A low-cost and simple technique for encryption of two-dimensional patterns and shapes is suggested and demonstrated. The method is based on the superposition of random grids.

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The Wigner distribution function (WDF) is used to study the propagation of partially coherent beams through optical systems. The width and divergence of multimode beams are defined in terms of moments of the WDF. It is shown that these and other parameters of partially coherent beams of arbitrary form may be calculated using geometrical ray traces. Generalized transformation laws of these beam parameters by an ABCD optical system are obtained. These laws are tested experimentally for multimode beams and thin lenses. The applications of the ray tracing method can be extended to a non-ABCD system with mild aberrations.

Mapping of temperature of a premixed hydrogen-oxygen flame by moire deflectometry is demonstrated. The technique is based on deflection mapping of rays from a collimated light beam due to gradients of the refractive index across the flame. For an axially symmetric flame the radial distribution of the refractive index was derived by Abel transformation. The temperature profile of the flame was calculated for a known gas composition assuming ideal gas behavior.

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