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In general, the 2-D interpolator can be formulated as Z k , l   f   p  f   q C ( k ' p, l ' q ) , m  ( p ,q )S  x y  m , (10) (11) where f(.) is the one-dimensional impulse response of the corresponding interpolator; S is the input range of the 2-D interpolators; μx and μy indicate the local fractional displacement from the nearest pixel (k’, l’) at Cm in horizontal and vertical directions, respectively. The relationship between the local fractional displacement μx and μy and the corresponding pixel position k’ and l’ on the misaligned image Cm can be expressed as ~ k  k cos   l sin    x   M   x , (12) ~ l  k sin   l cos    y  M   y where M is the oversampling ratio and ~ ~ k  k , x  k  k .

4, iv/121- iv/124, ISBN 0-7803-8874-7, Mar. 2005, Philadelphia Optical data storage in photosensitive glasses and spin state transition compounds 33 X3 Optical data storage in photosensitive glasses and spin state transition compounds Matthieu Bellec, Lionel Canioni, Arnaud Royon, Bruno Bousquet, Jérôme Degert and Eric Freysz Centre de Physique Moléculaire Optique et Hertzienne (CPMOH), University of Bordeaux France Thierry Cardinal and Jean-François Létard Institut de Chimie de la Matière Condensée de Bordeaux (ICMCB), University of Bordeaux France 1.

2000). , Singh, K. (2009). Phase modulated gray-scale data pages for digital holographic data storage. Optics Communications, Vol. 282, No. 11, pp. , & Hong, J. (1996). Statistics of both optical and electrical noise in digital volume holographic data storage. Electronic Letters, Vol. 32, No. 1400–1402, ISSN 0013-5194 Haykin, S. (2002). Adaptive filter theory, Prentice Hall, 4th edition, ISBN 0130901261 He, A. & Mathew, G. (2006). Nonlinear equalization for holographic data storage systems.

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