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Acousto optic processing in white light
Volume 56, number 4
OPTICS COMMUNICATIONS
15 December 1985
ACOUSTO OPTIC PROCESSING IN WHITE L I G H T A. LACOURT Laboratoire d'Optique P.M. Duffieux, Associk au CNRS no 214, Universitb de Franche-Comtb, 25030 Besanqon Cedex, France Received 18 February 1985; revised manuscript received 20 June 1985
The wavelength dependence of the diffraction process into an acousto optic cell is taken into account for optical processing. The device is illuminated with spatially coherent or incoherent white fight depending upon the kind of process. It applies to broadening of the deflection range of the cell, to spectrum analysis and to 1-D triple correlation.
1. Introduction Acousto Optic Ceils (AOC) are commonly used for light modulatibn, deflection, correlation or radio frequency spectral analysis. Spatially coherent and quasi monochromatic illumination is generally used in order to avoid the dispersion effect of gratings and other problems dealing with Bragg phenomena. This paper is aimed at showing that operation in white light is possible and may offer advantages. For example, in the device described here, three input variables x, ~, t and three output variables ~, ),, f are available, allowing multidimensional or multifunetional architectures [1]. Possibilities of the set-up are illustrated by various experiments. First a larger magnification of the deflection range of the ceil is shown. That applies to the concept of a spectrum analyser yielding a direct visualization of the signal spectrum. Then is built-up a triple 1D-correlator between the power spectrum of a time dependent function and two space dependent functions. In either case, no speckle noise occurs. The results are discussed in the last section.
X1
)(earth
X
t
TAoct
/~__ ~L.~_-"__~
slit S1
~S(t)
X~ ,L
t'
X~
t
a
t
t
.)
silt s 2
Fig. 1. Schematic diagram of the device. S is a point white light source; AOC the Acomtic Optic Cell. G is a passive grating. The power spectrum Of the RF signal Sw(t) is projected onto the output plane x3Ya.
2. Principle
white light source is supposed to be rectangular shaped. The AOC is a modulator featuring a large interactive region, with acoustic velocity us . It is adjusted at the Bragg angle for the v0 mean frequency of light. The temporal frequency f0 of the acoustic carrier propagating into the cell and the corresponding spatial frequency N O are linked by f0 = N0v s. The incident and emerging directions of light at the AOC are def'med by their direct cosines: u 1 and u~ respective. ly. Similarly, u 2 and u~ define the incident and emerging directions at grating G. The spatial frequency of G is iV'. As the AOC works at Bragg conditions for the v0 frequency, we have
2.1. Set-up, notations
u l(vo) = - u l (vo) = UlO,
The basic diagram of the device is drawn in fig. 1. In the following, the power spectrum of the point
ul (vo) - Ul (vo) -- -2ulO = - N o X o
226
with Xo = c/v o.
(1)
(1')
0 030-4018/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 56, number 4
OPTICS COMMUNICATIONS
The slit S2 is located so that only the diffracted v0-frequency beam travels through it. The same beam reaches the grating G under the minimum of deviation condition
u 2 % ) = - u [ ( ~ 0 ) = u20,
(2)
u[O,o) - u20,o) = -2U2o = --,V'Xo.
(2')
2.2 White light diffraction by the A O C The monochromatic diffraction pattern of AOCs is widely investigated [ 2 - 4 ] . We extend published resuits to the case of white light illumination. Let s(t) be a RF electric signal modulating the amplitude of the acoustic carrier. Due to the Schlieren slit $2, the device acts as a diffracting pupil whose transparency is s(t - X/Os). Consider a white light beam incident onto the AOC along the Ulo direction. Provided the Bragg condition is not drastically critical (this is true if the amplitude of s(t) is small) and neglecting the Doppler frequency shift, each spectral component )` gives a Fraunhofer diffraction pattern at x2-Plane. This pattern is centered on the u~ CA)-direction which satisfies the grating formula f
U1 CA) - Ul0 - N0)`.
PwcA) =Tw(-'u 10, X) = X-2 ITw [NoC A - XO)Vs/X]12 (5) or
t,w (v) = v2 I~Sw(-f0Av/%)l 2
(6)
with A~ = v - v0 . Except for the v2 factor, the power spectrum of the light Pw(v) is similar to the W-K power spectrum of the RF signal. The RF signal is optofrequency converted and the frequencies are linked by: fifo = V/VO. Practically, there are two ways for eliminating the distortion introduced by t,2. The first solution consists in working with a limited spectral band so that Av is much smaller than v0. However the working spectral range of the device is reduced. The second method is based on a 1Iv 2 filtering process of the input rectangular power spectrum. Then eq. (6) reduces to
ew (v) = s 017w ( - f o a"/Vo)l 2.
(7)
Such a power spectrum is displayed at the output plane x 3 of the spectroscope (L, G, L) set in cascade with the previous set-up, yielding a straightforward access to the power spectrum of the RF signal. The advantages of the method are discussed in the follow. ing.
(3)
The intensity distribution in each monochromatic diffraction pattern is proportional to t
15 December 1985
t
iw (Ul,)`) = ) - 2 1 7w {os [u 1 _ u~ CA)]/)`} 12,
(4)
w h e r e "w is the Fourier transform of s(x/os) truncated by the finite width w of the cell. As the incident white light power spectrum is broad, the diffraction patterns generated by each ~peetral component overlap, yielding a chromatic blurring of the power spectrum of the RF signal propagating in the AOC. Next section gives the procedure cancelling out such a blurring.
2.3. Power spectrum o f the output light This section describes the power spectrum PwcA) of light travelling through the slit S2. It is given by the superposition of the various spectral components which travel through $2, whose angular position ul is u~ = --ulO. From eqs. (3), (4) and (1') we have
3. Application 1. Magnification of the deflection range of the cell The magnification of the deflection range of the cell can be easily demonstrated with a sinusoidal modulation of the acoustic carrier. Let s(O = cos(2rtAft). Provided A f > os/w , eq. (7) yields
ew(V) ~-I1 {sine2 [-(fo z~/Vo + ~/)w/os] + sinc2 ["(fo aV/Vo - a f ) w/us] }.
(8)
This equation shows that the power spectrum (fig. 2) consists of two bands, whose center frequencies v0 -+ Au are given by Av/t,0 = +-Af/fo. Their bandwidths are 2VoVs[foW. The grating formula for G can be expressed as
8u'2 = IW(X0 - X) = N~XAv/vO ,
(9)
and the deflection angles generated by the modula. tion frequency Af are 227
Volume 56, number 4
OPTICS COMMUNICATIONS
15 December 1985
4. Application 2. Spectrum analysis
0
Since the second stage of the device works as a spectrometer, the irradiance distribution at the output plane is an image of the RF signal power spectrum Eq. (9) expresses the relation between angular deviation of light at the output of the device, 5u~, and frequency variation of light, Av, from mean frequency v0 . On the other hand, eq. (7) gives the power spectrum of light at the input slit of the spectrometer." Substituting eq. (9) into eq. (7) yields
1
ew(x3) = 103 I~w(-(fo/N'X)x3/,b)l 2
L Fig. 2. Effective power spectrum yielded from cosine RF signal.
5u~(Af) = + N ' k A f / f 0 .
(10)
As a comparison, the same frequency shift of the carrier when the AOC is illuminated in monochromatic light h 0 produces a deflection angle 8ul (Af)
8u i ( a f ) = Xo zV'/os
(12)
with x 3 = ~fiu~. Fig. 3 shows examples of power spectra recorded at the output plane o f the device. The RF resolution limit was evaluated to be 47 kHz while the RF spectral range was found to be 40 MHz, covering all the free spectral range of the spectrometer. It corresponds to a time bandwidth product of 850. The distortion that can be seen in fig. 3b is due to the X term in the argument of eq. (12), which is a space variant scale factor.
(10')
yielding a magnification ratio 5. A p p l i c a t i o n
m = 5u'2(Af)lSu ~ (Af) = +-(X/Xo)N'/N O.
3. Triple c o r r e l a t o r
(11)
The experimental set-up includes an Isomet LS 110-500 cell. At the center frequency f 0 = 100 MHz, • fringe frequency is . N O = 162 m m - I . Th e the acoustic spatial frequency of grating G is N ' = 610 mm - I . The mean magnification calculated with X = X0 is m --- 3.8. The theoretical time bandwidth product is the same as that with monochromatic illumination, i.e. 1100 (with 14 mm aperture).
Consider the device in fig. 4. It is similar to that shown in fig. 1 apart from the slit S 1 which is removed and replaced by a space-dependent achromatic distribution, F(x 1). The slit S 2 is also replaced by a transmittance T(x2). If the AOC acts as a simple grating (i.e. when s(t) = constant) it can be shown that the device is an intensity correlator o f F(x 1) and T(x2) [6,7]
Fig. 3. Effective power spectra of RF signals recorded at the output plane of the device. The central peaks come from addition of a bias (see eq. (4):/3 = 0). (a): sinusoidal signal; (b): square signal; (e): chirp signal. 228
Volume 56, number 4 x1
x
XearciFi x ) ^
m
,l~ss I
~s,i,
OPTICS COMMUNICATIONS x2
--
x3
-
['-r
[
FS(x1, v) = F(x 1 )
15 December 1985
* ["Sw(OsXl/X~)[2,
(15)
neglecting a X2 coefficient as previously mentioned (eq. (7)) and stating u] - u~ CA)= Xl/~- Finally the grating effect of the carrier permits the substitution o f F ' into F in eq. (13) which leads to 7w (x 3 , V) = F(Nox3 IN')
Fig, 4, Triple col'relator, F ( / 1 ): spatially i n c o h e r e n t and
achromatic distribution. T(x 1): transparency.
• 17w [(vslX,~)Nox31N'] 12 , T[Nox31(N' - No) ]. (16) ~'(x3) =F(Nox3/N' ) * T[Nox3/(N' - N o ) ] .
(13)
The effect of any signal s(t) can be taken into account by separating the grating effect of the carrier in the cell from the pupilar effect of the modulation. Then we can consider the "virtual" diffraction pattern of the modulation, brought back to the input plane and replace the input distribution by F'(x 1 u) = F(x 1) *7w(X 1/X~),
(14)
where ~'w is the intensity distribution in the virtual diffraction pattern of the modulation at wavelength X. From eq. (4), we have
Such a result is a triple correlation between two optical intensity distributions and the power spectrum of the RF signal s(t). Examples of correlations are shown in fig. 5.
6. Discussion and conclusion
The experiments show that acousto optical signal processing can be performed in white light under some conditions. First, the Bragg condition cannot be fullfilled simultaneously for a wide range of
Fig. 5. Correlations of RF power spectra and optical intensity distributions.
229
Volume 56, number 4
OPTICS COMMUNICATIONS
wavelengths. The working conditions call for the Raman-Nath regime despite of a loss of efficiency. Second the 1/X~factor in eq. (4) must be taken into account as a precise spectrum analysis is concerned. Third, as can be seen from eq. (7), a non distorted image of the RF signal power spectrum implies a vscaled spectroscope. It is worth noting that the processor exhibits at its output an angular deflection 8u~ that is independent of the acoustic wavelength into the AOC, but depends only on the relative time frequency shift Af/fo and of the grating frequency N'. Thus a broad deviation range is available even at low RF unlike the monochromatic case (eqs. (10) and (10')). Notice that the device is also usable as a tunable filter suitable for spectrum shaping. The same advantage exists in the spectrum analysis configuration, i.e. even low center frequency and narrow band RF spectra can be displayed. Another at. tractive feature of this application is the linear correspondance between optical and radio frequency scales, v and f, so that calibrated optical spectrometers are useful to perform precise radio frequency spectral measurement. Most of the triple product processors are spatially multiplexed and time integrating devices [9]. The system being based on a wavelength multiplexing combined with a space integrating process, it exhibits a large range window [2]. Notice that the triple product could be optically displayed putting the input slit of a spectroscope along x 3-axis (eq. (16)). The use of the device as a spectral modulator of white light can be examinated but information re-
230
15 December 1985
trieval through the power spectrum of the light gives an access to the autocorrelation function of the actual signal only. A time holographic method [8] could be a convenient manner for recording the signal. Two ways are to be considered. The first one consists in superposing a time impulse reference to the actual signal. This applies to pulsed signals. In the second one, the zero order diffracted light could be used as a time reference when mixed with the first order beam. This is nothing but polychromatic optical heterodyninff.
Acknowledgement
"
I thank J £ . Goedgebuer from Laboratoire d'Optique P.M. Duffieux (Universit~ de Besanqon) and Drs. J. Gresser and P. Arabs from ISEA (Universit~ de HauteAlsace) for fruitful discussions about that work.
References
[1 ] D. Psaltis and D. Casasent, Optical Engineering 19 (1980) 193. [2] R.A. Sprague, Optical Engineering 16 (1977) 467. [3] A. Vanderlugt, Appl. Optic* 21 (1982) 1092. [4] R.V. Johmon, Appl. Optic* 17 (1978) 1507. [5] R.A. Sprague and C.L. Koliopoulos, Appl. Optics 15 (1976) 89. [6] J.D. Armitage, A. Lohmann and D.P. Paris, Japan J. Appl. Physics 4 (1965) 273. [7] A. Lacottrt, Optics Comm. 27 (1978) 47. [8] C. Froehly, A. Lacouxt and J.C. Vienot, Nouv. Rev. Optique 4 (1973) 183. [9] D. Casasent and G. Sflbershatz, Appl. Optics 21 (1982) 2076.
OPTICS COMMUNICATIONS
15 December 1985
ACOUSTO OPTIC PROCESSING IN WHITE L I G H T A. LACOURT Laboratoire d'Optique P.M. Duffieux, Associk au CNRS no 214, Universitb de Franche-Comtb, 25030 Besanqon Cedex, France Received 18 February 1985; revised manuscript received 20 June 1985
The wavelength dependence of the diffraction process into an acousto optic cell is taken into account for optical processing. The device is illuminated with spatially coherent or incoherent white fight depending upon the kind of process. It applies to broadening of the deflection range of the cell, to spectrum analysis and to 1-D triple correlation.
1. Introduction Acousto Optic Ceils (AOC) are commonly used for light modulatibn, deflection, correlation or radio frequency spectral analysis. Spatially coherent and quasi monochromatic illumination is generally used in order to avoid the dispersion effect of gratings and other problems dealing with Bragg phenomena. This paper is aimed at showing that operation in white light is possible and may offer advantages. For example, in the device described here, three input variables x, ~, t and three output variables ~, ),, f are available, allowing multidimensional or multifunetional architectures [1]. Possibilities of the set-up are illustrated by various experiments. First a larger magnification of the deflection range of the ceil is shown. That applies to the concept of a spectrum analyser yielding a direct visualization of the signal spectrum. Then is built-up a triple 1D-correlator between the power spectrum of a time dependent function and two space dependent functions. In either case, no speckle noise occurs. The results are discussed in the last section.
X1
)(earth
X
t
TAoct
/~__ ~L.~_-"__~
slit S1
~S(t)
X~ ,L
t'
X~
t
a
t
t
.)
silt s 2
Fig. 1. Schematic diagram of the device. S is a point white light source; AOC the Acomtic Optic Cell. G is a passive grating. The power spectrum Of the RF signal Sw(t) is projected onto the output plane x3Ya.
2. Principle
white light source is supposed to be rectangular shaped. The AOC is a modulator featuring a large interactive region, with acoustic velocity us . It is adjusted at the Bragg angle for the v0 mean frequency of light. The temporal frequency f0 of the acoustic carrier propagating into the cell and the corresponding spatial frequency N O are linked by f0 = N0v s. The incident and emerging directions of light at the AOC are def'med by their direct cosines: u 1 and u~ respective. ly. Similarly, u 2 and u~ define the incident and emerging directions at grating G. The spatial frequency of G is iV'. As the AOC works at Bragg conditions for the v0 frequency, we have
2.1. Set-up, notations
u l(vo) = - u l (vo) = UlO,
The basic diagram of the device is drawn in fig. 1. In the following, the power spectrum of the point
ul (vo) - Ul (vo) -- -2ulO = - N o X o
226
with Xo = c/v o.
(1)
(1')
0 030-4018/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 56, number 4
OPTICS COMMUNICATIONS
The slit S2 is located so that only the diffracted v0-frequency beam travels through it. The same beam reaches the grating G under the minimum of deviation condition
u 2 % ) = - u [ ( ~ 0 ) = u20,
(2)
u[O,o) - u20,o) = -2U2o = --,V'Xo.
(2')
2.2 White light diffraction by the A O C The monochromatic diffraction pattern of AOCs is widely investigated [ 2 - 4 ] . We extend published resuits to the case of white light illumination. Let s(t) be a RF electric signal modulating the amplitude of the acoustic carrier. Due to the Schlieren slit $2, the device acts as a diffracting pupil whose transparency is s(t - X/Os). Consider a white light beam incident onto the AOC along the Ulo direction. Provided the Bragg condition is not drastically critical (this is true if the amplitude of s(t) is small) and neglecting the Doppler frequency shift, each spectral component )` gives a Fraunhofer diffraction pattern at x2-Plane. This pattern is centered on the u~ CA)-direction which satisfies the grating formula f
U1 CA) - Ul0 - N0)`.
PwcA) =Tw(-'u 10, X) = X-2 ITw [NoC A - XO)Vs/X]12 (5) or
t,w (v) = v2 I~Sw(-f0Av/%)l 2
(6)
with A~ = v - v0 . Except for the v2 factor, the power spectrum of the light Pw(v) is similar to the W-K power spectrum of the RF signal. The RF signal is optofrequency converted and the frequencies are linked by: fifo = V/VO. Practically, there are two ways for eliminating the distortion introduced by t,2. The first solution consists in working with a limited spectral band so that Av is much smaller than v0. However the working spectral range of the device is reduced. The second method is based on a 1Iv 2 filtering process of the input rectangular power spectrum. Then eq. (6) reduces to
ew (v) = s 017w ( - f o a"/Vo)l 2.
(7)
Such a power spectrum is displayed at the output plane x 3 of the spectroscope (L, G, L) set in cascade with the previous set-up, yielding a straightforward access to the power spectrum of the RF signal. The advantages of the method are discussed in the follow. ing.
(3)
The intensity distribution in each monochromatic diffraction pattern is proportional to t
15 December 1985
t
iw (Ul,)`) = ) - 2 1 7w {os [u 1 _ u~ CA)]/)`} 12,
(4)
w h e r e "w is the Fourier transform of s(x/os) truncated by the finite width w of the cell. As the incident white light power spectrum is broad, the diffraction patterns generated by each ~peetral component overlap, yielding a chromatic blurring of the power spectrum of the RF signal propagating in the AOC. Next section gives the procedure cancelling out such a blurring.
2.3. Power spectrum o f the output light This section describes the power spectrum PwcA) of light travelling through the slit S2. It is given by the superposition of the various spectral components which travel through $2, whose angular position ul is u~ = --ulO. From eqs. (3), (4) and (1') we have
3. Application 1. Magnification of the deflection range of the cell The magnification of the deflection range of the cell can be easily demonstrated with a sinusoidal modulation of the acoustic carrier. Let s(O = cos(2rtAft). Provided A f > os/w , eq. (7) yields
ew(V) ~-I1 {sine2 [-(fo z~/Vo + ~/)w/os] + sinc2 ["(fo aV/Vo - a f ) w/us] }.
(8)
This equation shows that the power spectrum (fig. 2) consists of two bands, whose center frequencies v0 -+ Au are given by Av/t,0 = +-Af/fo. Their bandwidths are 2VoVs[foW. The grating formula for G can be expressed as
8u'2 = IW(X0 - X) = N~XAv/vO ,
(9)
and the deflection angles generated by the modula. tion frequency Af are 227
Volume 56, number 4
OPTICS COMMUNICATIONS
15 December 1985
4. Application 2. Spectrum analysis
0
Since the second stage of the device works as a spectrometer, the irradiance distribution at the output plane is an image of the RF signal power spectrum Eq. (9) expresses the relation between angular deviation of light at the output of the device, 5u~, and frequency variation of light, Av, from mean frequency v0 . On the other hand, eq. (7) gives the power spectrum of light at the input slit of the spectrometer." Substituting eq. (9) into eq. (7) yields
1
ew(x3) = 103 I~w(-(fo/N'X)x3/,b)l 2
L Fig. 2. Effective power spectrum yielded from cosine RF signal.
5u~(Af) = + N ' k A f / f 0 .
(10)
As a comparison, the same frequency shift of the carrier when the AOC is illuminated in monochromatic light h 0 produces a deflection angle 8ul (Af)
8u i ( a f ) = Xo zV'/os
(12)
with x 3 = ~fiu~. Fig. 3 shows examples of power spectra recorded at the output plane o f the device. The RF resolution limit was evaluated to be 47 kHz while the RF spectral range was found to be 40 MHz, covering all the free spectral range of the spectrometer. It corresponds to a time bandwidth product of 850. The distortion that can be seen in fig. 3b is due to the X term in the argument of eq. (12), which is a space variant scale factor.
(10')
yielding a magnification ratio 5. A p p l i c a t i o n
m = 5u'2(Af)lSu ~ (Af) = +-(X/Xo)N'/N O.
3. Triple c o r r e l a t o r
(11)
The experimental set-up includes an Isomet LS 110-500 cell. At the center frequency f 0 = 100 MHz, • fringe frequency is . N O = 162 m m - I . Th e the acoustic spatial frequency of grating G is N ' = 610 mm - I . The mean magnification calculated with X = X0 is m --- 3.8. The theoretical time bandwidth product is the same as that with monochromatic illumination, i.e. 1100 (with 14 mm aperture).
Consider the device in fig. 4. It is similar to that shown in fig. 1 apart from the slit S 1 which is removed and replaced by a space-dependent achromatic distribution, F(x 1). The slit S 2 is also replaced by a transmittance T(x2). If the AOC acts as a simple grating (i.e. when s(t) = constant) it can be shown that the device is an intensity correlator o f F(x 1) and T(x2) [6,7]
Fig. 3. Effective power spectra of RF signals recorded at the output plane of the device. The central peaks come from addition of a bias (see eq. (4):/3 = 0). (a): sinusoidal signal; (b): square signal; (e): chirp signal. 228
Volume 56, number 4 x1
x
XearciFi x ) ^
m
,l~ss I
~s,i,
OPTICS COMMUNICATIONS x2
--
x3
-
['-r
[
FS(x1, v) = F(x 1 )
15 December 1985
* ["Sw(OsXl/X~)[2,
(15)
neglecting a X2 coefficient as previously mentioned (eq. (7)) and stating u] - u~ CA)= Xl/~- Finally the grating effect of the carrier permits the substitution o f F ' into F in eq. (13) which leads to 7w (x 3 , V) = F(Nox3 IN')
Fig, 4, Triple col'relator, F ( / 1 ): spatially i n c o h e r e n t and
achromatic distribution. T(x 1): transparency.
• 17w [(vslX,~)Nox31N'] 12 , T[Nox31(N' - No) ]. (16) ~'(x3) =F(Nox3/N' ) * T[Nox3/(N' - N o ) ] .
(13)
The effect of any signal s(t) can be taken into account by separating the grating effect of the carrier in the cell from the pupilar effect of the modulation. Then we can consider the "virtual" diffraction pattern of the modulation, brought back to the input plane and replace the input distribution by F'(x 1 u) = F(x 1) *7w(X 1/X~),
(14)
where ~'w is the intensity distribution in the virtual diffraction pattern of the modulation at wavelength X. From eq. (4), we have
Such a result is a triple correlation between two optical intensity distributions and the power spectrum of the RF signal s(t). Examples of correlations are shown in fig. 5.
6. Discussion and conclusion
The experiments show that acousto optical signal processing can be performed in white light under some conditions. First, the Bragg condition cannot be fullfilled simultaneously for a wide range of
Fig. 5. Correlations of RF power spectra and optical intensity distributions.
229
Volume 56, number 4
OPTICS COMMUNICATIONS
wavelengths. The working conditions call for the Raman-Nath regime despite of a loss of efficiency. Second the 1/X~factor in eq. (4) must be taken into account as a precise spectrum analysis is concerned. Third, as can be seen from eq. (7), a non distorted image of the RF signal power spectrum implies a vscaled spectroscope. It is worth noting that the processor exhibits at its output an angular deflection 8u~ that is independent of the acoustic wavelength into the AOC, but depends only on the relative time frequency shift Af/fo and of the grating frequency N'. Thus a broad deviation range is available even at low RF unlike the monochromatic case (eqs. (10) and (10')). Notice that the device is also usable as a tunable filter suitable for spectrum shaping. The same advantage exists in the spectrum analysis configuration, i.e. even low center frequency and narrow band RF spectra can be displayed. Another at. tractive feature of this application is the linear correspondance between optical and radio frequency scales, v and f, so that calibrated optical spectrometers are useful to perform precise radio frequency spectral measurement. Most of the triple product processors are spatially multiplexed and time integrating devices [9]. The system being based on a wavelength multiplexing combined with a space integrating process, it exhibits a large range window [2]. Notice that the triple product could be optically displayed putting the input slit of a spectroscope along x 3-axis (eq. (16)). The use of the device as a spectral modulator of white light can be examinated but information re-
230
15 December 1985
trieval through the power spectrum of the light gives an access to the autocorrelation function of the actual signal only. A time holographic method [8] could be a convenient manner for recording the signal. Two ways are to be considered. The first one consists in superposing a time impulse reference to the actual signal. This applies to pulsed signals. In the second one, the zero order diffracted light could be used as a time reference when mixed with the first order beam. This is nothing but polychromatic optical heterodyninff.
Acknowledgement
"
I thank J £ . Goedgebuer from Laboratoire d'Optique P.M. Duffieux (Universit~ de Besanqon) and Drs. J. Gresser and P. Arabs from ISEA (Universit~ de HauteAlsace) for fruitful discussions about that work.
References
[1 ] D. Psaltis and D. Casasent, Optical Engineering 19 (1980) 193. [2] R.A. Sprague, Optical Engineering 16 (1977) 467. [3] A. Vanderlugt, Appl. Optic* 21 (1982) 1092. [4] R.V. Johmon, Appl. Optic* 17 (1978) 1507. [5] R.A. Sprague and C.L. Koliopoulos, Appl. Optics 15 (1976) 89. [6] J.D. Armitage, A. Lohmann and D.P. Paris, Japan J. Appl. Physics 4 (1965) 273. [7] A. Lacottrt, Optics Comm. 27 (1978) 47. [8] C. Froehly, A. Lacouxt and J.C. Vienot, Nouv. Rev. Optique 4 (1973) 183. [9] D. Casasent and G. Sflbershatz, Appl. Optics 21 (1982) 2076.