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Recording of time-varying electrical signals with one-dimensional holograms
Volume 7. number 2
I:ebruary
OPTICS COMhfUNICATIONS
RECORDING
OF TIME-VARYING
ELECTRICAL
WITH ONE-DIMENSIONAL
Rcccived
4 Deccmbcr
I973
SIGNALS
HOLOGRAMS
1972
A mcthud of opticall) recording and reconstructing electrical signals in the form of one-dimensional holograms is deccribcd. l,or this purpcw a pulsed laser beam is modulat~?d according to the information to be stored. This beam is superimposed on a spatially and temporaIl> constant refercrux beam, and the resulting interference pattern is rccorded on a film which is moved past the light distribution. The one-dimensional holograms thus recorded appear arranged in narrow tracks which partially overlap. l,or reconstruction the film is driven past a spatiall) and temporally constant reconstructing ~vave. The illuminated holograms reconstruct a closely spaced chain of points which succcssivcly pass by a dctcctor in which they produce an alternating current which. after appropriate nmplif’icotion and filtering. represents the original signal.
1. Introduction WC are investigating a method designed to provide the coherent optical recording of time-varying electrical signals. The basic idea of the method is to modulate the intensity- of a laser beam according to the signal to be
stored and to superimpose this modulated beam with a constant reference wave. Since the signals to be rccorded represent one-dimensional events ~ time being the only parameter - they can be recorded in the form of partially overlapping one-dimensional holograms on a moving film. One-dimensional holograms are narrow tracks on
SEQUENTIAL HOLOGRAPHIC DATA STORAGE I:ig. I. Schematic
IS8
rcprescntation
of recording
setup.
Volume 7, number 2
OPTICS COMMUNICATIONS
the film. Their characteristic values, such as transmission and phase structure, vary only longitudinally. whereas perpendicular to this direction they remain constant. Such a method of recording a time varying signal holographically is described below.
February 1973
To ensure faithful wave reconstruction and maximum storage density, the film transport speed, pulse repetition frequency and pulse width must be chosen such that the following criteria are satisfied: 1 the film can be considered stationary during its exposure, i.e.,
2. Recording Fig. I shows the recording arrangement.
An externally or internally pulsed gas or solid-state laser is chosen as a light source. The beam splitter BS 1 divides the beam into the reference wave (RW) and the object wave
(OW). The object wave is modulated by the modulator M according to the signal to be stored. The amplitude of the object wave varies from pulse to pulse corresponding to the time variation of the signal: whereas the amplitude of the pulses of the reference wave remains constant. The object wave is convergent and the reference wave divergent. Both waves are superposed and result in a pulsed interference field whose contrast varies according to the signal to be stored. This interference field is focused on the moving film with the aid of a cy lindrical lens, such that a one dimensional hologramm is recorded every time a pulse is applied, whereby the holograms partially overlap.
where 6x is the translation of the film during the exposure, 6t is the pulse duration and uH is the hologram speed ; 2, in the interval between two successive exposures the film is transported by the distance Ax. which is chosen such that the image points reconstructed by adjacent holograms are resolved; 3, the pulse repetition frequency is. at last twice the higher cutoff frequency of the signal to be recorded as required by sampling theory+. The resulting holograms differ only with respect to their contrast and their location on the recorded track. A high pulse produces high contrast in the hologram, a low pulse low contrast. Since the diffraction efficiency of a hologram depends directly on the hologram contrast, the various holograms reconstruct image points whose intensity corresponds to the signal at the instant of scanning [ 11 .
3. Reconstruction To reconstruct the stored signal, the film on which the superposed holograms are recorded is transported past a spatially and temporally constant reconstructing wave so that a section of the hologram track is illuminated. The superposed holograms in this section reconstruct a closely spaced chain of real image points (fig. 2). The intensity of each reconstructed image point represents the amplitude of the signal at the instant of scanning. The chain of image points passes by a stationary detector where it produces an alternating current, which is amplified and, after appropriate low pass filtering, represents the original signal. .t According to sampling theory, B continuous function can be completely represented by a discontinuous szqucnce of samples if the sampling frequency Jk is such that: f; > 21, (j, being the upper
cutoff
frequency
of the signal).
159
OPTICS COhlMUNICATIONS
Volume 7, number 2
E, - exp t-ik
4. Experiments 4.1. Preliminary
static experimer~ts
In order to investigate the feasibility of this method. preliminary static and dynamic experiments were carried out, in the course of which various beam-guiding concepts were studied. The use of symmetrical sources (fig. 3) described below proved particularly advantageous with respect to the specific problems involved in the method. It can be shown [2] that using symmetrical sources the reconstruction of the stored information is, in the first approximation invariant to hologram translations normal to the recording plane. This property greatly reduces the mechanical tolerance problems and will be discussed elsewhere 131. A further substantial advantage of symmetrical sources consists of the possibility of doubling the attainable storage density for a given object wave apcrture ratio as compared to a recording with a plane reference wave. To demonstrate this we will proceed from fig. 4 and calculate the field distribution E(x’) that arises in the reconstruction plane z = z. if the hologram is shifted in the x direction over a distance AX. The associated Fresnel diffraction integral
I:‘(x’) -
I:ebruary
1973
[zO + (x-x~)~/?~~]}.
I:, -exp{ik(z,
t(x-~,)~/22,]}.
/:;1 -exp{ik(zO
+(x~x’)~/?z~]},
E, being the object wave, E, the reference wave and I:‘,, the Huygens waves. For small ti. this yields
This result has been derived neglecting higher order terms as well as the influence of the smaller hologram
s
(I$)‘:‘; )T E,E,, dx ho1
must for this purpose be solved: Fig. 4. Determining lation.
x t
’
0 OBJECTSOURCE A
I:ig. 3. Symmetrical wave.
I60
source\
REFERENCE SOURCE
for object
wwc
and reference
the image shift in a given hologram
trans-
Volume
7, number
__---
2
CH 1 -I I
OPTICS
COMMUNICATIONS
LASER I
I
ES M CH
BEAM SPLITTER : MIRROR CHOPPER
February
1973
= lzrl is exactly twice the hologram shift (As = FAX). However, if the object wave were recorded with a plane reference wave (z, = -), image translation and hologram translation would be identical (As = AX). For a given object wave aperture ratio, this increased image translation in case of symmetrical object and reference wave sources allows. the storage density to be doubled compared to a recording with a plane reference wave without any deterioration in the resolution of the reconstructed image points. To verify this experimentally, the arrangement of the symmetrical sources shown in fig. 3 was used for the doubled-exposure of a photographic plate (Agfa Scientia 8 E 75) which was shifted during the Interval between two exposures by AX = 2.0 pm. The object wave was produced with a lens with an aperture ratio of 1:4.5 and a focal length of 63 mm. Fig. 5 shows the discrete reconstructed image points. The vertical marks between the points were recorded during reconstruction in another experiment which was conducted to determine whether any lateral image displacements had occurred. On the other hand recording with a plane reference wave, would have required a hologram translation of at last Ax = 1.23 Af/d e 3.5 pm to construct resolved image points according to the Rayleigh criterion. 4.2. Preliminary dynamic experiments
Fig. 6. Dynamic
recording
of binary
signals Ax = 4 pm,
aperture of the shifted hologram. Considerations which will take into account these effects will be reported in future. It is evident from the above equation that a hologram shift of Ax produces an image translation of As = Ax (1 + zu/zr). Thus the image shift for the case Izu 1
Fig. 7. Reconstruction
To investigate the general feasibility of the described method, a digital signal was recorded using symmetrical sources in a preliminary dynamic test (fig. 6). The beam of a cw HeeNe laser was mechanically- chopped with a chopper wheel and the resulting binary signal stored holographically on a continuously translated photographic plate (Agfa Scientica 8 E 75). The duty cycle was adjusted to the hologram speed and to the given
of the stored
signal.
161
Volume
7, number
2
OPTICS (‘O%lI11UNI(‘ATIONS
data rate according to the criteria given in section I. I. The distance Ax separatinp adjacent holograms was 4 pm. Fig. 7 shows the sequence ot‘ reconstructed image points. dicates
The bright point below the chain of points inthe horizontal position of the detector. The
storage
density
experiment
attained
is the result of a preliminary
Ireliability but also the possibility
higher storage problems
densities
associated
in addition
with guiding
1973
of attaining
to solving
tolerance
the film.
References
and has since been improved.
Our results show that holography only for block-organized
can be used not
but also for linearly
optical memories. Compared to point ing using modulated light, holography
I62
higher
February
organized
by point recordoffers not only
( I ] I{. Kiemle and D. R&c, Finfiihrung m die Tcchnik dcr Holographic (Akademixhc Vcrlagsgescll\chaft, Frankfurt/Main. 1969). 121 E. Storck and H. R&11, Ubcr eine spoielle hologaphischc Anordnung, DGaO-Tagung, Bad Hersfeld (1972). 131 H. Rtill and E. Storck, to be publised.
I:ebruary
OPTICS COMhfUNICATIONS
RECORDING
OF TIME-VARYING
ELECTRICAL
WITH ONE-DIMENSIONAL
Rcccived
4 Deccmbcr
I973
SIGNALS
HOLOGRAMS
1972
A mcthud of opticall) recording and reconstructing electrical signals in the form of one-dimensional holograms is deccribcd. l,or this purpcw a pulsed laser beam is modulat~?d according to the information to be stored. This beam is superimposed on a spatially and temporaIl> constant refercrux beam, and the resulting interference pattern is rccorded on a film which is moved past the light distribution. The one-dimensional holograms thus recorded appear arranged in narrow tracks which partially overlap. l,or reconstruction the film is driven past a spatiall) and temporally constant reconstructing ~vave. The illuminated holograms reconstruct a closely spaced chain of points which succcssivcly pass by a dctcctor in which they produce an alternating current which. after appropriate nmplif’icotion and filtering. represents the original signal.
1. Introduction WC are investigating a method designed to provide the coherent optical recording of time-varying electrical signals. The basic idea of the method is to modulate the intensity- of a laser beam according to the signal to be
stored and to superimpose this modulated beam with a constant reference wave. Since the signals to be rccorded represent one-dimensional events ~ time being the only parameter - they can be recorded in the form of partially overlapping one-dimensional holograms on a moving film. One-dimensional holograms are narrow tracks on
SEQUENTIAL HOLOGRAPHIC DATA STORAGE I:ig. I. Schematic
IS8
rcprescntation
of recording
setup.
Volume 7, number 2
OPTICS COMMUNICATIONS
the film. Their characteristic values, such as transmission and phase structure, vary only longitudinally. whereas perpendicular to this direction they remain constant. Such a method of recording a time varying signal holographically is described below.
February 1973
To ensure faithful wave reconstruction and maximum storage density, the film transport speed, pulse repetition frequency and pulse width must be chosen such that the following criteria are satisfied: 1 the film can be considered stationary during its exposure, i.e.,
2. Recording Fig. I shows the recording arrangement.
An externally or internally pulsed gas or solid-state laser is chosen as a light source. The beam splitter BS 1 divides the beam into the reference wave (RW) and the object wave
(OW). The object wave is modulated by the modulator M according to the signal to be stored. The amplitude of the object wave varies from pulse to pulse corresponding to the time variation of the signal: whereas the amplitude of the pulses of the reference wave remains constant. The object wave is convergent and the reference wave divergent. Both waves are superposed and result in a pulsed interference field whose contrast varies according to the signal to be stored. This interference field is focused on the moving film with the aid of a cy lindrical lens, such that a one dimensional hologramm is recorded every time a pulse is applied, whereby the holograms partially overlap.
where 6x is the translation of the film during the exposure, 6t is the pulse duration and uH is the hologram speed ; 2, in the interval between two successive exposures the film is transported by the distance Ax. which is chosen such that the image points reconstructed by adjacent holograms are resolved; 3, the pulse repetition frequency is. at last twice the higher cutoff frequency of the signal to be recorded as required by sampling theory+. The resulting holograms differ only with respect to their contrast and their location on the recorded track. A high pulse produces high contrast in the hologram, a low pulse low contrast. Since the diffraction efficiency of a hologram depends directly on the hologram contrast, the various holograms reconstruct image points whose intensity corresponds to the signal at the instant of scanning [ 11 .
3. Reconstruction To reconstruct the stored signal, the film on which the superposed holograms are recorded is transported past a spatially and temporally constant reconstructing wave so that a section of the hologram track is illuminated. The superposed holograms in this section reconstruct a closely spaced chain of real image points (fig. 2). The intensity of each reconstructed image point represents the amplitude of the signal at the instant of scanning. The chain of image points passes by a stationary detector where it produces an alternating current, which is amplified and, after appropriate low pass filtering, represents the original signal. .t According to sampling theory, B continuous function can be completely represented by a discontinuous szqucnce of samples if the sampling frequency Jk is such that: f; > 21, (j, being the upper
cutoff
frequency
of the signal).
159
OPTICS COhlMUNICATIONS
Volume 7, number 2
E, - exp t-ik
4. Experiments 4.1. Preliminary
static experimer~ts
In order to investigate the feasibility of this method. preliminary static and dynamic experiments were carried out, in the course of which various beam-guiding concepts were studied. The use of symmetrical sources (fig. 3) described below proved particularly advantageous with respect to the specific problems involved in the method. It can be shown [2] that using symmetrical sources the reconstruction of the stored information is, in the first approximation invariant to hologram translations normal to the recording plane. This property greatly reduces the mechanical tolerance problems and will be discussed elsewhere 131. A further substantial advantage of symmetrical sources consists of the possibility of doubling the attainable storage density for a given object wave apcrture ratio as compared to a recording with a plane reference wave. To demonstrate this we will proceed from fig. 4 and calculate the field distribution E(x’) that arises in the reconstruction plane z = z. if the hologram is shifted in the x direction over a distance AX. The associated Fresnel diffraction integral
I:‘(x’) -
I:ebruary
1973
[zO + (x-x~)~/?~~]}.
I:, -exp{ik(z,
t(x-~,)~/22,]}.
/:;1 -exp{ik(zO
+(x~x’)~/?z~]},
E, being the object wave, E, the reference wave and I:‘,, the Huygens waves. For small ti. this yields
This result has been derived neglecting higher order terms as well as the influence of the smaller hologram
s
(I$)‘:‘; )T E,E,, dx ho1
must for this purpose be solved: Fig. 4. Determining lation.
x t
’
0 OBJECTSOURCE A
I:ig. 3. Symmetrical wave.
I60
source\
REFERENCE SOURCE
for object
wwc
and reference
the image shift in a given hologram
trans-
Volume
7, number
__---
2
CH 1 -I I
OPTICS
COMMUNICATIONS
LASER I
I
ES M CH
BEAM SPLITTER : MIRROR CHOPPER
February
1973
= lzrl is exactly twice the hologram shift (As = FAX). However, if the object wave were recorded with a plane reference wave (z, = -), image translation and hologram translation would be identical (As = AX). For a given object wave aperture ratio, this increased image translation in case of symmetrical object and reference wave sources allows. the storage density to be doubled compared to a recording with a plane reference wave without any deterioration in the resolution of the reconstructed image points. To verify this experimentally, the arrangement of the symmetrical sources shown in fig. 3 was used for the doubled-exposure of a photographic plate (Agfa Scientia 8 E 75) which was shifted during the Interval between two exposures by AX = 2.0 pm. The object wave was produced with a lens with an aperture ratio of 1:4.5 and a focal length of 63 mm. Fig. 5 shows the discrete reconstructed image points. The vertical marks between the points were recorded during reconstruction in another experiment which was conducted to determine whether any lateral image displacements had occurred. On the other hand recording with a plane reference wave, would have required a hologram translation of at last Ax = 1.23 Af/d e 3.5 pm to construct resolved image points according to the Rayleigh criterion. 4.2. Preliminary dynamic experiments
Fig. 6. Dynamic
recording
of binary
signals Ax = 4 pm,
aperture of the shifted hologram. Considerations which will take into account these effects will be reported in future. It is evident from the above equation that a hologram shift of Ax produces an image translation of As = Ax (1 + zu/zr). Thus the image shift for the case Izu 1
Fig. 7. Reconstruction
To investigate the general feasibility of the described method, a digital signal was recorded using symmetrical sources in a preliminary dynamic test (fig. 6). The beam of a cw HeeNe laser was mechanically- chopped with a chopper wheel and the resulting binary signal stored holographically on a continuously translated photographic plate (Agfa Scientica 8 E 75). The duty cycle was adjusted to the hologram speed and to the given
of the stored
signal.
161
Volume
7, number
2
OPTICS (‘O%lI11UNI(‘ATIONS
data rate according to the criteria given in section I. I. The distance Ax separatinp adjacent holograms was 4 pm. Fig. 7 shows the sequence ot‘ reconstructed image points. dicates
The bright point below the chain of points inthe horizontal position of the detector. The
storage
density
experiment
attained
is the result of a preliminary
Ireliability but also the possibility
higher storage problems
densities
associated
in addition
with guiding
1973
of attaining
to solving
tolerance
the film.
References
and has since been improved.
Our results show that holography only for block-organized
can be used not
but also for linearly
optical memories. Compared to point ing using modulated light, holography
I62
higher
February
organized
by point recordoffers not only
( I ] I{. Kiemle and D. R&c, Finfiihrung m die Tcchnik dcr Holographic (Akademixhc Vcrlagsgescll\chaft, Frankfurt/Main. 1969). 121 E. Storck and H. R&11, Ubcr eine spoielle hologaphischc Anordnung, DGaO-Tagung, Bad Hersfeld (1972). 131 H. Rtill and E. Storck, to be publised.