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We quantitatively investigate the axial imaging properties of dynamic phase-contrast microscopy, with a special focus on typical combinations of tracer particles and magnifications that are used for velocimetry analysis. We show, for the first time, that a dynamic phase-contrast microscope, which is the integration of an all-optical novelty filter in a commercially available inverted microscope, can visualize three-dimensional velocity fields with a significantly reduced optical sectioning depth. The depth of field for dynamic phase-contrast microscopy is extracted from the three-dimensional response function and compared with the respective values for incoherent bright-field illumination. These results are then used to perform a depth-resolved particle image velocimetry analysis of Hagen-Poiseuille as well as electro-osmotically actuated flows in a microchannel. OCIS codes: 110.0180, 180.4315, 180.6900, 190.7070.

A fast computation algorithm for fine-pixel aerial images is presented that modifies the transmission cross coefficient approach of Hopkins as a product of two matrices. The spatial frequency of the image is calculated by the sum of diagonal and off-diagonal elements of the matrix. Let N, [N.sub.F], and M be the number of the point sources, the sampling number for fast Fourier transform, and the sampling number in the spatial frequency domain ranging twice the pupil size, respectively. The calculation time of this method is proportional to BN[[(M- 1)/2].sup.4], while that of a conventional source integration method is [2ANN.sub.F][log.sub.2] [N.sub.F], where A and B are constants and generally B < A If [N.sub.F] is sufficiently greater than M or M is small enough, which is the fine-pixel condition, this method runs faster than the source integration method. If the coherence factor is 0.9 and M [less than or equal to] 55, this method runs faster than the source integration even under the Nyquist sampling condition. OCIS codes: 110.4980, 110.5220, 110.2990.

Equations for Rayleigh scattering in a mixture of gases are derived and compared to frequent approximations in the literature. The traditional Rayleigh scattering equation as modified by King for scatter from a pure gas is correct, whereas another version sometimes appearing in modern literature is erroneous. Use of a mixture's refractive index, which is equivalent to assuming the isotropic molecular polarizabilities of the component gases are identical, is an approximation. Another common approximation is using only number-density weighting of the King factors. Approximation errors can be large when the major components of a mixture have disparate optical properties. Fortunately, the errors for Earth's air are much smaller and comparable to errors from other sources. OCIS codes: 290.5870, 290.1310, 010.1320, 280.3640.

We present a method for orientation-selective edge detection and enhancement based on the irradiance transport equation. The proposed technique distinguishes the sign of the derivative of the intensity pattern along an arbitrarily selected direction. The method is based on the capacity of liquid-crystal displays to generate simultaneously a contrast reverted replica of the image displayed on it. When both images (the original one and its replica) are imagined across a slightly defocused plane, one obtains an image with enhanced first derivatives. Unlike most Fourier methods, the proposed technique works well with a low-coherence light source, and it does not require precise alignment. The proposed method does not involve numerical processing, and thus it could be potentially useful for processing large images in real-time applications. Validation experiments are presented. [c] 2010 Optical Society of America OCIS codes: 100.2980, 100.2810.