Symmetrically recoded modified signed-digit optical addition and subtraction

Symmetrically recoded modified signed-digit number algorithms are proposed for carry-free arithmetic. The superiority of the new algorithms is established over all other two-step-based symbolic-substitution optical implementations.     

Optoelectronic Recoded and Nonrecoded Trinary Signed-Digit Adder that uses Optical Correlation

A symbolic-substitution-based optical numeric processor that uses recoded and nonrecoded trinary signed-digit (TSD) number representations is proposed. Also, we propose new joint spatial encodings for the TSD numbers that reduce the symbolic-substitution computation rules involved in the processor. Optoelectronic implementation of the proposed recoded adder is feasible. Also, the nonrecoded TSD addition can be performed optically in two steps. Both the proposed recoded and nonrecoded adders are more compact than a recently reported modified signed-digit counterpart and use fewer correlators and spatial light modulators.     

Simultaneous machining of parallel grooves in SnO(2) thin films using a Nd:YAG laser and a kinoform

A kinoform is used to split the beam of a Nd:YAG laser into six beams. The laser beams are, by means of optical fibers and collimating-focusing optics, transferred to the surface to be machined. Thus multiple grooves can be machined simultaneously. For demonstration, 100-μm-wide grooves are simultaneously machined into a SnO(2) thin film deposited on a glass substrate. The resulting grooves are well isolated. This result shows that the technique could be used, for example, in solar cell manufacturing to increase the efficiency of laser scribing.     

A clustering performance measure based on fuzzy set decomposition

Clustering is primarily used to uncover the true underlying structure of a given data set and, for this purpose, it is desirable to subject the same data to several different clustering algorithms. This paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms. The goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration. Several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings.     

Distortion in a 2-D scan pattern generated by combining a plane mirror and a regular polygon scanner

The distortion in a 2-D scan pattern generated by a system of a plane mirror and a regular polygon scanner was investigated using the matrix formulation of reflection by plane mirrors. A particular configuration involving the two scan elements was identified which does not introduce any distortion in its 2-D scan pattern.     

An intrinsic dimensionality estimator from near-neighbor information

The intrinsic dimensionality of a set of patterns is important in determining an appropriate number of features for representing the data and whether a reasonable two- or three-dimensional representation of the data exists. We propose an intuitively appealing, noniterative estimator for intrinsic dimensionality which is based on nearneighbor information. We give plausible arguments supporting the consistency of this estimator. The method works well in identifying the true dimensionality for a variety of artificial data sets and is fairly insensitive to the number of samples and to the algorithmic parameters. Comparisons between this new method and the global eigenvalue approach demonstrate the utility of our estimator.