We present a simple and effective method for estimating arbitrary phase steps in the presence of noise in phase-shifting interferometry. The method is based on the linear prediction property of the sinusoids. Simulation and experimental results obtained from a holographic interferometry prove the efficiency and feasibility of the proposed method.
Cramer-Rao Bounds (CRB) for the expected variance in the parameter space were examined for Diffuse Optical
Tomography (DOT), to define the lower bound (CRLB) of an ideal system. The results show that the relative
standard deviation in the optical parameter estimate follows an inverse quadratic function with respect to signal
to noise ratio (SNR). The CRLB was estimated for three methods of including spatial constraints. The CRLB
estimate decreased by a factor of 10 when parameter reduction using spatial constraints (hard-priors) was enforced
whereas, inclusion of spatial-priors in the regularization matrix (soft-priors) decreased the CRLB estimate only
by a factor of 4. The maximum reduction in variance from the use of spatial-priors, occurred in the background of
the imaging domain as opposed to localized target regions. As expected, the variance in the recovered properties
increased as the number of parameters to be estimated increased. Additionally, increasing SNR beyond a certain
point did not influence the outcome of the optical property estimation when prior information was available.