Abstract

Here we study the optical phase errors introduced into an optical correlator by the input and filter plane magneto-optic spatial light modulators. We measure and characterize the magnitude of these phase errors, evaluate their effects on the correlation results, and present a means of correction by a design modification of the binary phase-only optical-filter function. The efficacy of the phase-correction technique is quantified and is found to restore the correlation characteristics to those obtained in the absence of errors, to a high degree. The phase errors of other correlator system elements are also discussed and treated in a similar fashion.

© 1992 Optical Society of America

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References

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1991 (2)

1990 (1)

1989 (2)

1988 (3)

1986 (2)

Bahri, Z.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Casasent, D.

Diep, J.

Downie, J. D.

Ennis, D. J.

Farn, M. W.

Goodman, J. W.

Horner, J. L.

Jared, D. A.

Jeong, J. W.

Jeong, S. I.

Kang, M. H.

Kim, H. M.

Liu, H-K.

Ma, P. W.

Mahlab, U.

Mok, F.

Ochoa, E.

Psaltis, D.

Reid, M. B.

Rosen, J.

Shamir, J.

Vijaya Kumar, B. V. K.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Xia, S-F.

Appl. Opt. (6)

Opt. Lett. (4)

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the complete correlator system. The filter SLM and polarizer P2 are nearly coincident, as are the correlation plane detector and polarizer P3.

Fig. 2
Fig. 2

Measured phase distribution of a plane wave on transmission through the input plane MOSLM. The P–V deviation suffered by the wave front is 0.57λ, where λ = 633 nm.

Fig. 3
Fig. 3

Centered combination wrench image used for correlation simulations and experiment.

Fig. 4
Fig. 4

Simulation results of the effects of the correlator system component phase errors on the resulting correlation peak. Phase errors in the input plane greatly diminish the translation invariance of the system, while phase errors in the filter plane do not affect the translation-invariant properties.

Fig. 5
Fig. 5

Centered open-end wrench image used to test the discrimination capabilities of the modified phase-corrected niters designed to recognize the similar combination wrench image. The number of pixels on in this image equals that of the combination wrench.

Fig. 6
Fig. 6

(a) Experimental correlation peak for the centered combination wrench obtained by using an uncorrected filter. (b) Experimental correlation peak obtained by using a modified filter corrected for input SLM, filter SLM, and polarizer phase errors.

Tables (4)

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Table I Measured Phase Characteristics of Our Laboratory Correlator with GGG Semetex MOSLM’s and Melles-Griot Polarizersa

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Table II Computer Simulation Effects of the Various Types of Phase Error on the Output Correlation Peak for Both Uncorrected and Corrected Filters Made of the Combination Wrench Imagea

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Table III Simulation Results for the Discrimination Capabilities of the Uncorrected and Corrected Filters for the Case of Two Similar Objects—the Combination Wrench and the Open-End Wrencha

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Table IV Experimental Correlation-Peak Results from the Laboratory Correlator for Modified Phase-Corrected Filters Made for the Combination Wrench Imagea

Equations (10)

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c ( x , y ) = F 1 { F { s ( x , y ) ϕ i ( x , y ) } H * ( u , υ ) } ,
ϕ i ( x , y ) = exp [ j 2 π λ z ( x , y ) ] ,
c ( x , y ) = F 1 { F { s ( x , y ) } H * ( u , υ ) Φ f ( u , υ ) } = F 1 { S ( u , υ ) H * ( u , υ ) Φ f ( u , υ ) } = c 0 ( x , y ) * * F 1 { Φ f ( u , υ ) } ,
H ( u , υ ) = M { F { s ( x , y ) } } = M { S ( u , υ ) } ,
M { S ( u , υ ) } = { + 1 S ( u , υ ) Region 1 1 S ( u , υ ) Region 2 .
s ( x , y ) = s ( x , y ) ϕ i ( x , y ) .
H ( u , υ ) = M { F { s ( x , y ) Φ i ( x , y ) } } .
U f p = S ( u , υ ) Φ ( u , υ ) ,
H ( u , υ ) = M { S ( u , υ ) Φ ( u , υ ) } .
H ( u , υ ) = M { F { s ( x , y ) Φ i ( x , y ) } ϕ f ( u , υ ) Φ p ( u , υ ) } .

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