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Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh-Sommerfeld diffraction solution. OCIS codes: 050.1755, 050.1940, 070.2580, 070.7345.

Orthogonal projection sampling mode was proposed to reconstruct the incomplete-data flow field in optical computerized tomography (OCT). With numerical simulation technique, a two-peak plane symmetric flow field was reconstructed in different sampling modes and discussed in simulated results is the reconstructive accuracy with error indexes, such as mean square error (MSE) and peak error (PE). The corresponding experiments were researched with a Fabry-Perot rotary interferometer. The results indicated that the errors were drastically reduced and the precision was improved when orthogonal projection sampling mode was adopted in the reconstruction of the incomplete data field. The MSE obtained with orthogonal sampling mode was decreased 72.81% from that of the sequential projection sampling mode (the difference between the MSE obtained with the orthogonal sampling mode and that with the sequential sampling mode divided by the MSE of the sequential sampling mode) and the PE was decreased by 73.97%. The precision obtained from the experimental results reached 10%, which showed the orthogonal projection sampling could be a practicable sampling mode for the incomplete data field reconstruction in OCT and could provide some guidance for the flow-field measurement and apparatus design in the practical situation. OCIS codes: 110.6960, 100.3010, 200.3050, 100.6950.

We propose a fast surface-profiling algorithm based on white-light interferometry by use of sampling theory. We first provide a generalized sampling theorem that reconstructs the squared-envelope function of the white-light interferogram from sampled values of the interferogram and then propose the new algorithm based on the theorem. The algorithm extends the sampling interval to 1.425 [micro]m when an optical filter with a center wavelength of 600 nm and a bandwidth of 60 nm is used. The sampling interval is 6-14 times wider than those used in conventional systems. The algorithm has been installed in a commercial system that achieved the world's fastest scanning speed of 80 [micro]m/s. The height resolution of the system is of the order of 10 nm for a measurement range of greater than 100 [micro]m. OCIS codes: 120.6660, 120.3180.

Experimental results for the noise of photon-correlation and photon-structure functions are presented. The noise dependences on the mean count rate and on the sampling time are investigated by means of a specifically built linear fluctuation analyzer, and the results are compared with theoretical predictions. The predicted mean count rate dependence and sampling time dependence of the noise are confirmed by the experimental analysis. Some discrepancies between analytical expressions and experimental results are observed in the crossover predictions. The results show that the structure function has better noise performance for relatively high mean count rates and for long sampling times, which strongly suggests a wider use of this statistical estimator in measurements requiring good accuracy, as in the case of uniform sampling.