Optical signal processing

Image/signal processing is a wide research area of analysis, transformation, compression, and reconstruction of visual information with application to different fields of Science and Technology, such as Biomedicine, Industrial inspection, Control and security systems, Robotic vision, etc.

Essentially, detection and localization of objects is reduced to the performance of correlation operation of the given object with the observed picture and subsequent comparison of the result with a threshold. The optical correlator was introduced by Vander Lugt 30 years ago, that opened the "era" of coherent  Optical Image Processing. 

During the last decade the traditional area of optical information processing - Fourier Optics have been enlarged by the introducing bilinear distributions such as the Ambiguity function, the Wigner distribution, spectrogram etc., which represent a signal in position-frequency  plane. The key role in this  task belongs to the discovery of the optical fractional Fourier transform (FT). The fractional FT is a generalization of the ordinary FT and produces the rotation of the phase plane. The fractional FT can be performed by simple optical set up, which is similar to the FT one. The fractional FT is now used for signal analysis, filtering, encoding, watermarking, phase retrieval,etc.

Besides the fractional FT, other fractional transforms play an important role in signal processing. Thus the fractional Hilbert transform was found to be very promising for edge detection. Recently we have proposed a general procedure for the fractionalization of a linear cyclic transform, which permits to generate different types of the fractional Fourier transform  as well as other fractional transforms, including fractional Sine, Cosine, Hankel, and Hartley transforms etc. 

Our current work is 

  • Analysis a wide class of fractional transforms with respect to their implementation in optical image processing.

  • Design and study of the efficiency of the different optical fractional correlators.


[1]: T. Alieva and M. L. Calvo, "Fractionalization of the linear cyclic transforms," J. Opt. Soc. Am. A 17, 2330-2338 (2000).

[2]: T. Alieva, M. J. Bastiaans, and M. L. Calvo, "Fractional Transforms in Optical Information Processing," EURASIP J. Appl. Signal Process. 2005, 1498-1519 (2005).