A necessary and sufficient scalar condition for a Mueller matrix M to describe a non-depolarizing optical system is obtained. By computing only one scalar parameter, it can be determined whether a given Mueller matrix M describes a non-depolarizing, or a depolarizing optical system. The following theorem is stated: a necessary and sufficient condition for a given Mueller matrix M to describe a non-depolarizing optical system is Tr(M ^T M) = 4m ² ₀₀.

We define the width, divergence, and curvature radius for non-Gaussian and nonspherical light beams. A complex beam parameter is also defined as a function of the three previous ones. We then prove that the ABCD law remains valid for transforming the new complex beam parameter when a non-Gaussian and nonspherical, orthogonal, or cylindrical symmetric laser beam passes through a real ABCD optical system. The product of the minimum width multiplied by the divergence of the beam is invariant under ABCD transformations. Some examples are given.

Principal-component decomposition is applied to the analysis of noise for infrared images. It provides a set of eigenimages, the principal components, that represents spatial patterns associated with different types of noise. We provide a method to classify the principal components into processes that explain a given amount of the variance of the images under analysis. Each process can reconstruct the set of data, thus allowing a calculation of the weight of the given process in the total noise. The method is successfully applied to an actual set of infrared images. The extension of the method to images in the visible spectrum is possible and would provide similar results.

A fiber-optic sensor based on surface-plasmon resonance for the determination of the refractive index is used for measuring the degree of salinity of water. The transducing element consists of a multilayer structure deposited on a side-polished monomode optical fiber. Measuring the attenuation of the power transmitted by the fiber shows that a linear relation with the refractive index of the outer medium of the structure is obtained. The system is characterized by use of a varying refractive index obtained with a mixture of water and ethylene glycol. Experimental results show that the sensor can be used as a salinity-degree measurement device with environmental applications.

In this work, a Fourier transform technique for automatic analysis of moire´ deflectograms is presented. A squared grating is used to multiplex the information of the deflection in two orthogonal directions in one image. This procedure avoids the necessity of rotating the gratings to obtain the complete deflection information. With this method only two fringe patterns, reference and distorted, are needed to determine the complete deflection information. To deal with irregularly shaped processing areas, a Gerchberg extrapolation method is used. The automatic determination of the carrier as well as the size and position of the reconstruction windows permit the complete and automatic measurement of the deflection produced by an ophthalmic lens in two orthogonal directions. Afterwards, the refractive power maps can be obtained. Experimental results obtained with a progressive addition lens are presented and comparison with measurements obtained with a commercial focimeter are shown showing a good agreement. © 1999 Society of Photo-Optical Instrumentation Engineers.