Efficient computation of optical disk readout by use of the chirp z transform

Computation of the readout signal of an optical disk involves Fourier transforms from the objective lens pupil to the disk and, after interaction with the disk, from the disk to the objective pupil. Traditionally, the complex two-dimensional Fourier transform is numerically evaluated as a two-dimensional fast Fourier transform. To obtain sufficient resolution in the involved planes, one must choose sampling grid sizes of typically 1,024 x 1,024 or higher, resulting in a substantial computation time if the calculation is to be repeated many times. Discussed is an alternative method for evaluating the Fourier transform, based on the chirp z transform, by which a considerable improvement in efficiency can be obtained without loss of accuracy.