Abstract

Rotation-invariant pattern recognition can be performed by encoding the Fourier transform of a circular-harmonic (CH) component of the reference pattern. This technique has recently been applied to a binary phase-only version of the filter (BPOF). However, the recording medium is not capable of recording the complex Fourier transform. A cosine CH BPOF is obtained by encoding binary versions of the real part of the CH filter and a sine CH BPOF is obtained by encoding binary versions of the imaginary part. Rotation invariance is lost when either of these filters is used alone. However, by successively applying the filters and summing the successive output intensities, full rotational invariance can be recovered. The disadvantage of this method is that two separate filters are required. Full rotational invariance can be obtained in a single filter by multiplying the complex Fourier transform by a Fresnel lens. In the binarization process, the desired CH filter is encoded onto a converging lens, and the undesired complex conjugate of the CH filter is encoded onto a diverging lens. This process can be successfully integrated into the short version of the correlator. Computer simulations and experimental results using the MOSLM show that this single filter has full rotational invariance.

© 1990 Optical Society of America