It is shown how a coherent optical signal that contains only a finite number of Hermite–Gauss modes can be reconstructed from the knowledge of its Radon–Wigner transform—associated with the intensity distribution in a fractional-Fourier-transform optical system—at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.
© 2002 Optical Society of America
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.5070) Image processing : Phase retrieval
(200.1130) Optics in computing : Algebraic optical processing
Tatiana Alieva and Martin J. Bastiaans, "Finite-mode analysis by means of intensity information in fractional optical systems," J. Opt. Soc. Am. A 19, 481-484 (2002)