Holography in White Light* OLOF BRYNGDAHL

IBM Research Laboratory, San Jose, California 95114 AND

ADOLF LOHMANN Department of Applied Physics and Information Science,

University of California, San Diego, La Jolla, California 92037 (Received 16 August 1969)

INDEX HEADINGS: Holography; Coherence; Interference.

In this paper we want to report on some experiments on hologram formation and reconstruction with a white-light source.

A hologram is a record of interference fringes. In polychromatic light, each wavelength λ produces its own elementary fringe system. If all these elementary fringe systems coincide in scale and position, a broad-band source can be tolerated. Under these cir­cumstances it will be possible to record on black-and-white film a hologram from a black-and-white object in natural white light, as emitted from a xenon-arc lamp, for example. Looking for such circumstances is the same as searching for a situation in which the degree of spatial coherence remains high even for a broad-band source.

The following two features, which will be discussed below, are useful for expanding the temporal-coherence tolerances: (1) The interference fringes on the hologram shall be achromatic fringes

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282 LETTERS TO THE EDITOR Vol. 60

FIG. 1. Recording of the hologram in natural white light. O: Object; G: grating; S: screen ; H : hologram.

and (2) the hologram shall be recorded in or close to the image plane of the object. Holograms with either the first feature1,2 or with the second 3 have been made previously. In 1966 Burch and Ennos* suggested a method that combines both features. Our own method,5 which has both features, is simpler but perhaps less general. Dyes and Ward6 have applied our technique successfully.

The purpose of this letter is to describe the two coherence-relax­ing features that are incorporated into our setup. We used it for recording holograms in natural white light on black-and-white and on color material.

The history of achromatic interference fringes7 goes back to Talbot. The most popular version of these achromatic fringes is nothing but the image of a grating, such as a Ronchi ruling. Ob­viously, the coherence requirements for the formation of a grating image are rather generous.8 A less direct but relevant way to explain the generation of these achromatic fringes is based on Abbe's theory of image formation. Suppose the light source is fairly small. When this source is imaged through the grating into the diffraction or aperture plane, we will see several source images, side by side, one for each grating diffraction order. These source images will exhibit lateral color dispersion, except in the zeroth order. Suppose now that only the + l s t and the —1st orders can pass through two holes in a screen. These two diffraction orders act as two mutually coherent sources, which form interference fringes in the so-called image plane of the grating. The period of those interference fringes depends on the wavelength and on the angle between the two interfering waves, of course. But the two grating-order sources are properly dispersed so that the ele­mentary fringes from all wavelengths coincide perfectly. Not only the + lst and —1st orders, but any pair of diffraction orders will produce perfect achromatic interference fringes.

These achromatic fringes have already been exploited several times in holography.1 Similar chromatic tolerances are feasible if the grating is replaced by a Fresnel zone plate9 or by a scatter plate.2 The essential feature is that the grating or its replacement acts as a beam splitter (division of wave amplitude) that is imaged into the plane of the hologram. Then, all rays emerging from one point on the beam splitter will be combined again on the hologram, irrespective of wavelength and direction. The path lengths through both arms of the interferometers thus formed ought to be equal. This is fairly easy to achieve if the arms share the lenses, mirrors, and other optical elements. In the language of interferometry, this means that the achromatic fringes are localized in the image plane of the grating. That is obviously the best location for the hologram.

FIG. 2. Reconstruction in natural white light.G: Grating; H : hologram; Z + 1, – 1: zeroth, plus first, minus first diffraction order of H.

FIG. 3. Holography in natural white light. (a) and (b): Holograms; (c) and (d): magnified sections of holograms; (e) and (f): reconstructed images; left: image holography; right: near-field holography.

To produce an achromatic hologram, it is also necessary for the diffraction pattern from the object to be fairly independent of λ in the plane of the hologram. This will be the case if the wave from the object happens to form an image on the hologram. An image is only a special case of a diffraction pattern. The necessary lenses have to be free from chromatic aberration, of course. It is well known that the chromatic tolerences for these so-called image holograms3 are rather generous. The chromatic tolerances become particularly generous if the angle between object wave and refer­ence wave varies with λ in such a manner that the interference fringes have a λ-independent period. The angular dispersion necessary for this to happen is the same as occurs in grating diffraction, as already described.

Now we understand why the two features (1) achromatic fringes (=grating image) and (2) image holography are favorable for getting generous tolerances for the temporal coherence. We must arrange for these two features to be compatible. The problem is that the two features require that both the grating and the object be imaged onto the hologram. This implies that object 0 and grating G are in close contact in the same plane (Fig. 1). If the object has finite depth, the grating should be very close to it or possibly in the middle of it. In the diffraction plane midway be­tween the object 0 and the hologram H, we may observe several

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FIG. 4. 3D holography in natural white light. (a) Hologram; (b) and (c) : reconstructions in different planes. The height of the numbers was 2.5 mm and the two planes were 70 mm apart.

grating diffraction orders, each surrounded by the Fraunhofer diffraction pattern of the object. These diffraction patterns will be clearly separated if the grating constant is finer than the finest object details. We select as the object wave, for example, the + lst diffraction order by means of a window in a screen S. The reference wave Z is created by a small pinhole in the center of the zeroth diffraction order. This trick for generating a reference wave behind the object was invented by Räntsch10 in connection with inter­ference microscopy. Since then, this trick has been used several times in holography.5,6,11 To obtain the proper angular dispersion between the object wave and the reference wave, we can in principle select any two grating orders. But the zeroth order is particularly desirable as the reference wave because the center of the Fraunhofer diffraction pattern coincides for all wavelengths. According to the analysis of Leith and Upatnieks,12 it would be somewhat better to let the zeroth order carry the object wave and the + lst order provide the reference wave. I t might be possible to follow this suggestion if Hg light were used, but with the wide spectrum from the xenon arc in our setup, we have to use the zeroth order to illuminate the pinhole for the reference wave. In

reconstruction (Fig. 2), we can use white light again, but we have to predisperse it with the same grating G before the light hits the hologram H. This predispersion precompensates the dispersion in the + 1st order of the grating-like hologram. The unwanted direct light (Z) and the light (—1) forming the twin image can be eliminated by a proper screen in a secondary diffraction plane to the right of H in Fig. 2.

In our first experiment, we used a plane black-and-white object in contact with a Ronchi ruling as grating. The light source was a xenon-arc lamp, which could be used also in reconstruction. The object was sharply focused onto the hologram [Fig. 3(a)] or slightly defocused [Fig. 3(b)]. Figures 3(c) and (d) show magni­fied sections of the holograms in Figs. 3(a) and (b). The recon­structed images [Figs. 3 (e) and (f) ] were satisfactory in both cases. Another hologram [Fig. 4 (a) ] made from an object consisting of two black-and-white transparencies at a finite distance behind each other yielded a reconstructed image of similar quality, clearly exhibiting the two different depth positions by change of focus [see Figs. 4(b) and (c)]. We also recorded holograms, again in xenon-arc light, on Agfa Scientia color material which has rather good resolution. The object consisted of pieces of Wratten color filters at different depth positions. A 3D effect was clearly notice­able, but the color reproduction was not quite faithful at sharp edges of the object. At the time of the experiments, we suspected that these color defects were due to the limited dynamic range or to overlap of the three color bands or to the nonlinearities of the color film. We did not pursue this problem because we had no control over the photographic process. However, other effects might have been the causes of these color edge defects. For example, the finite size of the pinhole for the reference wave might have created a halo effect similar to that known from phase con­trast13 in which the finite size of the 90°-phase plate is responsible for a halo at sharp edges in the image. Recently, Nassenstein and Eggers14 demonstrated that the anomalous dispersion of color film can be important for holography. This effect might have also influenced our results. Further experiments, possibly with a krypton laser, together with a theoretical study, are needed in order to find out how much the chromatic tolerances can be relaxed in holography.

We appreciate A. Nafarrate's experimental contributions.

* Presented at the 1967 Fall meeting of the Optical Society [J. Opt. Soc. Am. 57, 1412A (1967)], and at the NEREM Conference in Boston, 1967.

1 E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963); 57, 975 (1967); W. H. Carter, P. D. Engeling, and A. A. Dougal, IEEE J. Quantum Electron. QE-2, 44 (1966); R. E. Brooks, L. O. Hefiinger, and R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966); M. De and L. Sévigny, Appl. Phys. Letters 10, 78 (1967). 2 E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964) ; J. M. Burch, J. W. Gates, R. G. N. Hall, and L. H. Tanner, Nature 212, 1347 (1966); L. O. Hefiinger, R. F. Wuerker, and R. E. Brooks. J. Appl. Phys. 37, 642 (1966); J. W. C. Gates, J. Phys. E1, 989 (1968); L. H. Tanner, J. Phys. E2, 288 (1969).

3 J. M. Burch and A. E. Ennos, J. Opt. Soc. Am. 56, 541A (1966); W. H. Carter, P. D. Engeling, and A. A. Dougal, IEEE J. Quantum Electron. QE-2, 44 (1966); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966); R. F. van Ligten and H. Osterberg, Nature 211, 282 (1966); A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 56, 537A (1966); L. Rosen, Appl. Phys. Letters 9, 337 (1966); G. W. Stroke, Phys. Letters 23, 325 (1966); W. E. Kock, L. Rosen, and G. W. Stroke, Proc. IEEE 55, 80 (1967); L. Rosen, Proc. IEEE 55, 79 (1967); L. Rosen and W. Clark, Appl. Phys. Letters 10, 140 (1967); O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968).

4 J. M. Burch and A. E. Ennos. J. Opt. Soc. Am. 56, 541A (1966). 5 O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 57, 1412A (1967); IEEE NEREM Record 9, 154 (1967). 6 W. A. Dyes and J. H. Ward, J. Opt. Soc. Am. 58, 723A (1968); IEEE NEREM Record 10, 116 (1968).

' F. Talbot, Phil. Mag. (3) 9, 401 (1836); E. Hurion, J. de Phys. (2) 1, 303 (1882); Lord Rayleigh, Phil. Mag. (5) 28, 86 (1898); R. W. Ditchburn, Light (Blackie & Son, Ltd., London, 1963), 2nd ed., pp. 148-152. 8 A. Lohmann, Opt. Acta 9. 1 (1962). 9 M. Kato and T. Suzuki, J. Opt. Soc. Am. 59, 303 (1969). 10 K. Räntsch, German Patent No. 822 023 (1949). 11 A. Lohmann, Optik 11, 478 (1954); R. Fleischmann and A. Lohmann, Z. Physik 159. 348 (1960); W. D. Montgomery, Appl. Opt. 7, 83 (1968); O. Bryngdahl and A. Lohmann, J. Opt. Soc. Am. 58, 141 (1968) ; R. L. Lamberts, J. Opt. Soc. Am. 59, 501A (1969); Ph.D. thesis, U. of Rochester, 1969.

12 E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 57, 975 (1967). 13 E. Menzel, Optik 5, 385 (1949); H. Wolter, Naturwiss. 37, 272 (1950). 14 H. Nassenstein and J. Eggers, Phys. Letters 28A, 141 (1968).