Phase-only filters codified with Burckhardt's method.

The main techniques for optical pattern recognition are those based on the correlation between a test and an image. Phase-only filters (POFs) have good features for the recogni­ tion process: high discrimination capability between simi­ lar objects and high sharp correlation peaks. Nevertheless, most of the graphic devices and spatial light modulators, such as CRTs, liquid crystal TVs (LCTVs), plotters, etc., can plot exclusively intensity variations, and therefore, they can only modulate the amplitude. With those kinds of devices it is not possible to obtain directly a POF. Flavin and Horner proposed a method to codify POFs which presents ampli­ tude-only variations. In this work we propose another method for the amplitude encoded phase-only filters based on Burckhardt's method. This codification method allows phase-only filters to be written on an amplitude modulating device. The graphic device to be used is the laser printer which presents good features for the generation of holograms by computer. We present experimental results of the impulse response and of the correlation obtained by using a CGH made with the proposed technique. Burckhardt's method is based on the possibility of the decomposition of a complex value into three complex num­ bers with positive amplitudes and phases equal to 0, 2π/3, and 47r/3. This is a simplification of Lee's method which has four components with phases equal to 0,π/2, π, and 3π/2. Then, the transmission of each pixel on the filter, A exp(ƒФ), is replaced by the following equation: Fig. 1. Scene used in the detection process. The target to be recognized is the upper butterfly (B1).