SPECTROSCOPIC ORIGINS AND APPLICATIONS OF WHITE-LIGHT REFLECTION HOLOGRAPHY

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SPECTROSCOPIC ORIGINS AND APPLICATIONS

OF WHITE-LIGHT REFLECTION HOLOGRAPHY

George Storke

To cite this version:

George Storke. SPECTROSCOPIC ORIGINS AND APPLICATIONS OF WHITE-LIGHT

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JOURNAL DE PHYSIQUE Colloque C 2, supplkment au no 3-4, Tome 28, mars-avril1967, page C 2

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196

SPECTROSCOPIC ORIGINS AND APPLICATIONS

OF WHITE-LIGHT REFLECTION HOLOGRAPHY

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The University of Michigan Ann Arbor, Michigan, U. S. A.

Manuscript submitted 25 April 1966

Rksumk. - Des dkveloppements spectroscopiques et interfkrometriques sont a l'origine de nou- veaux dkveloppements en imagerie holographique ( 2 ) qui, a son tour, s'est trouvke avoir d'impor- tantes applications en spectroscopie et mEme en interfkromktrie. Nous dkcrivons quelques travaux inkdits, notamment ceux qui ont trait aux rkcentes expkriences sur les hologrammes par rkflexion en lumiere blanche de G. W. Stroke et A. E. Labeyrie.

Abstract. - Spectroscopic and interferometric foundations are basic to the new developments in holographic imaging (3) which, in turn, have been found to have important applications to

spectroscopy and indeed to interferometry. Some previously unpublished work is described, notably that related to the recent development of the (( white-light reflection hologram n by G. W. Stroke

and A. E. Labeyrie.

Introduction. - Recent advances in holography show that the field of two-step diffraction imaging has much wider and, perhaps, much more sophisti- cated ramifications in physical optics, than might have appeared from its original name of (( wavefront- reconstruction imaging )) [I-31 or, indeed, more recently, from the name of (( laser photography )) and from the spectacular achievements of (( three-dimensional photography )), which were first reported in 1964 and 1965 by E. N. Leith, J. Upatnieks and G . W. Stroke [4-61. New applications to microscopy, (( intensity interferometry )), image-synthesis and filtering, as well as to (( aposteriori image compensation )) and spectroscopy have already been demonstrated,

(1) Parts of this work were first communicated privately to

the National Science Foundation, Washington, D. C . (October 1965 to January 1966). Parts were also publicly presented in a number of places, among which the meeting of the Optical Society of America,

arch

16, 1966.

(2) Pour une documentation gbnkrale, cf. G. W. STROKE An Introduction to coherent Optics and Holography 1) (Ac. Press.

Inc. New York et London 1966), 270 pages y compris la reproduction de trois articles originaux de Gabor (( Image par recons-

truction de front d'onde )).

(3) For a general background, see e. g. G. W. Stroke, ((An Introduction to Coherent Optics and Holography )) (Academic

Press, Inc. New York and London, 1966) [270 pages, including reprints of the three origina ; (( wavefront-reconstruction ima-

ging )) papers by D. Gabor].

notably in the work by the author and his students, mostly in only the last few months. These new advances in holography are based, to a large extent, on the principles of (( Fourier-transform holography )) first proposed by G. W. Stroke in 1964 [4], and since developed by him and his students, as well as by others.

A particular simplification in holography, both

theoretical and experimental, is characteristic of Fourier-transform holography, as compared to the earlier forms of wavefront-reconstruction imaging, including the Fresnel holography with so-called (( carrier )) waves, such as that first described by Leith and Upatnieks [6] and others [4, 51. Unlike the (( Fres- nel-transform )) holograms, which have no inversion in the mathematical sense, and suffer from aberra- tions, (( Fourier-transform )) holograms can be inver- ted, both physically and mathematically, by a second Fourier transformation, for instance by illuminating the hologram with a plane wave, and by recording the two symmetrical side-band images in the focal plane of a well-corrected lens. Some of the physical charac- teristics of Fourier-transform holograms can be recognized, by noting that Fourier-transform holograms are obtained whenever a superposition of sinu- soIda1 (( interference gratings )), one per object point, or wavelength, can be recorded.

I t has now been shown by Stroke and his students that Fourier-transform holograms can be recorded

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SPECTROSCOPIC ORIGINS AND APPLICATIONS C 2 - 197 both with and without lenses, and indeed not only

with spherical (respectively plane) wavefronts, originating from a (( point )) source, but also with (( reference )) wavefronts originating from extended sources, and indeed also in non-coherent light !

A posteriori compensation for the resolution (( loss )) which would result from the uncompensated use of an extended source, in place of the point source, forms only one example of the possible ramifications of Fourier-transform holography [7, 81. Another example is found in the newly demonstrated principle of holographic Fourier transform spectroscopy [9], which yields spectra directly; without computing, from holograms recorded in interferometers with comple- tely stationary elements.

In contrast with a widely held belief, the author and his students have recently demonstrated 1121 that the original (( Gabor )> (c in line t ) scheme of holographic recording yields perfectly separable cc twin 1)

images, without any phase-recording problems. The more recently introduced c t off-axis )) schemes [13] using prisms or equivalent off-set lenses [notably in spatial filtering (Leith and Upatnieks, Vander Lugt)], respectively mirrors [(Stroke) [4, 5, 141, notably in 3-dimensional lensless photography], have advantages arising from experimental rather than from any basic considerations.

Important advances in holography have been introduced recently by many authors (see, e. g. references in ref. 14). Here we wish to note more particularly the following advances introduced since 1963,

black-and-white holograms upon illumination (in the reconstruction) with ordinary white light [15] [16].

6. The (( equivalence )) between the new method of holography with extended sources [7, 81 and the

crystallographic equivalent of the ct heavy atom ))

technique, as used notably in protein crystal synthesis was formally demonstrated in a recent article in Nature [17] (in collaboration with Prof. M. G. Ross- mann and associates), following previous independent indications of this analogy by W. L. Bragg [IS] and by Stroke 1191. This formal cc equivalence )> may in

particular be taken as a form of (( existence )) proof for the solution of the (( phase problem )) in crystallo- graphy with the aid of holographic principles on which the author has been working for the last several years [14] [in part now in collaboration with Prof. M. G. Rossmann].

The ramifications of these and other advances may best be interpreted by the list of references given, with the indicative titles, including the additional references [20-271.

In what follows we shall particularly single out some previously unpublished theoretical and experimental details about our new method of (( white-ligth reflection holography D. [Additional details may be found

in the unpublished (( these de dipl6me )) of A. Labey- rie reporting aspects of our work carried out under the direction of the author].

Spectroscopic foundation of N white-light reflection

holography D.

-

The arrangement of figure 1 which

and which are particularly relevant to our work. 1. The formalism of Fourier-transform holography, [4,5, 141 and several extensions, including (( lensless )) Fourier-transform holograms [21].

2. Holography with (( extended )) reference sources, including applications to image coding and to cc a posteriori )) resolution-retrieving (( compensation [7]

P I -

3. Holography with incoherent light [24] including applications to Fourier-transform cc spectrography )) (without computing) [9] and to image formation [14]. 4. The principle of double-exposed and of multiple-

exposed holograms (introduced jointly with Professor D. Gabor [lo]) and its applications to image-synthesis (complex amplitude addition and subtraction), image- coding and decoding and to interferometry [25] [26]. 5. A new type of reflection hologram [15] using a Lippmann-Bragg diffraction principle in cc thick )) holographic emulsions, and extending work by Yu. N. Denisyuk to obtain cc white-light reflection holograms )) capable of yielding color images from the

&

OBJECT

RECONSTRUCTED

IMAGE

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C 2

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198 GEORGE W. STROKE

obtained by illuminating the black-and-white reflection hologram with ordinary white light (from a 300 watt zirconium arc) as recorded on Kodachrome I1 film with a Retina reflex 35 mm camera : it should be clear that the limited depth of field of the camera does not permit to show the holographic perfection of the three-dimensional reconstruction in a single view. The hologram was recorded in 6 328

A

light from a 60- milliwatt Model 125 Spectra Physics cw laser on a commercially obtained Kodak 649 F plate, having an emulsion thickness estimated to be some 5 microns :

the emulsion was artificially swelled (perhaps by a factor of 5 to 10 times) by immersion in water (maintained by covering the plate with a cover glass), and the reconstruction of the image, as well as the recording, were thus carried out ct in immersion )). Very satisfactory reconstruction of three-dimensional objects were obtained without immersion : figure 4 shows a white-light reconstruction thus obtained of a model of a diamond molecule, and figure 5 shows an enlarged view of a section of the model obtained, for comparison, using 6 328

A

laser light.

An elementary theory of the recording and reconstruction processes may be given as follows [for background and details see ref. 151 :

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SPECTROSCOPIC ORIGINS A N D APPLICATIONS

FIG. 5.

be neglected, and that the fields throughout the depth of the emulsion may be written as

Ao(x, Y , 2, t ) and A,(x, Y , 2, t )

respectively.

By interference, the resulting complex amplitude of the field throughout the depth of the emulsion is A(x7 Y , z , t ) = Ao(x, Y , 2 , t )

+ A,(K

Y , 2 , t ) (1)

The corresponding intensity recorded in the emulsion is

The experiments described above show that the hologram described by eqn 3 will tend to behave as a Bragg-like crystal with a cc scattering power )) given by eqn 3. [For the crystallographic background and terminology, see. e. g. A. Guinier, ref. [29]. This may be understood, in a simple way, as we first noted in our ref. 15, for the case where both A, and A, are plane waves, incident onto the plate, from opposite directions, along the z-axis (see figure 1). In that case, the hologram intensity may be written in the form (assuming A, = 1).

where k = 2 n/A and where A, =

I

A, [ expicp (x, y), with 1 being the recording laser wavelength.

For the purpose of discussing the theory of the reconstruction process, one may at first discuss the reconstruction in its general form, remembering that crystallographic considerations require us to associate with eqn 3 also Bragg's law (see figure la)

where we recall that the elementary (( Bragg )) interference planes (e. g. those corresponding to the recording with the two plane waves) are cc parallel )) to the plane bisecting the directions of incidence of the beams A, and A,, and where d is the spacing of these elementary planes. We may also recall that the spacing d is related to the (( angle )) a between the two beams (see figure la) by the equation

d = A

2 sin (42)

so that for the case of near-normal incidence used in the recording of (( reflection )) holograms the spacing d is approximately equal to A/2. As usual, in crystallographic terms, the angle 8 refers to the angle of the incident (and ct reflected )) or ct diffracted ))) beams

with the Bragg planes, as shown.

Under these conditions, and bearing in mind the spectral and angular selectivity of the diffracted waves, as determined by Bragg's law of eqn 5., illumination of the hologram given by eqn 3 may be considered as corresponding to an illumination with a wave A,, provided (and this is essential) that the geometrical shape of the white-light (or indeed monochromatic) wavefront used in the reconstruction is the same as the shape of the wavefront used in the recording, and provided also that the wavefront used in the reconstruction is incident along the same direction relative to the Bragg planes as the recording wavefront A,.

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C 2

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200 GEORGE W. STROKE Under the holographic conditions (see e. g. ref. [14])

where A, A: = 1 (which would be the case when A, is a plane wave, or a suitably curved wave), eqn 7 may be interpreted as immediately showing that the third term ( A , A:) A, corresponds to the desired (c monochromatic )) reconstruction of the object, while the other terms correspond to waves propagating in the opposite direction from the (c reconstructed 1) wave A,.

Additional details of both the recording and the reconstruction processes may be made clear in discussing the recording of (( multi-color )) holograms, such as those first described in our ref. 16. We now give some of the additional details which we had obtained in view of that work and which were basic to that work, but which could not be incorporated into the short brief n which appeared in the April issue of the Bell System Technical Journal.

We may recall that laser light had generally been considered as essential in holography heretofore, before the cc white-light )) holography method [15]

just described, not only in the recording of holograms, but indeed also in the reconstruction of holograms, for instance in the first method of color holography described by Pennington and Lin [35] [in which two lasers, a 6 328

A

He-Ne laser and a 4 880 Argon-ion laser were used in the reconstruction, as well as in the recording, in a scheme of which the geometricd layout is illustrated in figure 6a]. Because it immediately appeared clear to us that our method of (( white- light )) holography with a single-laser recording could be extended to (c multicolor white-light )) holography using, in the recording for example the same two lasers as used in the work by Lin and Pennington, the multicolor work was carried out as a part of a joint effort [16] and permitted to verify that the basic principles of which we now give some additional details.

RECORDING PROCESS.

-

The physical principles of

our method of white-light multi-color holography are quite comparable to our method described for single-color white-light reconstruction. In essence, the multi-color reflection hologram is simply an intensity superposition (in the same emulsion) of two (or more) singlealor reflection holograms of the type described above and in our ref. 1151. For each of the component colors, the color selection in the reconstruction with white light may be attributed to a multi-layer interference effect and a (( high-dispersion )) spectral image separation (see figure 61, resulting from a ct stratification )) of the emulsion caused, in the recording, by the interference between the reference field and the field scattered by the object,

very much like in the original Lippmann color photography method 1301 described in 1894, in which images rather than holograms, as in our case, were recorded by the stationary interference field formed in the emulsion. The spacing of the stratifications (along the z-direction) in the recording is 4 2 in case where both fields are plane waves incident normally onto the plate. In the case of scattering by an arbitrary object (Fig. la), the multilayer stratification maxima are locally dis- placed along r, according to the local values of the phase of the resultant scattered electric-field vector (as measured with respect to the reference field). In addition, the resultant local intensity modulation of the processed photographic emulsion (in depth, say along z, for a given x-coordinate in the plane of the hologram) is determined by the resultant magnitude of the scattered field vector. For the case when the hologram is illuminated in several wavelengths (either simultaneously or indeed successively), the resultant intensity in the emulsion is simply the sum of the intensities given by eqn 3 for the single-color holo- gram component, under usual holographic conditions

[14]. We may note that the elementary stratifications

(for the case of normal incidence, used to simplify the discussion) will have a spacing dA = R/2, so that the ratio

d,/A

of the stratifications to wavelength will remain constant, i. e.

RECONSTRUCTION. - In the reconstruction (Fig. 1 b)

illumination of the hologram with ordinary white light (e. g. electric light, sun, zirconium arc, etc.) from the reference beam side produces from each single-color hologram component one spectrally selected cc single-color )) reconstructed wave, capable of forming an image by wavefront reconstruction, according to the principles first described by Gabor [I]. Moreover, because of Bragg's law, which we may write as

A sin 8,

+

sin 0, = m

-

d,

where

Oi

and 0, are the angles of (( incidence and of (( reflection >) (in the crystallographic sense), and m and integer, it follows from eqn. 8 and eqn. 9, that all of the reconstructed waves of different colors will be diffracted (i. e. c t reflected u), upon illumination in white light from a given angle Bi, in the same direction 0,, which is essential for the reconstruction of

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SPECTROSCOPIC ORIGINS AND APPLICATIONS C 2

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201

same angle Oi as used for the reference beam in the recording is the usual condition for good color reconstruction).

Because of the (( spectroscopic )) dispersion equation dO,/d, rzl 2 tan %,/A resulting by differentiation from eqn. 9 (see also ref. [36]), it is seen that each elementary layer d, of the (( high-dispersion )) white- light reflection holograms (Fig. 6) will only reflect, in the desired direction, its own characteristic color

A

[while ct dispersing )) the remaining ct unwanted )) colors from the white-light source out of the field of view]. [Note that the (( low dispersion )) holograms, on the other hand, do not permit white-light recons-

truction (see figure 6)] but they are suitable as (( trans- mission )) holograms.

LOW-DISPERSION

1

H IGH-DISPERSION

REFERENCE

Fro. 6.

In summary, we may say that the color reconstruction from the black-and-white hologram results from a superposition of ct single-color )) reconstructed waves, in which 1) the local phase modulation is determined by the local displacements of the reflecting multilayer stratifications, 2) the local amplitude modulation is determined by the local intensity modulation of the hologram, and 3) the color selection is obtained by Bragg diffraction from the grating-like stratifications of each of the component (( single- color )) holograms.

Conclusion. - It should be clear from the preceding discussion that spectroscopic and interferometric principles, as well as grating-diffraction principles are fundamentally involved both in the theory and in the experimental aspects of holography, and notably in (( multi-color white-light reflection holography )). Additional background regarding grating diffraction theory may be found in ref. [36].

We may summarize the status of our work perhaps as follows :

Two of the new methods of holography recently introduced by the author with his students have already found to be based on spectroscopic considerations and to have spectroscopic applications.

1. A new type of (( white-light volume reflection hologram )), based on spectroscopic considerations and a Lippmann-Bragg diffraction effect has just been attained (Stroke and Labeyrie 1151) : it has permitted us to obtain color images of objects from

black-and-white holograms (recorded in laser light) upon illumination of the hologram with ordinary white light (with a suitable wavefront shape). Exten-

sions of our method of (( white-light reflection holography )) to multi-color imaging has also been success- ful [16], and so has been the attainment of holographi- cally recorded (( Bragg )) diffraction gratings, having very high dispersions (characteristic of lattice spacings on the order of 3,000 fringes per millimeter) and appli- cable to spectroscopy.

2. A holographic method of Fourier-transform spectrography (Stroke and Funkhouser [9]) which we have previously described has permitted us to record Fourier-transform holograms of the spectrum (e. g. of mercury) photographically, in a beam-splitting inter- ferometer having no moving elements and to recons- truct the spectrum by a second optical Fourier trans-

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C 2

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202 GEORGE W. STROKE incorrect marking of the spectrum lines, as reported

i n ref. [9] and [14] has now been corrected).

Acknowledgement. - The author is pleased t o acknowledge fruitful discussions and assistance of his several students, and may fruitful discussions with a n d suggestions from Professor Dennis Gabor.

Note added in proof : We have recently verified that jxed Kodak 649 F emulsions, used for our method of (( Lippmann- Bragg reflection holography )) [IS] [16] could be (( re-swollen )) to their original recording thickness, as required for faithful color reconstruction, by immersion in an aqeous 4 to 5 per cent solution of triethanolamine (available from Union Car- bide) according to the method described by L. H. Lin,

R. J. Collier and C . V. Lo Bianco [J. Opt. Soc. Amer. 56,1414 (1966) Abstract ; to appear in AppIied Optics, Vol. 6 (1967)l.

[I] GABOR (D.), (( A New Microscopic Principale )), Nature, 1948, 161, 777.

121 GABOR (D.), (( Microscopy by Reconstructed Wave- fronts, I. )), Proc. Roy. Soc. (London), 1949- A 197, 454.

f.31 GABOR (D.), (( Microscopy by Reconstructed Wave- fronts, 11. )), Proc. Roy. Soc. (London), 1951, B 64, 449.

[4] STROKE (G. W.), cc An Introduction to Optics of Coherent and Non-Coherent Electromagnetic Radiations D, 1st edition (The University of Mi- chigan, May 1964), 77 pages.

(51 STROKE (G. W.), ct Theoretical and Experimental Foundations of Optical Holography (Wavefront- Reconstruction Imaging) )) in Optical Information Processing, J. T. Tippett et ali, ed. (M. I. T. Press 1965), presented 9 November 1964.

161 LEITH (E. N.) and UPATNIEKS (J.), ct Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects )I, J. Opt. Soc. Amer.

1964, 5 4 , 295.

171 STROKE (G. W.), RESTRICK (R.), FUNKHOUSER (A.) and BRUMM (D.), (( Resolution-Retrieving Com- pensation of Source Effects by Correlative Reconstruction in High-Resolution Holography )), Physics Lett., 1965, 18, 274.

[8] STROKE (G. W.), RESTRICK (R.), FUNKHOUSER (A.) and BRUMM (D.), (( Resolution-Retrieving Com- pensation of Source Effects in Holography with Extended Sources )), Appl. Phys. Lett., 15 sept. 1965, 7, No 6.

[9] STROKE (G. W.) and FUNKHOUSER (A.), (( Fourier- Transform Spectroscopy using Holographic Ima- ging without Computing and with Stationary Interferometers D, Physics Lett., 1965, 16, 272. [lo] GABOR (D.), STROKE (G. W.), RESTRICK (R.), FUN-

KHOUSER (A.) and BRUMM (D.), (( Optical Image Synthesis (Complex Amplitude Addition and Subtraction) by Holographic Fourier Transfor- mation D. Physics Lett., 1965, 18, 116.

[ I l l for additional background, see e. g. STROKE (G. W.) and FALCONER (D. G.), ((Attainment of High Resolutions in Wavefront-Reconstruction-Ima- ging D, Physics Lett., 1964, 13, 306.

[I21 STROKE (G. W.), BRUMM (D.), FUNKHOUSER (A.), LABEYRIE (A.) and RESTRICK (R. C.), (( On the absence of phase-recording or (( twin-image )) separation problems in (( Gabor 1) (in-line) holo-

graphy )), British, J. Appl. Physics, April 1966, 17, 497-500

(+

2 plates), communicated by D. Gabor.

[I31 LEITH (E. N.) and UPATNIEKS (J.), (( Wavefront reconstruction photography )), Physics Today, August 1965, 18, 26-32.

[14] STROKE (G. W.), c( An Introduction to Coherent Optics and Holography (Academic Press, New York and London, 1966) [xii

+

270 pages ;

including reprints of three original (( wavefront- reconstruction imaging papers by D. Gabor]. [15] STROKE (G. W.) and LABEYRIE (A. E.), (( White-Light Reconstruction of Holographic Images using the Lippmann-Bragg Diffraction Effect D, Physics Letters, 1966, 20, 368-370.

[I61 LIN (L. H.), PENNINGTON (K. S.), STROKE (G. W.) and LABEYRIE (A. E.), (( Multicolor Holographic Image Reconstruction with White-Light Illumi- nation )), Bell System Techn. Jour., 1966, XLV (NO 4).

[I71 TOLLIN (P.), MAIN (P.), ROSSMANN (M. G.), STROKE (G. W.) and RESTRICK (R. C.), c( Holography and its Crystallographic Equivalent B, Nature, 1966, 209, 603-604.

[I81 BRAGG (W. L.), Nature, 1950, 166, 399.

[19] STROKE (G. W.), ct Lensless Photography )), Intern. Sci. Technology, 1965, No 41, pages 52-60. [20] STROKE (G. W.) and FALCONER (D. G.), (( Attainment

of High Resolutions in Holography by Multi- directional Illumination and Moving Scatterers )), Physics Letters, 1965, 16, 272-274.

[21] STROKE (G. W.), (( Lensless Fourier-transform Method for Optical Holography )), Appl. Phys. Letters, 1965, 6, 201-203.

[22] STROKE (G. W.), (( Attainment of High Resolutions in Image-Forming X-ray Microscopy with Lens- less Fourier-transform Holograms and Correla- tive Source-Effect Compensation )), in Procee- dings of the IVth X-Ray Congress (Paris, Septem- ber 7-10, 1965) [Hermann, Paris, in print]. 1231 STROKE (G. W.), BRUMM (D.) and FUNKHOUSER (A.),

(( Three-dimensional Holography with (( Lensless )) Fourier-transform Holograms and Coarse PIN Polaroid Film )), J. Opt. Soc. Amer., 1965, 55, 1327-1328.

[24] STROKE (G. W.) and RESTRICK (R.), (( Holography with Spatially Non-Coherent Light D, Appl. Phys. Letters, 1965, 7, 229-231.

LAB E STROKE

(G. W.) and LABEYRIE (A.), (( Two-Beam Interferometry by Successive Recording of Intensities in a Single Hologram B, Appl. Physics Letters, 1966, 8, 42-44.

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SPECTROSCOPIC ORIGINS AND APPLICATIONS C 2

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203 [27] GABOR (D.) and STROKE (G. W.), BRUMM (D.),

FUNKHOUSER (A.) and LABEYRIE (A.), (( Recons- truction of Phase Objets by Holography u, Nature, 1965, 208, 1159-1162.

[28] LABEYRIE ( A . Dipl6me #Etudes Sup6rieures (Faculti? des Sciences de Paris, 1966, unpublished), (( Quelques nouvelles mkthodes en holographie )) (travail effectui? a l'universiti? de Michigan, Electro-Optical Sciences Labo- ratory, sous la direction du Professeur George W. Stroke).

[29] GUINIER (A.), (( X-Ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies 1) (W. H. Freeman & Co., San Francisco and London, 1963), 378 pages.

[30] LIPPMANN (G.), (( Sur la thCorie de la Photographie des Couleurs Simples et Compostes par la MB- thode Interfkrentielle n, J. Physique 1894, 3 , 97- 107.

[31] IVES (H. E.), (( An Experimental Study of the Lipp-

mann Color Photograph D, Astrophys. J., 1908, 325-352.

[32] DENISYUK (Yu. N.), (( Photographic Reconstruction of the Optical Properties of an Object in its Own Scattered Field D, Soviet Physics-Doklady, Decem- ber 1962, 7, No 6, English translation pages 543-

545.

1331 DENISYUK (Yu. N.), ((On the Reproduction of the Optical Properties of an Object by the Wave Field of its Scattered Radiation )), Optics and Spectroscopy, 1963, 15, 279-284.

[34] DENISWK (Yu. N.), ((On the Reproduction of the Optical Properties of an Object by the Wave Field of its Scattered Radiation I1 )) (?) (Received 19 July 1963).

[35] PENNINGTON (K. S.) and LIN (L. H.), (( Multicolor Wavefront Reconstruction D, Applied Physics Letter, 1965, 7, 56-57.