Optical apparatus and method for producing the same

Optical measuring and testing apparatus incorporating a holographically recorded, single-frequency, optically thin, phase grating. When this phase grating is illuminated by a quasi-monochromatic spatially coherent light source, it acts as a basic common path interferometer and constitutes a highly efficient source for a high contrast, stable, interference fringe pattern. In one embodiment, elements are repositioned to move the light source with respect to the grating thereby to alter the number of fringes in a given area. In another embodiment the grating moves in a plane that is orthogonal to an axis from the light source. This motion causes the fringe pattern to move past detecting means thereby to sense motion of the grating. In a third embodiment, a phase grating operates as a Fourier filter in a coherent optical processor which generates equal height contour lines from the information contained in two vertical stereo photographs.

BACKGROUND OF THE INVENTION 
This invention generally relates to the field of optical measuring and 
testing and more specifically to apparatus for producing, controlling and 
utilizing fringe patterns for measuring and testing operations. 
There are two basic methods for producing fringe patterns: (1) an 
interferometric technique that utilizes interference phenomena, and (2) a 
Moire technique that utilizes shadow casting and/or pattern 
multiplication. 
There are a wide variety of measuring and testing procedures that utilize 
interference fringe patterns and there are many ways to produce and 
control interference fringes. Generally, an interference fringe pattern is 
produced when at least two coherent beams of light are brought together 
and interact. When two coherent beams interact, they destructively 
interfere to produce dark spots or bands and constructively interfere to 
produce bright spots or bands. 
Moire fringes are produced when two similar, geometrically regular patterns 
consisting of well defined clear and opaque areas are juxtaposed and 
transilluminated. Some examples of geometrically regular patterns used to 
generate Moire fringes include (1) Ronchi rulings, (2) sets of concentric 
circles, and (3) radial grids. The generation of Moire fringes can be 
considered as shadow casting; that is, the shadow of the first pattern 
falling onto the second pattern produces the Moire fringes. The 
mathematical function describing Moire fringes is obtained by multiplying 
the intensity transmissions or irradiances of the overlapped geometrically 
regular patterns. 
Fringes generated by both interference and Moire techniques are used by 
ophthalmologists for testing retinal acuity. In one such apparatus, light 
from a laser is divided into two coherent beams by an optical element 
consisting of two adjoined dove prisms. These two beams are converged and 
directed into the eye where they interact to produce an interference 
fringe pattern on the retina. 
In another apparatus used in the field of ophthalmology a laser source and 
an ordinary Ronchi ruling form an interference fringe pattern. The laser 
source produces a laser beam that is directed to the Ronchi ruling. The 
Ronchi ruling splits the incident beam into multiple coherent beams of 
widely varying strengths. It is necessary to use complicated motions of 
numerous optical and mechanical components to select only two coherent 
beams and to control the spacing of interference fringes eventually 
projected onto the retina. In yet another ophthalmic apparatus, two Ronchi 
rulings are used. They produce Moire fringes that are eventually imaged 
onto the retina. 
Ophthalmologists use the foregoing apparatus that implement either the 
Moire or interference techniques to test and measure retinal acuity. This 
measurement is obtained by varying the "fineness" of the fringes projected 
onto the retina and monitoring the patient's ability to resolve them. The 
patient's ability to resolve a fringe pattern of a certain "fineness" 
converts directly into a measurement of retinal acuity. 
In an entirely different measuring application, fringe patterns from 
interferometric or Moire apparatus are used to accurately position two 
elements relative to each other. With interferometric techniques, an 
incoming beam of light is generally split into two parts. One part is 
reflected from a reference position; the other, from a movable element. 
The reflected beams are recombined to produce an output fringe pattern 
that "moves" as the movable element moves. In one example of a Moire 
technique, two high contrast Ronchi rulings of slightly different spatial 
frequencies are juxtaposed and transilluminated. One ruling is stationary 
while the other is movable in a predetermined plane. Photodetectors sense 
the variations in the light that passes through the gratings and produce 
signals that indicate the motion. 
Certain disadvantages exist in apparatus that utilize the interferometric 
techniques to form fringe patterns in various applications, including the 
ophthalmic and position detection applications. For example, in such 
apparatus the two light beams generally travel through different light 
paths that contain distinct optical elements. If the elements in each path 
are not matched optically, aberrations distort the fringe pattern. Matched 
optical elements can eliminate the aberration problem; however, they 
significantly increase the overall expense of the apparatus. Moreover, 
this apparatus is subject to various outside influences, such as vibration 
and thermal change. These influences can cause fringe pattern motion or 
noise and lead to improper measurements. 
Moire techniques also have many limitations. When small spacings and high 
accuracies are required, the geometrically regular patterns used to 
generate Moire fringes are quite difficult and expensive to produce. In 
applications where one ruling moves next to a fixed ruling, the spacing 
between the rulings must be held constant or errors result. Also, Moire 
fringes are localized, i.e., they exist in a very small region of space, 
and additional optical components are often required to image the Moire 
fringes into desired regions. 
Recently, an amplitude grating and a spatially coherent, 
quasi-monochromatic light source have been used to generate interference 
fringes. An amplitude grating is a generally transparent to 
semi-transparent media whose opacity is altered in accordance with some 
spatially periodic pattern. An amplitude grating "breaks up" or diffracts 
an incoming beam of light into a series of diffracted cones or orders. The 
strength, or amount, of light in each order depends upon the exact shape 
of the periodic opacity of the amplitude grating. Although various 
diffracted orders could be approximately the same strength, scalar 
diffraction theory for a thin amplitude grating predicts that the dominant 
strength will lie in the zero order undiffracted light and that the 
strength of other diffracted orders will vary. Indeed, practical 
applications bear out this prediction. 
In one such application, it is proposed to pass light from a source through 
an amplitude grating to produce different order cones of diffracted light: 
for example, zero order and fist order cones. To compensate for the 
different intensities, the diffracted light cones are reflected back 
through the grating. After the second passage through the grating, the 
zero order cone of the reflected first order cone and the first order cone 
of the reflected zero order cone have equal strengths and are combined to 
form a high contrast interference fringe field. This double pass system is 
quite stable because it closely approximates a common path interferometer. 
In a common path interferometer the interfering beams traverse the same 
optical path. Therefore, perturbations affect both beams simultaneously 
and do not distort the output fringe pattern which is sensitive only to 
differences between the two optical paths. However, problems in such a 
double pass system do occur because it is difficult to control grating 
substrate aberrations and mirror-grating separation. 
Further improvements have been made with the advent of holographically 
produced amplitude gratings. Holographic amplitude gratings are produced 
by exposing a high resolution photographic emulsion to the precise 
interference pattern of a laser two-beam interferometer. During ordinary 
photographic processing, the photosensitive silver halide in the emulsion 
converts into opaque metallic silver to form the amplitude grating. 
In an application of one such holographic grating, a double frequency 
holographic grating produces a so called "shearing" pattern. This grating 
is produced by sequentially exposing a single photographic emulsion to a 
first laser interference pattern of a first spatial frequency, f.sub.1, 
and then to a second laser interference pattern of a second spatial 
frequency, f.sub.2. Equal amplitude transmission modulations at both 
frequencies f.sub.1 and f.sub.2 are achieved by adjusting the exposure to 
the first and second laser patterns. Ordinarily, the two sequential 
exposures are identical, but if f.sub.1 and f.sub.2 are very different or 
if one laser pattern is in red light and the other is in green light, the 
sequential exposures must be compensated for the spectral and frequency 
responses of the photographic plate. These exposure adjustments to achieve 
equal amplitude transmission modulations in f.sub.1 and f.sub.2 are 
usually done by trial and error. 
Upon illumination with spatially coherent, quasi-monochromatic light, this 
double frequency grating produces two first order light cones of equal 
strength, one light cone being associated with each of the f.sub.1 and 
f.sub.2 frequencies. These two first order light cones interact to form a 
very stable, high contrast fringe pattern. Such a double frequency 
holographic shearing interferometer also is a common path interferometer. 
While it is simple to construct, it is necessary to separate the zero 
order cone from the interacting first order cones. This separation 
requirement limits the f/number of the input light cone and the amount of 
shear obtainable. Moreover, if the two first order cones have high 
diffraction angles an astigmatic distortion of the output fringe field 
exists. In addition, the efficiency, or ratio of output fringe field power 
to input power, is only about 2%. 
For many years people have bleached photographically recorded amplitude 
gratings to obtain "phase gratings". One basic type of bleaching, known as 
volume bleaching, chemically converts the opaque silver in the 
photographic emulsion into a transparent, high index silver salt. A second 
type of bleaching, known as tanning, chemically removes the developed 
silver within the emulsion and leaves a void. A tanned phase grating has a 
corrugated surface. Whereas an amplitude grating selectively absorbs 
light, a bleached phase grating selectively introduces phase delays across 
the input light beam. As a result, a phase grating is much more efficient 
than an amplitude grating; that is, the ratio of first order power to 
input power is greater. 
However, bleached gratings are generally characterized by substantial 
problems. They are very noisy and also may deterioriate physically back 
into amplitude gratings upon extended exposure to light. Bleached gratings 
also have a lower spatial frequency response than amplitude gratings. 
Although volume bleached gratings are less noisy and have a higher spatial 
frequency response than their tanned counterparts, they generally are 
weaker and less efficient. 
The efficiency of a volume bleached grating can be increased by increasing 
its thickness. However, any substantial increase in thickness drastically 
changes the basic diffraction properties of the grating. Any amplitude or 
phase grating can be considered optically thick when the optical, or 
active, thickness of the emulsion is more than five times the grating 
spacing. A grating can be considered optically thin if the optical, or 
active, thickness of the emulsion is less than half the grating spacing. 
Properties of thick gratings are accurately predicted by electromagnetic 
theory while properties of thin gratings are described by scalar 
diffraction theory. For example, a thick phase grating output consists of 
only the zero order and one first order diffracted cone. In addition, 
diffraction takes place only for a plane wave input at a certain specified 
angle with respect to the grating. On the other hand, a thin grating of 
the same spacing produces multiple orders (i.e. the 0, .+-.1, .+-.2, 
.+-.3, etc. orders) with either a spherical wave or plane wave input at an 
arbitrary angle with respect to the grating. 
Distinctions between optically thin amplitude and optically thin phase 
gratings are accurately predicted by scalar diffraction theory. When a 
pure sinusoidal amplitude transmission perturbation exists in a thin 
amplitude grating, only the zero and .+-.1 diffracted orders exist. When a 
pure sinusoidal phase perturbation occurs in a thin phase grating, many 
orders (e.g., the 0, .+-.1, .+-.2, .+-.3, and other orders) are observed. 
The strengths of the phase grating orders are proportional to the 
normalized Bessel functions [J.sub.n (m/2)].sup.2, where n is the order 
number (e.g., n=0, .+-.1, .+-.2, . . . ) and m is the strength or size of 
the phase perturbation in radians. When the amplitude grating perturbation 
departs from a pure sinusoidal form, additional diffracted orders are 
generated. The strengths of these additional orders are directly related 
to the strengths of the Fourier components associated with the grating 
perturbation function. 
With a phase grating, the diffracted orders associated with a 
non-sinusoidal phase perturbation are predicted by convolving the 
individual outputs from each Fourier component of the phase perturbation. 
Such a multiple convolution reveals complicated phase relationships 
between multiple orders associated with just one particular Fourier 
component. In addition, diffracted orders corresponding to sum and 
difference frequencies are generated when the phase perturbation consists 
of more than one fundamental spatial frequency. For example, one might 
consider bleaching the previously discussed double-frequency holographic 
grating to improve its poor efficiency. Although bleaching will increase 
the overall efficiency of such a grating, the bleached grating, in 
accordance with the convolutional operation, produces sum and difference 
frequency diffraction cones that are in addition to and that interact with 
the desired fundamental frequency diffraction cones. It is then possible 
for the sum and difference frequency diffraction cones to destroy the 
fringe field. 
Therefore, it is the object of this invention to provide an improved 
holographic phase grating for producing a high contrast interference 
pattern. 
Another object of this invention is to provide an improved method for 
producing a holographic phase grating that is useful in a wide variety of 
applications. 
Still another object of this invention is to provide an improved 
interferometer that utilizes a holographic phase grating. 
Another object of this invention is to provide an improved holographic 
grating that is useful in a number of applications including the testing 
of retinal acuity. 
Yet another object of this invention is to provide apparatus for testing 
retinal acuity. 
Another object of this invention is to provide an improved holographic 
grating that is useful in a number of applications including position 
detection. 
Yet another object of this invention is to provide apparatus for accurate 
detection of position information. 
Still another object of this invention is to provide a holographic phase 
grating which acts as an optical Fourier plane filter. 
Another object of this invention is to provide an improved holographic 
grating that is useful in a number of applications including the 
generation of equal height contours from a pair of vertical stereo 
photographs. 
Yet another object of this invention is to provide apparatus for the 
generation of equal height contours from a pair of vertical stereo 
photographs. 
SUMMARY 
In accordance with various aspects of my invention, I produce a single 
frequency holographic phase grating by exposing a photographic emulsion to 
a single frequency, two-beam interference pattern. After developing the 
emulsion, I bleach the plate to produce a very clear, low noise phase 
grating. By controlling the exposure and processing procedures I control 
the effective emulsion thickness, the relative strengths of the diffracted 
orders of light from the grating and the relative phases of the diffracted 
orders. 
My holographic diffraction grating can be used as an element in an 
interferometer for producing light interference patterns that are useful 
in a wide range of applications. In each application the grating is 
illuminated by a source of quasi-monochromatic, spatially coherent light 
and produces diverging diffraction cones of different orders. The light in 
each diffraction cone of two different orders has equal strength, and the 
cones overlap thereby to produce a bright, high constrast, low noise 
interference pattern. The form of the fringes comprising the interference 
pattern depends on the shape of the wavefront incident upon the grating. 
In accordance with one specific embodiment of this invention, I place a 
focusing element between the light source and grating for producing a 
point source of light at a focal point that is slightly displaced from the 
grating. Other optical elements positioned in the resulting interference 
fringe field project the interference pattern through the eye and onto the 
retina. The fineness of the pattern on the retina is controlled accurately 
by positioning the focal point with respect to the grating. This system 
can accurately measure retinal acuity in the presence of corneal or eye 
lens opacities known as cataracts. 
In accordance with another specific embodiment of this invention, a 
quasi-monochromatic, spatially coherent light source is positioned 
adjacent to one side of my holographic grating and directs light to the 
grating along an axis. Photodetectors are disposed on the opposite side of 
the grating to receive the interference pattern. Relative motion between 
the photodetection means and the grating in a plane that is normal to the 
light axis is readily detected and accurately measured by the 
photodetectors. 
In accordance with still another embodiment of this invention, my 
holographic phase grating is positioned in the Fourier plane of a coherent 
optical processor. The processor input consists of light from two 
transilluminated vertical stereo transparencies. The unique properties of 
my holographic phase grating create a dark, usually irregular interference 
fringe in each of the processor output images. Each of these interference 
fringes is an equal height contour line in the perspective of its 
associated image. 
This invention is pointed out with particularity in the appended claims. 
The above and further objects and advantages of this invention may be 
better understood by referring to the following description taken in 
conjunction with the accompanying drawings.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
A. Holographic Grating 
FIG. 1 depicts, in diagrammatic form, the arrangement of apparatus 
necessary for exposing a photographic plate during the production of a 
holographic phase grating. The holographic phase grating produced in 
accordance with the arrangement shown in FIG. 1 and the procedures 
outlined in FIG. 2 is essential to the operation of the diverse 
embodiments of the invention that are shown in the other Figures. 
Specifically, this apparatus includes a laser source 10 which directs 
light along an axis 11. The other apparatus in FIG. 1 splits the light 
into parts that travel over two separate paths and are then brought back 
together to expose a photographic plate 12. 
A conventional beamsplitter 13 separates the light into two parts. A first 
part travels along a first path that includes mirrors 14 and 15 for 
reflecting the light into an objective lens and pinhole 16, thereby to 
produce a spherical wave that emanates from a point source at the pinhole. 
The wave appears in a cone 17 and is directed toward the photographic 
plate along an axis 18. The second path established by the beamsplitter 13 
includes a mirror 20 and an objective lens and pinhole 21 that produce a 
spherical wave cone 22 that emanates from a point source at that pinhole 
along an axis 23. The light waves from these two point sources combine; 
they destructively interfere to produce dark bands and constructively 
interfere to produce bright bands at the photographic plate 12. 
The photographic plate 12 mounts on a rotary table which positions the 
photographic plate 12 and accurately establishes an angle .theta. between 
the axes 18 and 23. The spatial frequency, .xi., of the interference 
pattern at plate 12 is closely approximated by the equation 
##EQU1## 
where .lambda. is the laser wavelength. Although the fringes produced at 
the plate 12 are slightly hyperbolic, they are excellent approximations to 
rectilinear bands and therefore are shown as such in various Figures. 
Increasingly better approximations to rectilinear bands are achieved by 
increasing the distance along the axes 18 and 23 between the plate 12 and 
the pinholes 16 and 21, respectively. 
The apparatus diagrammed in FIG. 1 has been used to manufacture gratings 
having the desirable properties that characterize my invention. The 
equipment is simple and relatively inexpensive. For example, the laser 10 
can comprise a TEM.sub.00 mode laser; the beamsplitter 13, a conventional 
variable density beamsplitter that enables the intensity of the two beams 
to be equalized. The mirrors 14, 15 and 20 are standard planar mirrors. 
The objective lens comprises a conventional 10X microscope objective, and 
the pinhole matches that objective lens. The distances 18 and 23 are 
approximately 2 meters. With this specific arrangement, I am able to 
obtain a 500 line-per-millimeter interference fringe pattern over a 
3".times.3" area with maximum fringe displacement error of about 0.00254 
millimeters. 
Once the apparatus in FIG. 1 is arranged, the emulsion on the photographic 
film can be exposed to the interference pattern as shown as Step I in FIG. 
2. During this exposure step, certain controls must be exercised to assure 
a holographic grating of good quality. For example, the exposure should be 
made in an environment that is not subjected to vibrations. Thermal 
disturbances should be minimized as any air flow between the beamsplitter 
13 and the photographic plate 12 can distort the resulting fringes. In 
applications where very high densities and minimal distortions are 
required the distances along axes 18 and 23 must be increased to 5 or even 
10 meters. Precise determinations of .lambda. and .theta. must be made. 
Although this basic apparatus can be used to produce highly accurate 
holographic phase gratings, the maximum accuracy ultimately then will be 
determined by the accuracy of angular measuring equipment, the stability 
of the single frequency laser, the optical table stability, and the 
atmospheric and thermal controls that are exercised. 
In order to produce a phase grating with special properties that enable the 
construction of the various disclosed embodiments, it is first necessary 
to produce an amplitude grating. Given the various properties of 
commercially available photographic emulsions and developers, a thin 
emulsion photographic plate and a chemically compatible developer are 
selected. A process of heavily overexposing and underdeveloping the 
emulsion reduces the optical thickness of the processed emulsion to a 
fraction of its original physical thickness. Thus, by utilizing the 
controls set forth in steps 1 and 2 of FIG. 2, one produces an amplitude 
grating characterized by having: 
1. an optically thin emulsion conforming to scalar diffraction theory; 
2. a specific form for the absorbtion function which converts to a 
correspondingly specific phase transmission function after bleaching; and 
3. a specific amplitude or strength of the absorbtion function which 
converts to a specific peak to peak phase modulation after bleaching. 
Specific plate types, exposures, development times and developers are 
discussed later. 
Once the development of step 2 is complete, the photographic plate is 
washed in an acid short-stop solution in step 3. The solution contains an 
acid hardener. A two-minute treatment in a hardening bath produces 
acceptable results. 
In step 4 the emulsion of the photographic plate is fixed and hardened. A 
standard fixing bath and acid hardener have been used successfully, the 
plate being immersed in the bath for about ten minutes. 
Next (step 5) the emulsion is prewashed for thirty seconds and hypo-cleared 
in a hypo clearing bath for about two minutes. In step 6 the emulsion is 
washed (e.g., twenty minutes in filtered water) and then soaked in a 
methanol bath until all residual sensitizing dye is removed (step 7). Once 
the methanol bath has been completed, the plate is dried in a light blow 
air drying operation. 
All the foregoing steps are conventional photographic processing steps that 
utilize commercially available chemicals. Upon completion of step 7 an 
amplitude grating has been produced. Steps 8 and 9 then convert this 
amplitude grating into a phase grating having the desired characteristics. 
More specifically, after the photographic plate is dried thoroughly in step 
7, it is bleached during step 8 in a bromine vapor until the plate is 
clear. Once the bleaching operation has been completed, the plate is 
rinsed in a methanol bath to remove residual Br.sub.2 and dried thoroughly 
by a light blow air drying operation in step 9. 
It now will be beneficial to discuss certain characteristics of these 
holographic phase gratings that are particularly desirable. First, the 
exposure and development times and the emulsion have been chosen to 
produce "thin" gratings. As a specific example, I have made 393.7 
line-per-millimeter gratings on Kodak 131-01 plates according to the 
foregoing processing procedure using an average exposure of 200 
ergs/cm.sup.2 and a development time of 15 seconds in standard Kodak D-19 
developer at 80.degree. F. Uniform development is achieved by using a 
large development tank and rapid manual agitation of the plate. After 
complete processing in accordance with the steps of FIG. 2, the resulting 
thin phase grating diffracts both input spherical waves as well as input 
plane waves; as previously stated, a thick grating diffracts only input 
plane waves incident at a particular angle with respect to the grating. 
Measurements have shown that a thin phase grating manufactured according to 
the foregoing process has a pure sinusoidal phase transmission function 
whose peak-to-peak phase delay produces equal strength zero and .+-.1 
diffraction orders. The 200 ergs/cm.sup.2 exposure produces an average 
amplitude transmission of approximately 0.45 for the developed, but 
unbleached, Kodak 131-01 plates. Experimental data has confirmed that a 
pure sinusoidal phase transmission function is maintained when the thin 
grating has an average amplitude transmission of 0.5 or less in its 
developed but unbleached state. The strength or peak-to-peak phase delay 
of the final phase grating is adjusted by controlling the initial exposure 
(Step 1, FIG. 2) within the limits set by an average amplitude 
transmission of 0.5 (measured after Step 7 in FIG. 2). A very weak phase 
grating produced with low exposure levels exhibits a strong zero order 
diffraction, a weak first order, and an even weaker second order. Stronger 
gratings produced with higher exposure levels exhibit increasingly more 
powerful first and second order diffraction and decreased zero order 
diffraction. Equal strength zero and .+-.1 diffraction orders or equal 
strength zero and .+-.2 diffraction orders are achieved by a trial and 
error adjustment of the initial exposure. 
The advantages of such a thin phase grating that produces two different 
diffraction orders of equal strength will now become apparent in the 
following discussion of an interferometer that utilizes such a phase 
grating. 
B. Interferometer 
Referring now to FIG. 3, an interferometer is depicted in schematic form 
that includes a helium neon laser 30 which directs light along an axis 31 
to a negative lens 32. The negative lens 32 expands the beam slightly so 
that it completely fills a microscope objective 33. The microscope 
objective 33 focuses this light at a focal point FP displaced a distance 
Z.sub.1 from a holographic grating 34 constructed as described above. The 
laser 30, negative lens 32 and microscope objective 33 constitute a source 
of a quasi-monochromatic, diverging spherical wave that emanates from the 
focal point FP. In one embodiment, the cone from the focal point FP is an 
f/2 cone. 
When the spherical wave from the point source at the focal point FP strikes 
the grating 34, it produces a number of cones of diffraction. According to 
scalar diffraction theory, the strength of the diffracted cones is 
governed by the Bessel function [J.sub.n (m/2)].sup.2 where n is the 
diffraction order number and m is the grating transmission function 
peak-to-peak phase delay in radians. The previously specified exposure and 
development times yield a value of m=2.870 at .lambda.=6328 A. The zero 
and first order diffraction cones are of equal intensity because [J.sub.0 
(1.435)].sup.2 =[J.sub.1 (1.435)].sup.2. Moreover, the diffraction angles 
are such that the zero order cone overlaps both first order cones while 
the first order cones merely abut each other. At some point at a distance 
Z.sub.2 from the grating 34, an output such as is shown in FIG. 3 is 
produced. The zero order cone appears as a planar circle 35 and the two 
first order cones appear as planar circles 36A and 36B. Areas 37A and 37B 
are areas of overlap and the fringes are produced in those areas. 
Moreover, the fringes in the areas 37A and 37B are out of phase with each 
other. Thus, if the centrally located fringe in area 37A is a dark band, 
the corresponding fringe in area 37B is a light, or bright, band. By 
"light" and "dark" bands, I do not means bands having the same intensity 
across the band, as the bands are shown in the drawings. The fringe 
intensity actually varies smoothly and is proportional to the square of a 
sine function, although the eye may perceive distinct alternating bands 
under some illumination conditions. 
The 180.degree. phase shift between the fringes in areas 37A and 37B is a 
direct result of having a pure sinusoidal phase transmission function 
associated with grating 34. When the phase transmission function of 34 
departs from a pure sinusoid, the fringes in the areas 37A and 37B will 
have some other phase relationship not equal to 180.degree.. The 
180.degree. phase shift is not essential to the production of high 
contrast fringe patterns; but it is important in a position detecting 
application where quadrature electrical signals are derived from the 
central fringes. Control of the grating transmission function form is 
achieved by selecting the proper combination of emulsion, developer, 
exposure and development time as previously discussed. 
The interferometer shown in FIG. 3 has several properties. If the distance 
Z.sub.1 is varied, the number of fringes within the overlap areas 37A and 
37B changes. Specifically, decreasing the distance Z.sub.1 decreases the 
number of fringes that appear in the overlap areas. As Z.sub.1 is varied, 
fringes "flow" into or out of the areas 37A and 37B. Although this "fringe 
flow" may cause the central fringes to widen or narrow, it does not move 
the central fringes; they remain located at the centers of their 
respective areas. The importance of this central fringe behavior with 
Z.sub.1 variations will be discussed later. If the grating 34 is moved in 
a plane that in normal to the axis 31 and perpendicular to the direction 
of the fringes, all the fringes in the areas 37A and 37B appear to slide 
through those areas, but the number of fringes in those areas remains 
unchanged. If the distance Z.sub.2 varies, the number of fringes also 
remain the same, but in this case their sizes change, the fringe widths 
becoming smaller as Z.sub.2 decreases. The interferometer parameters are 
related by the equation: 
EQU T=(Z.sub.2 +Z.sub.1)/.xi.Z.sub.1 (2) 
where T is the fringe period in overlap regions 37A and 37B, .xi. is the 
spatial frequency of the grating 34 defined by equation (1) and Z.sub.1 
and Z.sub.2 are the positive distances shown in FIG. 3. 
The holographic grating interferometer in FIG. 3 is very stable and free of 
fringe distortion from outside influences because it is essentially a 
common path interferometer. Atmospheric changes, air currents and thermal 
instabilities do not distort the fringes. Moreover, the intensity of the 
light in each of the diffraction cones is much greater than that usually 
obtained from amplitude gratings because the phase grating essentially is 
transparent and relies entirely on time delays within the grating 34 to 
produce the diffraction cones. As a result the overall brightness of the 
fringe pattern is increased. Moreover, as the intensities in each of the 
zero-order and first-order cones are equal, the destructive and 
constructive interferences tend to be complete so the dark bands are 
essentially black while the bright bands are essentially twice as bright 
as the average light. Thus the grating enables the production of a simple 
common path interferometer that produces bright, high-contrast fringes. 
The foregoing properties lay a basis for understanding three specific 
applications of a bleached phase grating that can be applied in diverse 
fields. In one, the distance Z.sub.1 is intentionally varied to alter the 
number of fringes that appear in a given area. Apparatus embodying this 
feature is particularly adapted for use in a retinal acuity tester that is 
discussed with reference to FIGS. 4 through 7B. In another application, 
the Z.sub.1 and Z.sub.2 distances remain essentially unchanged, but the 
grating is allowed to move thereby to shift the fringes. Apparatus 
embodying this feature is particularly adapted for use in positioning 
systems. In a third application auxiliary optics are placed before the 
grating to form two spatially coherent sources from the light transmitted 
by two stereo transparencies. These two spatially coherent sources are 
superimposed at the grating surface, or at Z.sub.1 =0. The output at 
Z.sub.2 =.infin. is a null fringe or contour line which is observed at the 
rear focal plane of a lens positioned behind the grating. The phase 
grating used in this application is similar to the one previously 
discussed except that instead of having zero and first order diffractions 
equal in strength, zero and second orders of equal strength are used. 
C. Retinal Acuity Tester 
The retinal acuity tester in FIG. 4 includes a laser 40 that can comprise a 
low-power TEM.sub.OO mode helium-neon cylindrical or other like laser. 
Light from the laser is directed along an axis 41A through a filter wheel 
42. The filter wheel 42 contains a number of conventional metallic coated 
neutral density filters. These filters control the intensity of the light 
that is transmitted to the remaining elements in the retinal acuity 
tester. In this manner it is possible to control the brightness of the 
fringes eventually projected onto a patient's retina. 
A negative lens 43 and microscope objective lens 44 that are movable along 
the axis 41A focus the light at a focal point FP. The negative lens 43 
expands the beam from the laser slightly so as to completely fill the 
microscope objective lens 44 aperture with a uniform light distribution. A 
-4 mm focal length biconcave lens is a satisfactory negative lens. The 
microscope objective 44 is a conventional objective lens, a 10X N.A. 0.25 
objective lens being satisfactory. 
The grating 45 comprises a holographically recorded, single frequency phase 
grating that is produced as described earlier. The grating frequency is 
400 l/mm (lines per millimeter) to allow for ideal separation of zero and 
.+-.1 orders from the N.A. 0.25 objective input cone. The grating 45 also 
is optically thin and responsive to the spherical wave eminating from the 
focal point FP, and the zero and first order diffractions have equal 
strengths. As becomes apparent later, there is no reason to control the 
phase of output fringes from the grating 45 when the grating is used in a 
retinal acuity testing apparatus. Therefore, the added constraints in the 
processing procedure associated with preserving a pure sinusoidal phase 
perturbation are eliminated. A convenient development time compatible with 
the requirement of producing an optically thin emulsion is chosen. Then 
exposure time is adjusted by trial and error until the desired strength of 
phase modulation is achieved. 
In this case, a modulation producing equal strength zero and 35 1 orders is 
obtained. Thin, very clean, low-noise, 400 l/mm phase gratings for the 
retinal acuity tester can be produced on Kodak (120-01 plates using an 
average exposure of 1000 ergs/cm.sup.2 at 6328 A. These plates are 
developed for 100 seconds in Kodak D-19 developer at 68.degree. F. (steps 
1 and 2 in FIG. 2). Steps 3 through 9 in FIG. 2 are used to complete the 
processing. 
The grating 45 produces the diverging cones of different order 
diffractions. More specifically, there is a zero order cone represented by 
circle 35 and first order cones represented by abutting circles 36A and 
36B. These cones are of equal strength so that they produce high contrast 
fringes as shown in areas 37A and 37B where the zero and first order cones 
overlap. In this specific embodiment, an axis 41B extends from the center 
of the grating 45 through the center of the area 37A. A dove prism 46 is 
positioned to receive the fringe field and is disposed with its 
longitudinal axis on the axis 41B. As the dove prism 46 is rotated about 
its longitudinal axis, the angle of fringe orientation within the fringe 
field 37A also rotates about the axis 41B through twice the prism rotation 
angle. 
The fringe field propagates through the dove prism 46 to an aperture wheel 
47. One aperture in the aperture wheel 47 is selectively aligned with the 
axis 41B by rotating the aperture wheel 47. An eyepiece 48 receives light 
transmitted through the selected aperture. This eyepiece 48 forms twin 
point sources within an eye pupil 49 of the patient. These point sources 
correspond to the point sources formed in FIG. 1 by the objective lenses 
and pinholes 16 and 21. The fringe field in the area 37A thereupon 
propagates through the eye and is projected onto the retina 50. 
During testing, a patient positions his eye pupil 49 on the axis 41B near 
the eyepiece 48 to intercept the twin point sources from the eyepiece 48. 
When his eye is in the proper position, the patient will sense or "see" 
the fringe pattern projected onto his retina 50. The cornea and eye lens 
have negligible optical power in such an arrangement and therefore have a 
negligible effect upon the fringe pattern projected onto the retina. 
The negative lens 43 and microscope objective 44 are positioned on a slider 
51 that can be moved along the axis 41A thereby to reposition the focal 
point (FP) with respect to the grating 45. As the slider 51 and focal 
point (FP) are repositioned, the number of fringes within fringe field 37A 
changes. The ability of the patient to see or discern a pattern of a given 
number of fringes within the field projected onto his retina is directly 
equated to standard measurements of acuity. 
During retinal examination the dove prism 46 and aperture wheel 47 play 
subtle, but important, roles because the retinal test is rather 
subjective. The examiner is able to control the orientation of the fringes 
by rotating the dove prism 46 thereby to determine whether a patient's 
claim of being able to see a pattern in a certain orientation is actually 
valid. To the extent that retinal response might exhibit orientational 
variations, the nature of such variations also can be evaluated. 
The diameter of the aperture selected by positioning the aperture wheel 47 
controls the size of the retinal area stimulated by the fringe pattern. 
This field control is important in determining the extent of any macular 
degeneration. The retinal fields offered by the various apertures in wheel 
47 range, in one specific example, from 20.degree. to 0.5.degree.; these 
fields correspond to circular regions that are stimulated on the retina 
ranging from 5.0 to 0.15 mm. in diameter. 
FIG. 5 illustrates a number of different patterns as they will be perceived 
by a patient who is being examined utilizing the apparatus shown in FIG. 
4. If the slider 51 is located in an intermediate position, the patient 
could perceive the fringe pattern of alternate dark and bright bands that 
are shown as pattern A. If a laser that emits red light is used, the light 
areas are red and the dark areas are black. Thus, the patient perceives a 
series of straight red and black lines. If the slider 51 is moved along 
the axis 41A in FIG. 4 toward the grating 45, the number of fringes 
decreases and the patient perceives pattern B that contains fewer and 
wider fringes. Likewise, motion of the slider 51 in a direction away from 
the grating 45 beyond the intermediate position increases the number of 
fringes as shown in pattern C. If, on the other hand, the slider 51 is in 
the same position that produces pattern A, a 22.5.degree. rotation of the 
dove prism 46 in FIG. 4 rotates the fringes 45.degree. to an orientation 
shown in pattern D. 
Another embodiment of the retinal acuity tester is shown in FIG. 6. This 
tester differs from the retinal acuity tester shown in FIG. 4 by the 
addition of a viewing system for the examiner. This viewing system can be 
added because the common path principle applies to the overlapped orders 
producing the area 37A. Various viewing system designs could be used 
because the choice of specific components is not dictated by fringe 
distortion cnsiderations. However, the components of the viewing system 
should be of reasonable quality to insure best viewing system performance. 
The viewing system, as shown in FIG. 6, includes a beamsplitter 52 that is 
disposed between the aperture wheel 47 and the eyepiece 48. The 
beamsplitter 52 directs white light from a fiber optics light guide 53 
through the eyepiece 48 onto the eye. The source of light for the light 
guide can comprise a standard low-power fiber optics illuminator (not 
shown). Light reflected from the eye passes through the eyepiece 48, the 
beamsplitter 52 and the aperture in aperture wheel 47 aligned with the 
axis 41B to another beamsplitter 54. Normally the largest aperture is 
aligned to provide the largest field of view. The beamsplitter 54 directs 
this light to a concave mirror 55 that forms a real image of the eye 
surface near the beamsplitter 54. Lens 56 relays the real image of the eye 
surface through a polarizer 57 to the focal plane of an eyepiece 58 for 
observation. The polarizer 57 coacts with another crossed polarizer 59 
between the dove prism 46 and the beamsplitter 54 to eliminate that 
portion of the fringe field reflected from beamsplitter 54 toward eyepiece 
58. Viewing system aberrations are reduced by locating the aperture wheel 
47 at the center of curvature of mirror 55 and using a symmetrical relay 
lens 56 at 1:1 conjugates. 
Even with good chin rests one of the most frequently encountered problems 
in ophthalmic examinations is the proper positioning of the patient's eye. 
With a properly aligned viewing system of the type disclosed in FIG. 6, 
the exact center of the image observed through eyepiece 58 is centered 
between the twin coherent point sources formed by eyepiece 48. Thus, when 
the examiner properly positions a patient's eye pupil to intercept the 
twin coherent point sources he will observe a clear, centralized image of 
the eye pupil through eyepiece 58. The viewing system is especially 
valuable for testing cataract patients because it enables precise location 
of the twin coherent point sources at any existing opening in a cataract. 
FIGS. 7A and 7B are two views of a retinal acuity tester constructed in 
accordance with this invention. This specific tester embodies the elements 
that are disclosed in FIG. 4. More specifically, the tester includes a 
housing 60 having a conventional laser unit 61 extending from one end 62 
of the housing 60. The laser 61 is connected to a conventional laser power 
supply 63. 
The various elements within the housing 60 are supported on a base plate 
64. A first element includes an upright stand 65 that supports the filter 
wheel 42. The examiner rotates a portion of the circumference of the 
filter wheel 42 that extends through a slot in a top plate 67 of the 
housing 60 to position the appropriate filter on the light axis. Although 
the angular position of the filter wheel 42 might be maintained by 
friction, a more positive positioning means would incorporate some detent 
indexing mechanism for interacting between the upright stand 65 and the 
filter wheel 42. 
The negative lens 43 and microscope objective lens 44 shown in FIG. 4 are 
mounted in a housing 70 carried on the slider 51. A rotary cam 71 has a 
shaft that extends through a side wall 72 of the housing 60 and is 
supported on a stand 72A. This shaft carries a positioning knob 73, a 
scale 74 and a detent mechanism that is not shown. The scale 74 is 
graduated directly in equivalent Snellen acuities ranging from 20/15 
through 20/400. As the examiner rotates the knob 73, the cam 71 rotates 
and longitudinally displaces the slider 51 and both the negative lens 43 
and the microscope objective lens 44 thereby to vary the position of the 
focal point FP shown in FIG. 4. In this embodiment the slider 51 is 
constituted by a cam follower that contacts the cam 72 and is supported in 
a slide 75. The slide 75 also houses springs to bias the slider 51 against 
the cam 71. 
Another upright stand 76 is mounted to the base plate 64. This stand 76 
carries the grating 45. Thus, when the power supply 63 is activated, the 
light emanating from the laser 61 passes through the filter wheel 42, the 
negative lens 43, the microscope objective lens 44 to the grating 45 
thereby to produce zero and first order diffraction cones that have equal 
strengths and that overlap. In one specific arrangement the distance 
between the grating 45 and the focal point varies over a range from about 
0.6 mm to 25 mm. That range of distances enables the apparatus to produce 
fringe patterns that correspond to acuity measurements from 20/400 through 
20/15. 
There is also located at a fixed position on the base plate 64 another 
stand 77. This stand is skewed slightly with respect to the housing 60 in 
order to position the longitudinal axis of the dove prism 46 on the axis 
41 B shown in FIG. 4. The stand 77 carries a rotatable wheel 80. A portion 
of the wheel 80 extends through another slot in the top 67. The wheel 80 
carries the dove prism 46 so that rotation of the wheel 80 by the examiner 
rotates the dove prism 46 and changes the orientation of the fringes, as 
shown in pattern D of FIG. 5. 
The next element in the tester is an end wall 81 that supports the aperture 
wheel 47 and the eyepiece 48 on the axis 41B in FIG. 4. A portion of the 
aperture wheel 47 extends through a slot in wall 60 allowing the examiner 
to center the various apertures on axis 41B shown in FIG. 4. In addition, 
the end wall 81 contains two notches 82 and 83 in an exterior portion of 
the wall. These notches are offset on opposite sides of the eyepiece 48. 
They alloy the patient to position his nose with respect to the housing 
during examination. For example, the patient would position his nose in 
the notch 82 during examination of his right eye. 
From the foregoing discussion, it will be apparent that the retinal acuity 
tester disclosed in FIGS. 7A and 7B is compact and easy to construct. All 
the optical elements, except the grating 45, are conventional elements 
that are readily available and relatively inexpensive. Such elements are 
used because the retinal acuity tester is an example of a common path 
interferometer and because the fringes are not subject to thermal 
variations, vibrations or other environmental perturbations. 
D. Position Encoder 
In accordance with another aspect of this invention, the interferometer 
shown in FIG. 3 is readily adapted to use in a position control system. As 
previously indicated, the fringes in the areas of overlap 37A and 37B in 
FIG. 3 move through the area of overlap in the direction of motion of the 
grating. Moreover, if the distance Z.sub.1 between the focal point FP and 
the grating remains constant, the number of fringes in the area of overlap 
remains constant. On the other hand, if the distance Z.sub.2 varies, then 
the number of fringes within the area of overlap remains the same but the 
area of the overlap varies, as would be expected in a projection type 
system. 
A specific embodiment of a position encoder that can be used in a wide 
variety of measurement and control functions is disclosed in FIG. 8A. In 
FIG. 8A, light emanates from a point source 100 of quasi-monochromatic, 
spatially coherent light. A holographically recorded, single-frequency 
phase grating 101 is mounted in a carrier 102 that moves in in the X 
direction of an XY plane that is orthogonal to the light, or Z, axis. 
Light from the source 100 is diffracted into equal strength zero and first 
order cones by the grating 101 that is supported in a carrier 102. The 
zero order distribution is represented as a planar circle 103 while the 
two first order distributions are depicted by planar circles 104 and 105. 
The fringes in the areas of overlap 106 and 107 are projected onto 
photodetectors 110 and 111 that generate input signals for a position 
detection circuit 112, such circuits being well known in the art. 
Referring to FIG. 8B, the photodetectors 110 and 111 are horizontally 
oriented in the central fringe that is produced in each of the areas of 
overlap 106 and 107; i.e., on axes 120 and 121 respectively. As previously 
explained, controlling the form of the grating phase transmission function 
causes the fringes in one area of overlap to be 180.degree. out of phase 
with the fringes in the other area of overlap. As shown in FIG. 8B the 
photodetector 110 is aligned with a dark band at the central fringe 
position while the photodetector 111 is aligned with a bright band at the 
central fringe position. For purposes of the photodetection, this 
particular embodiment is particularly simplified if the light source 100 
generates red or near infrared light as photodetection cells, such as 
photodiodes, are particularly sensitive in this region of the spectrum. 
If the carrier 102 moves slightly to the right in FIG. 8A along the X axis, 
the fringes shift with it. After an incremental motion, the bands that 
impinge the photodetectors 110 and 111 in FIG. 8B shift to the positions 
shown in FIG. 8C. Now a bright band impinges the photodetector 110, and a 
dark band impinges the photodector 111. If the grating 101 has a phase 
pattern of 400 lines per millimeter, this binary change represents a 
translation along the X axis of approximately 0.000050 inches. Yet even 
with this accuracy, this apparatus is relatively easy to construct because 
the bands that impinge the photodetectors are relatively wide. For 
example, bands having a width of about 0.1 inch are obtained when Z.sub.2 
equals about 2 inches and Z.sub.1 equals 0.001 inches. See equation (1). 
Bands of this width facilitate the placement of the photodetectors because 
their positions can be established with fairly loose tolerances. 
This apparatus is essentially insensitive to any changes in the distance 
between the grating 101 and the photodetectors 110 and 111 along axes 120 
and 121. As previously indicated, the size of the fringe fields 106 and 
107 changes if Z.sub.2 changes, but the number of fringes within the 
fields does not change. Thus, in FIG. 8B the photodetectors 110 and 111 
remain centered on their respective central fringes, notwithstanding any 
variations in the distance Z.sub.2 along axes 120 and 121. 
The point source 110 shown in FIG. 8A comprises elements such as the laser 
40, negative lens 43 and microscope objective 44 in FIG. 6. With a source 
of this construction, the laser radiation is allowed to overfill the 
objective, thus producing a well bounded radiation field with radial 
symmetry as shown in FIG. 8A. 
On the other hand a simple laser diode could also be used by itself or in 
combination with the microscope objective 33. The shape of the laser diode 
radiating region is approximately rectangular instead of circular. 
Therefore, when the laser diode is used by itself, the zero and .+-.1 
order distributions are not the radially symmetrical and sharply bounded 
circles 103, 104 and 105 in FIG. 8A. However, FIG. 8A does constitute an 
approximate representation of the actual irradiance distributions in the 
XY plane when the spatially coherent, quasi-monochromatic source comprises 
only a laser diode. When a laser diode and microscope objective are used 
in combination, the laser diode radiation is allowed to overfill the 
microscope objective. Thus, a well-bounded radiation field with greater 
radial symmetry is produced. With any such "source", the discussions 
concerning the various position encoders is totally valid and unaffected 
by the use of the idealized representations 103, 104 and 105, FIG. 8A. 
While the apparatus in FIG. 8A is useful in making measurements in one 
direction, FIG. 9A discloses a carrier that moves in both the X and Y 
directions. The grating 123 differs from the grating 101 in FIG. 8A and 
the difference is most readily understood by referring to FIGS. 1 and 2. 
In forming the grating 123, the photographic plate 12 is exposed as 
previously described with reference to step 1 in FIG. 2. However, the 
plate is then turned 90.degree. and exposed again before it is developed. 
This double exposure produces superimposed horizontal and vertical single 
frequency interference patterns. 
Referring again to FIG. 9A, when the grating 123 is illuminated with any 
point source of quasi-monochromatic, spatially coherent light, the grating 
produces five diffraction cones of interest that are approximated in FIG. 
9A and are shown more clearly by a planar projection in FIG. 9B. The 
vertical phase pattern on the grating produces cones represented by 
circles 103 through 105 as previously described, these cones producing 
areas of overlap 106A and 107A. However, the horizontally disposed phase 
pattern produces a pair of first order cones in the vertical direction 
designated by reference numerals 114 and 115. Four areas of overlap are 
important. Arcuate wedge areas 106A and 107A correspond to the areas 106 
and 107 shown in FIG. 8B that are independent of the influence exerted by 
the first order cones 114 and 115. Arcuate wedge areas 116A and 117A are 
formed by overlapping the zero order cone 103 and the first order cones 
114 and 115, and they are independent of any influence by the first order 
cones 104 and 105. The photodetectors are aligned on the central fringe 
for each area of overlap. Photodetectors 110 and 111 aligned with the 
areas 106A and 107A respond to motion along the X axis as previously 
discussed. Photodetectors 120 and 121 are aligned with the areas 116A and 
117A. They sense vertical motion along the Y axis. These four 
photodetectors are then coupled to the position detection circuit 124 that 
responds to these signals either for indicating XY motion or for providing 
an input to an XY positioning servo mechanism. 
FIG. 10 illustrates, diagrammatically, apparatus that generates quadrature 
signals. Basically this apparatus employs the apparatus shown in FIG. 8A 
with the addition of photodetectors 125 and 126. Photodetectors 110 and 
111 are shifted upwardly but remain positioned on the central fringes. The 
additional photodetectors 125 and 126 are positioned one-quarter fringe 
period to the right of each central fringe (i.e. 90.degree. out of phase 
or in a quadrature position). Thus, as will be readily apparent, the 
signals from these four photodetectors provide quadrature signals that 
inherently provide both position and direction information. 
In each of the foregoing applications, it is assumed that the Z.sub.1 
distance between the point source of light and the grating remains 
constant. As apparent, however, such a constant dimensions might be 
difficult to achieve in some practical applications. FIGS. 11A and 11B 
disclose apparatus which is essentially insensitive to a reasonable range 
of variations in the Z.sub.1 dimension. This again is shown in connection 
with an apparatus for detecting translation along the X direction only. 
The resulting signals are conveyed to a position detection system 127 that 
includes an up-down counter to count the passage of fringes and to provide 
an accurate indication of motion. 
More specifically, a laser light source 100 transmits light through the 
grating 101 to produce zero and first order cones 103, 104 and 105 with 
areas of overlap 106 and 107. As shown in FIG. 11B, photodetectors 110 and 
111 then provide a first set of signals. Another light source 130 is 
disposed below the light source 100. It is positioned to produce a 
zero-order cone 133 and first-order cones 134 and 135 that lie below the 
diffraction cones produced by light from the source 100. The horizontal, 
or X, position of source 130 is adjusted to produce overlap areas 136 and 
137 whose central fringes are 90.degree. out of phase with the central 
fringes of overlap areas 106 and 107. Photodetectors 140 and 141 are 
aligned with these central fringes in overlap areas 136 and 137. With this 
arrangement, quadrature signals are generated from four central fringes 
whose position is unaffected by variations in Z.sub.1. Increasing Z.sub.1 
causes the width of the central fringes to decrease, but so long as the 
photodetector aperture can resolve the central fringes, an accurate 
quadrature signal is produced. 
E. Contour Generator 
The single frequency holographic phase grating previously disclosed in 
conjunction with the position sensing and retinal acuity testing 
applications can be readily adapted for use as a Fourier plane filter. 
FIG. 12A shows a grating filter optical subtraction system whose critical 
component is the single frequency holographic phase grating 207. The 
general system of FIG. 12A is very well known as a coherent optical 
processor. A laser 200 and beam expander/collimator 201 are the source of 
a spatially coherent, quasi-monochromatic plane wave 203. Two vertical 
stereo transparencies 204 and 205 are placed in the front focal plane of a 
lens 206 and transilluminated by the plane wave 203. The Fourier transform 
of the wave transmitted by both stereo transparencies appears at the 
holographic phase grating 207. The grating 207 is mounted on a 
micropositioner and located along an axis to constitute a cosinusoidal 
phase filter to the Fourier transform light distribution. Lens 208 then 
forms output images at plane 209 from the filtered Fourier transform 
distribution. 
The important output images shown in FIG. 12B are coherent superpositions 
of two real image distributions. Therefore, "output images" 210 and 211 
are not images in the classical sense. The important feature in "output 
image" 210 is a dark fringe which corresponds to an equal height contour 
line. The contour line of 210 is a perspective contour line which appears 
in the perspective of original transparency 205 and its classical image 
205A. The "output image" 211 contains the same equal height contour line 
as 210 but in this case the contour line is displayed in the perspective 
of original transparency 204 and its classical image 204A. The contour 
line in the "output image" 210 results when the zero order cone produced 
by grating 207 in response to light from transparancy 205 is overlapped 
with the +2 order produced by grating 207 in response to light from 
transparency 204. Similarly, the contour line in "output image" 211 
results from overlapping the zero order and the -2 order diffraction cones 
from grating 207 that are produced in response to light from 
transparencies 204 and 205, respectively. The lens 208 forms real, 
classical images of the contour lines in plane 209. Other equal height 
contour lines can be produced by mechanically changing the separation B of 
the original transparencies 204 and 205. 
The critical component in this system is the grating 207 which produces the 
various order classical images that are overlapped to form contour lines. 
More specifically, grating 207 is a 90 l/mm, optionally thin, 
holographically produced phase grating. In this particular application the 
peak to peak phase delay of the grating transmission function is 3.68 
radians, the value required to produce equal strength zero and .+-.2 order 
diffraction cones. In addition, the phase transmission function must be a 
pure cosinusoidal function to allow the second order diffraction cones to 
be 180.degree. out of phase with the zero order diffraction cone so that a 
complete optical subtraction can occur between the overlapped orders. 
Where the classical images 204A and 205A are identical, the optical 
subtraction is complete and a dark contour line or contour fringe is 
produced. 
The grating 207 can be produced on an AGFA 8E75 emulsion which is exposed 
to a 90 l/mm interference pattern generated by the optical system of FIG. 
1. The average exposure is 2000 ergs/cm.sup.2 at 6328 A with a 45 second 
development time in Kodak D-76 developer at 80.degree. F. When producing 
relatively low frequency gratings, the tanning action of certain 
developers can cause undesirable phase perturbations. For this reason, the 
weakly tanning D-76 developer and chemically compatible AGFA 8E75 emulsion 
were chosen for the production of the 90 l/mm grating. The previously 
discussed exposure adjustment procedures are used to achieve equal 
strength zero and second order diffraction from the final phase grating 
while maintaining a pure sinusoidal phase perturbation function. The 
remaining steps 3 through 9 in FIG. 2 are used to complete the processing. 
In summary, there has been disclosed a basic inteferometer construction 
that utilizes a holographically recorded optically thin, single-frequency, 
bromine-vapor bleached, phase grating for producing stable, high-contrast 
fringe patterns with high efficiency. Moreover, there has been disclosed 
three diverse applications of this interferometer for testing retinal 
acuity, for sensing or controlling the position of a mechanical element 
and for generating contour lines. Moreover, a specific example of the 
retinal acuity tester has been disclosed. 
It will be apparent from the foregoing discussion, however, that the 
specific embodiments of this invention that have been disclosed are merely 
representative. The basic principles can be employed in a wide variety of 
applications with the attainment of some or all of the advantages of this 
invention. Therefore, it is an object of the appended claims to cover all 
such variations and modifications as come within the true spirit and scope 
of this invention.