High-efficiency in-line multiple imaging by means of multiple phase holograms

Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

I The Self-Imaging Phenomenon and its Applications

Coded aperture imaging in high energy astronomy represents an important technical advance in instrumentation over the full energy range from X- to γ-rays and is playing a unique role in those spectral ranges where other techniques become ineffective or impracticable due to limitations connected to the physics of interactions of photons with matter. The theory underlying this method of indirect imaging is of strong relevance both in design optimization of new instruments and in the data analysis process. The coded aperture imaging method is herein reviewed with emphasis on topics of mainly practical interest along with a description of already developed and forthcoming implementations.

Coded aperture imaging in X- and gamma-ray astronomy

Binary phase elements in photoresist have been implemented which transform a uniform beam of light into an array of output light spots by means of the fractional Talbot effect. Arrays of more than 30 x 30 light spots with varying spot shapes have been achieved with compression ratios of up to 1:9.

Making an array illuminator based on the Talbot effect

Three-dimensional display techniques can be classified as binocular and autostereoscopic types, still and animated types, nontransmitted and transmitted types, and nonholographic and holographic types. This paper deals mainly with autostereoscopic still nontransmitted techniques. Holographic and nonholographic tecniques are described on about equal footing. For the sake of brevity, emphasis is placed upon those techniques that appeared in the past several years. However, some old techniques of historical and/or practical importance are also mentioned because rather few textbooks are available in this field. In the final part, state of the art of three-dimensional display for animated and transmitted images (three-dimensional television) is described. Speculations on the direction of the development are presented.

Three-dimensional displays

Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging

Multiple imaging devices are capable of producing simultaneously a number of images of one object. Several methods have been suggested to realize such an optical system. They make use of the imaging properties of a fly's-eye lens or of an array of pinholes, or they utilize birefringence. More recently, multiple image generation has been achieved by forming the convolution of the object with an array of δ functions in an ordinary spatial filtering arrangement. The complex filter is realized by the Fourier transform hologram of the cor­ responding array of point sources. The second Fourier trans­ form lens, however, has to transmit more than twice the full information of the multiplied image array. Since the most im­ portant application of multiple imaging is semiconductor device fabrication as has been discussed earlier, the resolving power has to be very high, so that up to now no lenses are available that are capable of imaging the multiple array of images of a usual etching mask. I t is for this reason that to date, images of etching masks are transferred to the semiconductor wafer by contact printing. In this communication, we propose to use an arrangement dif­ ferent from that in Ref. 4, such that the multiplied images do not have to be transmitted by any additional optical component. Par t of this communication has already been mentioned in a paper presented at a holography meeting organized by the Battelle Institute at Frankfurt /M, Germany, on 2 December 1967. The principle of operation is illustrated by Fig. 1. The hologram of the array of point sources is produced in the usual way by recording the interference pattern caused by coherent superposition of the spherical waves emanating from the ref­ erence point and the signal points the spatial positions of which correspond to the desired positions of the images to be formed. Multiple imaging is then performed in the reconstruction process by replacing the reference point source by the real image to be multiplied. This can be achieved in the well-known way by means of a lens that images the object through the hologram into the surrounding of the reference point. In this case, an additional real image of the object is formed in the surrounding of each signal point. The behavior of the hologram can be easily understood by thinking of a point hologram as of a generalized Fresnel zone plate with its well-known lenslike properties. Indeed, this hologram of the distribution of point sources may be considered as some special kind of a fly's-eye lens, in which the lenses are replaced by Fresnel zone plates. But there is a rather important difference. Contrary to lenses, the single point holograms may overlap completely without disturbing each other. For this reason, the aperture of each point hologram determining the diffraction limited size of the image point can be made equal to the aperture of the hologram of the whole point distribution provided that suitable spherical waves are used in the recording process. There is no relationship between the diameter of this aperture and the distances of the images to be formed. Limitations to the resolution of this multiple imaging device are mainly introduced by aberrations. In the special case of small plane objects, which are of dominant interest in semicon-

Multiple imaging by means of point holograms.

Two methods have recently been suggested for the generation of stereoscopic images of x-ray objects by producing holograms from a sequence of x-ray photographs of different perspective. Redman et al. superimposed time sequentially the focused x-ray images on the hologram, which between exposures was rotated by the angle describing successive viewing directions. Since in the recording process the reference beam is rotated by the same amount, the hologram being illuminated with one reference wave reconstructs the sequence of images in the vicinity of the axis of rotation. They seem to be illuminated from different directions by a corresponding number of light sources. By means of an additional converging lens these virtual sources are imaged on to the pupil of the eye of the observer, who will see a succession of views of corresponding perspective of the object, when he moves his head. To our knowledge this method is a special application of the more general principle of image separation by pupil separation in multiple exposure holography as suggested by van Ligten andLawton. A less sophisticated arrangement was reported by Kasahara et al. They recorded a sequence of spatially separated Fresnel holograms, each of which contained the information of the x-ray image viewed from a different position. In this experiment, however, the photographic plate recording the hologram was moved behind a diaphragm containing the aperture. This has several disadvantages: (1) the reconstructed virtual image seems to be pseudoscopic; (2) the conjugate complex wavefronts displaying the real images cannot be utilized, since these individual images are superimposed in a wrong way; (3) for plane holograms a plane reference wavefront has to be used. We want to draw attention to the point that it is more advantageous to compose the hologram of the different views of the ob-

3-d display of x-ray images by means of holography.

In 1968, Dicke had suggested that multiple-pinhole camera systems would have significant advantages concerning the SNR in X-ray and gamma-ray astronomy if the multiple images could be somehow synthesized into a single image. The practical development of an image-synthesis method based on these suggestions is discussed. A formulation of the SNR gain theory which is particularly suited for dealing with the proposal by Dicke is considered. It is found that the SNR gain is by no means uniform in all X-ray astronomy applications.

X-Ray and gamma-Ray Imaging with Multiple-Pinhole Cameras Using a posteriori Image Synthesis.

A new type of hologram capable of multiple imaging or reconstructing point images is proposed. These holograms are produced by using extended but correlated signal and reference sources in the recording process. The theory of multiple imaging using spatially incoherent light is developed. Some preliminary experiments are described, demonstrating that a resolution in excess of 110 line pairs/mm can be obtained in the multiplied images, even if sources of 5-mm diam were used in the recording process.

G. Groh

Papers

Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging

Multiple imaging by means of point holograms.

3-d display of x-ray images by means of holography.

X-Ray and gamma-Ray Imaging with Multiple-Pinhole Cameras Using a posteriori Image Synthesis.

Multiple Imaging by Means of Holograms of Correlated Objects