Image motion and distortion stabilization for predetection scene information processing sensors

The specification discloses a method and apparatus for stabilizing images in the reference frame of a forward or down looking infrared receiver moving relative to the scene. An infrared modulator (14) is disposed in the image plane of the receiver for imaging infrared energy from the scene. The modulator (14), normally nonreflecting of infrared energy incident thereon, is capable of having reflective spots written on selected locations thereon to reflect infrared energy incident at those locations. Detectors (24) positioned to detect infrared energy reflected from the modulator provide an output signal representing the radiance values of the sampled scene element. A microprocessor (30) is connected to the detector, responsive to the detected output signal, to detect image motion caused by relative motion between the receiver and the scene from the detected information. The microprocessor (30) provides transform information about the transformation from reference frame to modulator coordinates such that infrared energy reflected from the modulator will appear stabilized to a sampling frame in the computer during relative motion between the telescope and the scene. Interface electronics (32) connected to the microprocessor (30) converts selected sampling points in the window frame coordinates to modulator coordinates at which coordinates an electron gun (21) writes reflective spots on the modulator.

TECHNICAL FIELD 
The invention pertains to methods and apparatus for electronically 
stabilizing images observed in the focal plane of a sensor under 
conditions of relative motion between the sensor and the object, and more 
particularly to methods and apparatus for stabilizing images for 
predetection scene processing in forward looking and down looking infrared 
receivers. 
BACKGROUND ART 
In conventional sensors in which the image of a scene is focused on the 
detector plane, rotation or translational movement of the sensor causes 
the image of the scene to move and distort relative to the detector. Under 
such conditions, a fixed reference frame in the scene is not a fixed 
reference frame in the image plane. To compensate for image motion to 
prevent blur, conventional sensors must sample scene information at very 
high frame rates. The greater the sensor motion, the higher the frame rate 
must be with concomitant greater bandwidth requirements. 
A major disadvantage of using fast frame rates is that scene frames lose 
their value quickly since they cannot easily be correlated with new frames 
having different distortion. Physical stabilization of the sensor line of 
sight has been attempted with only partial success. Such stabilization 
corrects for only part of the image motion, the part in the near vicinity 
of the relative velocity vector or the track point in the scene. This 
procedure makes the useful field of view small and increasingly smaller at 
higher relative velocities. Therefore, a need arises for a method and 
apparatus for stabilizing images in a sampling coordinate frame in a 
computer to compensate for relative motion between the object and the 
sensor. 
DISCLOSURE OF THE INVENTION 
In accordance with the present invention, apparatus is disclosed for 
stabilizing the image of a scene being viewed by a forward or down looking 
infrared receiver moving relative to the scene. An infrared modulator is 
disposed in the image plane of the receiver for imaging infrared energy 
from the scene. The modulator is normally nonreflecting to infrared energy 
incident thereon, but is capable of having reflecting spots written at 
selected locations thereon to reflect infrared energy incident at those 
locations. Detectors positioned to detect motion of the image on the 
modulator caused by infrared energy reflected from the modulator provide 
an output signal representative of the radiance of the sampled scene 
element. A microprocessor is connected to the detector, responsive to the 
detected output signal to detect motion of the image on the modulator 
caused by relative motion between the receiver and the scene from the 
detected information. The microprocessor provides a signal indicative of 
the sampling coordinates on the modulator from which infrared energy 
reflected from the modulator will appear stabilized to a sampling frame in 
the computer during relative motion between the telescope and the scene. 
Control means responsive to the microprocessor converts selected sampling 
points in the window frame coordinates to modulator coordinates and 
directs a cathode ray tube to write reflective spots on the modulator at 
the modulator coordinates. 
In accordance with another aspect of the invention, a method is disclosed 
for stabilizing the image of a forward or down looking infrared receiver 
moving relative to the scene being viewed. Radiance values derived from 
the last set of observations made of the scene are stored. A current set 
of radiance values corresponding to selected points in the scene is 
obtained by rapidly writing a series of reflecting spots on a thermoptic 
modulator. The time rate of change of the radiance values is determined by 
comparing current radiance values with stored radiance values from the 
preceding set of observations. The spatial rate of change of the current 
radiance values is then determined from the current radiance values. The 
time and spatial rates of change of the radiance values are then processed 
to determine transform values representing the motion of the image caused 
by relative motion between the telescope and the scene. A set of sample 
points having coordinates in the window frame is then transformed into 
modulator coordinates such that a scene element reflected from the 
modulator at these modulator coordinates will appear stabilized in the 
window frame during relative motion between the telescope and the scene.

DETAILED DESCRIPTION 
The emerging technology of thermoptic materials has made possible a variety 
of new light control devices which have particular application in forward 
and down looking infrared sensors. The physical phenomenon on which the 
thermoptic technology is based is the sudden change in optical properties 
of certain materials at specific phase transition temperatures. For 
thermoptic materials such as vanadium dioxide (VO.sub.2), the change in 
crystal structure from the monoclinic to rutile states is 
thermodynamically favored above the phase transition temperature with a 
consequent sudden change in optical properties which produce nonreflecting 
and reflecting states from a film stack. Switching times between states 
can be extremely short, on the order of nanoseconds. Reflecting spots can 
be written on these normally nonreflecting materials by inducing localized 
changes in temperature. By proper control of the ambient temperature, the 
spots can be maintained indefinitely or permitted to vanish rapidly after 
being written. Spot sizes have been written as small as five microns by 
lasers and as small as twenty microns by electron beam heating. Large area 
optical quality VO.sub.2 film surfaces have been manufactured and 
programmable spots have been obtained using CRT tubes with thermoptic film 
faceplates. For further information about the optical properties of 
vanadium dioxide thin films and the use of such films as infrared 
modulators, reference is made to the copending application of Dayton D. 
Eden, Ser. No. 023,221, filed Mar. 23, 1979, entitled "Optical Modulation 
of Vanadium Oxide Thin Films", now issued as U.S. Pat. No. 4,283,113. 
Infrared modulators using these new thermoptic materials have been 
constructed in which scene sampling patterns can be programmed in real 
time in the image plane to move and distort in exactly the same way as the 
image. The sampling spot in this electronically stabilized reference frame 
in a computer maintains its position in the scene for all sensor motions 
that do not move that part of the scene out of the field of the view. As a 
result, the true optical image is made to correspond mathematically to a 
sampling frame image that is not distorted, displaced or lost from the 
field of view. Since high frame speeds are not required, bandwidth 
requirements are accordingly reduced. 
In the preferred embodiment, an infrared sensor may employ a programmable 
infrared modulator ahead of the detectors to perform a variety of optical 
processing functions on the incoming infrared scene image prior to 
detection. The modulator, placed in the focal plane of an infrared sensor, 
is capable of reflecting all or part of the infrared image falling on the 
modulator to an infrared detector when part or all of the modulator is 
switched to its reflecting (metal) state. In its normal (semiconductor) 
state, the modulator does not reflect infrared energy and infrared energy 
from the scene passes through or is absorbed by the modulator with minimum 
reflection. When the modulator is in its normal, nonreflecting state, the 
detectors have no view of the outside world. Such an arrangement is 
referred to as a "dark field" infrared telescope. 
When information from the real world scene is desired, a localized spot of 
predetermined size is written at a desired location on the modulator. The 
optical path of the detector is thereby coupled with the optical path of 
the telescope by a reflecting spot which allows energy intercepted by the 
spot on the modulator to be reflected to the detectors. The location of 
the reflective spot on the modulator determines the location of the scene 
element to be sampled. The size of the spot, which can also be varied, 
determines the instantaneous field of view (IFOV) of the sensor, and 
therefore, the area of the scene to be sampled, which determines the 
resolution. Any part of the telescope viewable scene can thus be randomly 
accessed with any degree of resolution within the limits of the 
programmable spot size and the optical resolution limits of the infrared 
telescope. 
FIG. 1 schematically illustrates the dark field telescope and the 
associated electronics employed in the image stabilization system. A scene 
10 emitting thermal energy at wavelengths in the infrared region of the 
electromagnetic spectrum, is viewed through a lens 12 which focuses 
infrared radiation onto the faceplate of a thermoptic modulator 14. The 
modulator 14 contains a stack of thin films 16 disposed on a substrate 
material 18 at the faceplate thereof. Film stack 16, which is typically 
less than 5 microns in thickness, contains several layers of thin films, 
at least one of which is a phase transition material such as vanadium 
dioxide thin film, having a thickness typically about 2000 A. The film 
stack is designed such that its reflective and nonreflective 
characteristics are optimized for operation at wavelengths in the range 
0.4 to 12 microns by appropriate choices of the indices of refraction and 
the thicknesses of the films and substrate material. The film stack 16 is 
maintained at a temperature of about 50.degree. C., which is about 
15.degree. below the transition temperature of the vanadium oxide thin 
film. At this temperature, reflective spots written on the faceplate of 
modulator 14 by localized heating decay rapidly as the heated region 
returns to ambient temperature. This permits a set of observations of the 
scene to be made by rapidly scanning a series of reflecting spots written 
at specific coordinates on the modulator. 
The thermal emission of the entire scene 10 is therefore viewed at the 
faceplate of modulator 14. As the result of a command to the modulator 
drive electronics 20, a reflective spot of selected size is written at 
selected coordinates (X.sub.m, Y.sub.m) on the modulator to reflect the 
portion of the scene incident at the spot to the infrared detectors 24. 
The modulator drive electronics generates the necessary voltages to drive 
an electron gun or laser in the modulator of predetermined size to be 
directed at selected coordinates on the faceplate of modulator 14 at which 
point a reflecting spot 22 is written. In the preferred embodiment, a 
cathode ray tube with an electron gun and electrostatic deflecting plates 
or alternatively, an electromagnetic deflection coil, is employed in the 
thermoptic modulator. Alternatively, a scanable laser may also be used in 
place of an electron gun. 
Detectors 24 generate a signal responsive to the intensity of the infrared 
photon flux or radiance values detected at coordinates (X.sub.m, Y.sub.m) 
on the modulator 14. Conventional infrared detectors, such as the indium 
antimonide detectors, have been employed for this purpose, and other 
detectors, such as lead selenide or mercury cadmium telluride, are also 
suitable, depending upon the wavelength at which the telescope is designed 
to operate. The detectors may be employed in an array to provide greater 
sensitivity and reduction of detector noise. To facilitate collection of 
the radiation reflected from the modulator, additional optics 26 may be 
provided between the modulator and the detectors. 
The signals generated by detectors 24 are fed to a signal processor 28, 
where the signals are amplified and converted into digital form for 
processing by the sensor microprocessor 30. Such a signal processor may 
include conventional electronics such as preamplifiers, post-amplifiers, 
filters and analog to digital converters. The digitized output signal of 
signal processor 28 is fed to the sensor microprocessor 30, which 
processes information about the radiance values observed at detectors 24 
and which also controls the operation of the dark field telescope. For 
further details concerning the dark field telescope, reference is made to 
the copending application of James D. Billingsley and Dayton D. Eden, Ser. 
No. 023,221 filed Aug. 11, 1981. 
Under control of the sensor microprocessor 30, information about the 
radiance values obtained at detectors 24 is processed in accordance with 
the method hereafter described. Microprocessor 30 determines the location 
of points on the modulator in a computer reference or "window" frame from 
which information sampled from the scene will appear stabilized despite 
relative motion between the telescope and the scene. Microprocessor 30 may 
be any conventional microprocessor capable of carrying out the arithmetic 
functions hereafter described. Microprocessor 30 processes data about 
current and previously observed radiance values, as well as information 
about the "window" frame coordinates from which transform data is 
generated to permit selected sample points in window frame coordinates to 
be transformed to modulator coordinates. The transform data along with 
selected sample points in window frame coordinates are then furnished to 
conventional interface electronics 32, where the window frame coordinates 
are transformed to modulator coordinates by simple arithmetic operations 
and appropriate signals are generated for commanding the modulator drive 
electronics 20 so that reflecting spots are written at the proper 
coordinates on the modulator 14. Interface electronics 32 contains 
conventional digital or analog circuitry for carrying out addition and 
multiplication operations necessary to make the coordinates transformation 
as well as conventional table lookup electronics necessary to generate the 
required control signals for the modulator drive electronics. The 
interfacing electronics 32 will send three separate control signals to the 
modulator drive electronics 20: a signal which turns the beam on and off, 
a signal which specifies the size of the spot and a signal which specifies 
the coordinates on the modulator at which the spot is to be written. The 
spot size, scanning times and synchronous sampling rates are all under the 
control of the sensor microprocessor 30. 
Referring to FIG. 2, the operation of the present invention can now be 
understood by considering that at some initial time, a scene (in the 
object space) lies in the field of view of the telescope. At this instant, 
there is a one-to-one correspondence between points in the scene and 
images of these points within the field of view. Because any point in the 
scene is specified by three coordinates, a transformation between the 
object space and the image space maps a subset of three-dimensional 
Euclidean space into a subset of two-dimensional Euclidean space. However, 
unless the telescope remains fixed in position and attitude relative to 
the scene, the image of each observed point will move about in the 
modulator coordinate frame. Moreover, incremental motion of different 
image points will be different depending upon the character of the 
relative motion. For example, if the motion of the telescope consists of a 
simple roll about the optical axis, points on one side of the axis will 
move up, while points on the other side will move down. Moreover, the 
magnitude of the observed motion is proportional to the distance from the 
axis. If the modulator or image frame moves toward the earth, the image 
points will move outwardly of the origin in the modulator frame at rates 
dependent upon their distance from the origin. Generally speaking, motion 
in the image frame is considerably complex and it can be seen that 
components of translation, rotation and changes in scale (magnification or 
minification) are required to describe image motion. 
FIG. 3A illustrates the distortion of an image which occurs over time when 
a telescope is moving relative to the scene. The closed dots represent the 
position of nine points distributed about the origin of the modulator 
coordinate system (X.sub.m, Y.sub.m) at some initial time t.sub.o ; the 
open dots represent the position of each of the nine points after some 
period of time t. The lines connecting the closed and open circles 
represent the motion of each of the respective points in the modulator 
frame or image space over time t. As shown in FIG. 3A, the image of the 
nine points is distorted after time t due to the relative motion between 
the scene and the telescope. The six degrees of sensor motion include 
three translational degrees of freedom, X, Y, and Z, and three rotational 
degrees of freedom, pitch, yaw and roll about the optical axis. 
FIG. 3B illustrates the position of the nine points in stabilized window 
frame in the computer at times t.sub.o and t. As shown in FIG. 3B, the 
image of the nine points appears stationary. While the sensor 
microprocessor 30 keeps track of what occurs at the modulator by means of 
the computational window frame, transformation is required between the 
window frame coordinates and image frame coordinates if points in the 
window frame are to be accessed on the modulator. 
The image stabilization procedure of the present invention can be seen as 
establishing a computational reference window frame in the sensor 
microprocessor in which the coordinates of the image of fixed points in 
space do not change in time. Transformation is required from the 
stabilized window frame to the modulator frame because the scene 
processing clearly must access the modulator. The capacity to access 
arbitrary points on the thermoptic modulator at high speeds makes image 
stabilization procedures feasible. 
The mathematical development of the image stabilization procedure will now 
be described. Vectors are represented by lower case Roman or Greek 
letters, with a bar (-) below each letter. Matrices are represented by 
upper case Roman or Greek letters. 
A general description of the transformation between object space to image 
space can be written as follows: 
EQU y.sub.1 (t)=.beta.(t)+B(t)z (1) 
where .beta. (t) is a two-dimensional column vector, 
B(t) is a 2.times.2 non-singular matrix, 
z is a two-dimensional column vector that denotes a point in object space, 
and 
y.sub.1 (t) is a two-dimensional column vector which provides x and y 
coordinates of the image of z (t). 
Similarly, a transformation from window space to image space can be written 
as follows: 
EQU y.sub.2 (t)=.alpha.(t)+A(t)x (2) 
Where 
.alpha. (t) is a two-dimensional column vector, 
A(t) is a 2.times.2 non-singular matrix, 
x is a two-dimensional column vector that denotes a fixed point in window 
space, and 
y.sub.2 (t) is the two-dimensional mathematical image of x in the "real" 
image space. 
The transformation from window space to object space is obtained by 
equating y.sub.1 to y.sub.2, then solving for z (t). z is a function of 
time because some residual relative motion exists between the window frame 
and the object frame. This motion is sensed and nulled by change in the 
window frame parameters on the modulator. This yields: 
EQU z(t)=B.sup.-1 (t)[A(t)x+.alpha.(t)-.beta.(t)] (3) 
Equation (3) permits selection of a point in the computational window frame 
and have that point stationary in object space. Equation (2) provides the 
necessary intermediate step that properly locates the selected point on 
the modulator. The transformation of the window frame to the modulator 
using these equations produces a sampling frame that follows the motions 
and distortions of the image. Theoretically, A(t) and .alpha.(t) can be 
determined from the rotational and translational motion of the telescope. 
More importantly, however, A(t) and .alpha.(t) can be determined from 
observations of the scene. Thus, direct knowledge of the sensor's motion 
is not needed to stabilize the scene and sampling process. 
Stabilization is possible by observing and nulling z in a closed loop 
control process that reproduces the window frame velocity components on 
the modulator. The representation of a fixed window frame on the modulator 
requires variation of six independent parameters: y axis location, 
rotation angle and scale and x axis location, rotation angle and scale. 
The representation of the window frame on the modulator and the 
corresponding representation of the object frame on the modulator (as the 
image) is anamorphic, nonorthogonal and nonstationary. 
The representation of the window frame on the modulator is as a moving 
frame. However, the moving frame can be regarded as fixed and the object 
frame as moving. Since equations (1), (2) and (3) represent affine 
transformations, it can be shown from the theory of Lie Groups that: 
##EQU1## 
for a suitable choice of of .mu..sub.1, .mu..sub.2 . . . where X.sub.1, 
X.sub.2 . . . are the infinitesimal generators of the motion. The 
parameters .mu..sub.i are derived from the detected radiance values. 
It can be shown from equations (3) and (4) that: 
##EQU2## 
Using (3) and (6), the left-hand side of (5) becomes 
##EQU3## 
The above can be rewritten as 
##EQU4## 
which is seen to be equation (5) given the previous definitions of .mu., M 
and x. 
The basic equations needed to obtain the principal result can be written as 
follows: 
##EQU5## 
Equation (7) is obtained by formally differentiating equation (3) with 
respect to t: 
EQU z=B.sup.-1 (Ax+.alpha.-.beta.)+B.sup.-1 (Ax+.alpha.-.beta.) 
The term involving A x is equal to 0, because the window frame is chosen to 
be a time independent reference frame. 
The expression for B.sup.-1 can be put in more suitable form as follows: 
From BB.sup.-1 =I, differentiation with respect to time yields: 
##EQU6## 
The above expression for z can now be written as 
##EQU7## 
Using the definitions of equation (8), it follows that: 
EQU z=B.sup.-1 (.LAMBDA..sub.A -.LAMBDA..sub.B)Ax+B.sup.-1 [.lambda..sub.A 
-.lambda..sub.B +(.LAMBDA..sub.A -.LAMBDA..sub.B).alpha.] 
It is seen that negating all terms in the previous equation yields equation 
(7). 
By equating equations (5) and (7) as indicated by equation (4), and 
comparing like terms, the following results are obtained: 
EQU B.sup.-1 AM=B.sup.-1 (.LAMBDA..sub.B -.LAMBDA..sub.A)A 
and 
EQU B.sup.-1 A.mu.=B.sup.-1 [.lambda..sub.B -.lambda..sub.A +(.LAMBDA..sub.B 
-.LAMBDA..sub.A).alpha.] 
If the first equation is solved for .LAMBDA..sub.B -.LAMBDA..sub.A and the 
second equation solved for .lambda..sub.B -.lambda..sub.A, there results: 
EQU .LAMBDA..sub.B -.LAMBDA..sub.A =AMA.sup.-1 
EQU .lambda..sub.B -.lambda..sub.A =A.mu.-AMA.sup.-1 .alpha. (9) 
To determine the generalized velocities, .mu..sub.1, .mu..sub.2 . . . 
.mu..sub.6, observations of radiance values in the object space must be 
made, rather than coordinates of z. .mu. and M can be found from radiance 
values. Thus, let F (t, x) be any contrast feature observed in the window 
frame. Then it can be shown that: 
##EQU8## 
Given that the infinitesimal generators X.sub.1 X.sub.2 . . . X.sub.n are 
the same, the .mu..sub.i of equations (4) and (10) are identical. These 
.mu..sub.i do not depend upon the particular point being observed, but are 
spatially invariant over the scene. 
As earlier stated, the stabilization of images seen by the modulator 
requires the .alpha. vector and the A matrix in equation (2) to be 
determined so that conversion can be made from window space to image space 
or back again. The observable data F (t, x) are radiance observations of 
points in object space. Thus, the time and spatial derivatives specified 
by equation (10) pertain to rates of change of observed radiance values. 
The procedure for obtaining .alpha. and A is now described by reference to 
FIG. 4 in which the components of the dark field telescope and the 
functional features of the stabilization subroutine under the control of 
the main program of the microprocessor are shown schematically. Since the 
six parameter algorithm requires not only current but previously obtained 
radiance values, some startup procedure is necessary when the 
stabilization routine is started and prior observations are not available. 
In the startup procedure, the values .alpha., A, .lambda..sub.A and 
.LAMBDA..sub.A are initialized as shown by the block 33. It is assumed 
that at time t=0, the transformation from window to image space is the 
identity transformation. 
##EQU9## 
Thus, .lambda..sub.A and .LAMBDA..sub.A are initially set to zero, because 
no a priori knowledge is assumed to infer time rates of change of the 
scene. This results in an initial lag or startup transient, before scene 
lock is established. These initialized values are fed from microprocessor 
30 to the interface electronics 32 where these values will be used to 
obtain coordinates on the modulator which can be accessed by the electron 
gun 21. The main program 36 executed by the microprocessor 30 requests 
start of the stabilization subroutines at 38 by choosing a sample point 
set in the window frame. FIG. 5 shows one possible sample point set. These 
sample point coordinates are then fed to the interface electronics 32 
where the coordinates are transformed to coordinates in the modulator 
frame. In the startup procedure, the above values of .alpha..sub.o and 
A.sub.o make the modulator coordinates the same as those in the window 
frame. 
In the next step, an initial sample of radiance values is obtained by 
writing a set of reflecting spots on the modulator at the modulator 
coordinates corresponding to each point in the sample set and observing 
the radiance value for each sample point at the detectors 24. 
The objective of the sampling is to provide data used in equation (10) to 
determine values for .mu..sub.1, .mu..sub.2, . . . .mu..sub.6. Because the 
number of unknown .mu..sub.i is six, a solution requires at least six 
distinct sample sets in the window coordinate frame. In the preferred 
embodiment, nine sampling sets are used from which the .mu..sub.i are 
determined by a method of least squares. The nine sampling sets in the 
window frame are shown in FIG. 5. It is understood, of course, that if the 
telescope is moving relative to the scene, the set will be represented 
differently in the modulator frame. It can be seen in FIG. 5 that in the 
preferred embodiment, the nine central sampling sets comprise a first 
sampling set at the origin and eight additional sampling sets equally 
spaced on a circle centered at the origin. Within a sampling set, the 
vertical and horizontal separation between adjacent points is represented 
by the distance "h". 
The central point of each set in FIG. 5 is used to obtain time derivatives 
required by the left-hand side of equation (10). The surrounding points 
are used to obtain spatial derivatives required by the right-hand side of 
equation (10). Thus, radiance values are observed at five separate points 
for each sample set. Stated differently, a set of observations consists of 
45 individual radiance values obtained by rapidly writing the 45 
reflecting spots in series. The configuration of sampling points in the 
window frame is shown in FIG. 5. 
In the next step of the startup procedure, new values for .alpha. and A are 
now computed. Integration by the Euler method procedure results in 
incrementing A by .LAMBDA..sub.A A.multidot..DELTA.t and incrementing 
.alpha. by (.lambda..sub.A +.LAMBDA..sub.A .multidot..alpha.) .DELTA.t. 
This step is represented at 40 by the block entitled "TRANSFORM UPDATE". 
Generating new values for .alpha. and A is equivalent to moving the window 
frame relative to the modulator frame. Because in starting up, 
.LAMBDA..sub.A and .lambda..sub.A are initialized to zero, this procedure 
yields no change in .alpha. and A. Thus, .alpha..sub.1 =.alpha..sub.0 and 
A.sub.1 =A.sub.0. However, when initial estimates are available for 
.LAMBDA..sub.A and .lambda..sub.A, scene track lock can be achieved more 
quickly. For example, if the position and velocity of the telescope are 
known, together with the attitude, this information will be used to 
initialize .LAMBDA..sub.A and .lambda..sub.A to non-zero values. Even if 
this information is imprecise, lock-on is more quickly achieved with 
non-zero values. 
This completes the startup procedure and provides a set of radiance values 
which can be stored for use in determining the time derivatives of the 
radiance values obtained from the next set of observations. 
Once a set of radiance values has been obtained, the six parameter 
algorithm for obtaining .alpha. and A may be executed by the stabilization 
subroutine 42. 
In Step 1 of the algorithm, timer interrupt 34 causes a new sample of 
radiance values to be obtained by selecting a sample point set such as 
that shown in FIG. 5 and transmitting the coordinates of this point set to 
the interface electronics 32, where the appropriate modulator coordinates 
are determined and appropriate signals are generated for directing the 
modulator drive electronics 20 to write the reflecting spots on the 
modulator. The window frame coordinates of the sampling points will, in 
general, be different from the modulator frame coordinates of those same 
points (FIG. 5). The values of .alpha. and A are used to determine the 
coordinates of the sample points in the modulator from the coordinates of 
the sample points in the window by equation (2). At block 40, the values 
of .alpha. and A are updated by applying the results of the sample 
measurements and stabilization computations. 
In Step 2 of the algorithm, shown by the block 44 entitled "FIND 
DERIVATIVES," the time derivatives required by equation (10) are computed 
from current and preceding sets of radiance values; spatial derivatives 
require current values only. The current radiance values are processed by 
the signal processor and fed in digitized form to the sensor 
microprocessor 30. The previous set of radiance values, stored at 46, is 
used in determining the time derivatives of the radiance values. The time 
and spatial derivatives are then used to compute the nine equations in the 
six unknowns, .mu..sub.1, .mu..sub.2, . . . .mu..sub.6. These nine 
equations in six unknowns may be represented by the matrix equation: 
EQU C.lambda.=d, (11) 
where C is a 9.times.6 matrix and d is a 9.times.1 vector. To see how each 
of the nine equations is found, consider a typical location such as shown 
in FIG. 5. 
If F (x.sub.i, t) is the observed radiance at time t for the point x.sub.i, 
i=1, 2, . . . 9, in the window space, the time derivative can be 
approximated as follows: 
##EQU10## 
The d vector in equation (11) consists of nine values obtained by equation 
(12). 
##EQU11## 
The spatial derivatives of the equation (10) are found as follows: 
##EQU12## 
For simplicity of notation, let 
##EQU13## 
Then the C matrix of equation (11) can be written: 
##EQU14## 
It can be seen that the time derivatives require the radiance values for 
the nine central locations to be saved at each sampling time, t.sub.k, 
because when time is advanced by increment, .DELTA.t, the following 
replacements occur: 
EQU F(x.sub.i,t.sub.k).fwdarw.F(x.sub.i,t.sub.k-1) and F(x.sub.i,t.sub.k 
+.DELTA.t).fwdarw.F(x.sub.i,t.sub.k) 
The spatial derivatives, however, are computed from current radiance values 
such that only nine of the 45 total values must be saved from one sampling 
time to the next. These nine values then replace the previously saved 
radiance values. These replacement and store functions are indicated at 
block 46. 
In the third step of the algorithm represented at 48 by the block entitled 
".lambda. SOLVER," the nine equations in six unknowns represented by 
equation (11) are solved for .lambda. by a least squares algorithm. This 
is equivalent to finding .mu. and M, because 
##EQU15## 
That is, the values of .mu..sub.i in equation (17) are the same as those 
given for defining .mu. and M, following equation (5). 
In Step 4, the .lambda..sub.A matrix and the .lambda..sub.A vector are now 
updated. This step is shown in FIG. 5 in block 50 entitled "VELOCITY 
UPDATE." From equation (9) it is seen that: 
EQU .DELTA..LAMBDA.=AMA.sup.-1 (18) 
Similarly, equation (9) shows that 
EQU .DELTA..lambda.=A.mu.-AMA.sup.-1 .alpha. (19) 
Greater control of the response rate can be achieved by applying feedback 
factors to the increments calculated in equations (18) and (19). Thus, let 
.DELTA..LAMBDA. and .DELTA..lambda. be represented as follows: 
##EQU16## 
The subscripts in the two equations above are used to correspond to those 
in the definitions of .mu. and M that follow equation (5). Six feedback 
factors are provided as preloads, say, f.sub.i, i=1, 2, . . . 6. These 
f.sub.i can be determined mathematically from stability analysis of the 
particular system and experimentally modified for the particular system. 
The components of the .LAMBDA..sub.A matrix and .lambda..sub.A vector are 
replaced as follows: 
##EQU17## 
In the last step of the algorithm, represented by block 40, the .alpha. 
vector and the A matrix are updated from the newly computed values of 
.DELTA..LAMBDA. and .DELTA..lambda. by applying equation (8). This step is 
outlined in the block entitled "TRANSFORM UPDATE." As a consequence of 
computing updated values of .LAMBDA..sub.A and .lambda..sub.A, the window 
frame may be moved relative to the modulator frame by recomputing the 
coordinates of the window space sample points in image space using A and 
.alpha. and equation (2). Thus, from .LAMBDA..sub.A =AA.sup.-1 it follows 
that: 
EQU A=.LAMBDA..sub.A A (23) 
Similarly, from .lambda..sub.A =.alpha.-.LAMBDA..sub.A .alpha., one obtains 
EQU .alpha.=.lambda..sub.A +.LAMBDA..sub.A .alpha. (24) 
The integration can be done by the simple Euler method, yielding 
EQU A+A.multidot..DELTA.t.fwdarw.A (25) 
Equivalently, the value of A is incremented by .DELTA.t 
Similarly, 
EQU .alpha.+.alpha..multidot..DELTA.t.fwdarw..alpha. (26) 
This means that the value of .alpha. is incremented by 
(.alpha..multidot..DELTA.t) 
The updated values of A and .alpha. are now furnished to the interface 
electronics 32. At this point subroutine 42 is terminated and control is 
returned to the main program 36. Equation (2) is now used in the interface 
electronics 32 to transform the desired sampling locations in window 
coordinates to modulator coordinates. The main program can now acquire 
images of the scene by selecting sampling points in window coordinates 
that define the pattern to be used to obtain the image. These sample 
points having coordinates in the window frame are then transferred into 
modulator coordinates such that a scene element reflected from the 
modulator at these modulator coordinates will appear stabilized in the 
window frame during relative motion between the telescope and the scene. 
The algorithm described above is now repeated, controlled by the timer 
interrupt 34, starting with the acquisition of a new set of radiance 
values. 
Thus, the above procedure provides a method for stabilizing the images in 
the sensor microprocessor's frame of reference. Of course, other 
stabilization procedures can be derived to accomplish the same result and 
other thermoptic materials may be employed to detect sample scene radiance 
values at other wavelengths, including wavelengths in the visible. 
Although particular embodiments of the invention have been illustrated in 
the drawings and described herein, it is understood that the invention is 
not limited to the embodiments disclosed but is capable of rearrangement, 
modification and substitution of parts and elements without departing from 
the spirit of the invention.