The Fourier transformation is an important tool in information processing. It is closely related to other widely used transformations and distributions, such as the wavelet transform, the Wigner distribution, the ambiguity function, etc. A few decades ago, a generalization of the Fourier transform known as the fractional Fourier transform was introduced, leading to attractive applications in optics and signal processing. In the one-dimensional case, the fractional Fourier transformation describes the rotation of a signal in phase space. For two-dimensional signals, other phase-space rotators exist, including the gyrator and the image rotator. This chapter is devoted to these basic phase-space rotators and to their applications in optical and digital signal processing. Special attention is paid to experimental implementations of optical systems performing phase-space rotations. Many applications of phase-space rotators, such as beam characterization, mode conversion, filtering, encryption, etc., require fast changing of the transformation parameters. The design of quasi-real-time programmable optical systems using spatial light modulators is proposed for this task.
|Title of host publication||Optical and digital image processing : fundamentals and applications|
|Editors||G. Cristóbal, P. Schelkens, H. Thienpont|
|Place of Publication||Weinheim|
|Number of pages||21|
|Publication status||Published - 2011|
Rodrigo, J. A., Alieva, T., & Bastiaans, M. J. (2011). Phase-space rotators and their applications in optics. In G. Cristóbal, P. Schelkens, & H. Thienpont (Eds.), Optical and digital image processing : fundamentals and applications (pp. 251-271). Wiley-VCH Verlag. https://doi.org/10.1002/9783527635245.ch12