Abstract
Using matrix based techniques it is shown how the Space-Bandwidth Product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner Distribution Function (WDF), can be tracked through any quadratic phase optical system whose operation is described by the Linear Canonical Transform (LCT). We extend this to include offset optical elements and systems, which are described by a more general transform-the Special Affine Fourier Transform (SAFT) or Offset LCT. It is shown that by decomposing the overall system matrix associated with the SAFT, into a product of the matrices representing the individual optical components, the spatial extent, its location and the signals bandwidth can be determined at any point in the optical system. This approach has application in many areas of optical signal processing; for example, numerical simulation, optical and digital compression, speckle metrology, optical encryption, optical filtering and the recording of processed images. The method is shown to be a simple tool of fundamental importance in the context of the entropy of the propagated signal and by tracking the Space Bandwidth product we can determine the quantity of information according to the Nyquist sampling theorem. We also discuss future work in relation to superresolution.
