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Holographic multiplexing by use of Fresnel holograms
Volume
OPTICS COMMUNICATIONS
2, number 6
HOLOGRA
PHIC
MULTIPLEXING
Laboratoire
BY
USE
OF
November
FRESNEL
HOLOGRAMS
1970
*
S. C. SOM ** and R. A. LESSARD d’optique et Hyperfr&quence. D+partement de Physique. Universit& Laval, f&&bee lOe, Qu&bec, Canada Received
2 October
1970
field has been A new technique of holographic multiplexing based on the division of the “aperture” briefly discussed. Some experimental results are presented with a short discussion of the quality of the reconstructed images. 1. INTRODUCTION
Several authors [l-4] have considered the carrier multiplexing and the spatial multiplexing techniques in holography. In an earlier communication [5] we considered a new technique based on Fourier transform holograms recorded and reconstructed by use of a lens. The advantages of this technique are that only one carrier is necessary and that the entire area of the photographic plate is exposed to each of the multiple holograms that can be stored in the plate. Although Fourier transform holography has certain advantages, there are situations where it would be desirable not to have to use a lens. We have therefore extended the technique to the experimental situation in which no lens is used and the recorded hologram is more nearly of the Fresnel transform type than the “lensless” Fourier transform type.
and the plane of the hologram, and divide this aperture into segments. The aperture should be large and its shape determined by the kind of segmentations used. Two suitable methods of segmentation, appropriate for circular apertures, were considered in ref. [5]. These are the methods of (i) division of radius and (ii) division of azimuth angle of the aperture. In practice, any of these methods of segmentations can be implemented by use of suitable masks. Previously reported [5] experimental results were obtained with masks implementing division of radius type segmentation. In the present communication, results that have been obtained with masks implementing the other type of segmentation will be presented. Three such masks, suitable for multiplexing three signals, are shown in figs. la, lb and lc in reduced size.
3. EXPERIMENTAL 2. THE TECHNIQUE The technique reported in ref. [5] basically depends on the division of the aperture of the lens used for Fourier transformation into suitable segments and utilizing a particular group of these segments for recording the hologram of one signal as well as for its subsequent reconstruction. Although there is no lens aperture in the present experimental situation, the concept can still be used if we imagine a geometrical aperture between the plane of the input signal * Work supported by the Defence Research Canada under grant DRB 2801-24. ** On leave from the Department of Applied Calcutta University, Calcutta 9, India.
Board of Physics,
ARRANGEMENT
Fig. 2 shows the experimental arrangement for recording the holograms. T is the input signal transparency backed by a suitable diffusing glass plate G. M is the mask to be used with each of the input signals that are to be multiplexed. H is the recording photographic plate. The distances dl and d2 are such that the plate is reasonably well covered by light coming through the mask from the input plane. In the present experiment dl and d2 were both about 35 cm. The radius of the sector masks was 11 cm and the size of each signal transparency was about 2 cm X 2 cm. The size of the plate used was 10 cm X 12 cm. The experimental arrangement for reconstruction is shown in fig. 3. The plate H is rotated through 180’ about the vertical axis from its pre259
Volume 2, number 6
OPTICS
COMMUNICATIONS
Fig. 1. Masks for multiplexing
November
three signals. REFERENCE \BEAM
GT
Fig. 2. Experimental
nrrangement
for recording
holograms.
y ____---+_---_
c-Fig. 3. Experimental 260
d, arrangement
for reconstruction
of signals.
1970
OPTICS
Volume 2, number 6
COMMUNICATIONS
vious position so that the conjugate, rather than the primary, reconstructions are obtained on the optical axis. The mask is also similarly rotated and placed at the same relative position with respect to the plate as it was during recording the holograms.
4. EXPERIMENTAL
November 1970
nal, in the plane M shown in fig. 3. The mask has to be placed in the manner described in the previous section. Slight adjustment of the mask in its position may be necessary. Figs. 5, 6 and 7 show, in photographs, such separate reconstructions of the three signals which are shown in simultaneous reconstruction in fig. 4.
RESULTS 5. CONCLUSION
Suppose we have three input signals generated by three transparencies T1, T2, and T3. With one of the masks, which are shown in fig. 1, we use the transparency T1 and the plate is exposed to record the hologram of the signal corresponding to Tl. Next the transparency T2 is used with another of the three masks and the hologram is recorded. Lastly, the transparency T3 is used with the third mask and the hologram is recorded as usual. If, after necessary processing, the plate is placed in position and illuminated by a replica of the reference beam, as shown in fig. 3, all three of the input signals will be, reconstructed simultaneously at the plane T’ (fig. 3). Fig. 4 shows, in photograph, such reconstruction of three different input signals, one of which is a binary signal. To reconstruct any one of the three signals separately, it is necessary to use the corresponding mask, which was used during recording the hologram of that sig-
Fig. 4. Simultaneous reconstruction of signals.
The present experiment, although performed with a limited number of signals, conclusively demonstrates the usefulness of the new technique in achieving multiplexing also in Fresnel transform holography. The quality of the reconstructed images, as seen in the photographs, is satisfactory except for the presence of background granularity generated mainly by the diffusing glass plate. A full theoretical investigation of this technique, which is under way, shows that the resolution in the reconstructed image will be determined by the size and, to some extent, the structure of the masks, in addition to the usual causes. However, if the aperture of the mask is reasonably large, so that it accepts the entire cone of light received by the plate from any point of the input plane, the use of the masks will not generate severe loss of resolution compared to other usual and well-known causes.
Fig. 5. Separate reconstruction of signals. 261
Volume
2. number
Fig.
6
6. Separ:lte
OPTICS
reconstruction
Fig.
01 signals.
REFERENCES [I) E. S. Lcith and J. Epatnielcs. (1964) 1293. 121 E:. Ii. Leith, A.Koxm;~, S.Mnssey. Appl. Opt.
262
J. Opt. SW. Am.
J. Upatnicks, 5 (1966) 1303.
.I. Marks
COMMUNICATIONS
34 anti
Novcmher
7.
Separnte
reconstruction
1070
of signals.
[3] R. J. Collier antI K. S. Pennington, App. Opt. (j (1967) 1091. [A] EI.,J.CauLfield. Appl. Opt. 9 (1970) 1218. [5] S. C. Som and R. A. Lessard. Opt. Commun. 2 (1970) 12x.
OPTICS COMMUNICATIONS
2, number 6
HOLOGRA
PHIC
MULTIPLEXING
Laboratoire
BY
USE
OF
November
FRESNEL
HOLOGRAMS
1970
*
S. C. SOM ** and R. A. LESSARD d’optique et Hyperfr&quence. D+partement de Physique. Universit& Laval, f&&bee lOe, Qu&bec, Canada Received
2 October
1970
field has been A new technique of holographic multiplexing based on the division of the “aperture” briefly discussed. Some experimental results are presented with a short discussion of the quality of the reconstructed images. 1. INTRODUCTION
Several authors [l-4] have considered the carrier multiplexing and the spatial multiplexing techniques in holography. In an earlier communication [5] we considered a new technique based on Fourier transform holograms recorded and reconstructed by use of a lens. The advantages of this technique are that only one carrier is necessary and that the entire area of the photographic plate is exposed to each of the multiple holograms that can be stored in the plate. Although Fourier transform holography has certain advantages, there are situations where it would be desirable not to have to use a lens. We have therefore extended the technique to the experimental situation in which no lens is used and the recorded hologram is more nearly of the Fresnel transform type than the “lensless” Fourier transform type.
and the plane of the hologram, and divide this aperture into segments. The aperture should be large and its shape determined by the kind of segmentations used. Two suitable methods of segmentation, appropriate for circular apertures, were considered in ref. [5]. These are the methods of (i) division of radius and (ii) division of azimuth angle of the aperture. In practice, any of these methods of segmentations can be implemented by use of suitable masks. Previously reported [5] experimental results were obtained with masks implementing division of radius type segmentation. In the present communication, results that have been obtained with masks implementing the other type of segmentation will be presented. Three such masks, suitable for multiplexing three signals, are shown in figs. la, lb and lc in reduced size.
3. EXPERIMENTAL 2. THE TECHNIQUE The technique reported in ref. [5] basically depends on the division of the aperture of the lens used for Fourier transformation into suitable segments and utilizing a particular group of these segments for recording the hologram of one signal as well as for its subsequent reconstruction. Although there is no lens aperture in the present experimental situation, the concept can still be used if we imagine a geometrical aperture between the plane of the input signal * Work supported by the Defence Research Canada under grant DRB 2801-24. ** On leave from the Department of Applied Calcutta University, Calcutta 9, India.
Board of Physics,
ARRANGEMENT
Fig. 2 shows the experimental arrangement for recording the holograms. T is the input signal transparency backed by a suitable diffusing glass plate G. M is the mask to be used with each of the input signals that are to be multiplexed. H is the recording photographic plate. The distances dl and d2 are such that the plate is reasonably well covered by light coming through the mask from the input plane. In the present experiment dl and d2 were both about 35 cm. The radius of the sector masks was 11 cm and the size of each signal transparency was about 2 cm X 2 cm. The size of the plate used was 10 cm X 12 cm. The experimental arrangement for reconstruction is shown in fig. 3. The plate H is rotated through 180’ about the vertical axis from its pre259
Volume 2, number 6
OPTICS
COMMUNICATIONS
Fig. 1. Masks for multiplexing
November
three signals. REFERENCE \BEAM
GT
Fig. 2. Experimental
nrrangement
for recording
holograms.
y ____---+_---_
c-Fig. 3. Experimental 260
d, arrangement
for reconstruction
of signals.
1970
OPTICS
Volume 2, number 6
COMMUNICATIONS
vious position so that the conjugate, rather than the primary, reconstructions are obtained on the optical axis. The mask is also similarly rotated and placed at the same relative position with respect to the plate as it was during recording the holograms.
4. EXPERIMENTAL
November 1970
nal, in the plane M shown in fig. 3. The mask has to be placed in the manner described in the previous section. Slight adjustment of the mask in its position may be necessary. Figs. 5, 6 and 7 show, in photographs, such separate reconstructions of the three signals which are shown in simultaneous reconstruction in fig. 4.
RESULTS 5. CONCLUSION
Suppose we have three input signals generated by three transparencies T1, T2, and T3. With one of the masks, which are shown in fig. 1, we use the transparency T1 and the plate is exposed to record the hologram of the signal corresponding to Tl. Next the transparency T2 is used with another of the three masks and the hologram is recorded. Lastly, the transparency T3 is used with the third mask and the hologram is recorded as usual. If, after necessary processing, the plate is placed in position and illuminated by a replica of the reference beam, as shown in fig. 3, all three of the input signals will be, reconstructed simultaneously at the plane T’ (fig. 3). Fig. 4 shows, in photograph, such reconstruction of three different input signals, one of which is a binary signal. To reconstruct any one of the three signals separately, it is necessary to use the corresponding mask, which was used during recording the hologram of that sig-
Fig. 4. Simultaneous reconstruction of signals.
The present experiment, although performed with a limited number of signals, conclusively demonstrates the usefulness of the new technique in achieving multiplexing also in Fresnel transform holography. The quality of the reconstructed images, as seen in the photographs, is satisfactory except for the presence of background granularity generated mainly by the diffusing glass plate. A full theoretical investigation of this technique, which is under way, shows that the resolution in the reconstructed image will be determined by the size and, to some extent, the structure of the masks, in addition to the usual causes. However, if the aperture of the mask is reasonably large, so that it accepts the entire cone of light received by the plate from any point of the input plane, the use of the masks will not generate severe loss of resolution compared to other usual and well-known causes.
Fig. 5. Separate reconstruction of signals. 261
Volume
2. number
Fig.
6
6. Separ:lte
OPTICS
reconstruction
Fig.
01 signals.
REFERENCES [I) E. S. Lcith and J. Epatnielcs. (1964) 1293. 121 E:. Ii. Leith, A.Koxm;~, S.Mnssey. Appl. Opt.
262
J. Opt. SW. Am.
J. Upatnicks, 5 (1966) 1303.
.I. Marks
COMMUNICATIONS
34 anti
Novcmher
7.
Separnte
reconstruction
1070
of signals.
[3] R. J. Collier antI K. S. Pennington, App. Opt. (j (1967) 1091. [A] EI.,J.CauLfield. Appl. Opt. 9 (1970) 1218. [5] S. C. Som and R. A. Lessard. Opt. Commun. 2 (1970) 12x.