Abstract

The optimality of correlation filters is an important issue in applications of pattern recognition. We consider here both binary phase-only filters (BPOFs) and amplitude encoded binary phase-only filters (AE BPOFs) and study the results of optimizing the filters for a real world object (the Space Shuttle). We find that while only small improvements result from optimizing a BPOF, optimization of the AE BPOF is quite important in obtaining a useful correlation function. In the case of an AE BPOF, both signal-to-noise and peak-to-sidelobe measures must be studied. Computer simulation and experimental correlation results are presented.

© 1990 Optical Society of America

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References

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    [CrossRef]
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1989 (5)

1988 (2)

1987 (1)

1986 (1)

1984 (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).

Dickey, F. M.

Farn, M. W.

Feldman, M. R.

Flannery, D. L.

Flavin, M. A.

Gianino, P. D.

Goodman, J. W.

Guest, C. C.

Horner, J. L.

Kallman, R. R.

Kim, M. S.

Loomis, J. S.

Milkovich, M. E.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).

Romero, L. A.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).

Vijaya Kumar, B. V. K.

Appl. Opt. (7)

Opt. Eng. (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698–704 (1984).

Opt. Lett. (2)

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Figures (14)

Fig. 1
Fig. 1

Complex real and imaginary planes with decision line angle β.

Fig. 2
Fig. 2

Schematic diagram of a three-lens correlator system. Lenses 1 and 2 together have focal length f. Lens 3 has focal length f3 and performs both phase correction and the inverse transform 1/f′ is the power of lens 3 used to perform transform and in practice f′ ≈ f.

Fig. 3
Fig. 3

Schematic illustration of MOSLM/polarizer configurations for (a) binary phase operation and (b) binary amplitude operation. Upon passage through the MOSLM the incident polarization is rotated either ±θ degrees.

Fig. 4
Fig. 4

Centered Shuttle at 45°.

Fig. 5
Fig. 5

Simulation results for the BPOF made for the centered Shuttle object.

Fig. 6
Fig. 6

Experimental results for the BPOF made for the centered Shuttle object: (a) β = 0° and (b) β = 90°.

Fig. 7
Fig. 7

Most odd test object.

Fig. 8
Fig. 8

Simulation results for the BPOF made for the most odd test object.

Fig. 9
Fig. 9

The 45° Shuttle shifted to the upper left-hand corner.

Fig. 10
Fig. 10

Simulation results for the BPOF made for the 45° Shuttle shifted to the upper left-hand corner.

Fig. 11
Fig. 11

Experimental results for the BPOF made for the shifted Shuttle object: (a) β = 54° and (b) β = 90°.

Fig. 12
Fig. 12

Simulation results for the AE BPOF made for the centered Shuttle object.

Fig. 13
Fig. 13

Experimental results for the AE BPOF made for the centered Shuttle object: (a) β = 90° and (b) β = 270°.

Fig. 14
Fig. 14

Simulation results for the AE BPOF made for the shifted Shuttle object.

Equations (6)

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c ( 0 , 0 ) 2 = | H ( u , v ) S ( u , v ) d u d v | 2 ,
γ = c ( 0 , 0 ) 2 c ( x , y ) 2 d x d y - c ( 0 , 0 ) 2 ,
denom = c ( x , y ) 2 d x d y - c ( 0 , 0 ) 2 = C ( u , v ) 2 d u d v - c ( 0 , 0 ) 2 = H ( u , v ) 2 S ( u , v ) 2 d u d v - c ( 0 , 0 ) 2 ,
γ = H ( u , v ) S ( u , v ) d u d v 2 H ( u , v ) 2 S ( u , v ) 2 d u d v - H ( u , v ) S ( u , v ) d u d v 2 .
s ( x , y ) = π / 4 + s t ( x , y ) π / 2 · rect ( x 2 π ) ,
s t ( x , y ) = m = 0 sin [ ( 2 m + 1 ) x ] ( 2 m + 1 ) .

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