Optical illustration of a varied fractional Fouriertransform order and the Radon–igner display

Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image–processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time– and spatial–frequency analyses. The given approach for producing this display starts with a onedimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free–space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon-Wigner display has been demonstrated experimentally.