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Determining optimal matched filter parameters David Casasent and Alan Furman Carnegie-Mellon University, Department of Electrical Engineering, Pittsburgh, Pennsylvania 15213. Received 6 March 1976. The coherent optical frequency plane correlator 1 is poten- tially one of the most powerful pattern recognition systems. Since the development of the holographic matched spatial filter, many optical image correlation demonstrations using this optical configuration have appeared. In this Letter we report on a simple method for determining the optimal pa- rameters used in the synthesis of a holographic matched spatial filter. These parameters include exposure, beam balance ratio K (the ratio of the intensities of the reference and signal beams), and the choice of the spatial frequency band in which K is set. The effect of these parameters on the diffraction efficiency (η) and signal-to-noise ratio (SNR) of the correlations and cross-correlations are best determined experimentally on representative imagery. We will shortly publish the theoretical considerations and detailed experi- mental results for these issues. At present we report only on a convenient experimental technique for data collection using a wedge-ring detector array 3 in the optical Fourier transform plane. The issue of automatic control of the beam balance ratio has been proposed earlier. 4 The detector array (or diffraction pattern sampling unit) consists of sixty-four separate photodiodes on a common 2.5-cm diam silicon substrate. The array contains thirty-two semiannular ring-shaped elements in one semicircle and thirty-two wedge-shaped elements in the other semicircle, with all sixty-four outputs available in parallel on separate leads. The detector elements are operated in the photovoltaic Fig. 1. SNR of the correlation peak vs the spatial frequency band in which the beam balance ratio K was sent equal to 2. mode and are capable of visible to near ir (1-μm) spectral re- sponse, 60-dB dynamic range, less than 0.1-μsec risetime, less than 0.1% crosstalk between elements, and parallel readout. The unit used in the experiments described digitally displays the outputs of manually selected detector elements. When this detector array is placed in the transform plane at the in- tersection of the object and reference beams, the outputs of the thirty-two annular ring-shaped elements (the wedge- shaped elements are not used in this application) provide a measure of the relative power (integrated over the area of the ring element) in thirty-two different spatial frequency bands in the object and reference beams. To demonstrate the utility of this device in holographic matched spatial filter synthesis, a 35-mm transparency of a representative aerial image was illuminated with collimated 633-nm laser light. Its Fourier transform was produced on the detector array in the back focal plane of a 495-mm focal length lens. The outputs of sets of the thirty-two ring ele- ments were grouped to provide an integrated response in nine spatial frequency bands (see the first three columns in Table I) covering the 0-50-cycles/mm range. The uneven divisions of the bands are due to the width of the elements, which in- creases with radial distance. The noncontinuous spatial frequency coverage is due to small isolating channels between ring elements. A series of thirty-six Fourier holograms of an aerial image were made on nine 101 mm × 127 mm Kodak 649 F plates with four spatially separated exposures, at 2:1 exposure time steps per plate. For each plate, K 2 for a different band (A to I in Table I). This was achieved by varying the intensity of the object beam by a variable beam splitter in that path. Prior to making these spatially separated holograms, the intensity m each of the nine spatial frequency bands was recorded for Table I. Summarized Wedge-Ring Detector Data 1690 APPLIED OPTICS / Vol. 15. No. 7 / July 1976
