Apparatus for de-emphasizing low spatial frequencies in optical imaging systems

Apparatus is disclosed for de-emphasizing low spatial frequencies in a two-dimensional optical imaging system. The apparatus (10) includes a source of incoherent light (12) adapted to be directed toward a source of optical information (14); first (17) and second (19) coplanar strips of pupils (16, 18) for transmitting light from the source of optical information (14), the strips (17, 19) being parallel to one another, the pupils (16) of the first strip being randomly distributed therein and circular in shape, the pupils (18) of the second strip being randomly distributed therein and ring shaped; a lens system (20) positioned to focus light passing through the strips (17, 19) of pupils (16, 18) onto an output plane (22); and a Ronchi grating (24) positioned between the lens (20) system and the output plane (22) and parallel thereto at a distance from the output plane (22) such as to provide interlacing of the images through the two strips of pupils, the grid lines (25 ) of the grating being parallel to the strips (17, 18) of pupils.

BACKGROUND OF THE INVENTION 
This invention relates to optical systems and, more particularly, to 
improved apparatus for de-emphasizing low spatial frequencies in optical 
imaging systems. 
It is a characteristic of all optical pupils that low spatial frequencies 
are emphasized. This emphasis of low frequencies causes a derogation and 
often a complete masking of important optical information. 
Various attempts have been made to eliminate this low spatial frequency 
bias. For example, in our paper Low Frequency De-Emphasis of the 
Modulation Transfer Function, I. One Dimensional Case, Optical 
Communications, Vol. 41, p. 388 (1982), N. Konforti and I disclosed an 
optical system in which an input image of an object is directed through a 
pair of pupils and an imaging lens. The lens is adjusted so that the 
object's image is projected onto an output image plane in the form of a 
photosensitive plate positioned behind a Ronchi ruling or grating. In this 
particular arrangement, the pupils are rectangular in shape and their 
centers are equidistant from the symmetry axis of the optical system. Each 
pupil provides an optical transfer function which is different from that 
of the other pupil. The two pupils are selected to have equal 
transmissivity, so that equal optical energy is transmitted through each 
pupil. One pupil is in the form of a single rectangle while the other 
pupil is formed of two rectangles. 
The grating lines of the Ronchi grating are perpendicular to a line 
extending between the two pupils. The grating period and the distance 
between the grating and the photosensitive plate are chosen in accordance 
with geometric relationships specified in the paper. The images projected 
through the two pupils are sampled and interlaced by the Ronchi grating to 
form a single composite image on the photosensitive plate. This composite 
image is recorded on the photographic plate and, after developing, is 
analyzed with coherent illumination. The coherent light is diffracted by 
the recorded grating pattern and a first order beam is selected by an 
aperture properly located. The image formed by the beam associated with 
the first diffraction order is the desired output. 
It is also postulated in the paper that one could generate a real-time 
version of the composite image by utilizing the photosensitive surface of 
a television camera in place of the photographic plate. The system 
disclosed in this paper is limited to the suppression of low spatial 
frequencies of the optical transfer function in only one dimension as a 
result of the rectangular pupils utilized. Another limitation of this 
sytem is the low level of illumination available at the output image plane 
due to the limited amount of light transmitted through the small pupils. 
H. Bartelt and A. W. Lohmann, in their paper Optical Processing of 
One-Dimensional Signals, Optics Communications, Vol. 42, p. 87 (1982), 
discuss a general optical system for processing data which are not 
two-dimensional. The system utilizes two pupils in the form of single and 
double slits, respectively. A desired optical transfer function is 
synthesized by sequentially recording the results of two different 
filtering operations using a television camera and storing the data in an 
image memory. The two results are subtracted digitally and displayed on a 
monitor. Accordingly, while electronic sensing apparatus may be used as 
the photosensitive surface in systems of this type, a two step process is 
required to produce the result. As a consequence of the two-step process 
the output image is not available optically, thus preventing further 
optical processing or manipulation of the image. The amount of light 
reaching the output image plane is also severely limited. 
C. Han and K. Murata, in their paper Two-Step Incoherent Optical Method for 
the Realization of a Rho Filter, Optics Letters, Vol. 8, p. 587 (1983), 
discuss an optical subtraction process in which individual circular 
statistical filters having a conventional low pass response with different 
cut-off frequencies are used to obtain a two dimensional rho filter by 
substraction of the optical transfer functions. Such a filter provides a 
linearly increasing transfer function for low spatial frequencies. Each of 
the two circular statistical amplitude filters has different sized opaque 
disks randomly distributed over its total aperture. The filters are 
placed, one after the other, in the system between an incoherently 
illuminated input image and a lens which forms an image on a vidicon 
receiving plane. Each image is separately digitized and stored in a 
digital image memory. By subtraction of the digitally stored images, a 
resultant image is obtained and displayed on the television monitor. This 
resultant image has the appropriate spatial frequencies de-emphasized. 
However, the process requires two steps to complete and, therefore, does 
not enable a real time solution. Moreover, the output image is not 
available optically, thus preventing further optical processing or 
manipulation of the image. 
In our paper Low Frequency De-Emphasis of the Modulation Transfer Function, 
II. Two-Dimensional Case, Proceedings of the Tenth International Optical 
Computer Conference, p. 214, April, 1983, Boston, Mass., N. Konforti and I 
disclose a non-interacting circularly symmetric system utilizing two 
pupils, one circular and the other ring shaped, for de-emphasizing low 
spatial frequency components in two dimensions. The arrangement of the 
various system components is similar to that described above in the 
earlier Marom and Konforti paper. A Ronchi grating is employed to produce 
superposed interlacing images on a photosensitive material. Criteria are 
given for the design and placement of the Ronchi grating to obtain the 
appropriate composite image which may then be filtered to obtain the 
substractive result of the optical transfer functions of the two pupils. 
The criteria for selecting the dimensions of the pupils to obtain a 
band-pass filter characteristic are also provided. This filter system may 
be used to de-emphasize the low spatial frequencies and to allow a more 
correct presentation of optical information. This system also severely 
limits the amount of light reaching the output image plane. 
It is one purpose of the present invention to provide an improved system 
for de-emphasizing low spatial frequencies in the optical analysis of 
incoherently illuminated two dimensional objects. 
It is another purpose of the present invention to provide an improved 
system of low spatial frequency de-emphasis for incoherently illuminated 
two-dimensional objects which may be operated in real time and which 
transmits substantial amounts of light to the output image plane. 
It is yet another purpose of the present invention to provide an optical 
image of an object with low spatial frequencies de-emphasized, whereby 
this image may be optically processed, analyzed and manipulated without 
the need of an electronic to optic converter. 
SUMMARY OF THE INVENTION 
The foregoing purposes and other objects of the present invention are 
realized in an optical imaging system where de-emphasizing of low spatial 
frequencies in two dimensions takes place. In this system the small pupils 
of prior art methods are replaced by two long rectangular areas or strips 
which are spaced equidistant from the axis of the imaging system and which 
have their longer dimensions parallel to one another. Each of the strips 
includes a plurality of pupils randomly spaced over the total area of the 
strip. This system has the advantage of providing a substantial increase 
in the light available at the output image plane, of producing selectable 
optical filter transfer functions, and of accomplishing spatial frequency 
de-emphasis in a single rather than a two step process thereby allowing 
real time processing. The system of the present invention also provides an 
optical output image which may be optically processed, analyzed and 
manipulated without the need of an electronic to optical converter. 
Other features and advantages of the invention will become apparent from a 
reading of the specification taken in conjunction with the drawings in 
which like reference designators refer to like elements throughout the 
several views.

DETAILED DESCRIPTION OF THE INVENTION 
It is a natural phenomenon that pupils in optical imaging systems produce 
images with emphasized low spatial frequencies. Such emphasis may act to 
mask or otherwise obscure useful information contained in an image. FIG. 1 
is an example of the naturally occurring spatial frequency response of a 
pupil. It will be recognized by those skilled in the art that such 
heightened low frequency response will often mask a substantial portion of 
useful information. 
The prior art arrangements discussed above disclose various methods for 
de-emphasizing low spatial frequencies so that more useful information is 
obtained. These arrangements all use some method of subtracting the 
optical transfer functions of two pupils transmitting two images of the 
same scene. FIGS. 2(a) and 2(b) are illustrations of the optical transfer 
functions of two pupils such as those used in the prior art. FIG. 2(c) 
illustrates the resulting function after subtraction of the two functions 
of FIGS. 2(a) and (b). 
The physical arrangements for accomplishing the results illustrated in FIG. 
2 involve various lens systems with pupils interposed between the input 
image and the lens. The dimensions of the pupils and optical systems are 
carefully chosen so that the images obtained through them are of the same 
size, intensity, magnification, and have the same aberrations. This is 
usually accomplished by employing a single optical train. Images 
transmitted through the pupils are projected by the lens system onto means 
for electronically or optically filtering the information to accomplish 
the subtraction of the optical transfer functions. 
Some of the prior art methods discussed above severely limit the amount of 
light reaching the output image, or processing plane. Others of these 
methods require sequential processing operations and, thus, are not real 
time operations. Still others are limited to one dimensional processing. 
Still others do not present the output image optically. The present 
invention overcomes these limitations, as described below. 
FIG. 3 illustrates an arrangement 10 in accordance with the present 
invention which may be used for the processing of two dimensional 
information with substantially higher light intensities than those 
provided by prior art systems. The arrangement 10 includes a source of 
incoherent light 12 arranged to the left in FIG. 3 of a transparency 14 or 
other source of input image information lying in a plane defined by axes 
x.sub.1 and y.sub.1. The source of light 12 may be any of a number of 
types well known in the prior art. The source 12 projects light through 
the transparency 14 and through a plurality of circular pupils 16 randomly 
distributed in a first strip 17 and through a plurality of ring shaped 
pupils 18 randomly distributed in a second strip 19. The strips 17 and 19 
lie in a pupil plane defined by axes x.sub.2 and y.sub.2 and are spaced 
apart with their center lines at a distance d/2 from the symmetry axis z 
of the system FIG. 4 more clearly shows the distributed pupils 16 and 18 
as they appear in the aperture of an imaging lens 20, and an enlarged view 
of one of the pupils 16 and 18 is shown in the insert of FIG. 5. The 
imaging lens 20 is positioned behind the pupil plane and acts to project 
the images of the input object onto a light sensitive output image or 
processing screen 22 which lies in the plane defined by axes x.sub.4 and 
y.sub.4. 
Interposed between the lens 20 and the screen 22 is a Ronchi grating 24 
which has its grid lines 25 parallel to the axis x.sub.2 and hence 
parallel to the strips 17 and 19. The grid 24 is spaced from the screen 22 
a distance .DELTA. such that the images from the pupils 16, 18 are 
interlaced and produce a composite image which may be filtered (by 
coherent light or electronically), to give the desired substractive 
characteristic. The image intensity transmitted through the pupils 16 
should be equal to the image intensity transmitted through the pupils 18. 
Such equalization may be accomplished by using any of a number of uniform 
intensity attenuators (e.g., a neutral density filter) in conjunction with 
the appropriate strip 17, or 19. 
The Ronchi grating provides sampling of the images transmitted through the 
pupils 16, and 18 as well as the means for interlacing these images as 
indicated by ray lines 26 and 28 in FIG. 3. Since it is desirable that the 
images retain their full spectral context, a restriction is placed on the 
sampling frequency, i.e., the Ronchi grating frequency. Thus, if the 
highest resolvable detail in the image is .mu., the grating period shown 
as p in FIG. 3 should be at least two times smaller. Accordingly, assume 
that 
EQU p=.mu./2.5 (1) 
For a pupil of width W in an incoherent optical system, the maximal or 
cutoff frequency f.sub.c.o. passed by the system is 
EQU f.sub.c.o. =W/(.lambda.l) (2) 
where .lambda. is the central wavelength of the illuminating source and l 
is the separation between the pupil and the images planes, as shown in 
FIG. 3. Note that in the instance of circular and ring-shaped pupils, the 
dimension W above should be set equal to the diameter of the larger of the 
two types of pupils. Combining equations 1 and 2, it may be shown that the 
Ronchi grating period should be 
EQU p=.lambda.l/(2.5W) (3) 
For pupils separated by a distance d, it may be shown by virtue of 
geometrical considerations that 
EQU p/(2.DELTA.)=d/l (4) 
Eliminating the dependence on l yields 
EQU .DELTA.=1.25p.sup.2 W/(.lambda.d) (5) 
Since the grating 24 (providing the sampling function) is proximity imaged 
onto the output plane 22, the separation .DELTA. should be smaller than 
the corresponding Rayleight distance, i.e. 
EQU .DELTA..ltoreq.(p/2).sup.2 /.lambda. (6) 
Substitution into equation 5 yields 
EQU d/W.gtoreq.5 (7) 
Therefore, as design guidelines one should choose a Ronchi grating 24 with 
a period p which is on the order of 2 to 2.5 times smaller than the 
desired minimum image resolution .mu., should place it a distance .DELTA. 
equal to .mu..sup.2 /(25 .lambda.) in front of the image plane 22, should 
limit the diameter of the largest of the two pupils 16, 18 to 
W=.lambda.l/.mu. and should place them apart from each other at a distance 
d on the order of five times the largest pupil diameter. It is interesting 
to note that neither the distance between the plane of the pupils 16, 18 
and the lens 20 nor the exact positioning of the pupils 16, 18 along the 
axis x.sub.2 are critical to the operation of the system 10. 
One of each of the pupils 16 and 18 is shown in detail in FIG. 5. For 
purposes of the following analyses, the inner radius of the ring pupil 18 
is defined as r.sub.B, the outer radius of the pupil 18 is defined as 
r.sub.A, and the radius of the circular pupil 16 is normalized as 1. 
Considering the system of FIG. 3 it may shown that the composite optical 
transfer function of the ring pupil 18 (with radii r.sub.A and r.sub.B) 
and the circular pupil 16 (with unit radius) is given by: 
EQU C(x)=C.sub.1 (x;r.sub.A,r.sub.B)-.alpha.C.sub.2 (x;1,0) (8) 
where C.sub.1 is the autocorrelation of the pupil 18, x is the spatial 
frequency parameter, C.sub.2 is the autocorrelation of circular pupil 16 
whose "ring" radii are 1 and 0, and .alpha. is the attenuation factor of 
the circular pupil (defined as the ratio of the area of the ring pupil 18 
to that of the circular pupil 16). Due to the fact that there is no light 
amplification in the system of FIG. 3 when .alpha. is greater than 1, a 
factor of 1/.alpha. should be applied in its place to the ring pupil 18 
instead of the circular pupil 16. 
It may be shown that by proper choice of the values of r.sub.A, r.sub.B and 
.alpha., a wide variety of optical transfer functions may be obtained. 
For example, a band-pass transfer function may be obtained if the function 
C(x) and its first three derivatives vanish at the origin. These 
requirements lead to 
##EQU1## 
where .phi. is the mathematical constant known as the "Golden Ratio". 
On the other hand, if a rho-filter is desired where the optical transfer 
function is linear near the origin, the requirements are that 
C(0)=C"(0)=C'"(0)=0. From these equations, various systems may be designed 
having transfer functions with different linear slopes. FIG. 5 shows 
curves representing four different optical transfer functions which may be 
obtained using the system of FIG. 3, and the values of r.sub.A, r.sub.B 
and corresponding thereto. Curves I, II and III correspond to rho-filters, 
while curve IV corresponds to the bandpass filter derived above. 
The system of the present invention described above enables real time 
processing of information in two dimensions while substantially improving 
the level of illumination available at the output image plane. Real time 
processing may be accomplished using a video camera positioned at the 
output image plane in a manner disclosed in my earlier paper discussed 
above. 
An advantage of the invention is that an optical image having low spatial 
frequencies de-emphasized can be provided and processed without the aid of 
an electronic to optical converter. On the other hand, for some 
applications an electronic to optical converter can be employed. 
An alternate embodiment 50 of the invention is shown in FIG. 6. In this 
embodiment, as in the previously described embodiment 10, the source 12 of 
incoherent light projects light through the transparency or input image 
14. Positioned normal to the z axis is a second incoherent light source 
12'. The source 12' projects light though a transparency or input image 
14' which is an identical replica of the image 14. 
Light from the image 14 passes through a plurality of the circular pupils 
16 randomly arranged on a substrate 17' which is typically of sufficient 
size to cover the aperture of the imaging lens 20 positioned behind the 
plane of the pupils 16. In like manner, light from the image 14' passes 
through a plurality of the ring-shaped pupils 18 randomly arranged on a 
substrate 19' which is typically of sufficient size to cover the aperture 
of imaging lens 20' positioned behind the plane of the pupils 18. 
A beam-splitter, which may be in the form of a partially silvered mirror is 
positioned as shown in FIG. 6 so that light from the lens 20 is 
transmitted through the splitter 52 and through the Ronchi grating 24 to 
impringe on the output image plane 22 in a manner analogous to the 
operation of the system 10. Light from the lens 20' is reflected by the 
splitter 52 so that it too is directed through the Ronchi grating 24 to 
impinge on the output image plane 22. 
By comparing the system 10 with the system 50 it will be appreciated that 
the system 50 employs two separate light sources, input images, pupil 
planes, and lens to provide the two images which are combined by the 
splitter 52 and interlaced by the grating 24 to produce the desired 
composite image. One advantage of the system 50 is that the substrates 17' 
and 19' may each be made to cover the aperture of the corresponding lens, 
thus providing a substantial level of illumination at the output image 
plane 22. In implementing the system 50 one should be careful in meeting 
the requirement that the characteristics of the images (e.g., intensity, 
contrast, size) from the lens 20 and the lens 20' must be substantially 
identical. 
While particular embodiments of the invention have been described in 
detail, various other adaptations and modifications will become apparent 
to those skilled in the art. It is, therefore, to be understood that the 
invention is limited only by the claims appended hereto.