Abstract

We present a configuration for a real-time spatial image processor that is based upon an imaging setup in which a grating with Fourier coefficients with tunable phase is attached to the object plane. The illumination that is used for the proposed concept is spatially incoherent. By proper adjusting of the magnification of the imaging system to the spatial period of the grating and the sampling grid of the camera, the aliasing effect due to the digital sampling realizes a nonuniform and tunable spectral distribution (a filter) that is applied over the spectrum of the object. Preliminary numerical and experimental demonstration of the operation principle is provided with a spatial LiNbO3 hexagonal grating.

© 2009 Optical Society of America

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References

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1998 (1)

1997 (2)

1995 (2)

1994 (1)

1993 (2)

1992 (2)

1990 (1)

1979 (1)

Babbitt, W. R.

Braunecker, B.

Cartwright, C. M.

Chang, T. Y.

Fainman, Y.

D. M. Marom, D. Panasenko, P. Sun, and Y. Fainman, “Real time spatial-temporal signal processing by wave-mixing with cascaded second-order nonlinearities,” in Optics in Computing, OSA Technical Digest (Optical Society of America, 1999), paper OThC2.

Farkas, D.

Gaeta, C. J.

Gillespie, W. A.

Hauck, R.

Hong, J. H.

Huang, G.

Jin, G.

Joseph, J.

Kachru, R.

Kamra, K.

Knowlden, R.

Leger, J. R.

Lohmann, A. W.

Marom, D. M.

D. M. Marom, D. Panasenko, P. Sun, and Y. Fainman, “Real time spatial-temporal signal processing by wave-mixing with cascaded second-order nonlinearities,” in Optics in Computing, OSA Technical Digest (Optical Society of America, 1999), paper OThC2.

Mendlovic, D.

Mitchell, P. V.

Morphis, N.

Mossberg, T. W.

Panasenko, D.

D. M. Marom, D. Panasenko, P. Sun, and Y. Fainman, “Real time spatial-temporal signal processing by wave-mixing with cascaded second-order nonlinearities,” in Optics in Computing, OSA Technical Digest (Optical Society of America, 1999), paper OThC2.

Pepper, D. M.

Pillai, P. K. C.

Poon, T.-C.

Rhodes, W. T.

Schilling, B. W.

Schuler, J.

Shen, X. A.

Shinoda, K.

Singh, K.

Sirohi, R. S.

Sreedhar, P. R.

Sun, P.

D. M. Marom, D. Panasenko, P. Sun, and Y. Fainman, “Real time spatial-temporal signal processing by wave-mixing with cascaded second-order nonlinearities,” in Optics in Computing, OSA Technical Digest (Optical Society of America, 1999), paper OThC2.

Suzuki, Y.

Wang, Z. Q.

Wu, M.

Wu, M. H.

Yan, Y.

Yeh, P.

Zalevsky, Z.

Appl. Opt. (6)

J. Opt. Soc. Am. B (1)

Opt. Lett. (5)

Other (1)

D. M. Marom, D. Panasenko, P. Sun, and Y. Fainman, “Real time spatial-temporal signal processing by wave-mixing with cascaded second-order nonlinearities,” in Optics in Computing, OSA Technical Digest (Optical Society of America, 1999), paper OThC2.

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Figures (18)

Fig. 1
Fig. 1

Schematic illustration of the optical setup.

Fig. 2
Fig. 2

(a) Schematic illustration of the OTF and the notations we use. (b) Schematic illustration of the spectral distribution H ¯ ( μ ) due to replication of S ( μ ) .

Fig. 3
Fig. 3

Schematic illustration of the spectral replication due to the sampling at the detector plane.

Fig. 4
Fig. 4

Suggested experimental configuration.

Fig. 5
Fig. 5

(a) Binary amplitude mask that is to be attached to the aperture plane of the imaging lens. (b) Realization of all-pass and of low-pass filtering that is tuned by changing the phase of the tunable Li Nb O 3 grating from zero to π.

Fig. 6
Fig. 6

(a) SEM image of the Li Nb O 3 modulator with pixels of 35 μm . (b) Experimental setup.

Fig. 7
Fig. 7

(a) Captured target image without CG. The x and y axes are pixel indices. (b) After averaging rows. (c) Fourier transform of (b) with DC normalization. (d) Zoom-in to show the modulation value (0.02) and to show its position (sample 119 for + 1 order).

Fig. 8
Fig. 8

(a) Captured image of CG without object. The x and y axes are pixel indices. (b) After averaging rows. (c). Fourier transform of (b) with DC normalization. (d) Zoom-in to show position of + 1 order (sample 139).

Fig. 9
Fig. 9

(a. Captured image of CG with object. The x and y axes are pixel indices. (b) After averaging rows. (c) Fourier transform of (b) with DC normalization. (d) Zoom-in to show position of CG + 1 order (sample 139).

Fig. 10
Fig. 10

(a) Result after simulating the aliasing effect by decimation (in the Fourier domain). (b). Zoom-in to show the enhanced modulation value (0.045). (c) Result after simulating the aliasing effect by decimation (in the space domain).

Fig. 11
Fig. 11

Experimental setup for the 2D experiment.

Fig. 12
Fig. 12

(a) Original object and (b) its spectrum.

Fig. 13
Fig. 13

(a) Coding grating and (b) its spectrum.

Fig. 14
Fig. 14

(a) Captured image of the CG with target, prior to the aliasing effect. (b) The obtained spectrum.

Fig. 15
Fig. 15

Final results. (a) Applying aliasing on the resampled captured image results in a contrast enhanced target image. (b) The spectrum.

Fig. 16
Fig. 16

Numerical simulations. (a) Original object with contrast of first harmonic of 0.167. (b) Enhanced object with contrast of first harmonic of 0.235.

Fig. 17
Fig. 17

Numerical simulation with USAF resolution target. The USAF resolution target was tested under the same conditions as in Fig. 16. Frequencies beyond the tested bandwidth were deliberately filtered out. (a) USAF target and (b) the enhanced USAF target.

Fig. 18
Fig. 18

Simulations of the original OTF (solid curve) and the enhanced OTF (dotted curve).

Equations (13)

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H ¯ ( μ ) = H ( μ ) · [ s ( x ) · g ( x ) ] exp ( 2 π i μ x ) d x ,
H ( μ ) sinc ( 4 W m Z i μ b ) .
W m = b 2 2 ( 1 Z i + 1 Z o - 1 F ) .
1 Z i + 1 Z o = 1 F .
g ( x ) = n a n exp ( 2 π i n μ 0 x ) .
H ¯ ( μ ) = n a n H ( μ ) S ( μ n μ 0 ) ,
H m ( μ ) = H ( μ ) · rect ( μ m μ 0 μ 0 ) .
H ¯ ( μ ) = n a n H n ( μ ) S ( μ n μ 0 ) .
H ¯ d ( μ ) = H ¯ ( μ ) n δ ( μ n μ 0 ) .
H ¯ d ( inf ) ( μ ) = n a n H n ( μ ) S ( μ ) = S ( μ ) [ n a n H ( μ n μ 0 ) ] .
f ( x ) = h ( x ) · n a n exp ( 2 π i n μ 0 x ) ,
a n = 1 / μ 0 [ f ( x ) h ( x ) ] exp ( 2 π i n μ 0 x ) d x .
λ F 2 b M = 35 μm 2.5 .

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