Theoretical expression for the correlation signal of nonlinear joint-transform correlators

Generalized joint fractional fourier transform correlators: a compact approach

Fractional correlation was introduced recently. We generalize the architecture of a joint (Fourier) transform correlator (JTC) to achieve the joint fractional (Fourier) transform correlator (JFrTC) such that fractional correlation can be obtained. Here the Fourier transform in the JTC is replaced by the fractional Fourier transform, and four different JFrTC architectures can be implemented. The mathematical derivations for these JFrTC architectures are given, together with the simulation verifications. The JFrTC can provide a correlation signal similar to a delta function but with a small discrimination ratio, such that it is insensitive to additive noise. In a conventional JTC the distance between the two desired correlation signals at the output plane is fixed and depends on the distance between the input and the reference signals. However, with a given fractional order and an additional phase mask the separation distance between the two correlation signals at the output plane of a JFrTC can be larger or smaller than that of a JTC. This property is useful for the applications of real-time target tracking. Unlike in a previous approach [Appl. Opt. 36, 7402 (1997)], we need only two fractional Fourier transformations instead of three to achieve fractional correlation.

Position-invariant, rotation-invariant, and scale-invariant process for binary image recognition

A novel recognition process is presented that is invariant under position, rotation, and scale changes. The recognition process is based on the Fang-Häusler transform [Appl. Opt. 29, 704 (1990)] and is applied to the autoconvolved image, rather than to the image itself. This makes the recognition process sensitive not only to the image histogram but also to its detailed pattern, resulting in a more reliable process that is also applicable to binary images. The proposed recognition process is demonstrated, by use of a fast algorithm, on several types of binary images with a real transform kernel, which contains amplitude, as well as phase, information. Good recognition is achieved for both synthetic and scanned images. In addition, it is shown that the Fang-Hausler transform is also invariant under a general affine transformation of the spatial coordinates.

Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques

The implementation of non-zero-order joint-transform correlators (JTC's) is presented. The zero-order spectra (i.e., the autocorrelation power spectra) are removed from the joint-transform power spectrum by use of phase-shifting techniques by which the output diffraction and input spatial domain can more efficiently be utilized. Applications of the phase-shifting techniques to both conventional JTC's and phase-transformed input JTC's (PJTC's) are discussed. Compared with the conventional JTC, the PJTC has the advantages of higher light efficiency, a better signal-to-clutter ratio, and the simplicity to realize phase shifting. We anticipate that the proposed non-zero-order JTC's should have a significant impact on the future development of more efficient JTC's.

Invariant optical-pattern recognition based on a contour bank

We propose a new optical pattern-recognition method that is invariant to shift, rotation, and scale changes. By means of a zero-order circular-harmonic filter the input object can be transformed into a correlation peak whose outline retains a shape similar to the outline of the input object. After multilevel thresholding and binarization, a bank composed of many contours with different sizes is formed. The invariant recognition can be obtained by a small contour line being taking as a reference and its second-order circular-harmonic component being taken as a filter. In addition to the scale invariance the correlation peak is superior to the classical circular-harmonic filter and the phase-only circular-harmonic filter in terms of peak intensity, half-maximum width, and peak-to-sidelobe ratio.