Spatial frequency filter

A spatial frequency filter including: an optical system having detector means and means for projecting onto the detector means an image of an object area; and means for operating the optical system alternately in a first mode to develop a first system transfer function and a second mode to develop a second system transfer function which is matched to the first system transfer function in low spatial frequencies and divergent therefrom in high spatial frequencies, for imposing on the detector means a first representation of the image in the first mode and a second representation of the image in the second mode, thereby providing a fluctuating elemental image output from each element of the detector means which derives from a high spatial frequency object; and also including means for limiting the wavelength range of input radiation to the detector means.

FIELD OF INVENTION 
This invention relates to a spatial frequency filter, and more particularly 
to such a filter for optically distinguishing high spatial frequency image 
elements from low spatial frequency image elements. 
BACKGROUND OF INVENTION 
It is often useful to suppress low spatial frequencies and enhance high 
spatial frequencies in an optical image produced by telescopes, cameras, 
radiometers and the like, in order to distinguish the high spatial 
frequency image elements from the low spatial frequency image elements. 
This allows the high spatial frequencies to stand out and become easier to 
locate, detect, and track so that point sources can be easily 
distinguished from a very similar background when the background is 
characterized by spatial frequencies which are lower than the higher 
frequencies of the point source. 
Traditionally, the discrimination is performed electronically by massive 
data processing operations that require large computing capacity and a 
significant amount of time. 
One attempt optically to preprocess images preliminarily to distinguish 
between objects or sources which differ from their background relates to 
the use of a dual beam interferometer which provides two images to a 
detector: a defocussed image and a sharply focussed image, whereby point 
sources may be detected. U.S. Pat. No. 4,128,337, Dec. 5, 1978, Method and 
Apparatus for Interferometric Background Suppression, Theodore F. 
Zehnpfennig. 
It has further been suggested that techniques other than the 
focussing-defocussing approach may be used for discrimination purposes. In 
one proposal various techniques, such as introducing controlled amounts of 
spherical aberration, annular entrance apertures of various sizes, 
circular entrance apertures of various diameters, and transmittance 
variations, have been suggested to provide a spatial filter with two 
modulation transfer functions which match at lower spatial frequencies and 
diverge at higher spatial frequencies. To this end, pairs of optical 
systems were sought in which one member of the pair could be transformed 
into the other member and then back again with minimum mechanical 
disturbance to the instrument, using optical path difference variations 
and small oscillatory movements. It was found that one such pair could be 
formed by translating the central 30% portion of the primary mirror in a 
radiometer by one quarter wavelength to form one member, then the other 
member could be formed by removing the previous translation, translating 
the annular outer two percent of the primary mirror by one quarter 
wavelength, and finally oscillating the secondary mirror. See "Tailored 
Modulation Transfer Function and the Application to Dual Beam 
Interferometry", Scientific Report No. 1, Air Force Geophysics Laboratory, 
AFGL-TR-78-0077, Mar. 27, 1978, pages 1-29, Reference 1. Such an approach 
is difficult and costly to implement, and is subject to reliability and 
life problems because of the complexity of the mechanical and optical 
structures and interactions. Further, the treatment of a broad spectrum of 
input radiation has resulted in substantial mismatch of the various 
transfer functions which essentially defeats the matching at the low 
spatial frequencies and results in poor suppression. 
SUMMARY OF INVENTION 
It is therefore an object of this invention to provide an improved spatial 
frequency filter for optically discriminating between high and low spatial 
frequencies. 
It is a further object of this invention to provide such a spatial 
frequency filter which uses simple, easily implemented motions to provide 
the different transfer functions. 
It is a further object of this invention to provide such a spatial 
frequency filter which limits the input radiation wavelength. 
It is a further object of this invention to provide such a spatial 
frequency filter which requires only two different patterns of motion to 
provide two transfer functions which match at low spatial frequencies and 
diverge at high spatial frequencies. 
It is a further object of this invention to provide such a spatial 
frequency filter in which the regions of low spatial frequency matching 
and high spatial frequency divergence can be easily varied. 
It is a further object of this invention to provide such a spatial 
frequency system which may be implemented with a single optical system 
driven in two different modes by a simple actuator to obtain two different 
motions and resulting transfer functions. 
The invention results from the realization that a simple yet extremely 
effective optical spatial frequency filter can be made for preliminarily 
discriminating higher spatial frequencies from lower spatial frequencies 
by limiting the wavelength of incoming radiation and also by operating the 
optical system alternately in one mode and then another to provide two 
different transfer functions which suppress the low spatial frequency 
elements of the image and cause the high spatial frequency elements to 
fluctuate for easy detection. 
This invention features a spatial frequency filter including an optical 
system having detector means and means for projecting onto the detector 
means an image of an object area. There are means for operating the 
optical system alternately at least in the first mode to develop a first 
system transfer function and a second mode to develop a second transfer 
system function, which is matched to the first system transfer function in 
low spatial frequencies and divergent therefrom in high spatial 
frequencies. This imposes on the detector means a first representation of 
the image in the first mode and a second representation of the image in 
the second mode in order to produce a fluctuating elemental image output 
from each element of the detector means which derives from a high spatial 
frequency object. Means are provided for limiting the wavelength of input 
radiation to the detector means. 
The invention also features a spatial frequency filter having an optical 
system including detector means and means for projecting onto the detector 
means an image of an object area. There are means for gyrating the optical 
system alternately at least in a first mode to develop a first system 
transfer function and a second mode to develop a second system transfer 
function which is matched to the first system transfer function in low 
spatial frequencies and divergent therefrom in high spatial frequencies. 
In a preferred embodiment, the means for operating or the means for 
gyrating may move the means for projecting relative to the detector means, 
or may move the detector means relative to the projecting means. Or an 
optical element disposed in the optical path between the means for 
projecting and the detector means may be moved or gyrated by the means for 
operating or gyrating. There may be further included means for sensing 
fluctuations of the output of the detector means, and the means for 
sensing may include means for subtracting the image in one mode from the 
image in the other mode. The means for sensing may include a band pass 
filter and an AC coupling means interconnecting the band pass filter and 
the detector means, and the band pass filter may be tuned to the frequency 
of the alternation of the first and second modes. The means for operating 
or the means for gyrating may include piezoelectric means and may further 
include means for driving the optical system to move or gyrate at one or 
more radii for a first period of time in the first mode and to gyrate at 
one or more other radii for a second period of time in the second mode. At 
least one of the modes may include intermittent dwell periods.

Point sources contain all spatial frequencies and are distinguished from 
most other sources by the fact that those other sources have the lower 
spatial frequencies but do not have the higher spatial frequencies. Thus a 
system which can discriminate higher spatial frequencies from lower 
spatial frequencies will serve well to identify point sources in the 
presence of structured backgrounds. The spatial frequency filter according 
to this invention is such a device. 
There is shown in FIG. 1 a spatial frequency filter 10 according to this 
invention having an optical system 12 including some means for projecting 
such as a primary optical element, concave perforated mirror 14, and a 
convex secondary mirror 16, and a detector array viewing mirror 16 through 
perforation 20 in mirror 14. Optical system 12 may be located in a 
telescope or radiometer structure 22 and mirror 16 and mirror 14 may in 
fact constitute the Cassegrain system of such a radiometer. Image 
radiation directed at this radiometer 22 strikes mirror 14 and is 
reflected to convex mirror 16 and then focussed on the sensitive surface 
of detector 18. In accordance with this invention, the optical system is 
gyrated, for example in FIG. 1, by gyrating mirror 16 by some means 23 
such as piezoelectric actuators 24, 26, 28 and 30, shown more distinctly 
in plan view in FIG. 2A, which are driven by high voltage function 
generator 44, FIG. 1. Some means for limiting the wavelength range of 
input radiation to detector 18, such as spectral bandpass filter 45, is 
also included. It may be placed anywhere in the optical path, e.g. between 
mirror 14 and mirror 16 or between mirror 16 and detector 18, as indicated 
at 45a. This prevents wavelengths outside the region of interest from 
entering the system and degenerating the low spatial frequency match of 
the transfer functions which accomplish the low spatial frequency 
suppression. 
In operation, mirror 16 is gyrated first in one mode and then in a second 
mode alternately by actuators 24-30, resulting in first and second 
representations of the image being projected onto the face of detector 18. 
The two gyration modes performed by mirror 16 suppress low spatial 
frequency image elements and enhance high spatial frequency image elements 
so that the high spatial frequency image elements fluctuate on detector 
array 18 at the same rate or frequency at which the two modes are 
alternately interchanged. The fluctuating elements may be detected by 
sensor 32, which may include an AC coupling unit 34, such as a set of 
capacitors, and a temporal or electronic filter 36 which passes 
fluctuations in a band centered on the frequency of the alternating 
interchange of the two modes and blocks other frequencies. The output from 
sensor 32, having been suitably preliminarily processed to provide only 
the information from the fluctuating high spatial frequency elements of 
the image, is then directed to a data processor 38 which need only then 
process these higher spatial frequency image elements. The detector array 
may be a one or two dimensional array of lead sulfide, indium antiminide, 
or mercury cadmium telluride detector elements. Sensor 32 may be any 
suitable means by which the fluctuating signals to be detected, for 
example the output from the detector elements may be fed to an A to D 
converter so that the outputs from successive modes can be subtracted or 
algebraically combined to obtain the difference between the images 
produced in the two modes. 
Alternatively, the means for gyrating 23 may be mounted to detector 18: 
piezoelectric actuators 24a, 26a, 28a, and 30a (not visible) in FIG. 1. 
The arrangement of actuators 24a, 26a, 28a and 30a mounted to base plate 
25 of detector 18 is shown in greater detail in FIG. 2B. In another 
implementation, the means for gyrating 23b, FIG. 3, may be used to drive 
an intermediate optical element such as mirror 40 disposed in the optical 
path between detector 18 and mirror 16. Gyrating means 23b is fixed to a 
suitable mounting 42. Although in FIGS. 1 and 3 a single optical element 
is used to provide both modes, this is not a necessary limitation of the 
invention, as two different optical elements may be used, one to provide 
each mode. 
In one embodiment, high voltage function generator 44, FIG. 4, may include 
a mode B1 square wave generator 46 which operates at one Hz and a mode A 
square wave generator 48 which operates at one KHz. The output of 
generator 46 is provided on line 50 directly to OR gates 52 and 54 and the 
output of generator 48 is delivered directly to the same OR gates over 
line 56. The output of generator 46 is also provided over line 58 to the 
controlled input of generator 48. OR gates 52 and 54 control sine wave 
generator 60 and cosine wave generator 62, which operate at 10 KHz and 
whose outputs drive piezoelectric actuators 24-30. Actuator 24 is driven 
by a plus sine wave, actuator 26 by a minus cosine wave, actuator 28 by a 
minus sine wave and actuator 30 by a plus cosine wave. During the first 
part of the cycle of square wave generator 46, when the output on line 50 
is at zero, the mode A square wave generator 48 is enabled to provide a 1 
KHz square wave on line 56 to OR gates 52 and 54 to drive generators 60 
and 62 to provide their respective sine and cosine outputs at 5,000 volts 
maximum amplitude. During the second half of the cycle, when mode B1 
square wave generator 46 provides a positive output on line 50, mode A 
square wave generator 48 is disabled and the positive output from 
generator 46 is provided through OR gates 52 and 54 directly to generators 
60 and 62 to provide 3,000 volt maximum sine and cosine output. More 
specifically, in mode B1, the output waveforms of 60 are (in volts) equal 
to +3,000 sin (2.pi.10,000t) and -3000 sin (2.pi.10,000t), where t is 
time. Those of 62 are +3000 cos (2.pi.10,000t) and -3000 cos 
(2.pi.10,000t). 
The form of the wave shape may best be seen in FIG. 5. During the first 
half cycle, which at 1 Hz is equivalent to one half second during mode A, 
the 1 KHz signal from generator 48 provides a fractional gyration time of 
typically 30.5% and a fractional dwell time f equal to 69.5%. During the 
next half of the cycle or the next half second, when generator 46 output 
goes positive in mode B1, a constant output is provided to 60 and 62 for 
the entire half cycle, giving a constant gyration radius of R.sub.B1. 
The gyration patterns provided by the optical system of FIG. 1 driven by 
the circuits of FIG. 4 as explained with reference to the wave forms of 
FIG. 5 may include a circular gyration represented by the relatively low 
amplitude cylindrical form having a radius in the detector plane of 
R.sub.A, FIG. 6, in mode A, and in mode B1 may include a gyration 
represented by the cylindrical form of larger amplitude and smaller radius 
R.sub.B1. Although the gyration patterns in FIG. 6 and in FIG. 10 are 
illustrated as cylinders, this is for purposes of illustration only: the 
actual diffraction pattern appears as shown in FIG. 3 of Reference 2, 
cited infra. The central spike shown in mode A, FIG. 6, represents the 
intermittent, non-gyrated dwell periods in mode A. The cylindrical 
illustrations are abstractions illustrating the radius and relative 
duration spent at each gyration radius. Other than circular patterns may 
be utilized. For example, one or both of the patterns could be spiral so 
that the gyration pattern begins at the external radius and spirals 
inwardly to the central axis in one mode and then begins at the central 
axis and spirals outwardly in the other mode. Such a system should reduce 
accelerations, While typically there are two modes of gyration, this is 
not necessary as there may be more than two with various dwell periods as 
well. 
The means for projecting, optical system 12, has a modulation transfer 
function in one mode as indicated by the curve labelled "Mode A" in FIG. 
7, and in the other mode as indicated by the curve labelled "Mode B1" in 
FIG. 7. These curves are matched in the regions of low spatial frequency 
70 and diverge in the regions of high spatial frequency 72. In fact, the 
curve from mode B1 goes negative at high spatial frequencies while the 
curve from mode A stays positive. Thus the image areas containing spatial 
frequencies in the upper or higher region will fluctuate as they are 
successively interchanged on the detector face and cause fluctuations in 
the detector array elements receiving image elements derived from objects 
or sources of high spatial frequency. In comparison, in the lower spatial 
frequency region 70 the two curves mode A and mode B1 in FIG. 7 are 
matched and so there will be no fluctuation noticed in the lower spatial 
frequency regions. The combined modulation transfer function of spatial 
frequency filter 10 is indicated as curve A-B1 in FIG. 7, which has an 
effectively zero response in the lower regions and high response in the 
higher regions. The transition between the low spatial frequency region 
and the high spatial frequency region is the null point at which the 
spatial frequencies of the two modes are the same. 
The desired value for the null point .omega..sub.D is chosen by selecting 
the radii R.sub.A, R.sub.B1, and the fractional dwell time f in accordance 
with the expression: 
EQU J.sub.0 (2.pi.R.sub.B1 .omega..sub.D)=f+(1-f)J.sub.0 (2.pi.R.sub.A 
.omega..sub.D) (1) 
where J.sub.0 is the zero order Bessel function, f is the fraction of time 
spent dwelling without gyrations while in mode A, R.sub.A is the radius of 
mode A gyration, R.sub.B1 is the radius of mode B gyration, and 
.omega..sub.D is the spatial frequency of the null point at which the two 
transfer functions match. With R.sub.A equal to 1.615, R.sub.B1 equal to 
0.808, and f equal to 0.695, .omega..sub.D occurs at 0.20. The units of 
R.sub.A and R.sub.B1 are .lambda./d, where .lambda. is the wavelength of 
the center of the spectral passband and d is the diameter of the entrance 
aperture of the optics. The center wavelength of the spectral filter 45, 
FIG. 1, covers a broad enough band to include targets of interest and a 
narrow enough band to keep the low spatial frequency portion of the 
modulation transfer functions sufficiently matched to produce the desired 
low spatial frequency suppression. A further explanation of the background 
and details of implementation of the invention is contained in "Background 
Suppression With Variable Modulation Transfer Function Imaging Systems ", 
Zehnpfennig et al., SPIE Vol. 253, pp. 8-14, Reference 2, which is 
incorporated herein by reference. 
It is normally desirable to have .omega..sub.D at somewhere between 20% and 
50% of the cutoff frequency, but this can vary depending upon the spatial 
frequency of the objects desired to be identified. The cutoff frequency 
.omega..sub.c, measured in the image plane of a diffraction limited 
optical system, is equal to the diameter of the aperture divided by the 
product of the focal length and the wavelength of the radiation. 
In FIG. 7, while the modulation transfer functions have a workable match, 
that match is not precise. For example, see the slight negative excursion 
of curve A-B1 in region 76, FIG. 7. A more precise match indicated in 
region 76a, FIG. 8, of the modified A-B1 modulation transfer function can 
be obtained by having that transfer function cross the zero level twice, 
as indicated in FIG. 9, where the area 76a has been enlarged to show that 
in addition to the axis crossing at .omega..sub.D there is a previous 
crossing at .omega..sub.E. Again, these spatial frequencies .omega..sub.E 
and .omega..sub.D may be chosen by selection of g and R.sub.B2 as well as 
R.sub.A, R.sub.B1 and f, previously referred to with respect to expression 
(1), through the simultaneous solution of equations (2) and (3): 
EQU gJ.sub.0 (2.pi.R.sub.B1 .omega..sub.D)+(1-g)J.sub.0 (2.pi.R.sub.B2 
.omega..sub.D)=f+(1-f)J.sub.0 (2.pi.R.sub.A .omega..sub.D) (2) 
EQU gJ.sub.0 (2.pi.R.sub.B1 .omega..sub.E)+(1-g)J.sub.0 (2.pi.R.sub.B2 
.omega..sub.E)=f+(1-f)J.sub.0 (2.pi.R.sub.A .omega..sub.E) (3) 
where R.sub.B2 is the radius of a second gyration pattern in mode B, and g 
is the fraction of the time when in mode B which is spent gyrating at 
radius R.sub.B1. 
The resulting gyration patterns are shown in FIG. 10, where the general 
form of mode A is unchanged from mode A of FIG. 6, but mode B includes 
now, in addition to the smaller-radius R.sub.B1 pattern, a second pattern 
of larger radius R.sub.B2. This second gyration pattern in mode B may be 
derived by superimposing a second set of square waves indicated in dashed 
line in FIG. 5 as mode B2 on the existing signal wave form mode B1. This 
may be done simply by adding an additional mode B2 square wave generator 
at 1 KHz 46a in line 50, FIG. 4. Thus the filter of this invention is 
easily tuned to a particular range of high spatial frequencies versus low 
spatial frequencies and may be modified to improve the match in the low 
frequency regions as required by circumstances. 
Thus far we have taken the ungyrated modulation transfer function 100, FIG. 
11, of the optic elements and gyrated it in mode B to provide the 
modulation transfer function 102, and have further gyrated the optical 
elements in mode A to obtain modulation transfer function 104, FIG. 12. 
The transfer function 106, FIG. 13, of the detector array in mode B is 
identical to the transfer function 108, FIG. 14, of the detector array in 
mode A. This results in a system transfer function 110, FIG. 15, in mode 
B, derived from the product of transfer functions 102 and 106. In mode A 
there results the transfer function 112, FIG. 16, from the product of 
transfer functions 104 and 108. The combination, by subtraction of the two 
transfer functions 110 and 112, then results in the system transfer 
function 114, FIG. 17. 
However, the invention is not restricted to the gyration of the optical 
elements. The detector elements may also be gyrated according to the 
invention. In that case the transfer function 120, FIG. 18, of the optics 
in mode B is identical to the transfer function 122, FIG. 19, of the 
optics in mode A. However, with the detector gyrated the detector's 
transfer function 124, FIG. 20, in mode B, takes a different form than the 
detector's transfer function 126, FIG. 21, in mode A. The product of 
transfer functions 120 and 124 result in transfer function 128, FIG. 22, 
for mode B, and the product of transfer functions 122 and 126 result in 
the transfer function 130, FIG. 23, for mode A. The resulting system 
transfer function 132, FIG. 24, is the same as the system transfer 
function 114 in FIG. 17; any part of the optical system, either the 
detector array or one or more of the optical elements, may be gyrated to 
accomplish the same result. 
Although the embodiments disclosed herein relate to two-dimensional 
gyrations, this is not a necessary limitation of the invention. For 
example, a one-dimensional or linear motion can be effected using only one 
of the sine or cosine generators in FIG. 4. In that case the motion 
pattern would be represented as a line or lines instead of a circle or 
circles as illustrated in FIGS. 6 and 10. 
Other embodiments will occur to those skilled in the art and are within the 
following claims: