- Email: [email protected]
Associative space-and-time domain recall of picosecond light signals via photochemical hole burning holography
Volume 65, number 3
OPTICS COMMUNICATIONS
1 February 1988
ASSOCIATIVE SPACE-AND-TIME D O M A I N RECALL OF P I C O S E C O N D L I G H T SIGNALS VIA P H O T O C H E M I C A L H O L E B U R N I N G H O L O G R A P H Y A. REBANE Institute of Physics, Estonian S.S.R. Acad. of Sci., 142 Riia Str., Tartu, 202400, USSR
Received 4 August 1987
A new version of space-and-timedomain holographyin media with photochemicalhole burning is proposed where holographic recall is completed by partial space-timeepisodes of the ultrafast scene. Associative holographic storage and recall of picosecond light signals is experimentallydemonstrated. 1. Introduction Combining the method of persistent photochemical hole burning (PHB) in low-temperature impurity media [1-4] with the principles of optical holography makes possible to perform holographic recording and playback of space-and-time domain behaviour of ultra-short light signals [5-8]. The phenomenon of PHB provides the recording and long term storage of the intensity spectrum of incident object light field with an accuracy to 10-3-10 -4 cm-~, while the introduction of an additional reference pulse provides the storage and playback of the phases of the quasimonochromatic components of the object light field as well. For the sake of convenience it has earlier been assumed that the role of the reference signal in recording and playback of space-time holograms in PHB media should be performed by special 6-like reference pulses, i.e. pulses with the duration very short as compared to the duration of the object pulse [7,8]. At a first glance one may conclude that in an opposite case, i.e. when the duration of the reference pulse is comparable to or even longer than the duration of the object pulse, the signal recalled from the hologram should be temporally hopelessly distorted and dispersed. The purpose of the present paper is to demonstrate that the role of the reference signals in recording and playback of space-and-time domain holograms can be accomplished in an associative
manner by separate space-time fragments (episodes) of the object light field. Recall of such kind of associative holograms is performed, analogously to an associative recall of ordinary space-domain holograms, by feeding into the hologram one or several fragments of the stored-in signal. It is experimentally shown that by recording associative holograms in spectrally selective media not only the reproduction of the spatial image do occur but also the recall of the temporal features of the original signal takes place. In other words, one can reproduce from the hologram the whole event provided a single episode of this event is still available for the readout procedure. Further prospects of this approach are also discussed.
2. Experimental The experimental setup was similar to that described in refs. [4,5]: laser pulses with 2-3 ps duration and 6 c m - ~spectral width were generated with 82 MHz repetition rate by a picosecond dye laser synchronously pumped by an actively mode-locked argon ion laser. The sample was prepared from polystyrene activated with octaethylporphin molecules at concentrations 10-3-10 -4 and had the dimensions 15 X 15 X 5 mm. The sample was contained at 2 K temperature in a liquid-He cryostat with pass-through optical windows. The inhomogeneously broadened
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
175
Volume 65, number 3
B
OPTICS COMMUNICATIONS
E
~P
T
,S
I
Fig. 1, Schematic of the experimental setup. B - beam expander: E - Michelson echelon; S - beamstop used to eliminate parts of the beam during readout of the hologram; D - mat glass beam disperser: C - cwostat: H - hologram: P - photographic camera: SC - synchroscan streak camera: M - semitransparent mirror: T - transparency. absorption b a n d used for P H B at 620 nm wavelength had a 200 c m - 1 width. The starting value o f the optical thickness o f the sample (pre to P H B ) was 2.0-2.5. To record a hologram, exposures about 10 mJ cm -2 were needed, to p e r f o r m the readout the exposures were 2 - 3 orders o f m a g n i t u d e less. The time interval required to write a hologram d e p e n d e d on the sample illumination conditions and varied from tens to several h u n d r e d s o f seconds. During this long interval o f time the PHB-action of 10 m- 101 ~identical light pulses was a c c u m u l a t e d in the m e d i u m o f the hologram. T e m p o r a l resolution o f the light signals with an accuracy to 2 0 - 1 5 ps was p r o v i d e d in the e x p e r i m e n t by a synchroscan streak camera. To record t e m p o rally averaged spatial images a photographic c a m e r a was used.
3. Results and discussion The output b e a m o f the laser was e x p a n d e d in a telescope and passed through a Michelson echelon (fig. 1 ). The optical path through the neighbouring segments o f the echelon differed by 34 ps. At the output of the echelon the laser pulse a p p e a r e d to be divided up in eight pulses. Each o f the eight pulses c o r r e s p o n d e d to a fraction o f the input pulse crosssection travelled through a certain segment o f the echelon so that the relative delays o f the segments 176
1 FebruaD' 1988
were correspondingly 34 ps, 68 ps, 102 ps, etc. The total d u r a t i o n o f the pulse train d i d not exceed, as it is required in space-time holography, the phase relaxation time ~ _ 500 ps o f the excited electronic state o f the i m p u r i t y centers responsible for PHB. By inserting into the laser b e a m various transparencies the spatial outlines of the light pulses could also be tailored, say, in the form o f stripes, fragments of printed text etc. In order to write a hologram, mutual interference o f various parts o f the incident object light field had to be arranged by making all the spatial parts o f the object pulse meet each other all over the hologram. To do this a mat glass plate was inserted into the laser b e a m some 15 cm from the incident window of the cryostat. As a result the laser b e a m which at the output of the echelon c o m p r i s e d a train o f co-propagating pulses with spatially non-overlapping wavefronts, turned at the incident plane o f the hologram into a train o f pulses with each pulse illum i n a t i n g almost evenly the whole area o f the sample. In fig. 2a is presented a photograph o f a spatial image p r o d u c e d by object pulses scattered from the mat glass disperser. This image was observed when looking through the sample and the windows o f the cryostat during the writing exposure of the hologram. In fig. 2b the temporal structure o f the same light signal recorded with a streak camera is presented. F o r the purpose o f better visibility of the spatial image a transparency was used to shape the object pulse in such a way that only pulses with delays 0, 34, 68 and 170 ps of the whole echelon output train were present. To perform the read-out o f the hologram certain parts of the object beam were stopped so that they d i d not reach m a t glass. At the time both spatial (averaged over the time interval of the photographic c a m e r a exposure) and temporal images o f the light signal emerging from the hologram were recorded. In figs. 3a, b a photograph o f the spatial image and the streak camera record of the signal recalled from the hologram are presented. The readout o f the hologram was carried out with a space-time fragment comprising first three pulses out o f the four pulse sequence used to write the hologram. C o m p a r i n g the d a t a presented in fig. 2 and fig. 3 one can conclude that the hologram indeed had the ability to repro-
Volume 65, number 3
OPTICS COMMUNICATIONS
//[ \
1 February 1988
//
\
>-. I.-m
Z
Z !..i_1
ILl
z
z
I--
I--
0
100
200 PS
0
100
200 PS
Fig. 2. Photograph of the spatial image (a) and corresponding streak camera record (b) of the object signal used to write the hologram. Correspondence between spatial and temporal fragments is indicated by arrows.
Fig. 3. Photograph of the spatial image (a) and the streak camera record (b) of the signal recalled from the hologram. For the readout fragment see the bright part at the left of the photograph (a) and the three pulses with delays 0, 34 and 68 ps (b).
duce both the spatial and the t e m p o r a l structure o f the missing part o f the object signal. Note that the duration o f the readout signal was some 70 ps while the t e m p o r a l width o f the recalled pulse was less than the streak c a m e r a 15 ps t e m p o r a l resolution. By utilizing c o m b i n a t i o n s o f various space-time readout fragments it was established that the missing part o f the signal turned out only in case at least a fraction o f the readout signal p r e c e d e d in time during writing o f the hologram the missing part o f the signal. In the opposite case when the readout fragm e n t belonged entirely to the r e t a r d e d part o f the signal no recall was observed. This feature is naturally u n d e r s t o o d if one accounts for the causality properties o f space-time holography in P H B m e d i a [7,8]. During the readout o f the hologram it was also observed that the more readout signals p r e c e d e d the
missing part o f the scene, the more intense and detailed was the signal recalled from the hologram. This feature m a y be interpreted as a further p r o p e r t y o f an associative m e m o r y to reproduce the details o f the stored-in scene d e p e n d i n g on the a m o u n t o f the p r e l i m i n a r y i n f o r m a t i o n s u b m i t t e d for the readout. Figs. 4a, b display the photographs o f an associatively recorded and recalled picosecond space-time signal which had the form o f a p r i n t e d text each line o f which had a d u r a t i o n in time 2 ps, the interval between the following lines was 34 ps. By illuminating the hologram with some o f the first lines o f the text it was possible to read from ,he recalled image the rest o f the text while the streak camera records showed that the t e m p o r a l features o f the signal were r e p r o d u c e d as well. It should be noted that associative properties o f the t e m p o r a l recall observed in the described above 177
Volume 65, number 3
OPTICS COMMUNICATIONS
1 February 1988
a
43~2,
b
~SION~ AC*O|N~"
-
A' "
CtS.~ns PNY
~ t ~ /
Fig. 4. Photographs of the image of a picosecond space-time signal applied to record a hologram (a) and the image recalled from the recorded hologram (see the text). e x p e r i m e n t s m a n i f e s t e d t h e m s e l v e s to a c o n s i d e r a ble e x t e n t d u e to the fact t h a t d i f f e r e n t t e m p o r a l f r a g m e n t s o f the r e c o r d e d o b j e c t scene h a d an irregular, d i f f e r e n t f r o m o n e a n o t h e r spatial s t r u c t u r e [ 9,10]. In this sense p r e s e n t e x p e r i m e n t s do r e m i n d the r e p r o d u c t i o n o f a so-called p h a n t o m i m a g e obs e r v e d in c o n v e n t i o n a l holography. A s s o c i a t i v e r e a d o u t o f s p a c e - t i m e h o l o g r a m s can be p e r f o r m e d also d u e only to the t i m e - d o m a i n s t r u c t u r e o f the object signal p r o v i d e d the d i f f e r e n t f r a g m e n t s o f the object scene do not correlate strongly with each a n o t h e r in t i m e d o m a i n [ 1 0 , 1 1 ] . In this case to a c c o m p l i s h the r e a d o u t o f the h o l o g r a m a f r a g m e n t w h i c h possesses t e m p o r a l s t r u c t u r e coinc i d i n g w i t h an e p i s o d e b e l o n g i n g to the object scene is r e q u i r e d . It s h o u l d be n o t e d that tlfe possibility o f holog r a p h i c t e m p o r a l recall utilizing f r a g m e n t s o f the rec o r d e d signal has b e e n a l r e a d y i n d i c a t e d earlier by G a b o r [ 12 ] a n d the analogy b e t w e e n h o l o g r a p h i c recall a n d s o m e p r o p e r t i e s o f h u m a n m e m o r y was also p o i n t e d out.
Acknowledgements T h e a u t h o r is i n d e b t e d to K.K. R e b a n e a n d P.M. Saari for useful d i s c u s s i o n o f this w o r k a n d to R . K .
178
K a a r l i for t a k i n g part in the e x p e r i m e n t s . T h e a u t h o r also w a n t s to t h a n k I. R e n g e for p r e p a r i n g the samples.
References [ 1] A.A. Gorokhovskii, R.K. Kaarli and L.A. Rebane. JETP Lett. 20 (1974) 474, [2] B.M. Kharlamov, R.I. Personov and L.A. Bykovskaya, Optics Comm. 16 (1974) 282. [3] L.A. Rebane, A.A. Gorokhovskii and J.V. Kikasa. Appl. Phys. B29 (1982) 235. [41 J. Friedrich and D. Haarer, Angew. Chem. Int. Ed. Engl. 23 (1984) 113. [ 5 ] A. Rebane, R. Kaarli, P. Saari, A. Anijalg and K. Timpman, Optics Comm. 47 (1983) 173. [6] A. Rebane and R. Kaarli, Chem. Phys. Lett. 101 (1983) 317. [7] P. Saari, R. Kaarli and A. Rebane, J. Opt. Soc. Am. B 3 (1986) 527. [8 ] P. Saari and A. Rebane, Proc. Acad. Sci. of Estonian SSR 33 (1984) 322. [ 9 ] A. Rebane and R. Kaarli, Proc. Acad. Sci. of Estonian SSR 36 (1987) 208. [10] A. Rebane, Abstract of V Intern. Symposium on Ultrafast phenomena in spectroscopy, Vilnius, 1987. [ 11 ] A. Rebane, Proc. Acad. Sci. of Estonian SSR (in print). [ 12 ] D. Gabor, Nature 217 (1968) 1288.
OPTICS COMMUNICATIONS
1 February 1988
ASSOCIATIVE SPACE-AND-TIME D O M A I N RECALL OF P I C O S E C O N D L I G H T SIGNALS VIA P H O T O C H E M I C A L H O L E B U R N I N G H O L O G R A P H Y A. REBANE Institute of Physics, Estonian S.S.R. Acad. of Sci., 142 Riia Str., Tartu, 202400, USSR
Received 4 August 1987
A new version of space-and-timedomain holographyin media with photochemicalhole burning is proposed where holographic recall is completed by partial space-timeepisodes of the ultrafast scene. Associative holographic storage and recall of picosecond light signals is experimentallydemonstrated. 1. Introduction Combining the method of persistent photochemical hole burning (PHB) in low-temperature impurity media [1-4] with the principles of optical holography makes possible to perform holographic recording and playback of space-and-time domain behaviour of ultra-short light signals [5-8]. The phenomenon of PHB provides the recording and long term storage of the intensity spectrum of incident object light field with an accuracy to 10-3-10 -4 cm-~, while the introduction of an additional reference pulse provides the storage and playback of the phases of the quasimonochromatic components of the object light field as well. For the sake of convenience it has earlier been assumed that the role of the reference signal in recording and playback of space-time holograms in PHB media should be performed by special 6-like reference pulses, i.e. pulses with the duration very short as compared to the duration of the object pulse [7,8]. At a first glance one may conclude that in an opposite case, i.e. when the duration of the reference pulse is comparable to or even longer than the duration of the object pulse, the signal recalled from the hologram should be temporally hopelessly distorted and dispersed. The purpose of the present paper is to demonstrate that the role of the reference signals in recording and playback of space-and-time domain holograms can be accomplished in an associative
manner by separate space-time fragments (episodes) of the object light field. Recall of such kind of associative holograms is performed, analogously to an associative recall of ordinary space-domain holograms, by feeding into the hologram one or several fragments of the stored-in signal. It is experimentally shown that by recording associative holograms in spectrally selective media not only the reproduction of the spatial image do occur but also the recall of the temporal features of the original signal takes place. In other words, one can reproduce from the hologram the whole event provided a single episode of this event is still available for the readout procedure. Further prospects of this approach are also discussed.
2. Experimental The experimental setup was similar to that described in refs. [4,5]: laser pulses with 2-3 ps duration and 6 c m - ~spectral width were generated with 82 MHz repetition rate by a picosecond dye laser synchronously pumped by an actively mode-locked argon ion laser. The sample was prepared from polystyrene activated with octaethylporphin molecules at concentrations 10-3-10 -4 and had the dimensions 15 X 15 X 5 mm. The sample was contained at 2 K temperature in a liquid-He cryostat with pass-through optical windows. The inhomogeneously broadened
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
175
Volume 65, number 3
B
OPTICS COMMUNICATIONS
E
~P
T
,S
I
Fig. 1, Schematic of the experimental setup. B - beam expander: E - Michelson echelon; S - beamstop used to eliminate parts of the beam during readout of the hologram; D - mat glass beam disperser: C - cwostat: H - hologram: P - photographic camera: SC - synchroscan streak camera: M - semitransparent mirror: T - transparency. absorption b a n d used for P H B at 620 nm wavelength had a 200 c m - 1 width. The starting value o f the optical thickness o f the sample (pre to P H B ) was 2.0-2.5. To record a hologram, exposures about 10 mJ cm -2 were needed, to p e r f o r m the readout the exposures were 2 - 3 orders o f m a g n i t u d e less. The time interval required to write a hologram d e p e n d e d on the sample illumination conditions and varied from tens to several h u n d r e d s o f seconds. During this long interval o f time the PHB-action of 10 m- 101 ~identical light pulses was a c c u m u l a t e d in the m e d i u m o f the hologram. T e m p o r a l resolution o f the light signals with an accuracy to 2 0 - 1 5 ps was p r o v i d e d in the e x p e r i m e n t by a synchroscan streak camera. To record t e m p o rally averaged spatial images a photographic c a m e r a was used.
3. Results and discussion The output b e a m o f the laser was e x p a n d e d in a telescope and passed through a Michelson echelon (fig. 1 ). The optical path through the neighbouring segments o f the echelon differed by 34 ps. At the output of the echelon the laser pulse a p p e a r e d to be divided up in eight pulses. Each o f the eight pulses c o r r e s p o n d e d to a fraction o f the input pulse crosssection travelled through a certain segment o f the echelon so that the relative delays o f the segments 176
1 FebruaD' 1988
were correspondingly 34 ps, 68 ps, 102 ps, etc. The total d u r a t i o n o f the pulse train d i d not exceed, as it is required in space-time holography, the phase relaxation time ~ _ 500 ps o f the excited electronic state o f the i m p u r i t y centers responsible for PHB. By inserting into the laser b e a m various transparencies the spatial outlines of the light pulses could also be tailored, say, in the form o f stripes, fragments of printed text etc. In order to write a hologram, mutual interference o f various parts o f the incident object light field had to be arranged by making all the spatial parts o f the object pulse meet each other all over the hologram. To do this a mat glass plate was inserted into the laser b e a m some 15 cm from the incident window of the cryostat. As a result the laser b e a m which at the output of the echelon c o m p r i s e d a train o f co-propagating pulses with spatially non-overlapping wavefronts, turned at the incident plane o f the hologram into a train o f pulses with each pulse illum i n a t i n g almost evenly the whole area o f the sample. In fig. 2a is presented a photograph o f a spatial image p r o d u c e d by object pulses scattered from the mat glass disperser. This image was observed when looking through the sample and the windows o f the cryostat during the writing exposure of the hologram. In fig. 2b the temporal structure o f the same light signal recorded with a streak camera is presented. F o r the purpose o f better visibility of the spatial image a transparency was used to shape the object pulse in such a way that only pulses with delays 0, 34, 68 and 170 ps of the whole echelon output train were present. To perform the read-out o f the hologram certain parts of the object beam were stopped so that they d i d not reach m a t glass. At the time both spatial (averaged over the time interval of the photographic c a m e r a exposure) and temporal images o f the light signal emerging from the hologram were recorded. In figs. 3a, b a photograph o f the spatial image and the streak camera record of the signal recalled from the hologram are presented. The readout o f the hologram was carried out with a space-time fragment comprising first three pulses out o f the four pulse sequence used to write the hologram. C o m p a r i n g the d a t a presented in fig. 2 and fig. 3 one can conclude that the hologram indeed had the ability to repro-
Volume 65, number 3
OPTICS COMMUNICATIONS
//[ \
1 February 1988
//
\
>-. I.-m
Z
Z !..i_1
ILl
z
z
I--
I--
0
100
200 PS
0
100
200 PS
Fig. 2. Photograph of the spatial image (a) and corresponding streak camera record (b) of the object signal used to write the hologram. Correspondence between spatial and temporal fragments is indicated by arrows.
Fig. 3. Photograph of the spatial image (a) and the streak camera record (b) of the signal recalled from the hologram. For the readout fragment see the bright part at the left of the photograph (a) and the three pulses with delays 0, 34 and 68 ps (b).
duce both the spatial and the t e m p o r a l structure o f the missing part o f the object signal. Note that the duration o f the readout signal was some 70 ps while the t e m p o r a l width o f the recalled pulse was less than the streak c a m e r a 15 ps t e m p o r a l resolution. By utilizing c o m b i n a t i o n s o f various space-time readout fragments it was established that the missing part o f the signal turned out only in case at least a fraction o f the readout signal p r e c e d e d in time during writing o f the hologram the missing part o f the signal. In the opposite case when the readout fragm e n t belonged entirely to the r e t a r d e d part o f the signal no recall was observed. This feature is naturally u n d e r s t o o d if one accounts for the causality properties o f space-time holography in P H B m e d i a [7,8]. During the readout o f the hologram it was also observed that the more readout signals p r e c e d e d the
missing part o f the scene, the more intense and detailed was the signal recalled from the hologram. This feature m a y be interpreted as a further p r o p e r t y o f an associative m e m o r y to reproduce the details o f the stored-in scene d e p e n d i n g on the a m o u n t o f the p r e l i m i n a r y i n f o r m a t i o n s u b m i t t e d for the readout. Figs. 4a, b display the photographs o f an associatively recorded and recalled picosecond space-time signal which had the form o f a p r i n t e d text each line o f which had a d u r a t i o n in time 2 ps, the interval between the following lines was 34 ps. By illuminating the hologram with some o f the first lines o f the text it was possible to read from ,he recalled image the rest o f the text while the streak camera records showed that the t e m p o r a l features o f the signal were r e p r o d u c e d as well. It should be noted that associative properties o f the t e m p o r a l recall observed in the described above 177
Volume 65, number 3
OPTICS COMMUNICATIONS
1 February 1988
a
43~2,
b
~SION~ AC*O|N~"
-
A' "
CtS.~ns PNY
~ t ~ /
Fig. 4. Photographs of the image of a picosecond space-time signal applied to record a hologram (a) and the image recalled from the recorded hologram (see the text). e x p e r i m e n t s m a n i f e s t e d t h e m s e l v e s to a c o n s i d e r a ble e x t e n t d u e to the fact t h a t d i f f e r e n t t e m p o r a l f r a g m e n t s o f the r e c o r d e d o b j e c t scene h a d an irregular, d i f f e r e n t f r o m o n e a n o t h e r spatial s t r u c t u r e [ 9,10]. In this sense p r e s e n t e x p e r i m e n t s do r e m i n d the r e p r o d u c t i o n o f a so-called p h a n t o m i m a g e obs e r v e d in c o n v e n t i o n a l holography. A s s o c i a t i v e r e a d o u t o f s p a c e - t i m e h o l o g r a m s can be p e r f o r m e d also d u e only to the t i m e - d o m a i n s t r u c t u r e o f the object signal p r o v i d e d the d i f f e r e n t f r a g m e n t s o f the object scene do not correlate strongly with each a n o t h e r in t i m e d o m a i n [ 1 0 , 1 1 ] . In this case to a c c o m p l i s h the r e a d o u t o f the h o l o g r a m a f r a g m e n t w h i c h possesses t e m p o r a l s t r u c t u r e coinc i d i n g w i t h an e p i s o d e b e l o n g i n g to the object scene is r e q u i r e d . It s h o u l d be n o t e d that tlfe possibility o f holog r a p h i c t e m p o r a l recall utilizing f r a g m e n t s o f the rec o r d e d signal has b e e n a l r e a d y i n d i c a t e d earlier by G a b o r [ 12 ] a n d the analogy b e t w e e n h o l o g r a p h i c recall a n d s o m e p r o p e r t i e s o f h u m a n m e m o r y was also p o i n t e d out.
Acknowledgements T h e a u t h o r is i n d e b t e d to K.K. R e b a n e a n d P.M. Saari for useful d i s c u s s i o n o f this w o r k a n d to R . K .
178
K a a r l i for t a k i n g part in the e x p e r i m e n t s . T h e a u t h o r also w a n t s to t h a n k I. R e n g e for p r e p a r i n g the samples.
References [ 1] A.A. Gorokhovskii, R.K. Kaarli and L.A. Rebane. JETP Lett. 20 (1974) 474, [2] B.M. Kharlamov, R.I. Personov and L.A. Bykovskaya, Optics Comm. 16 (1974) 282. [3] L.A. Rebane, A.A. Gorokhovskii and J.V. Kikasa. Appl. Phys. B29 (1982) 235. [41 J. Friedrich and D. Haarer, Angew. Chem. Int. Ed. Engl. 23 (1984) 113. [ 5 ] A. Rebane, R. Kaarli, P. Saari, A. Anijalg and K. Timpman, Optics Comm. 47 (1983) 173. [6] A. Rebane and R. Kaarli, Chem. Phys. Lett. 101 (1983) 317. [7] P. Saari, R. Kaarli and A. Rebane, J. Opt. Soc. Am. B 3 (1986) 527. [8 ] P. Saari and A. Rebane, Proc. Acad. Sci. of Estonian SSR 33 (1984) 322. [ 9 ] A. Rebane and R. Kaarli, Proc. Acad. Sci. of Estonian SSR 36 (1987) 208. [10] A. Rebane, Abstract of V Intern. Symposium on Ultrafast phenomena in spectroscopy, Vilnius, 1987. [ 11 ] A. Rebane, Proc. Acad. Sci. of Estonian SSR (in print). [ 12 ] D. Gabor, Nature 217 (1968) 1288.