Abstract

A volume holographic correlator is capable of inner product calculations between the input image and multiple stored images in parallel. The inner product that is the center value of the correlation can provide a scalar measure of change between two images. The inner product values are directly acquired by measuring the intensities of the correlation peaks on the CCD. However, the measured intensities are not exactly equal to the theoretical inner product values due to the redundancy correlation. The structure of the correlation peak for randomly interleaved images is analyzed. It can be regarded as two volumes, one pyramid and one prism. The relative inner product value is only determined by the height of the pyramid. The prism, caused by the redundancy correlation, appears as the background noise, which is the main source of the inner product calculation error. A calibration method is proposed to remove the prism from the measured intensity. Based on the geometric structure of the correlation peak, the theoretical expression of the inner product value for the pyramid is derived. A white image is employed as the input image and the measured correlation peak intensity is used to calibrate the inner product value. The calibration method can effectively eliminate the error caused by the redundancy correlation to achieve a high output accuracy of the volume holographic correlator. Experiments are demonstrated for the validity of the method.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

2009 (2)

2007 (2)

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32, 2972–2974 (2007).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

2006 (2)

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Y. Takashima and L. Hesselink, “Media tilt tolerance of bit-based and page-based holographic storage systems,” Opt. Lett. 31, 1513–1515 (2006).
[CrossRef]

2004 (1)

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

2003 (1)

1999 (2)

1997 (1)

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

1996 (1)

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35, 1847–1853 (1996).
[CrossRef]

1995 (1)

1994 (1)

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 (1994).
[CrossRef]

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Burr, G. W.

G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38, 6779–6784 (1999).
[CrossRef]

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 (1994).
[CrossRef]

Cao, L.

S. Wang, Q. Tan, L. Cao, Q. He, and G. Jin, “Multi-sample parallel estimation in volume holographic correlator for remote sensing image recognition,” Opt. Express 17, 21738–21747 (2009).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

Cao, L. C.

Coufal, H.

Denkewalter, R.

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Fu, H.

Goertzen, B. J.

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35, 1847–1853 (1996).
[CrossRef]

Gu, C.

Gu, H. R.

Hanssen, H.

He, Q.

S. Wang, Q. Tan, L. Cao, Q. He, and G. Jin, “Multi-sample parallel estimation in volume holographic correlator for remote sensing image recognition,” Opt. Express 17, 21738–21747 (2009).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

He, Q. S.

Heifetz, A.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Hesselink, L.

Y. Takashima and L. Hesselink, “Media tilt tolerance of bit-based and page-based holographic storage systems,” Opt. Lett. 31, 1513–1515 (2006).
[CrossRef]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Jin, G.

S. Wang, Q. Tan, L. Cao, Q. He, and G. Jin, “Multi-sample parallel estimation in volume holographic correlator for remote sensing image recognition,” Opt. Express 17, 21738–21747 (2009).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

Jin, G. F.

Kobras, S.

Lee, J. K.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Levene, M.

Liao, Y.

Lien, J.

Ma, Q.

Mitkas, P. A.

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35, 1847–1853 (1996).
[CrossRef]

Mok, F. H.

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 (1994).
[CrossRef]

Ni, K.

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Ouyang, C.

Psaltis, D.

M. Levene, G. J. Steckman, and D. Psaltis, “Method for controlling the shift invariance of optical correlators,” Appl. Opt. 38, 394–398 (1999).
[CrossRef]

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 (1994).
[CrossRef]

Pu, A.

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Qu, Z.

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

Qu, Z. Y.

Shahriar, M. S.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Shen, J. T.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Steckman, G. J.

Su, P.

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32, 2972–2974 (2007).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

Takashima, Y.

Tan, Q.

Tripathi, R.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

Wang, S.

Wang, S. L.

Wu, M. X.

Appl. Opt. (2)

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

Opt. Eng. (3)

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35, 1847–1853 (1996).
[CrossRef]

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45, 025201 (2006).
[CrossRef]

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Proc. IEEE (1)

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Proc. SPIE (2)

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 (1994).
[CrossRef]

K. Ni, Z. Qu, L. Cao, P. Su, Q. He, and G. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 68271J (2007).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Autocorrelation patterns of two different images. Point C is the inner product value in the center of the correlation.

Fig. 2.
Fig. 2.

(a) Autocorrelation pattern of the original image, (b) the cross-correlation pattern of two random images that are totally irrelevant to each other, (c) the autocorrelation pattern of the interleaved image that is randomized from the original image in (a).

Fig. 3.
Fig. 3.

(a) Correlation pattern of the interleaved images when the volume holographic correlator is not applied; (b) only a small integration area is used when the volume holographic correlator is applied; (c) the correlation peak in the integration area will be shown in the volume holographic correlator.

Fig. 4.
Fig. 4.

Schematic diagram of the calibration method. A white image is used as a reference to calibrate the inner product value.

Fig. 5.
Fig. 5.

Schematic diagram of the correlation peak. The correlation peak can be regarded as a pyramid on top of a prism. Vac is the value of the autocorrelation of the interleaved images. Vcc is the value of cross-correlation of any two interleaved images. Vbase is the value of the cross-correlation when these two images are totally irrelevant.

Fig. 6.
Fig. 6.

Experimental setup for verifying the calibration method used in the VHC. PBS, polarizing beam splitter; SLM, spatial light modulator; S, shutter; L1, L2, L3, and L4, lenses; M, mirror; λ/2, half-wave plate. The correlation peak is on the CCD.

Fig. 7.
Fig. 7.

Test images for the calibration method: (a) uninterleaved, (b) interleaved.

Fig. 8.
Fig. 8.

(a) Correlation spot array of the 96-channel volume holographic correlator when a white image is input (96 correlation spots on the CCD), (b) comparison of the calculated inner products using different methods.

Fig. 9.
Fig. 9.

Experimental results on the remote sensing images: (a) five subimages segmented from a big remote sensing image, (b) comparison between experimental results with and without the calibration method.

Tables (1)

Tables Icon

Table 1. Correlation Results of the Test Images

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

h=MNc2.
h=dMNc2.
R˜d=d/(MNc).
R˜dVcc/Vtop.
d=h+(dmaxh)dhdmaxh=MNc2+(MNcMNc2)dhdmaxh.
R˜d=ddmax=c+(1c)dhdmaxh.
Vbase(x,y)=shdxdy.
dhdmaxh=Vcc(x,y)Vbase(x,y)Vac(x,y)Vbase(x,y).
Vbase(x,y)=cVtop(x,y).
m=Vtop(x,y)/Vac(x,y).
R˜d=mVcc(x,y)mcVtop(x,y)Vtop(x,y)mcVtop(x,y)(1c)+c.

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