We consider the recently proposed double phase-encoding system [Opt. Lett. <b>20</b>, 767 (1995)]. We study the robustness of the decoding process, that is, the way in which a perturbation of the coded image modifies the decoded image. We demonstrate that the amplitude signal-to-noise ratio (SNR) in the decoded image is strictly (and not only statistically) equal to the SNR in the coded image for different kinds of coded-image perturbations. In optical implementations the intensity of the decoded image is measured at the output of the decoding system. We show that there exists a simple relation between the intensity SNR of the decoded image and the amplitude SNR of the coded image and that this relation is quasi-independent of the nature of the coded-image perturbation. The results presented could provide a simple and efficient way of determining the precision level of the components of the optical decoding system necessary to reach a predefined quality level of the decoded image.
© 1998 Optical Society of America
(070.4550) Fourier optics and signal processing : Correlators
(070.4560) Fourier optics and signal processing : Data processing by optical means
(100.1160) Image processing : Analog optical image processing
François Goudail, Franck Bollaro, Bahram Javidi, and Philippe Réfrégier, "Influence of a perturbation in a double phase-encoding system," J. Opt. Soc. Am. A 15, 2629-2638 (1998)