Abstract

Usually only a halftone (grayscale) modulation of light is used to present the processed and reference signals in the input plane of analog coherent optical (ACO) correlators, based on spatially integrating the product of two (processed and reference) signals. The halftone modulation requires two transparencies to record two signals separately, as the desired product of two spatial signals is obtained by sequential location of two spatial halftone records along the light path. Such an optical layout leads to the need for precision mutual alignment of two separate signal recordings. This paper presents a one-stage ACO correlation method based on combined halftone and position modulation of the light phase, which is produced by joint phase recording two signals on a single transparency. The joint phase recording provides the high optical efficiency of informational light modulation, automatically supports the spatial coincidence of corresponding elements of both recorded signals, and provides the same spatial scale for both recordings. The suggested method can also be used for introducing phase weight functions in the schemes of space–time ACO processing of wave signals. Advantages of ACO signal processing methods in comparison with corresponding electronic approaches are briefly noted.

© 2013 Optical Society of America

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References

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  1. A. Vander Lugt, “Optical signal processing,” in Space Integrating Correlators (Wiley, 2005), Chap. 13.
  2. B. Pernick, “Area-modulated signal recordings for coherent optical correlators,” Appl. Opt. 11, 1425–1426 (1972).
    [CrossRef]
  3. V. Ezhov, “Coherent-optical correlator with combined modulation of the spatial carrier,” Radiotekh. Elektron. (Minsk) 31, 298–307 (1986).
  4. V. Ezhov and A. Tarasov, “Coherent optical spectral analysis and correlation processing of signals recorded by combined modulation,” Tech. Cybern. 6, 156–166 (1980).
  5. V. Ezhov, “Coherent optical three-dimensional spectrum-correlation processing of wave signals based on space-time integration,” Appl. Opt. 51, 7900–7909 (2012).
    [CrossRef]
  6. R. Marks and S. Bell, “Astigmatic coherent processor analysis,” Opt. Eng. 17, 167–169 (1978).
    [CrossRef]
  7. A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

2012 (1)

1986 (1)

V. Ezhov, “Coherent-optical correlator with combined modulation of the spatial carrier,” Radiotekh. Elektron. (Minsk) 31, 298–307 (1986).

1980 (1)

V. Ezhov and A. Tarasov, “Coherent optical spectral analysis and correlation processing of signals recorded by combined modulation,” Tech. Cybern. 6, 156–166 (1980).

1978 (1)

R. Marks and S. Bell, “Astigmatic coherent processor analysis,” Opt. Eng. 17, 167–169 (1978).
[CrossRef]

1972 (1)

Andreev, A.

A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

Bell, S.

R. Marks and S. Bell, “Astigmatic coherent processor analysis,” Opt. Eng. 17, 167–169 (1978).
[CrossRef]

Ezhov, V.

V. Ezhov, “Coherent optical three-dimensional spectrum-correlation processing of wave signals based on space-time integration,” Appl. Opt. 51, 7900–7909 (2012).
[CrossRef]

V. Ezhov, “Coherent-optical correlator with combined modulation of the spatial carrier,” Radiotekh. Elektron. (Minsk) 31, 298–307 (1986).

V. Ezhov and A. Tarasov, “Coherent optical spectral analysis and correlation processing of signals recorded by combined modulation,” Tech. Cybern. 6, 156–166 (1980).

A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

Kompanets, I.

A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

Marks, R.

R. Marks and S. Bell, “Astigmatic coherent processor analysis,” Opt. Eng. 17, 167–169 (1978).
[CrossRef]

Pernick, B.

Sobolev, A.

A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

Tarasov, A.

V. Ezhov and A. Tarasov, “Coherent optical spectral analysis and correlation processing of signals recorded by combined modulation,” Tech. Cybern. 6, 156–166 (1980).

Vander Lugt, A.

A. Vander Lugt, “Optical signal processing,” in Space Integrating Correlators (Wiley, 2005), Chap. 13.

Appl. Opt. (2)

Opt. Eng. (1)

R. Marks and S. Bell, “Astigmatic coherent processor analysis,” Opt. Eng. 17, 167–169 (1978).
[CrossRef]

Radiotekh. Elektron. (Minsk) (1)

V. Ezhov, “Coherent-optical correlator with combined modulation of the spatial carrier,” Radiotekh. Elektron. (Minsk) 31, 298–307 (1986).

Tech. Cybern. (1)

V. Ezhov and A. Tarasov, “Coherent optical spectral analysis and correlation processing of signals recorded by combined modulation,” Tech. Cybern. 6, 156–166 (1980).

Other (2)

A. Andreev, V. Ezhov, I. Kompanets, and A. Sobolev, “Fast LC devices with lowest control voltage,” in Proceedings of 17th International Display Workshops 2010 (Curran Associates, 2012), pp. 1811–1812.

A. Vander Lugt, “Optical signal processing,” in Space Integrating Correlators (Wiley, 2005), Chap. 13.

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Figures (12)

Fig. 1.
Fig. 1.

Usual ACO correlation method with separate halftone recording two spatial signals, s1 and s2, on two transparencies and with spatial integration of the product of two signals by a spherical lens L with focal length f.

Fig. 2.
Fig. 2.

ACO correlator with joint in-plane recording of two real-amplitude spatial signals, s1 and s2, on a single transparency using a combination of halftone and aperture modulation of real-amplitude of light: (a) the record of two real-amplitude spatial signals, s1 and s2, by combining halftone and aperture modulation of absorption of the transparency and (b) optical scheme with on-axis point for obtaining the correlation function in the spectral plane Ξ.

Fig. 3.
Fig. 3.

ACO correlator with joint in-plane recording of two phase spatial signals, φ1 and φ2, on a single transparency using a combination of x-position modulation and y-position modulation of a real-amplitude spatial carrier: (a) unmodulated spatial carrier presented by halftone modulation of absorption of the transparency, (b) spatial carrier with record of one phase signal φ1 by x-position modulation, (c) spatial carrier with record of another phase signal φ2 by y-position modulation, and (d) spatial carrier with joint record of both phase signals φ1 and φ2 by combination of x- and y-position modulation of the spatial carrier; (e) optical scheme with off-axis point ξ0,η0 for obtaining the correlation function in the spectral plane Ξ.

Fig. 4.
Fig. 4.

Principle of operation of the one-stage ACO correlator, based on combined halftone and position phase modulation of light: (a) initial zero phase shift φout=0 at the point η0; (b) phase shift Δφ at the point η0 caused by changed position of the light source along the y-coordinate; (c) restoring zero phase shift φout=0 at the point η0 by halftone phase modulation of the Δφ value in the light source; (d) spatially stacked N 1D schemes, each illustrated by the picture (c) in this figure. with zero phase shift φout=0 along the η0-line; (e) one-stage scheme of ACO correlator while obtaining the correlation function at the point η0.

Fig. 5.
Fig. 5.

Experimental setup: mirrors Q1–Q4, the column-addressed electrically controlled transparency ECT for halftone phase modulation, the mask M for position phase modulation, the slit mask S.

Fig. 6.
Fig. 6.

Information phase signal s0π whose correlation function maximum is obtained in the experimental setup.

Fig. 7.
Fig. 7.

Appearance of the ECT.

Fig. 8.
Fig. 8.

Interference pattern in the plane Pimage of the experimental setup: (a) unmodulated light in the aperture of the switched-off ECT; (b) halftone phase modulation of light, according to the information signal, implemented by the switched-on ECT.

Fig. 9.
Fig. 9.

Masks in the input plane of the experimental setup: (a) slit mask S; (b) signal mask M with position phase modulation of light.

Fig. 10.
Fig. 10.

Light distributions in the spectral plane Ξ of the experimental setup: (a) the spectrum of the unmodulated light; (b) spectrum of halftone phase modulation of light according to the signal s0π; (c) spectrum of position phase modulation of light according to the signal s0π; (d) spectrum of combined halftone phase modulation and position phase modulation according to the signal s0π.

Fig. 11.
Fig. 11.

Multichannel one-stage ACO correlator with combined halftone and position phase modulation: (a) N channel multiplexing and spatial integration in each channel along y-coordinate; (b) spatial integration in each channel along x-coordinate.

Fig. 12.
Fig. 12.

Phase weight function in the ACO scheme of space–time processing of wave signals: (a) reception of wave with plane wavefront; (b) compensating the static spatial halftone phase modulation along the receiving array Xwave (produced by a spherical wave) using the weight phase function produced by the topology of the curved array xcurve of electro-optic elements.

Equations (10)

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Rc(x0)=sproc(x)sref(xx0)dx,
Ra(x0)=s(x)s*(xx0)dx,s(x)=Aexp(iφ),s*(x)=Aexp(iφ).
shalftone=exp(iφ)=exp(i2πα),
sposition=δ(yy0),
+s(y)δ(yy0)dy=s(y0)
F{sposition}=+δ(yy0)exp(i2πηy)dy=exp(i2πy0η).
F{spositionhalftone}=exp(i2πα)+δ(yy0)exp(i2πηy)dy=exp(i2πα)exp(i2πy0η)=exp[i2π(y0η+α)].
η0=αy0=φ2πy0,
Rc(x0)=exp{i2π[α(x)+η0y(xx0)]}dx
η0=α(x)y0(x)

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