Abstract

A channel model of the volume holographic correlator (VHC) is proposed and demonstrated to improve the accuracy in the scene matching application with the multi-sample parallel estimation (MPE) algorithm. A quantity related to the space-bandwidth product is used to describe the recognition ability in the scene matching system by MPE. A curve is given to optimize the number of samples with the required recognition accuracy. The theoretical simulation and the experimental results show the validity of the channel model. The proposed model provides essential theoretical predictions and implementation guidelines for using the multi-sample parallel estimation method to achieve the highest accuracy.

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References

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2010 (2)

E. Watanabe, A. Naito, and K. Kodate, “Ultrahigh-speed compact optical correlation system using holographic disc,” Proc. SPIE 7442, 1–8 (2010).

J. Joseph, A. Bhagatji, and K. Singh, “Content-addressable holographic data storage system for invariant pattern recognition of gray-scale images,” Appl. Opt. 49(3), 471–478 (2010).
[CrossRef] [PubMed]

2009 (1)

2007 (1)

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(20), 2973–2974 (2007).
[CrossRef]

2006 (3)

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(2), 025201 (2006).
[CrossRef]

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 (2006).
[CrossRef] [PubMed]

Y. Takashima and L. Hesselink, “Media tilt tolerance of bit-based and page-based holographic storage systems,” Opt. Lett. 31(10), 1513–1515 (2006).
[CrossRef] [PubMed]

2005 (1)

F. Saitoh, “Image template matching based on edge-spin correlation,” Electr. Eng. 153, 1592–1596 (2005).

2003 (1)

1998 (1)

1996 (2)

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]

1979 (1)

M. R. Vant, R. W. Herring, and E. Shaw, “Digital processing techniques for satellite-borne SAR,” Can. J. Rem. Sens. 5, 67 (1979).

1965 (1)

T. S. Huang, “PCM picture transmission,” IEEE Spectr. 2, 57–63 (1965).

1959 (1)

J. Capon, “A probabilistic mode for run length coding of picture,” IEEE Trans. Inf. Theory 5(4), 157–163 (1959).
[CrossRef]

Bernal, M.-P.

Bhagatji, A.

Burr, G. W.

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. C.

Capon, J.

J. Capon, “A probabilistic mode for run length coding of picture,” IEEE Trans. Inf. Theory 5(4), 157–163 (1959).
[CrossRef]

Coufal, H.

Devoe, R. G.

Grygier, R. K.

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(2), 025201 (2006).
[CrossRef]

Herring, R. W.

M. R. Vant, R. W. Herring, and E. Shaw, “Digital processing techniques for satellite-borne SAR,” Can. J. Rem. Sens. 5, 67 (1979).

Hesselink, L.

Hoffnagle, J. A.

Huang, T. S.

T. S. Huang, “PCM picture transmission,” IEEE Spectr. 2, 57–63 (1965).

Jefferson, C. M.

Jia, Y.

Jin, G. F.

Joseph, J.

Kodate, K.

E. Watanabe, A. Naito, and K. Kodate, “Ultrahigh-speed compact optical correlation system using holographic disc,” Proc. SPIE 7442, 1–8 (2010).

Lai, S. H.

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 (2006).
[CrossRef] [PubMed]

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(2), 025201 (2006).
[CrossRef]

Liao, Y.

Lundquist, P. M.

Macfarlane, R. M.

Moerner, W. E.

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]

Naito, A.

E. Watanabe, A. Naito, and K. Kodate, “Ultrahigh-speed compact optical correlation system using holographic disc,” Proc. SPIE 7442, 1–8 (2010).

Neifeld, M. A.

Ni, K.

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(20), 2973–2974 (2007).
[CrossRef]

Ouyang, C.

Poga, C.

Psaltis, D.

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]

Qu, Z. Y.

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(20), 2973–2974 (2007).
[CrossRef]

Saitoh, F.

F. Saitoh, “Image template matching based on edge-spin correlation,” Electr. Eng. 153, 1592–1596 (2005).

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(2), 025201 (2006).
[CrossRef]

Shaw, E.

M. R. Vant, R. W. Herring, and E. Shaw, “Digital processing techniques for satellite-borne SAR,” Can. J. Rem. Sens. 5, 67 (1979).

Shelby, R. M.

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(2), 025201 (2006).
[CrossRef]

Sincerbox, G. T.

Singh, K.

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(20), 2973–2974 (2007).
[CrossRef]

Takashima, Y.

Tan, Q. F.

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(2), 025201 (2006).
[CrossRef]

Vant, M. R.

M. R. Vant, R. W. Herring, and E. Shaw, “Digital processing techniques for satellite-borne SAR,” Can. J. Rem. Sens. 5, 67 (1979).

Wang, S. L.

Watanabe, E.

E. Watanabe, A. Naito, and K. Kodate, “Ultrahigh-speed compact optical correlation system using holographic disc,” Proc. SPIE 7442, 1–8 (2010).

Wei, S. D.

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 (2006).
[CrossRef] [PubMed]

Wimmer, P.

Wittmann, G.

Wu, M. X.

Appl. Opt. (2)

Can. J. Rem. Sens. (1)

M. R. Vant, R. W. Herring, and E. Shaw, “Digital processing techniques for satellite-borne SAR,” Can. J. Rem. Sens. 5, 67 (1979).

Electr. Eng. (1)

F. Saitoh, “Image template matching based on edge-spin correlation,” Electr. Eng. 153, 1592–1596 (2005).

IEEE Spectr. (1)

T. S. Huang, “PCM picture transmission,” IEEE Spectr. 2, 57–63 (1965).

IEEE Trans. Image Process. (1)

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 (2006).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

J. Capon, “A probabilistic mode for run length coding of picture,” IEEE Trans. Inf. Theory 5(4), 157–163 (1959).
[CrossRef]

Opt. Eng. (1)

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(2), 025201 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Proc. SPIE (2)

E. Watanabe, A. Naito, and K. Kodate, “Ultrahigh-speed compact optical correlation system using holographic disc,” Proc. SPIE 7442, 1–8 (2010).

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]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1966).

H. A. Jazwinskl, Stochastic process and filtering theory (Academic Press, 1970).

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Figures (8)

Fig. 1
Fig. 1

The schematic diagram of the segmentation process of the remote sensing image.

Fig. 2
Fig. 2

Typical correlation curve between a target image and the stored reference template images. The template image at pixel value 0 is perfectly matched to the target image. The correlation length and segmentation interval are only shown in the x direction.

Fig. 3
Fig. 3

Estimation model of multi-sample spots condition. (a) One-dimensional two-sample system. (b) Two-dimensional four-sample system. (c) Two-dimensional multi-sample system.

Fig. 4
Fig. 4

(a) Recognition error varies with p and the sample number of 2 × 2, 4 × 4, 6 × 6, 8 × 8, 10 × 10 and infinity. (b) Optimization line (blue) and limitation line (black) in the enlarged (a).

Fig. 5
Fig. 5

Experimental setup for testing the MPE method used in VHC. PBS is Polarizing Beam Splitter; SLM is Spatial Light Modulator; S is Shutter; L1, L2, L3, and L4 are Lenses; M is the Mirror; λ/2 is half-wave-plate.

Fig. 6
Fig. 6

Experimental results of the remote sensing image recognition. (a)The remote sensing reference image used in the experiment; (b) Detected correlation spots by inputting a white image; (c) Detected correlation spots by inputting the target image.

Fig. 7
Fig. 7

The results of the horizontal error and the vertical error for using 16 samples. (a) Horizontal error; (b) Vertical error.

Fig. 8
Fig. 8

The normalized error varies with the segmentation length t and the sample number 4 × 4, 6 × 6, 8 × 8, and 10 × 10.

Tables (2)

Tables Icon

Table 1 Different highest recognition accuracy and corresponding p with parameter n

Tables Icon

Table 2 Maximum error varies with segmentation length and sample number

Equations (21)

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f ( x , y ) = a e α | x | β | y | + b ,
M = ( 2 α 2 t x ) ( 2 β 2 t y ) = 16 α β t x t y .
{ σ x = σ VHC a α e β y α x , σ y = σ VHC a β e β y α x .
S x = 0 ,
S = ( z 1 f ( x ) ) 2 + ( z 2 f ( t x ) ) 2 .
2 a α e α | x | ( z 1 a e α | x | b ) + 2 a α e α | t x | ( z 2 a e α | t x | b ) = 0.
d x = e α ( t x ) d z 2 e α x d z 1 a α ( e 2 α x + e 2 α ( t x ) ) .
w = α 1 w 1 + α 2 w 2 + ... + α n w n ,
σ w 2 = α 1 2 σ w 1 2 + α 2 2 σ w 2 2 + ... + α n 2 σ w n 2 .
σ x = σ VHC a α e 2 α ( t x ) + e 2 α x .
e 2 α ( t x ) + e 2 α x 2 e α ( t x ) e α x = 2 e α t .
min ( σ x ) = σ VHC a α e 2 α t + 1 .
max ( σ x ) = σ VHC 2 a α e ( α t ) / 2 .
σ x = σ V H C a α e 2 α ( t x x ) 2 β ( t y y ) + e 2 α x 2 β ( t y y ) + e 2 α ( t x x ) 2 β y + e 2 α x 2 β y      = σ V H C a α ( e 2 α ( t x x ) + e 2 α x ) ( e 2 β ( t y y ) + e 2 β y ) .
{ max ( σ x ) = σ V H C 2 a α e ( β t y α t x ) / 2 = σ V H C 2 a α e ( β y α x ) , max ( σ y ) = σ V H C 2 a β e ( β t y α t x ) / 2 = σ V H C 2 a β e ( β y α x ) ,
{ σ x = σ VHC e ( α + β ) t / 2 a α ( 1 + e 2 α t + e 2 β t + e 2 α t 2 β t + ... + e 2 ( α + β ) ( n / 2 1 ) t )         = σ VHC e ( α + β ) t / 2 a α i = 1 n / 2 j = 1 n / 2 e 2 ( i 1 ) α t 2 ( j 1 ) β t σ y = σ VHC e ( α + β ) t / 2 a β ( 1 + e 2 α t + e 2 β t + e 2 α t 2 β t + ... + e 2 ( α + β ) ( n / 2 1 ) t )         = σ VHC e ( α + β ) t / 2 a β i = 1 n / 2 j = 1 n / 2 e 2 ( i 1 ) α t 2 ( j 1 ) β t .
{ σ x = σ VHC e ( α + β ) t / 2 2 a α i = 1 n / 2 j = 1 n / 2 e 2 ( i 1 ) α t 2 ( j 1 ) β t σ y = σ VHC e ( α + β ) t / 2 2 a β i = 1 n / 2 j = 1 n / 2 e 2 ( i 1 ) α t 2 ( j 1 ) β t .
w = t 2 a p i = 1 n / 2 j = 1 n / 2 e ( i + j 1 ) 2 p .
w = lim n t 2 a p i = 1 n / 2 j = 1 n / 2 e ( i + j 1 ) 2 p = t 2 a p ( e p e p ) .
w = 2.2 e 0.9 p 2.1 p = 2.2 e 3.6 / M 8.4 / M ,
n = 69.4 e 5.4 p + 1.8 p = 69.4 e 21.6 / M + 7.2 / M .

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