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REFERENCES
G. M. Brown and J. L. Sullivan, "The Computer-aided Holophotoelastic
Method". Exp. Mech. 20, 135-144 (1990) L. F. Collins, "Difference
Holography", Applied Optics 8, 203-205 (1968)
J. C. Dainty, ed., Laser Speckle and Related Phenomena, Berlin,
Springer-Verlag, 1984
D. Gabor, "Holography, 1948-1971", Science 177, 299-313 (1972)
M. E. Fourney, A. P. Waggoner, and K. V. Mate, "Recording Polarization
Effects via Holography", J. Opt. Soc. Am. 58, 701-702 (1968)
G. Lai and T. Yatagai, "Dual-reference holographic interferometry with a
double pulsed laser", Applied Optics Vol. 27, No. 18, pp 3855-3858, Sep.
15, 1988
D. B. Neumann, "Differential Holographic Interferometry", U.S. Pat. No.
4,464,052, Aug. 7, 1984
M. Nisida and H. Saito, "A New Interferometric Method of Two-dimensional
Stress Analysis". Exp. Mech. 4, 366-376 (1964)
M. Sharnoff, "Microdifferential Holography", J. Optical Soc. Amer. A 2,
1619-1628 (1985)
M. Sharnoff, "Differential Holography", U.S. Pat. No. 4,725,142, Feb. 16,
1988
T. Tsurata, N. Shiotake, and Y. Itoh, "Holographic Interferometry Using Two
Reference Beams", Japanese Journal of Applied Physics 7, No. 9, September
1968, pp. 1092-1100
OBJECT AND SUMMARY OF THE INVENTION
It is the principal object of this invention to produce accurate collation
of images that differ principally in fine detail, particularly where the
images or their differences are eventually to be scanned, determined,
processed, compared, or interpreted by digital techniques. The images are
encoded in pairs by means of a double reference wave holographic process,
one reference wave being used to encode one image of a pair, and the other
reference wave being used to encode the other image. The two holograms are
incoherently recorded on a single holographic plate or other unitary
holographic recording medium. Because the reference waves can be made
coherent with eachother, the images reconstructed when the two reference
waves simultaneously illuminate the developed holograms can be manipulated
coherently. Once the developed holographic plate, or other recording
medium, is returned to the position and orientation it occupied during its
exposure, the relative intensities and phases of the two reference waves
can be adjusted to produce nearly complete destructive interference
between the two reconstructed images. The small difference between the
original images is conveyed by the residual intensity in the interference
pattern of the two reconstructed images. This difference can then be
directly recorded by a digital scanner, such as a CCD based video camera
coupled to a memory bank and computer, with an accuracy and
signal-to-noise ratio very much higher than obtainable by direct digital
subtraction of the original images. Furthermore, the highly precise
registration of the reconstructed images and balance of their intensities
will be unaffected by further manipulation of the phases of the two
reference waves or by their alternate obstruction. Deliberately rephased
superpositions of the reconstructed images can also be scanned; or, if the
reference waves are made to impinge only one at a time upon the developed
holographic recording medium, the reconstructed images can be digitized
individually and processed by the computer in any way that it permits,
including any that requires or relies upon balance between the image
intensities.
When the images to be compared are more than two, a sequence of hologram
pairs is recorded in such fashion that the image encoded in one hologram
of any pair is encoded also in one hologram of at least one other pair,
there being, in all, sufficiently many holograms so that each of the
images is encoded in at least one of them.
While the invention is primarily optical in conception, the principles upon
which it depends are valid for any electromagnetic radiation and can be
put to practical use in any region of the spectrum for which a source of
coherent radiation is available and for which compactly arrayed sensors
appropriate for recording holograms can be constructed. In the soft Xray
portion of the spectrum, for instance, high-resolution photoresists are
the analogues of photographic film and are in current use both in Xray
holography and in lithography. Beamsplitters and focussing devices for
soft Xrays are likewise available, as are mirrors, collimating devices,
filters and attenuators, and polarizers; and a synchrotron source of
Xrays, equipped with monochromator and collimator, can generate a
spatially and temporally coherent beam of Xrays analogous to the beam of
visible light that emerges from a laser during operation.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a plan schematic view of an arrangement of apparatus that permits
a pair of holograms to be recorded sequentially in superposition.
FIG. 2 is a schematic drawing showing the relation between the position and
orientation of the holographic recording medium to one of the reference
waves, to the object wave, and to the reconstructed wave pertinent to the
apparatus of FIG. 1. The Figure shows also a method of forming an image
from the reconstructed wave.
FIG. 3 is a schematic drawing showing the relation between the position and
orientation of the holographic recording medium to the other of the
reference waves, to the object wave, and to the reconstructed wave
pertinent to the apparatus of FIG. 1.
FIG. 4 is a schematic drawing showing the relation between the two
reference waves, the object wave, and the reconstructed waves pertinent to
the apparatus of FIG. 1, and showing also their relation to the position
of a lens or other device intended to form images from the reconstructed
waves.
FIG. 5 is a schematic view of an arrangement of apparatus that permits a
pair of holograms to be recorded simultaneously in superposition.
FIG. 6 is a schematic view of a preferred embodiment of the invention in
which the reference waves are spatially filtered before impinging upon the
holographic plate.
FIG. 7 is a schematic view of a preferred embodiment of the invention as
adapted for use in photoelastic analysis.
BACKGROUND OF THE INVENTION
The present invention concerns the comparison of images which differ
slightly from one another. The images may be part of a sequence of
successive scenes, as of a vibrating object seen in various phases of its
motion; or they may part of a group of images formed simultaneously, as in
stereomicroscopy. Holographic interferometry poses an acute requirement
for accurate comparison of images, and it was in the course of their
activity in this area that the authors were led to the invention disclosed
herein. The invention is closely related to the art taught by Sharnoff in
U.S. Pat. No.4,725,142.
Central to that art is the principle that in holographic study of the fine
deformations or dynamics of a subject under test the holograms should be
recorded differentially in conjugate pairs. The conjugate images
reconstructed when the differential holograms of a pair are illuminated
one at a time can be scanned electronically and stored in a memory bank;
dynamic shifts in the amplitude or the phase of light coming from the
subject under test can then be determined from digital addition or
subtraction of the scanned images.
In the practical elaboration of this method to subjects of any complexity,
image collation presents a major difficulty. If the images to be scanned
are not put into registration to within a very small fraction of the
diameter of one pixel of the scanning device, errors of sampling make any
digital comparison intolerably noisy. The best signal-to-noise ratios that
the authors could obtain by digital subtraction of two identical
holographic scenes placed into registration by purely mechanical means
were a factor of 100 to 1000 lower than could be obtained, following the
art of Sharnoff, by direct holographic subtraction of the scene from
itself. The practice we teach below permits images to be digitally
subtracted without deficiency of registration, however complex and finely
detailed the images might be.
An important precursor to this practice was taught by Sharnoff in columns
15-17 and FIG. 9 of the disclosure of U.S. Pat. No. 4,725,142. Work
related to our practice appears to have been done by G. Lai and T. Yatagai
in "Dual-reference holographic interferometry with a double pulsed laser",
Applied Optics Vol. 27, No. 18, Sep. 15, 1988, pp 3855-3858.
DETAILED DESCRIPTION OF THE INVENTION
In the electronic comparison of images differing in final detail it is
important to position them so that they have exactly the same dimensions
and occupy, successively, exactly the same positions and orientations with
respect to the electronic imaging or sensing device. However the images
are projected onto said electronic imaging or sensing device, hereinafter
called simply a scanner, the positions of those features that the images
possess in common must appear to coincide to within a small fraction of
the diameter of the scanner's detection unit, or pixel. When the
coincidence between corresponding features that the images possess in
common has been satisfactorily effected, the images will be said to have
been collated. The process of securing satisfactory coincidence between
corresponding features that the images possess in common will be called
collation. The action that produces collation will be called collating,
and any material device, machine, or apparatus that makes collation
possible will be called a collator.
In the practice of the invention any two images whose comparison is desired
are collated interferometrically, the collation being judged by the degree
to which the two images are brought into destructive interference.
Destructive interference between corresponding details present in both
images will not take place unless they coincide to within one half
wavelength or less. Because the wavelength of light, typically 0.5 .mu.m
is so much smaller than the diameter of a typical pixel, typically 7.5 to
20 .mu.m in modern scanners like CCD TV cameras, collation by destructive
interference between two images is likely to be more accurate than any
purely mechanical method of collation. Like mechanical collation,
interferometric collation is facilitated by prior knowledge of the images,
or by the presence of bright, readily recognizable features or fiducial
marks common to both images. The collation may then be quickly judged by
the degree to which the bright, recognizable features or fiducial marks
have been brought into coincidence. In collation by destructive
interference, the proper superposition of the bright recognizable features
or fiducial marks would make them appear maximally black.
In the following description the word coherent will refer to waves,
holograms, beams of light or other radiation, or images that exhibit
interference, or to processes that depend upon interference. Thus, when
two coherent waves travel simultaneously through a common region of space,
a pattern of interference fringes is observable therein. The pattern will
be determined by the geometrical form of the wavefronts--equiphase
surfaces of the waves--and by the relative phases of the two waves at any
fixed reference point in space. The locations of the fringes, and
oft-times even the pattern itself, will be found to be affected by any
action that alters the relative phases of the waves at the fixed point in
question. If the waves are light waves, their interference patterns can be
photographed, and it can be confirmed that the locations of fringes are
affected by changes in the relative phases of the waves, for the
distribution of blackening on any of the photographic negatives would
represent the spatial distribution of the square of the coherent sum of
wave amplitudes. A photograph could also be made by exposing a negative
successively to the two coherent light waves one at a time, rather than
simultaneously. Negatives made in this way would be insensitive to change
in the relative phases of the waves at the reference point. Blackening in
such negatives would represent not a coherent sum of the waves, but only
the spatial distribution of the sum of their intensities.
The word incoherent will in the following description refer to waves,
holograms, beams of light or other radiation, or images that do not
exhibit interference, or to processes that do not depend upon coherence.
Thus, two light waves that are coherent can be made incoherent by
polarizing them orthogonally. For instance, if the waves travel
horizontally, this could be done by passing one through a Polaroid whose
axis is vertical and the other through a Polaroid whose axis lies
horizontally at right angles to the direction of its propagation. No
interference pattern is observable between light waves whose directions of
polarization are mutually perpendicular, and a photographic negative
exposed simultaneously to two such waves will exhibit no fringes of
interference between them even if the waves are derived from the same
laser. Digital addition or subtraction of two images successively exposed
to a TV camera or other scanner is incoherent even in cases in which the
images, were they present simultaneously, would be found coherent. In
particular, the result of the aforesaid addition or subtraction of
successively exposed images would not depend upon the relative phases
between the images when simultaneously present.
A hologram is a record of the pattern of interference between two waves
that are coherent. One of the two waves whose pattern of interference has
been recorded or is to be recorded in a hologram will be called the object
wave, whether or not it carries information directly from a real object
such as a subject under test. The other of the two waves whose pattern of
interference has been recorded or is to be recorded in a hologram will be
called the reference wave. Any wavefront of the reference wave will
normally be a geometrically simple surface such as a portion of a plane or
sphere. The geometrical simplicity of these wavefronts enables the
reference wave easily to be produced, controlled, and reproduced. If the
object wave and the reference wave are both light waves, and if
photographic emulsion on a holographic plate be exposed so as to record
the pattern of interference between the object wave and reference wave,
the developed photographic emulsion on the holographic plate is a
hologram. If the hologram be returned to the position and orientation
occupied by the photographic emulsion on the holographic plate during its
exposure to record the pattern of interference between the object wave and
the reference wave, and if it be thereupon illuminated by a wave having
the same wavelength as the reference wave, and having also wavefronts of
the same curvature and orientation as the wavefronts of the reference
wave, a remarkable phenomenon takes place: that portion of the object wave
that was incident upon and would have continued through and into the space
beyond the surface occupied by the photographic emulsion on the
holographic plate, had the photographic emulsion not been actually
present, is now produced through the hologram and into the space beyond
it, just as though the object wave continued to be incident upon the
surface occupied by the hologram, the hologram not being itself actually
present. The remarkable phenomenon will be called reconstruction of the
object wave, or simply reconstruction; and said portion of the object wave
will be called the reconstructed object wave, or, simply, the
reconstructed wave. An image can be formed from the reconstructed object
wave by means of a suitable optical system. The image is indistinguishable
from the image that said optical system would form from the object wave
when the object wave is present. The hologram will therefore be said to
encode the object wave. The hologram will be said also to encode any image
that can be formed from the reconstructed object wave. Any image formed
from the reconstructed object wave will be called a reconstructed image
and be said to have been formed or obtained by reconstruction from the
hologram in which the object wave had been encoded. It is well known in
the holographic art that when the object wave and the reference wave are
incident from different directions upon the photographic emulsion used to
record the pattern of their interference, images reconstructed from the
resulting hologram are or can be made disjoint from the reference wave.
A simple hologram is the record of the pattern of interference between an
object wave and a reference wave at a single instant of time or during an
interval within which there are no changes either in the object wave or in
the reference wave. If the object wave is obtained by reflection,
scattering, transmission, or diffraction of light used to illuminate a
subject under test, an image reconstructed from a simple hologram will be
an optical counterpart of the subject under test that depicts the subject
well. A composite hologram is a record of the pattern of interference
between an object wave and a reference wave sampled at two or more
instants of time, between which there may be changes in either or both of
the object wave and the relative phase of the reference wave. If the said
instants of time are discrete, it may be convenient to call form in which
the object wave exists at the first instant of time the first object wave
and to call the form in which the object wave exists at the second instant
of time the second object wave, and so forth, and to think of the first
object wave and second object wave as members of a group of object waves.
If the object wave is obtained by reflection, scattering, transmission, or
diffraction of light used to illuminate a subject under test, an image
reconstructed from a composite hologram may not be a perfectly
recognizable optical counterpart of the subject under test. If, for
instance, the subject under test undergoes a small deformation during the
sampling process, an image reconstructed from the composite hologram may
depict the subject under test superposed on a pattern of dark and bright
bands or fringes. The image is interpreted not as that of an object made
up of rigid disjoint segments of the subject under test, but as an
interferogram of the entire subject in various states of deformation. The
locations and intensities of the fringes of such an interferogram may be
affected by shifts in the relative phase of the reference wave during the
sampling process. Thus an image reconstructed from a composite hologram
need bear no simple or unique relation to the appearance of the subject
when undisturbed, or even to the deformations of the subject when
undergoing stress. There may indeed be no subject that when illuminated at
rest would resemble a reconstructed image that is an interferogram.
Nonetheless it will often be convenient in the following description to
call the group of object waves reconstructed from a composite hologram the
reconstructed wave, and to call an interferogram formed from the group of
waves reconstructed from a composite hologram a reconstructed image, just
as though the reconstructed wave or group of waves had been produced by
reconstruction from a simple hologram in which an image identical to said
interferogram had been encoded. When clarity is desired, such an image
will be called a composite image.
In our invention the images to be collated are obtained by reconstruction
from holograms in which they are originally or have been encoded. It will
be shown hereinbelow that if the images are to be accurately compared and
distinguished it is essential that a hologram in which any one image is
encoded be recorded incoherently from the hologram in which any other
image is encoded. When two holograms have no point in common in the
recording medium they are by nature incoherent. It will often be
convenient, however, to record two holograms as a pair superposed on a
common region of the recording medium, as was taught by Sharnoff in the
patent cited hereinabove.
There are two fundamental ways of superposing two holograms incoherently in
the same region of a holographic plate or other recording device. One way
is to record the two holograms successively. The other is to record them
simultaneously in an arrangement which causes the object wave and
reference wave whose pattern of interference is recorded in one of the two
holograms to be polarized perpendicularly to the object wave and reference
wave whose pattern of interference is recorded in the other of the two
holograms. Among several ways of ensuring this is, for instance, the use
of Polaroids or other polarizing devices in the fashion described
hereinabove. In order to permit the object wave encoded in the second or
two superposed holograms to be reconstructed independently of the object
wave encoded in the first of the two superposed holograms, the wavefronts
of the reference wave used to record the second hologram must differ in
curvature or in orientation from the wavefronts used to record the first
hologram. The two reference waves should have precisely equal wavelengths;
and so they should be derived from one and the same laser beam, or other
source of coherent radiation, in such fashion that the largest difference
of optical path-lengths between the primary beamsplitter and the
holographic plate not exceed the coherence length of the radiation. When
the two holograms to be superposed are to be recorded in sequence, rather
than simultaneously, no restriction need be imposed on the polarization of
either object wave or on the polarization of either reference wave.
Referring to FIG. 1, a sketch is shown of an arrangement of apparatus that
permits an object wave and two reference waves to be generated from a
single laser beam, the wavefronts of one of the two reference waves
differing in orientation from those of the other reference beam. The
external beam 2 of laser 1 is passed through shutter 3, forming shuttered
beam 4. This is directed at beamsplitter 5 where it is divided into two
sub-beams 6 and 7. Sub-beam 6 is directed upon beamsplitter 8, which
divides it further into sub-beam 9 and sub-beam 10. Sub-beam 9 is passed
through shutter 11, and the emerging portion 14 undergoes reflection at
mirror 15, forming the sub-beam 16. Sub-beam 16 is passed through
diverging lens 17, becoming the diverging beam 18 directed at 20, upon
which is mounted a holographic recording medium such as a holographic
plate coated with a photographic emulsion 19. Sub-beam 10 is passed
through shutter 13, and the emerging portion 21 is reflected at mirror 22,
forming sub-beam 23. Sub-beam 23 is passed through diverging lens 24,
becoming the diverging beam 25 directed at 20. Each of the diverging beams
indicated as 18 and 25 serves as a reference wave. Sub-beam 7 is passed
through shutter 12, and the emerging portion 26 is reflected at mirror 27,
forming sub-beam 28. Sub-beam 28 is diverged by passage through lens 29,
and directed as diverging beam 30 against the subject 31. Diffraction and
scattering of 30 by the subject is indicated by pencils 34 and 35
radiating outward from two representative points 32 and 33 of 31. Pencils
34 and 35 are representative and do not encompass all possible paths by
which the light of 30 might reach 19 after having been affected by subject
31; nonetheless, in combination they will be considered to represent the
object wave. The sum of the distances along 6, 9, 11, 14, 16, 17, and 18
must differ from the sum of distances along 7, 12, 26, 28, 29, 30, and 34
or 35 by less than the coherence length of the laser beam 2. Similarly,
the sum of distances along 6, 10, 13, 21, 23, 24, and 25 must differ from
the sum of distances along 7, 12, 26, 28, 29, 30, and 34 or 35 by less
than the coherence length of the laser beam 2. The timing of the exposure
or exposures of the photographic emulsion at 19 to 34-35, 18, and 25 is
controlled by shutter 3. The object wave 34-35 can be extinguished by
means of shutter 12. Reference wave 18 can be extinguished independently
of reference wave 25 by means of shutter 11, and reference wave 25 can be
extinguished independently of reference wave 18 by means of shutter 13.
Shutters 3 and 12 are both open, and at least one of shutters 11 and 13
are also open, during the exposure of the photographic emulsion at 19 to
record the pattern of interference between the object wave 34-35 and
reference wave 18. Shutters 3 and 12 are both open, and at least one of
shutters 11 and 13 are also open, during the exposure of the photographic
emulsion 20 to record the pattern of interference between 34-35 and 25. It
is to be understood that FIG. 1 is a plan view, and it is not necessary
that the plane in which sub-beams 6 and 7 travel coincide with the plane
in which sub-beams 9 and 10 travel or the plane in which sub-beams 9 and
16 travel. Nor is it necessary that the plane in which sub-beams 9 and 16
travel coincide with or be parallel with the plane in which sub-beams 10
and 23 travel. Whatever the actual paths and directions of the beams
indicated in FIG. 1, it is important only that reference waves 18 and 25
are projected towards a common region of 20 and that said common region is
accessible also to object wave 34-35.
The arrangement of apparatus shown in FIG. 1 is suitable for recording a
composite hologram, as follows: With the unexposed photographic emulsion
19 on the holographic plate held in place at 20, and with the subject in
place at 31, shutter 13 is held closed, and shutters 11 and 12 are kept
open. Shutter 3 is briefly opened, then closed; and at a later time it is
opened briefly again, and finally closed. If, during the interval between
the brief openings of the shutter 3 there is no change in the subject at
31 and no change in the disposition of apparatus, apart from shutter 3,
then the doubly exposed photographic emulsion of 20 becomes, upon
development, a simple hologram. If the subject at 31 undergoes motion or
deformation during the interval between the brief openings of the shutter
3, the doubly exposed photographic emulsion of 19 becomes, upon
development, a composite hologram. It is not necessary that all the
apparatus shown in FIG. 1 remain stationary during the recording of a
composite hologram. For instance, as taught by Sharnoff in the patent
cited hereinabove, during recording the mirror 15 could be given a
displacement in the direction perpendicular to its reflecting surface, it
being understood that the displacement itself be no larger than one
wavelength of the laser light. Owing to the exceeding smallness of this
displacement in comparison to the diameter of the laser beam 2 and
attendant sub-beams 14 and 16, the lateral displacement of reflected
sub-beam 16 will be imperceptible. Nonetheless, the sum of the optical
path lengths along 6, 9, 11, 14, 16, 17 of FIG. 1 will have been increased
by the amount 2h cos.theta., where h is the displacement of mirror 15 and
.theta. is the angle of incidence of sub-beam 14 upon it. The phase with
which the reference wave 18 impinges upon 20 will have been thereby
shifted by an amount (4.pi.h cos.theta.)/.lambda. radians, where .lambda.
is the wavelength of the light comprising sub-beam 14. One means of
securing the motion of mirror 15 is that of attaching it to a
piezoelectric transducer supplied with an appropriate voltage waveform, as
described by Sharnoff in the patent cited hereinabove.
In the reconstruction of a wave or an image encoded in the composite
hologram constituted, after its development, by the photographic emulsion
exposed to form a composite hologram as explained hereinabove, the
developed photographic emulsion 19' is placed at 20, in the same
orientation as during in its exposure. Shutters 3 and 11 are held open,
and shutters 12 and 13 are closed. The diverging beam 18 will impinge upon
20 as before, and its passage through the composite hologram 19' will
reconstruct the wave encoded therein. The diverging beam 18 will also pass
through the composite hologram into the space beyond it, but will travel
in a direction different from the direction followed by the reconstructed
wave. A converging lens of appropriate power can be placed in the space
beyond the composite hologram at such position as to intercept the
reconstructed wave but not transmitted reference wave. The power of the
converging lens can be preselected to ensure that the reconstructed wave
that the converging lens intercepts is focussed by its passage
therethrough as an image in any desired plane beyond said converging lens.
Referring to FIG. 2, the hologram 19' at 20 is illuminated by the
diverging beam 18, which serves as a reference wave which passes
therethrough as wave 44, creating by its passage through 19' the
reconstructed wave 36, 37. The converging lens 38 converts the
reconstructed wave 36, 37 into pencils 39 and 40 of light that are brought
to focus in points 41 and 42. The subject 30 and the pencils 34 and 35 are
not normally present during the reconstruction process but are included as
dotted lines in FIG. 3 in order to emphasize the relation of 36 and 37 to
the geometry FIG. 1. In particular, the points 41 and 42 are images of the
points labeled 32 and 33 in FIG. 1.
The arrangement of apparatus shown in FIG. 1 is suitable for recording a
superposed pair of simple holograms, as follows: With the unexposed
photographic emulsion 19 on the holographic plate in place at 20, and with
the subject in place at 31, shutter 13 is held closed, and shutters 11 and
12 are kept open. Shutter 3 is briefly opened, then closed. Shutter 11 is
then closed, and shutter 13 opened and held open while shutter 3 is
briefly opened a second time.
In the reconstruction of the object waves or images encoded in the
superposed pair of simple holograms constituted, after its development, by
the photographic emulsion exposed to form a superposed pair of simple
holograms as explained hereinabove, the developed photographic emulsion
19" is placed at 20, in the same orientation as during its exposure.
Shutters 3 and 11 are held open, and shutters 12 and 13 are closed. The
diverging beam 18 will impinge upon 20 as before, and its passage through
the superposed pair 19" of simple holograms will reconstruct that object
wave encoded in the simple hologram recorded when the diverging beam 18
incident upon 20 served as the reference wave. The arrangement of this
portion of the reconstruction process is as shown in FIG. 2, save that the
composite hologram 19' therein is to be replaced by a superposed pair of
simple holograms.
The second portion of the reconstruction proceeds with shutter 11 now
closed and shutter 13 now held open. The diverging beam 25 will impinge
upon 20 as during recording, and its passage through the superposed pair
19" of simple holograms will reconstruct that object wave encoded in the
simple hologram recorded when the diverging beam 25 incident upon 20
served as the reference wave. Diverging beam 25 will also pass through the
superposed pair 19" of simple holograms into the space beyond it, but will
travel in a direction different from the direction followed by the
reconstructed wave. Referring to FIG. 3, the hologram 19" is illuminated
by diverging beam 25, which serves as a reference wave which passes
therethrough as wave 43, creating by its passage through 19" the
reconstructed wave 36', 37'. The converging lens 38 converts the
reconstructed wave 36',37' into pencils 39' and 40' of light that are
brought to focus in points 41' and 42'. The subject 30 and the pencils 34
and 35 are not normally present during the reconstruction process but are
included as dotted lines in FIG. 3 in order to emphasize the relation of
36' and 37' to the geometry FIG. 1. In particular, the points 41' and 42'
are images of the points labeled 32 and 33 in FIG. 1.
If desired, reconstructed waves 36,37 and 36',37' can be simultaneously
projected into converging lens 38. This can be effected by reopening
shutter 11 while shutter 13 is held open.
It is important to note that if the subject 31 does not change during the
process of recording the superposed pair of simple holograms, the
reconstructed object wave 36,37 has wavefronts that are, part from
holographic reconstruction noise and other small irregularities that
attend holographic reconstruction, of the same form and orientation as the
wavefronts of the reconstructed object wave 36',37'. Consequently the
wavefronts within pencils 39 and 40 have nearly the same form and
orientation as the wavefronts within pencils 39' and 40', and the points
41 and 42 at which pencils 39 and 40 are brought to focus by converging
lens 38 coincide nearly with the points 41' and 42' at which pencils 39'
and 40' are brought to focus. Thus if, when shutter 11 is open and shutter
13 is closed, a scanner be placed in a plane containing points 41 and 42,
the image that it acquires will be found to be in fair registration with
the image acquired with the scanner in the same position, but with shutter
11 closed and shutter 13 open. Correspondingly, if all but a single
element of the subject at 31 remain unchanged during the process of
recording the superposed pair of simple holograms, the image formed by
converging lens 38 when illuminated by reconstructed object wave 36,37
will be found in fairly good registration, apart from the image of the
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