對於一個簡單的體積全像儲存相位解碼方法，並且能夠精確地讀取出資訊是必要的。此邊我們提出一個模組叫做雙頻光柵剪切干涉儀(Doubl-frequency grating based shearing interferometry簡稱DFGSI)。此模組是利用全像片，上記錄了兩種不同空間頻率的光柵，稱為雙頻光柵(Double-frequency grating，簡稱 DFG)。並配合四步相移技術來做全像儲存的四階相位訊號解碼，模擬得證用此模組可以消除碟片震動所造成的相位錯誤雜訊影響，進而讀出準確的資訊，達到誤碼率小於1%。實驗部分可以應證輸入一個完美訊號，此模組的剪切位移量可以達到符合預期的效果且能有效地消除雜訊得到較好的誤碼率。

A simple method to decode the stored phase signal of volume holographic data storage precisely is highly demanded. We promote a module called double-frequency-grating based shearing interferometry (DFGSI). Double-frequency grating is the Holographic film which is recorded by two different space frequency grating . We combine with the phase shift interferometry to decode the signal modulated by four step phase only. The simulation prove this module can remove the noise caused by shifting the disc laterally. Then, it can decode the signal correctly, and the bit error rate is less than 1%. The experiment prove that we input the perfect signal to this module. Then the displacement of shearing interferometer can achieve the effect we expected. In addition, it can remove the noise efficiently to have the better bit error rate.

1. K. Anderson and K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29, 1402-1404 (2004).
2. R. Fujimura, T. Shimura, and K. Kuroda, “Multiplexing capability in polychromatic reconstruction with selective detection method,” Opt. Express 18, 1091-1098 (2010).
3. T. Ochiai, D. Barada, T. Fukuda, Y. Hayasaki, K. Kuroda, and T. Yatagai, “Angular multiplex recording of data pages by dual-channel polarization holography,” Opt. Lett. 38, 748-750 (2013).
4. J. Zang, G. Kang, P. Li, Y. Liu, F. Fan, Y. Hong, Y. Huang, X. Tan, A. Wu, T. Shimura, and K. Kuroda, “Dual-channel recording based on the null reconstruction effect of orthogonal linear polarization holography,” Opt. Lett. 42, 1377-1380 (2017).
5. G. Barbastathis, M. Levene, and D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417 (1996).
6. H. Y. S. Li and D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
7. T. C. Teng, Y. W. Yu, and C. C. Sun, “Enlarging multiplexing capacity with reduced radial cross talk in volume holographic discs,” Opt. Express 14, 3187– 3192 (2006).
8. T. Nobukawa, Y. Wani, and T. Nomura, “Multiplexed recording with uncorrelated computer-generated reference patterns in coaxial holographic data storage,” Opt. Lett. 40, 2161–2164 (2015).
9. C. Li, L. Cao, Z. Wang, and G. Jin, “Hybrid polarization-angle multiplexing for volume holography in gold nanoparticle-doped photopolymer,” Opt. Lett. 39, 6891-6894 (2014).
10. C. C. Sun and W. C. Su, “Three-dimensional shifting selectivity of random phase encoding in volume holograms,” Appl. Opt. 40, 1253-1260 (2001).
11. D. Gabor, “A new Microscopic principle,” Nature 161, 777 (1948).
12. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393-400 (1963).
13. H. Coufal, D. Psaltis and G. T. Sincerbox, Eds, Holographic data storage, (Berlin, Germany, Springer-Verlag, 2000).
14. L. K. Anderson, “Holographic optical memory for bulk data storage,” Bell Lab. Record 45, 319-326 (1968).
15. W. H. Strehlow, R. L. Dennison and J. R. Packard, “Holographic data store,” J. Opt. Soc. Am 64, 543-544 (1974).
16. J. Heanue, M. Bashaw and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749-752 (1994).
17. N. Nishida, M. Sakaguchi and F. Saito, “Holographic coding plate: a new application of holographic memory,” Appl. Opt. 12,1663-1674 (1973).
18. L. D. Auria, J. P. Huignard, C. Slezak, and E. Spitz, “Experimental holographic read-write memory using 3-D storage,” Appl. Opt. 13, 808-818 (1974).
19. Y. Tsunoda, K. Tatsuno, K. Kataoka, and Y. Takeda, “Holographic video disk: an alternative approach to optical videodisks,” Appl. Opt. 15, 1398-1403 (1976).
20. K. Kubota, Y. Ono, M. Kondo, S. Sugama, N. Nishida, and M. Sakaguchi, “Holographic disk with high data transfer rate: its application to an audio response memory,” Appl. Opt. 19, 944-951(1980).
21. I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, and J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375-2379 (1996).
22. M. P. Bernal, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, and G. Wittmann, “A precision tester for studies of holographic optical storage materials and recording physics,” Appl. Opt. 35, 2360-2374 (1996).
23. G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, and B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639-641 (1997).
24. A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737 (1997).
25. S. S. Orlov, W. Phillips, E. Bjornson, Y. Takashima, P. Sundaram, L. Hesselink, R. Okas, D. Kwan, and R. Snyder, “High-transfer-rate high-capacity holographic disk data-storage system,” Appl. Opt. 43, 4902-4914 (2004).
26. G. W. Burr, F. H. Mok, and D. Psalts, “Angle and space multiplexed storage using the 90∘geometry,” Opt. Commun. 117, 49-55 (1995).
27. W. C. Su, Y. W. Chen, C. C. Sun, and Y. Ouyang, “Multi-layer storage of a shift-multiplexed holographic disc,” Opt. Eng. 42, 1528-1529 (2003).
28. G. A. Rakuljic, V. Leyva, and A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume hologram,” Opt. Lett. 17, 1471-1473 (1992)
29. S. Yin, H. Zhou, F. Zhao, M. Wen, Y. Zang, J. Zhang, and F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tnable diode-laser,” Opt. Commun. 101, 317-321 (1993).
30. C. Denz, G. Pauliat, and G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991)
31. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Encrypted holographic data storage based on orthogonal-phase-code multiplexing,” Appl. Opt. 34, 6012–6015 (1995).
32. C. C. Sun, W. C. Su, B. Wang, and Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67-74 (2000)
33. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, “Holographic data storage in three-dimensional media,” Appl. Opt. 5, 1303-1311 (1966).
34. A. Pu and D. Psaltis, in 1997 Optical Data Storage Topical Meeting (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 48–49.
35. K. Curtis, “Holographic Data Storage,” presented at Fall Research Review, Center for Magnetic Recording Research, University of California, San Diego, 26 October, 2005.
36. H. Horimai, “Collinear holography,” Proc. 5th Pacific Rim Conference on Lasers and Electro-Optics 1, 376–377 (2003).
37. K. Tanaka, H. Mori, M. Hara, K. Hirooka, A. Fukumoto, and K. Watanabe, “High density recording of 270 Gbits/inch2 in a coaxial holographic storage system,” Tech. Digest of ISOM 2007, MO–D–03.
38. H. Horimai, and X. Tan, “Advanced collinear holography,” Opt. Rev. 12, 90–92 (2005).
39. H. Horimai, X. D. Tan, and J. Li, “Collinear holography,” Appl. Opt. 44, 2575– 2579 (2005).
40. H. Horimai, and X. Tan, “Holographic versatile disc system,” Proc. of SPIE 5939, 593901 (2005).
41. Y. W. Yu, S. Xiao, C. Y. Cheng, and C. C. Sun, “One-shot and aberration-tolerable homodyne detection for holographic storage readout through double-frequency grating-based lateral shearing interferometry,” Opt. Express 24, 10412-10423 (2016).
42. 楊繼賢，使用微透鏡陣列之同軸全像儲存系統與其考慮材料紀錄動態範圍之模型建立，國立中央大學光電科學研究所碩士論文，中華民國一百零六年。
43. J. Liu, H. Horimai, X. Lin, Y. Huang, and X. Tan, “Phase modulated high density collinear holographic data storage system with phase retrieval reference beam locking and orthogonal reference encoding,” Opt. Express 26, 3828-3838 (2018).
44. J. Goodman, Introduction to Fourier Optics, 3rd eds. (McGraw-Hill, New York, 2002).
45. W. R. Klein, “Theoretical Efficiency of Bragg Devices,” Proc. IEEE 54, 803 (1966).
46. H. R. Carleton and W. T. Maloney, “A balanced optical heterodyne detector,” Appl. Opt. 7, 1241 (1968).
47. J. H. McElroy, “Infrared heterodyne solar radiometry,” Appl. Opt. 11, 1619 (1972).
48. Y. Fujii, J. I. Yamashita, S. Shikata, and S. Saito, “Incoherent optical heterodyne detection and its application to air pollution detection,” Appl. Opt. 17, 3444 (1978).
49. H. P. Yuen and V. W. S. Chan, “Noise in homodyne and heterodyne detection,” Opt. Lett. 8, 177 (1983).
50. R. Stierlin, R. Bättig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fibre-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445 (1986).
51. T. Okoshi, “Recent advances in coherent optical fiber communications systems,” J. Lightwave Commun. 5, 44 (1987).
52. M. J. Collett, R. Loudon and C. W. Gardiner, “Quantum theory of optical homodyne and heterodyne detection,” J. Mod. Opt. 34, 881 (1987).
53. K. Curtis, L. Dhar, A. Hill, W. Wilson and M. Ayres, Holographic Data Storage: From Theory to Practical Systems, (WILEY, 2009).
54. H. Mikami, T. Shimano, H. Kudo, J. Hashizume and H. Miyamoto, “Read-out signal amplification by homodyne detection scheme,” Joint International Symposium on Optical Memories and Optical Data Storage, presented at Waikoloa Hawaii, July 2008, paper TuA01.
55. S. Aoki, M. Yamada and T. Yamagami, “A novel deformable mirror for spherical aberration compensation,” Joint International Symposium on Optical Memories and Optical Data Storage, presented at Waikoloa Hawaii, July 2008, paper TuB02.
56. A. M. van der Lee and E. Altewischer, “Drive considerations for multi-layer discs,” presented at International Symposium on Optical Memories Takamatsu, Japan, October 2006, paper Mo-C-05.
57. K. Tanaka, M. Hara, K. Tokuyama, K. Takasaki, H. Okada, Y. Okamoto, H. Mori, A. Fukumoto and K. Okada, “Experimental verification of coherent addition technique for coaxial holographic data storage,” presented at Optical Data Storage Conference, Florida 2009.
58. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
59. Mark R. Ayres, and Boulder, “Method for holographic data retrieval by quadrature homodyne detection,” United States Patent, US 8,233,205 B2 (2012).
60. D. Nyssonen and J. M. Jerke, “Lens Testing with a Simple Wavefront Shearing Interferometer,” Appl. Opt. 12, 2061–2082 (1973).
61. M. V. R. K. Murty, “The Use of a Single Plane Parallel Plate as a Lateral Shearing Interferometer with a Visible Gas Laser Source,” Appl. Opt. 3, 531–534 (1964a)
62. P. Hariharan and D. Sen, “Cylic Shearing Interferometer,” J. Sci. Instrum. 37, 374 (1960).
63. D. Malacara, Optical Shop Testing, 3rd eds. (A Wiley-Interscience, 2007)
64. D. Kelsall, “Optical frequency response characteristics in the presence of spherical aberration measured by an automatically recording interferometric instrument,” Proc. Phys. Soc 73, 465 (1959).
65. J. C. Wyant, “Double Frequency Grating Lateral Shear Interferometer,” Appl. Opt. 12, 2057 (1973).
66. Y. Amnon and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, (A Wiley-Interscience, Canada, 1984)
67. R. C. Jones, “A New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am 31. 488-493 (1941).
68. D. P. Chrissoulidis, E. E. Kriezis, A. G. Papagiannakis, Electromagnetics and Optics, 1st eds. (World Scientific, USA, 1992).
69. C. Gu, G. Sornat, and J. Honh, “Bit-error rate and statistics of complex amplitude noise in holographic data storage,” Opt. Lett. 14, 1070 (1996).
70. 謝舒菁，同軸式體積全像儲存系統之研究與改良，國立中央大學光電所碩士論文，中華民國九十六年。