three parameters
for the rotational position (rotation group). The
position of the object is given by the 3-dimensional
coordinates of a point selected on the object. The
rotational position of the object is generally
described by the direction vector of a defined object
axis and the angle of rotation of the object about the object axis.
The direction vector of the object axis is a unit vector having the
length 1, i.e. the sum of the squares of its components is 1.
Related
W0' 95/27918 describes an arrangement for
determining 'the spatial position of a surgical
microscope with the aid of coded light signals which
are emitted by light emitting diodes, preferably in the
infrared range, and received by light receivers. A
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surgical microscope is generally mounted on an arm by
means of a cardan joint and can be moved
translationally in three directions in space and
rotated about three directions in space so that its
position in space can be adjusted as desired. On the
surgical microscope, the light emitting diodes or
optical fibres which are fed with light from the light
emitting diodes are mounted at specific points.
Alternatively, reflectors may also be mounted on the
surgical microscope. The light receivers are arranged
at various points in space and receive the light
signals specific to each of them. From this, the
spatial position of the surgical microscope is
determined. If the spatial position of the patient is
simultaneously known, the coordinates of the operating
site viewed through the surgical microscope are thus
known, which is indispensable for microsurgery.
In geodetic surveying, levelling staffs are
used for determining vertical points of reference and
for topographical surveying. They are also used in
construction surveying and in the construction of
traffic routes. A levelling staff is sighted with the
telescope optical system of the levelling instrument in
order to measure the difference in height between
levelling instrument and levelling staff. It is
assumed that the levelling staff is aligned
perpendicular to the optical axis of the telescope.
Since the optical axis of the telescope is usually
adjusted so that it is in a horizontal plane, an
operator must keep the levelling staff aligned as far
as possible perpendicular with the aid of the water
levels mounted thereon. Tilting of the levelling staff
results in an error in the height measurement.
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With the advent of automated digital levelling
instruments according to DE 34 24 806 C2, electronic
reading of the staff became possible for the first
time. For this purpose, the levelling staff has a code
pattern comprising black and white elements, a part of
which is produced as an image on a position-resolving
detector with the aid of the telescope optical system
of the electronic levelling instrument. Here, the code
pattern information present in the field of view of the
telescope is used to obtain the desired height
measurement by comparison with the code pattern of the
levelling staff, which pattern is stored as a reference
code pattern in the levelling instrument. Although the
measured code pattern is identified in this measurement
and evaluation method, tilting of the levelling staff
and the resulting contribution to the inaccuracy of
measurement are not taken into account.
A specific code pattern is disclosed in
DE 195 30 788 Cl. A levelling staff having a
rotationally symmetrical cross-section has, on its
lateral surface, code elements which form lines closed
rotationally symmetrically with respect to the
longitudinal axis of the levelling staff.
Consequently, the code pattern is visible from all
sides.
DE 44 38 759 Cl describes a method for
determining the tilt angle of coded levelling staffs in
the measuring direction by means of an electronic
levelling instrument. The tilt of the levelling staff
is taken into account exclusively in the measuring
direction, i.e. in the observation direction. The
resulting recording of the code pattern on the detector
is evaluated and the tilt angle is determined. Lateral
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tilting of the levelling staff, which thus takes place
transversely to the observation direction of the
levelling instrument, is however not taken into
account. A one-dimensional diode array is therefore
adequate as a detector.
Owing to a lateral tilt of the levelling staff,
an error also occurs in the height and distance
measurement. The point of intersection of the optical
axis of the levelling instrument with a tilted
levelling staff is further away from the bottom of the
levelling staff than in the case of exactly
perpendicular alignment of the levelling staff. An
insufficiently perpendicular alignment due to
inaccurate reading of the water level by the operator
therefore leads to erroneous measurements. There is
subsequently no possibility for correcting errors.
Moreover, often only a single operator is used today,
said operator operating the levelling instrument for
surveying. The levelling staff standing alone is
exposed to the wind, which leads to corresponding
deviations in the surveying.
In the case of a gun barrel - and the following
statement also applies analogously in the case of
directional aerials and radar aerials - the primary
concern is to determine its orientation in space or to
rotate the gun barrel into a specific predetermined
direction and to measure said rotation. The horizontal
and vertical angular position (azimuth and elevation)
of the gun barrel is controlled with the aid of
encoders which are mechanically connected to the gun
barrel. The encoders contain in general coded rotary
discs which execute a rotational movement by means of a
gear during rotation of the gun barrel and thus deliver
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electrical signals corresponding to the angles of
rotation. The mechanical play is disadvantageous in
the case of such controls. Moreover, the large thermal
loads and shocks lead to inaccuracies and to increased
wear.
Summary of the Invention
It is the object of the invention to provide a method by
means of which the position and the rotational position of an
object in three-dimensional space can be determined quickly
and without contact. Advantageous embodiments and further
developments of the invention are evident from the subclaims.
An optical measuring head is used for
determining the position and rotational position of an
object in space. The measuring head comprises an
imaging optical system and a detector which is
position-resolving in two dimensions and is arranged in
the focal plane of the imaging optical system. The
object with its object structures is focused onto the
detector by the imaging optical system. The object
structures are known from the outset as a priori
information. The object structures may contain the
geometric shape of the object and its dimensions or may
be marks at specific points on the object or they are a'
code pattern which is applied to the object. The image
of the object or of the object structures which is
present .in two-dimensional form on the detector is
evaluated in an evaluation unit connected to the
detector.
There are various possibilities for evaluating
the two-dimensional image information. For example,
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the image of the object can be compared with calculated
images. From the known geometry of the object or from
existing marks on the object or from an existing code
pattern on the object or from all these object
structures together, the expected detector image can be
calculated using the known properties of the imaging
optical system (and optionally the resolution of the
position-resolving detector) for any reasonable values
of the six position parameters stated at the outset.
Optimization methods are used for determining those
values of the position parameters which give the best
or at least a sufficiently good agreement between the
calculated image and the image actually recorded. Such
optimization methods are, for example, quasi-Newton
methods (determination of the least squares or of the
maximum likelihood, etc.), which are known from K.
Levenberg: "A Method for the Solution of Certain non-
linear Problems in Least Squares", Quart. Apl. Math. 2
(1944), pp. 164-168, or from D.W. Marquardt: "An
Algorithm for Least-squares Estimation of Nonlinear
Parameters", SIAM J. Appl. Math. 11 (1963), pp. 431-
441, or from J.J. More: "The Levenberg-Marquardt
Algorithm: Implementation and Theory", Numerical
Analysis, ed. G.A. Watson, Lecture Notes in Mathematics
630, Springer Verlag (1978), pp. 105-116.
Another possibility for evaluation is to
analyze the object structures focused on the detector
with respect to their geometrical parameters and to
determine the position parameters of the object
therefrom. Thus, the planar position and the
rotational position of the focused geometrical shapes
(e.g. edge contours) or of the code pattern on the
detector and the variation in the image scale changing
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as a function of the detector coordinates are first
measured and determined. If a code pattern is present,
all code elements of the code pattern focused on the
detector are preferably completely used since high
accuracy and especially high ruggedness and stability
of the evaluation result can thus be achieved. For
other requirements, such as, for example, for
particularly rapid availability of the results of the
measurement, however, the evaluation of only three
decoded code elements of the code pattern is
sufficient. The accuracy of the measurement is
somewhat limited. Alternatively, it is also possible
to evaluate only the focused edge contours of the
object.
From the determined geometrical parameters of
the detected object structures, the position parameters
of the object are determined with the aid of the
optical imaging equation and geometrical relationships
(vector algebra). By means of the position parameters,
which as mentioned at the outset include the position
vector, the direction vector of the object axis and the
angle of rotation of the object about the object axis,
the spatial position of the object, i.e. the position
and rotational position, is reconstructed.
Of course, said possibilities for evaluation
can also be combined with one another. For example, a
rough determination of the position parameters can be
effected by a rough evaluation of the edge contours or
of only a few code elements and an accurate evaluation
including the total recorded object geometry or all
recorded code elements can follow. For the accurate
evaluation, in particular the optimization method cited
above can also be used and the position parameters
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WO 99/49280 8 PCT/EP99/02041
determined from the rough evaluation can be employed as
starting parameters for the optimization.
Expediently, a three-dimensional Cartesian
coordinate system is chosen for determining the spatial
position of the object. The coordinates of the
measuring head and hence of the detector are known in
this coordinate system. The coordinate system may also
be chosen from the outset so that it agrees with the
detector coordinates. Of course, the position
parameters of the object can be converted into any
desired expedient coordinate system. In particular,
the rotational position of the object may also be
specified by two polar angles or by azimuth, elevation
and in each case the angle of rotation of the object
about the axis of rotation or by three Eulerian angles.
An optoelectronic detector capable of position
resolution in two dimensions is required for the
invention. Said detector may be, for example, a video
camera or two-dimensional CCD array. However, it is
also possible to use a plurality of one-dimensional CCD
arrays arranged side by side. The object is mapped
with such a detector and by means of the imaging
optical system. The object structures present in the
field of view of the imaging optical system are focused
and detected. The detector is adjusted with its light-
sensitive detector surface generally perpendicular to
the optical axis of the imaging optical system. The
point of intersection of the optical axis with the
light-sensitive detector surface may define the zero
point of the coordinate system of the detector.
When a CCD detector having discrete light-
sensitive pixel structures is used, the positional
resolution of the CCD detector can be further
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considerably increased by means of suitable optic
structures, in particular by means of suitable
structures of a code pattern. More than 10 times the
pixel resolution of the detector is thus achievable.
The particular measurement sensitivity is obtained if
the fundamental spatial frequency or one of the higher
harmonic spatial frequencies of the intensity
distribution caused by the code pattern on the detector
forms a low-frequency superposition pattern together
with the fundamental spatial frequency of the
radiation-sensitive structures of the detector. The
low-frequency superposition pattern acts in the same
way as a moire pattern. Moire patterns are known to be
very sensitive to a shift in the structures which
produce them. Here, this means that, even in the case
of a very small change in the intensity distribution on
the detector compared with its pixel structure, the
low-frequency superposition pattern changes
considerably in its spatial frequency. Thus, the
position of the focused code pattern on the detector
can be measured very precisely. Since a change in the
superposition pattern is caused by a change in the
position and rotational position of the object, the
position parameters of the object in space can
therefore be measured in a very sensitive and hence
highly precise manner.
If the object is a levelling staff, the
direction vector of its axis is also important in
addition to its position, since said vector describes
the tilt of the levelling staff from the perpendicular.
In addition to the known conventional levelling staffs
where a code pattern is applied to a flat surface, it
is also possible to use a levelling staff which is
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rotationally symmetrical with respect to its
longitudinal axis and has a rotationally symmetrical
bar code. In this case, the imaging optical system can
pick up the same code pattern even continuously from
all sides of the levelling staff. By determining the
direction vector of the levelling staff axis from the
focused code pattern or the detected contours of the
levelling staff, both the inclination of the levelling
staff in the direction of view of the imaging optical
system and the lateral inclination of the levelling
staff transverse to the direction of view of the
imaging optical system are determined. Thus, the
deviation of the levelling staff from the ideal
perpendicular is determined and is taken into account
in a corresponding correction for the surveying. This
correction is made automatically in every survey.
Consequently, it is even possible to dispense with
prior alignment of the levelling staff. As a result,
fast and precise surveying with only a single operator
and also independently of the wind conditions is
possible. If moreover, in the given case, the angle of
rotation of the levelling staff about its axis is also
determined - assuming a suitable code pattern or
specific marks - this automatically also gives the
sighting direction of a movable measuring head.
If the object is a gun barrel, this can be
equipped with various code patterns, analogously to the
case of the levelling staff. If only elevation and
azimuth of the gun barrel are to be determined, a code
pattern rotationally symmetrical with respect to the
longitudinal axis of the gun barrel or only the edge
contour of the gun barrel is sufficient. If a code
pattern comprising code lines aligned parallel to the
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longitudinal axis is additionally applied to the gun
barrel, its angle of rotation about its axis can
additionally be determined. The code lines may also be
stochastically oriented. Combinations of these code
patterns in which, for example, segments having
rotationally symmetrical code rings and segments having
parallel or stochastic code lines alternate can also be
used. A code pattern which is wound in a spiral manner
around the gun barrel and with which about the same
sensitivity for the direction vector of the gun barrel
axis and the angle of rotation of the gun barrel about
its axis can be achieved is also advantageous.
However, it is also possible to use a code pattern
having a completely irregular structure, as possessed,
for example, by military camouflage patterns. What is
decisive for all code patterns is that they are either
known per se or are determined by surveying.
Advantageously, such code patterns can be readily used
for the correlation procedures.
By means of the imaging optical system, the
contours of the gun barrel and/or of the code pattern
are recorded and the rotational position of the gun
barrel is determined without contact. Optionally, the
gun barrel can be actively illuminated, for example
with infrared light. The gun barrel or the applied
code pattern may also be luminescent. Generally firm
locking of imaging optical system and detector relative
to the gun barrel and the optical surveying result in
the great advantage that absolutely no mechanically
moving components are required for determining azimuth,
elevation and angle of rotation of the gun barrel.
This contactless measurement takes place rapidly and
gives precise results.
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If the object is an aid used in the medical
environment, in particular in automated microsurgery,
such as, for example, a surgical microscope, a surgical
tool (scalpel, drill, endoscopic aid, etc.) or a
radiation source for tumour treatment, good visibility
of the object structures of the aid must be ensured for
the measuring head. During handling of the aid, the
latter may be temporarily concealed by persons or
instruments and the direction of view of the measuring
head interrupted. However, if it is intended
constantly to measure the spatial position of the aid
under these conditions, it is useful if the object
structures to be detected by the measuring head are
located in an exposed area of the aid so that they are
as far as possible in the unobstructed direction of
view of the measuring head. When a code pattern is
used, it may also be applied to a plurality of points
on the aid or it may even cover the entire surface of
the aid. The measuring head may be movable in space
for an optimal recording, or preferably a plurality of
measuring heads distributed in space are used
simultaneously. The redundancy of the results
delivered by a plurality of measuring heads moreover
meets the requirement set in the medical sector for
particular equipment safety.
Otherwise, the object may also be the patient
itself, i.e. more precisely a frame which is firmly
connected to the patient and defines the coordinate
system of the patient. Precisely in operations on
tumours in the brain, such a frame is fixed to the
patient's head, the spatial position of the tumour
relative to the frame being determined, for example, by
computed tomography images. If the geometric
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structures of the frame or the code patterns applied to
the frame are recorded by the measuring heads and the
spatial position of the frame is determined, the
coordinates of the tumour are also known in the
coordinate system of the measuring heads. Since
moreover the spatial position of the surgical
microscope and of the surgical tool is determined with
the aid of the measuring heads, endoscopic navigation
through the brain to the tumour can be performed fully
automatically.
In all stated application examples of the
invention, it is possible that it may be difficult to
provide an object with a code pattern to be used or
that the object is already present as a complete
component. In such cases, it is possible to mount a
separate body provided with a code pattern
eccentrically on the object ("booster principle"). The
body may have a cylindrical shape. It is of course
also possible to mount a plurality of such bodies on
one object. If the object moves in space, the
separately mounted body, too, performs clearly coupled
movements, in particular rotational movements so that
the position and rotational position of the object can
always be computed.
In addition, an object can also be recorded
stereoscopically. For this purpose, either two
measuring heads can form a stereo base or the stereo
base is produced by a measuring head together with a
focusing mirror or a plurality of focusing mirrors, so
that the measuring head can record stereoscopic images
of the object. By means of this additional image
information, the accuracy of the position determination
of the object can be further increased - analogously to
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seeing with two eyes.
Finally, a distance measuring instrument can
also be connected to the measuring head or integrated
therein. With such additional information about the
distance of the object, it is also possible to increase
the accuracy of measurement. Moreover, the additional
information can ensure that the measured result
regarding the position of the object is available more quickly.
Brief Description of the Drawings
The embodiments of the invention are explained
in more detail below with reference to the drawing.
Fig. 1 shows a schematic representation of the
rotational position of an object
provided with a code pattern and the
recording of the object structures by a
measuring head comprising an optical
imaging system and a position-resolving
detector,
Fig. 2 shows a schematic representation of
detector recordings of the object for
different rotational positions,
Fig. 3 shows a representation of geometrical
relationships for determining the
rotational position and the position
vector of the object,
Fig. 4 shows a schematic representation of an
object in the form of a medical aid and
its recording by a plurality of
measuring heads,
~
Fig. 5a, b shows separate bodies which are provided
with a code pattern and are mounted on
the object to be surveyed,
Fig. 6a, b, c show a schematic representation for the
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stereo recording of the object and show
Fig. 7a, b a schematic representation of the measuring
head with a distance measuring instrument.
Detailed Description of the Preferred Embodiments
Fig. 1 schematically shows an object 1 in a
Cartesian coordinate system x, y, z. The object 1 has
a foot 3 and an object axis 4 and can be provided with
a code pattern 2b. The object contours 2a and/or the
code pattern 2b are either known from the outset or
they are surveyed so that the size, shape and the
spacing of the details of the object contours 2a and of
the individual code elements of the code pattern 2b
relative to the foot 3 of the object 1 are obtained.
In the simplest case, the object contours 2a are
straight lines. The object contours 2a shown in Fig. 1
are additionally rotationally symmetrical with respect
to the object axis 4, and, in the special case, the
angle of rotation K of the object 1 about the axis 4
cannot be determined from the object contours 2a alone.
With the aid of an imaging optical system 5
present in a measuring head 9, that part of the object
structures 2a, 2b present in the field of view of said
optical system is focused onto a two-dimensional
position-resolving optoelectronic detector 7. The
electrical signals of the detector 7 are evaluated in
an evaluation unit 8. According to the diagram in Fig.
1, the evaluation unit 8 is likewise integrated in the
measuring head 9. In principle, the evaluation unit 8
can of course also be present outside the measuring
head 9, for example in a separate electronics
arrangement or in a computer (PC).
A coordinate system XDet, YDet is defined in the
light-sensitive detector plane of the detector 7, the
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origin of said coordinate system being chosen at the
point of intersection of the optical axis 6 of the
imaging optical system 5 with the detector plane. The
optical axis 6 arranged perpendicularly to the detector
plane is lying parallel to the z axis of the coordinate
system x, y, Z. In the case of a horizontal imaging
optical system 5, the y axis is simultaneously the
normal to the Earth's surface. Of course, other
coordinate systems can also be used.
The position of the object 1 in space is
uniquely determined by six position parameters. They
arise from the components of the position vector ro,
the components of the direction vector v, which
contains only two independent parameters owing to its
unit vector property, and the angle of rotation x of
the object 1 about its axis 4. The position vector ro
points from the imaging optical system 5 to the foot 3
of the object 1. The direction vector v points in the
direction of the object axis 4 and thus indicates its
position in space. Instead of the direction vector v,
the position of the object axis 4 can also be described
by the angle S measured from the vertical y axis and
the horizontal angle cp measured from the y-z plane. In
the case of unique object contours 2a or a unique code
pattern 2b, the angle of rotation K about the object
axis 4 can be determined. The angle of rotation K can
be measured, for example, from the plane defined by the
position vector ro and by the direction vector v.
Thus, the complete rotational position of the object 1
is determined.
According to the invention, the position
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parameters of the object 1 are determined from the
planar position and the local mapping of the object
structures 2a, 2b focused on the detector 7. Depending
on the magnitude of the polar angles ((P, S) and of the
position vector ro, the position shown schematically in
Fig. 1 and the mapping of the object structures 2a, 2b
on the detector 7 change.
In this context, images of the object 1 at
various polar angles ((p, S) on the detector 7 are shown
schematically in Fig. 2. Each of the lines shown on
the detector coordinate system xDet, yDet corresponds
symbolically to the image of the same section of object
1 which is detected by the imaging optical system 5, in
each csae for a differen pair of polar angles ((p, S).
The individual code elements of any code pattern 2b
present are not shown here.
Fig. 2 reveals three groups of lines Gl, G2,
G3, which represent three different vertical angles S.
A small vertical angle S can be assigned to group Gl in
the upper region of Fig. 2, whereas a large angle S
gives rise to group G3. Within each group G1, G2, G3,
the horizontal angle cp varies, correspondingly large
negative or positive angles cp being assigned to the
lines at positive and negative coordinate values,
respectively, of XDet=
The different lengths of the lines depending on
cp and 8 indicate different imaging scales according to
the rotational position of the object 1. The imaging
scale of the object structures 2a, 2b varies along each
line since the object structures 2a, 2b are different
distances away from the imaging optical system 5 owing
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to the rotational position of the object 1. The
imaging scale is obtained from the quotient of the
known sizes of the object structures 2a, 2b on the
object 1 and the measured size of the object structures
2a, 2b on the detector 7. With the aid of the focal
distance f of the imaging optical system 5, the
distance between the imaging optical system 5 and the
object structures 2a, 2b on the object 1 is calculated
therefrom according to the laws of geometrical optics.
The geometrical situation in this context is
shown in Fig. 3. To present the principle more
clearly, the thickness of the object 1 is neglected.
The sighting point can then coincide with the foot 3
and both are given by the position vector ro. The
object structures 2a, 2b should in this case be a code
pattern 2b. The i th code element of the code pattern
2b is located at a fixed, known distance I L;Ifrom the
foot 3 of the object 1. It is assumed here that the
number i of the code element is known; this can be
obtained either by counting if the total code pattern
2b is focused on the detector 7 or by decoding a
sufficiently long focused section of the code pattern
2b. The i th code element is focused on the detector 7
at a distance ~pi~ from the optical axis 6 by te
imaging optical system 5 having the focal distance f.
The vectors pi and L; are three-dimensional, where pi
lies in the plane of the detector 7. In general, the
vectors pi and L; are not located in the plane of the
drawing in Fig. 3. Below, a distinction is made
between two cases.
In a first case, the position vector ro from
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the imaging optical system 5 to the foot 3 of the
object 1 should be predetermined. The predetermined
position vector ro means that the imaging optical
system 5 and the foot 3 of the object 1 are invariable
relative to one another. The position vector ro can be
determined by a simple mechanical measurement or, in
the case of higher requirements, also by laser
surveying or by a calibration measurement in which the
object 1 is present in a previously known spatial
position. Such mutual fixing of measuring head 9 and
object 1 may be the case, for example, when object 1 is
a gun barrel. With the known position vector ro, the
polar angles ((p, S) of the gun barrel are determined,
with the result that the latter can be brought or
adjusted to a predetermined rotational position.
Within the range of rotation of the gun barrel, code
pattern 2 must be capable of being at least partly
detected by the imaging optical system 5.
The distance ~,;a;from the imaging optical system
5 to the i th code element of the code pattern 2 is
determined in the following equations, where
ai = r= eZ - pi
and eZ is the unit vector in the positive z direction.
The vector ai is thus known, while ki is the
multiplication factor to be determined. The following
vector equation is applicable
Li = ki = a;. - ro.
By calculating the square of the absolute value, the
following quadratic equation for ki is obtained:
IasI2=ki2-2=(ro=ai)=Xi+ro2-Li2=0.
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There are thus two solutions for ki, which is shown in
Fig. 3 schematically by the two points of intersection
of the dashed arc with the direction of observation a;
to the i th code element. The uniqueness of the
solution is established by mapping the i th code
element on the detector 7. The mapping describes the
deviation of the shape of the focused code element (or
generally of object 1) from its shape which it has at
the "zero point" (polar angles cp = 0 and S= 0) of the
object 1.
The three-dimensional coordinates of the vector
L; are obtained on the basis of the distance k;a; to the
i th code element, determined from the above equations,
and of the vector ai determined from the detected
vector pi. This immediately gives the direction vector
Li
v= - , from which the polar angles (cp, S) can easily be
I L;
calculated by means of trigonometrical functions. Thus,
when position vector ro is known, the measurement of a
single code element is sufficient for calculating the
polar angles (cp, S). The accuracy of the polar angle
calculation can of course be substantially increased by
including more code elements of the code pattern 2b.
If in addition a code pattern 2b unique with respect to
the angle of rotation K is applied to the object 1, the
angle of rotation K of the object 1 about its axis 4
can also be determined from the focused code pattern
2b. Thus, the total rotational position of the object
1 is determined rapidly, precisely and without contact.
In a more extensive second case, the measuring
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head 9 and the object 1 are to be spatially variable
relative to one another. In this case, the position
vector ro is also unknown in addition to the rotational
position. The additional determination of the position
vector ro is essential particularly when the object 1
is a levelling staff, a surgical microscope or a
surgical tool (and can of course also be performed in
the case of the above-mentioned gun barrel) In the
case of surveys, the position vector ro - in particular
the distance Zo and the height H of the imaging optical
system 5 from the foot 3 of the levelling staff - is
even the measured quantity of actual interest. If at
the same time the direction vector v of the levelling
staff always deviating slightly from the exact
perpendicular is determined, this has the advantageous
effects, mentioned further above, on the accuracy of
the surveying and the handling during the levelling
process. It is even possible deliberately to dispense
with a perpendicular orientation of the levelling staff
and to omit the application of a water level on the
levelling staff. Finally, in the case of said medical
aids for diagnosis, therapy or surgery, a knowledge of
the position vector ro, of the direction vector v and
of the angle of rotation K is also important.
For simultaneous determination of ro and v, it
is sufficient in principle to select only three code
elements from the code pattern 2b focused on the
detector 7, to determine their code numbers i and to
apply the vector mathematics described by the above
equations to these code elements.
It is of course advantageous for the accuracy
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and reliability of the result to use additional or all
detected code elements for the evaluation and to apply
the vector mathematics described. Moreover, generally
known estimation and fit procedures from mathematics
can be used. Moreover, the above vector equations can
be solved with the aid of iteration procedures and
similar mathematical methods.
Instead of the code elements of code pattern
2b, details of object contours 2a or marks on the
object 1 can also be evaluated in an analogous manner.
Advantageously, the position parameters of the
object 1 which have been determined in this manner can
be used in subsequent optimization procedures and thus
determined even more accurately. The position
parameters are varied until the detector image of the
object structures 2a, 2b which are calculated from the
position parameters agree optimally with the image
information actually detected. In principle, however,
the optimization procedures can also be performed
independently of preceding calculations.
Fig. 4 schematically shows, as object 1, an aid
for the medical sector whose spatial position and
rotational position relative to a patient are of
decisive importance. Thus, the object 1 may be a
surgical microscope, a surgical tool, such as, for
example, a scalpel, a drill, an endoscope, etc., or a
frame firmly connected to the patient or a radiation
source for tumour treatment. As shown schematically in
Fig. 4, the object 1 may be provided with a code
pattern 2b in a plurality of areas on its surface. The
spatial position of the object 1 is changed, for
example, with the aid of a swivel arm 10. Moreover,
the object 1 is mounted on the swivel arm 10 so as to
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be rotatable at a pivot point 3 through the three
angles cp, S, x, so that its rotational position, too,
can be adjusted as desired. Thus, the object 1 - for
example in the case of a brain operation - can be
brought into any desired required spatial position on
the patient's head.
The object 1 can be picked up by a plurality of
measuring heads 9a, 9b, 9c and the object structures
2a, 2b can be evaluated according to the above
equations or with the aid of the optimization methods.
For reasons of redundancy and because of the possible
concealment of the object structures 2a, 2b by persons
or instruments, a plurality of measuring heads 9a, 9b,
9c are arranged in space. The spatial coordinates of
the pivot point 3 (position vector ro) and the
rotational position cp, 6, x of the object 1 can be
determined relative to each measuring head 9a, 9b, 9c.
Since the spatial positions of the measuring heads 9a,
9b, 9c relative to one another are known, the
positional parameters of the object 1 can be
transformed to a superior coordinate system, for
example into the coordinate system of the patient.
Thus, the exact spatial position of the surgical
microscope or of the surgical instruments relative to
the operating site can be displayed for the surgeon.
In addition, the surgical instrument can be guided
fully automatically.
Fig. 5a schematically shows an object 1 on
which a separate body la has been mounted. By means of
the novel surveying and evaluation of the object
structures 2a, 2b of the body la, the (6-dimensional)
spatial position of the body la and hence also that of
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the object 1 are determined. Advantageously, an object
1 which has insufficient structures for an intended use
can be subsequently equipped with a suitable body la.
Optionally, the body la can also be readily removed
again. Of course, a plurality of such bodies la can
also be fastened to an object 1 (Fig. 5b).
Fig. 6a shows a stereoscopic arrangement of two
measuring heads 9a, 9b, which permit a high accuracy of
the determination of the object position on the basis
of the additional image information. The measuring
heads 9a and 9b can on the one hand be firmly connected
to one another so that the mutual position of their
optical axes 6a, 6b is fixed. The axes 6a, 6b may make
an angle with one another. Because little mounting
work is required, they are preferably aligned parallel
to one another. On the other hand, it may be
advantageous to keep the two measuring heads 9a, 9b
variable relative to one another and to make a suitable
adjustment only when they are set up for surveying the
object 1. If the object 1 is brought into an initial,
previously known position, the mutual position of the
optical axes 6a, 6b of the measuring heads 9a, 9b can
be automatically set by self-calibration. Of course,
the measuring heads 9a, 9b can if required be housed in
a single housing.
A variant of the stereoscopic arrangement is
shown in Fig. 6b. Only one measuring head 9 is used,
which picks up one partial stereo image directly and
the other partial stereo image via a laterally arranged
mirror 15. The coupling of the light picked up via
this mirror 15 into the beam path of the measuring head
9 is effected either via a pivotable coupling mirror 16
which, depending on its position, lets through only one
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or only the other partial stereo image for image
mapping with the detector 7 of the measuring head 9, or
the coupling mirror 16 is controllable in its
reflection and transmission properties, for example
according to the function of an LCD shutter, in such a
way that the two partial stereo images reach the
detector 7 alternately at high transmission and at high
reflection of the coupling mirror 16. On the other
hand, it is possible to use a half-silvered coupling
mirror 16 which transmits the two partial stereo images
simultaneously to different detector regions of the
detector 7 or to two separate detectors 7. This is
possible with suitable tilting of the half-silvered
mirror 16 and of an imaging optical system 5 tailored
thereto.
Of course, a stereo basis can also be generated
by two mirrors 15a, 15b according to Fig. 6c, and the
associated partial stereo images can be received
alternately by the detector 7 via a rotatable mirror
17. The rotatable mirror 17 may also be replaced by a
rotatable or fixed prism. In the case of the fixed
prism or with a suitable mirror arrangement,
simultaneous focusing of both partial stereo images
onto different regions of the detector 7 can be
effected.
Instead of the stereo imaging or in addition
thereto, the distance to the object 1 can furthermore
be determined using a distance measuring instrument 18,
18a and can be used as further measuring information in
the evaluation. The measured distance value improves
the accuracy and/or the rapidity of the evaluation for
determining the position parameters for the object 1.
Electrooptical distance measuring instruments
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18, 18a are preferred. They are connected as an
independent device to the measuring head 9, for example
according to Fig. 7a, or integrated in the measuring
head 9, according to Fig. 7b. Fig. 7a furthermore
schematically shows a cooperative target mark 19
(reflective foil, reflector, retroreflector, etc.) to
which the distance is measured. Of course, the
distance measurement is also possible without
reflective aids and merely to the given surface of the
object 1 as an uncooperative target.
That version of an integrated distance
measuring instrument 18a which is shown in Fig. 7b has
the advantage that the imaging optical system 5 of the
measuring head 9 can also be used and the distance
along the optical axis 6 of the measuring head 9 can be
determined. Coupling of the emitted light of the
distance measuring instrument 18a into the optical beam
path of the measuring head 9 or coupling out of the
received light for detection in the distance measuring
instrument 18a are effected, for example, via a half-
silvered or wavelength-selective mirror 20.
The electrooptical distance measuring
instrument 18, 18a is usually operated in the visible
or infrared wavelength range. Wavelengths which are
outside the sensitivity of the detector 7 of the
measuring head 9 are preferred, or corresponding
filters for the detector 7 and/or for the distance
measuring instrument 18, 18a are used. With the use of
a wavelength-selective mirror 20, the latter may
optionally reflect the infrared light of the distance
measuring instrument 18a particularly well and at the
same time transmit the visible light to the detector 7
of the measuring head 9 particularly well. Otherwise,
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all types of electrooptical distance measuring
instruments 18, 18a can be used, including those which
have, for example, a biaxial design with separate
transmitted and received beam path or which are of
monoaxial design and simultaneously make use of the
same optical setup for the transmitted and received
radiation.
