在理論分析方面，我們對其在布拉格不匹配條件下的耦合方程式求解。首先利用弱耦合條件所作的某些近似來簡化方程式，再以此簡化後之方程式來求出一近似解，此近似解與Kogalnik’s formula 非常相似；利用此近似解所求得的相位關係代入完整耦合方程式中求出一通用解，此一通用解可以準確地近似至弱耦合條件下的近似解以及布拉格匹配條件下的通解。在實驗驗證方面，利用鈦酸鋇晶體非均向性自繞射所得到的結果與此準通用解的預測相當吻合。
在應用方面，則包含了四種利用鈦酸鋇晶體非均向性自繞射在光資訊處理的應用：一﹑光折變非同調─同調光學轉換器，利用鈦酸鋇晶體非均向性自繞射的非同調─同調光學轉換器具有高繞射效率的特性，因此具有減少晶體厚度來提升解析度的極大潛力，我們利用厚度1.2 mm的晶體得到40 lp/mm的解析度，繞射效率為51 %。二﹑中心對稱濾波器，由於非均向性自繞射的相位關係具有自卷積（auto-convolution）的特性，因此在中心對稱濾波器的應用方面具有不需要參考物的自動辨認特性，此外還具有大小不變（scale-invariant）的特性。三﹑剪影（shearing）干涉儀，此干涉儀則是利用鈦酸鋇晶體的即時全像特性，以雙重曝光的技巧來達成剪影干涉的目的，我們利用此剪影干涉儀來測量透鏡的等效焦距，結果與理論吻合。四﹑鈦酸鋇晶體折射率隨溫度變化的精密量測，利用非均向性自繞射布拉格條件的改變來測量鈦酸鋇晶體的非常態折射率（extraordinary refractive index）隨溫度的變化具有以下優點：量測精確度與晶體厚度無關，對於環境穩定性的要求較低，以及架構簡單。此架構也可以作為一溫度感測器。

In theoretical analysis, we solved the coupled equations under Bragg mismatching. We simplified the coupled equations under the weak coupling conditions and obtained an approximate solution. This approximate solution is similar to Kogalnik’s formula. Substituting the phase relation obtained from the approximate solution, we obtained a general solution. The general solution may be properly reduced to the approximate solution for weak coupling conditions and to the general solution under Bragg matching. In the experimental demonstration, the experimental results for ASD in BaTiO3 were found to fit the theory well.
For practical applications, four kinds of optical information processing based on ASD in BaTiO3 are proposed. (1) Incoherent-to-coherent optical converter (PICOC). PICOCs based on ASD in BaTiO3 have great potential for increasing resolution by reducing crystal thickness, owing to the high diffraction efficiency of ASD in BaTiO3. The resolution and diffraction efficiency for a thin crystal of 1.2 mm thickness are 40 lp/mm and 51 %, respectively. (2) Central-symmetry filter. According to the autoconvolution character in the phase relation of ASD, a central-symmetry filter possesses the character of auto-recognition and no reference object is required. In additional, scale-invariant filtering is performed. (3) Shearing interferometer. A shearing interferometer is implemented based on the double exposure technique due to the real-time hologram character of BaTiO3. We used this shearing interferometer to measure the effective focal length of a lens, and the measured results coincided with the theoretical prediction. (4) The precise measurement of the temperature-dependent refractive index change in BaTiO3. The measurement of temperature-dependent extraordinary refractive index change in BaTiO3 with the variation of the Bragg condition of ASD has the following advantages: the measurement precision is independent of the crystal thickness, the measurement can be implemented under an inferior condition, and the setup is simple. This algorithm can be applied to thermo-sensing.

1. F. T. S. Yu and S. Jutamulia, Optical signal processing, computing, and neural networks, John Wiley, New York (1992).
2. J. -P. Huignard and P. Gunter, Photorefractive Materials and Their Applications: I. Fundamental Phenomena, Springer-Verlag, New York (1988).
3. J. -P. Huignard and P. Gunter, Photorefractive Materials and Their Applications: II. Applications, Springer-Verlag, New York (1989).
4. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical holography, (1983).
5. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Bullman, J. J. Levinstein, and K. Nassau, “Optical-induced refractive index inhomogeneity in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72 (1966).
6. C. C. Sun, M. W. Chang, and K. Y. Hsu, “Matrix-matrix multiplication by use of anisotropic self-diffraction in BaTiO3,” Appl. Opt. 33, 4501-4507 (1994).
7. C. C. Sun, M. W. Chang, and K. Y. Hsu, “Optical information processing by using anisotropic diffraction In BaTiO3,” Int. J. Optoelectronics 11, 413-423 (1997).
8. C. C. Sun, B. Wang, and J. Y. Chang, “Photorefractive incoherent-to-coherent optical converter based on anisotropic self-diffraction in BaTiO3,” Appl. Opt. 37, 8247-8253 (1998).
9. C. C. Sun, B. Wang, W. C. Su, A. E. T. Chiou, and J. Y. Chang, “Optical filtering by use of anisotropic self-diffraction in BaTiO3,” Appl. Opt. 38, 3720-3725 (1999).
10. Ching-Cherng Sun and Bor Wang, “Optical information processing and computing with anisotropic diffraction in BaTiO3,” (Invited paper) Proc. SPIE 3801, 169-179 (1999).
11. D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
12. D. Gabor, “Microscopy by reconstructed wavefronts,” Proc. Roy. Soc. A197, 454 (1949).
13. D. Gabor, “Microscopy by reconstructed wavefronts: II,” Proc. Roy. Soc. B64, 449 (1951).
14. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Amer. 52, 1123 (1962).
15. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Amer. 53, 1377 (1963).
16. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffuced illumination and three-dimensional objects,” J. Opt. Soc. Amer. 54, 1295 (1964).
17. N. V. Kukhtarev, V. B. Makrov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949 (1979).
18. P. Yeh, Introduction to photorefractive nonlinear optics, John Wiley, New York (1993).
19. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).