UDC 772.99

PHYSICS

A. L. MIKAELYAN, V. I. BOBRINEV, L. Z. SOKOLOVA

RECORDING A LARGE NUMBER OF IMAGES BY THE METHOD OF SUPERIMPOSING HOLOGRAMS

(Presented by Academician A. M. Prokhorov, 18 VIII 1969)

One of the most important properties of holography is the possibility of successively recording, on one and the same area of a photosensitive surface, a large number of images which, upon reproduction, are easily separated from one another by changing the angle of inclination of the reading wave \((^1)\). This property can be used for the accumulation of large volumes of information and for the creation of new memory elements with a recording density several orders of magnitude higher than that of existing ones \((^2, ^3)\).

In the present work, the quality of images of the simplest objects is investigated for the successive recording of a large number of holograms, and the limiting possibilities of the indicated method are established with allowance for the influence of noise arising as a result of the granularity of photoemulsions \((^4)\).

In the experimental setup, the object was a set of point sources. Holograms of such objects were recorded successively on one and the same area of the photosensitive surface. For each object its own direction of the reference beam was set. Both in recording and in reading, the angle of rotation of the reference beam when photographing neighboring objects was about \(2'\). The exposure in photographing each hologram was chosen in such a way that the total blackening of the photoemulsion was of the order of 1. In this case the brightness of the reconstructed image is maximal. As the number of successive recordings increases, the brightness of the reconstructed image decreases, and it gradually disappears in the noise caused by scattering of light on inhomogeneities of the photoemulsion and on microcrystals of developed silver. With 5 successive exposures, the ratio of the brightness of the useful image to the brightness of the background was about 56 dB, while with 1000 exposures the noise already noticeably spoils the reconstructed image.

Figure 1 shows the reconstructed image of 360 successively photographed points (the two lower rows were photographed with a smaller exposure). It is easy to show that the ratio of the brightness of the image to the brightness of the noise decreases with increasing number of superimposed holograms \(L\) as \(1/L^2\). Suppose that the recording of holograms is carried out on a photosensitive material consisting of \(N\) randomly arranged photosensitive elements. In one recording, \(n\) elements are used; the total number of exposures must be such that all \(N\) elements are used. Owing to the random character of the distribution of the elements, upon illumination of the developed hologram a light background is created whose intensity is proportional to \(N\). The intensity of the light in the useful image is proportional to \(n^2\). Thus, if the image consists of \(M\) points, the signal-to-noise ratio is \(n^2/MN\).

Taking into account that \(n = N/L\), we obtain

\[ P_c / P_{\text{sh}} = N / ML^2 = NM / C^2, \tag{1} \]

Fig. 1

Fig. 2

where \(C = ML\) is the total amount of information recorded on the hologram and is equal to the product of the number of successive exposures by the number of individual points in each image, \(M\).

As we see, the signal-to-noise ratio is inversely proportional to the square of the number of exposures and increases with increasing \(N\), i.e., with the area of the hologram. It also follows from (1) that, for the same amount of information, the noise level decreases with increasing \(M\), i.e., with the amount of information recorded in one exposure.

Experiments confirm this conclusion. Images consisting of 32 discrete points were recorded. With satisfactory image quality it was possible to record up to 600 holograms on a region of the plate about 2 mm in diameter. In the reconstructed image shown in Fig. 2, the ratio \(P_{\mathrm{c}}/P_{\mathrm{ш}}\) is approximately 20. The experimentally obtained maximum amount of information, \(C \sim 2 \cdot 10^{4}\) bits (600 32-place binary numbers), as follows from formula (1), is approximately 3 times smaller than the calculated value. This discrepancy is explained by the fact that in (1) only the grain-noise of the emulsion is taken into account. In practice there are also other sources of noise: inhomogeneity of the substrate, irregularities of the photosensitive-layer surface, etc.

From (1) there also follows the important conclusion that the limiting recording density

\[ \frac{C}{S} = \sqrt{\frac{MN}{P_{\mathrm{c}}/P_{\mathrm{ш}}\,S}} \]

decreases with increasing hologram area. With a reduction in the noise level of the photographic material, the information-recording density can be increased and brought up to a value limited by diffraction phenomena. As can be shown [3], the limiting information-recording density is about \(\frac{\pi}{\lambda^{2}}\) bits/cm\(^2\) and can be achieved with photochromic materials [2] having a high concentration of color centers (\(\sim 10^{20}\) centers/cm\(^3\)).

Received
21 V 1969

REFERENCES

1. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am., 53, No. 12 (1963).
2. A. L. Mikaeliane, A. P. Axenchikov et al., J. IEEE on Quantum El., 11 (1968).
3. А. Л. Микаэлян, В. И. Бобринев и др., Радиотехника и электроника, 14, No. 1 (1969).
4. А. Л. Микаэлян, В. И. Бобринев, Письма ЖЭТФ, No. 5 (1966).