Guowen Lu

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

The implementation of non-zero-order joint-transform correlators (JTCs) 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 JTCs and phase-transformed input JTCs (PJTCs) 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 JTCs should have a significant impact on the future development of more efficient JTCs.

Performance of a phase-transformed input joint transform correlator

Conventionally a detected image is represented by an intensity array owing to the square-law nature of most detectors. However, this does not mean that we have to restrict ourselves to using intensity images for the correlation process. Transforming intensity images into phase images before correlation, which can be easily realized by a phase-modulation spatial light modulator, offers an alternative approach for high-performance pattern recognition. A phase-transformed input joint transform correlator is investigated in detail in terms of pattern discriminability, detection efficiency, and noise robustness. We show that the phase-transformed joint transform correlator has higher pattern discriminability and detection efficiency than the conventional joint transform correlator, and it also offers a better trade-off between the pattern discriminability and noise tolerance. A proof-of-concept experiment is also provided.

Short-time Fourier transform and wavelet transform with Fourier-domain processing

We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processing, which is suitable for optical implementation. We also systematically analyze the selection of the window functions, especially those based on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inverse STFT and the inverse WT. A couple of optical architectures based on Fourier-domain processing for the STFT and the WT, by which real-time signal processing can be realized, are proposed.

Speckle-induced phase error in laser-based phase-shifting projected fringe profilometry

Laser sources offer advantages over white-light sources in some phase-shifting projected fringe profilometry applications. These benefits, however, are gained at the cost of incurring speckle noise. Some basic statistics of speckle-induced phase-measurement errors are investigated based on the multiplicative noise model for image-plane speckles. First, the dependence of phase-error distribution and measurement uncertainty on speckle size and grating pitch is numerically studied, based on the Karhunen–Loeve expansion method. Then an analytical expression that relates phase-error distributions to optical system parameters is derived as a direct extension of the simulation results. This expression is useful for system design and optimization. Analysis shows that phase noise caused by speckles can be modeled as additive white Gaussian noise. Optical system design and noise-reduction algorithms are also briefly discussed, based on the simulation results.

Application of Phase Shift Optical Triangulation to Precision Gear Gauging

Traditionally, gear tooth profile is measured by coordinate measurement machines using mechanical probe scanning, which is very time consuming. Therefore, normally only a few lines are scanned across the gear tooth surface, which often do not faithfully represent the whole tooth surface profile. In this paper, a phase-shift optical triangulation technique is applied to the gear profile measurement, which has the advantages of redundant information, speed and non-contact nature. When examining a 2 cm2 area, comparative measurement accuracy better than 1 micrometers and resolution about 0.1 micrometers has been successfully demonstrated with the system; this corresponds to a 5 by 10-5 relative accuracy. The measurement result from the optical system displaced good correlation with those form a mechanical probe on a coordinate measurement machine. A few teeth/second measurement speed can also be expected. Different factors to effect the measurement accuracy are discussed, and the possible solutions are provided.

Kinoform-based Nipkow disk for a confocal microscope

A kinoform-based Nipkow-disk system, as applied to a real-time confocal microscope, is presented. The major advantage of this technique must be its high light efficiency (e.g., >80%), which significantly improves the performance of a confocal microscope. Our preliminary experiment indicates that there are potential applications to three-dimensional microscopic imaging as well as to object surface detection.

Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect

We present a novel technique for measuring phase modula- tion in a liquid crystal television (LCTV) panel using the fractional-Talbot effect. We show that the phase modulation property in an LCTV can be obtained by measuring the contrast ratio of the Fresnel diffraction field at one quarter of the Talbot distance. We also generate a multilevel phase grating that produces a Talbot array illuminator to verify the experimental measurement result.

Absolute measurement of surface profiles with phase-shifting projected fringe profilometry

Phase-shifting projected fringe profilometry (PSPFP) is a powerful tool in the profile inspection of a large variety of rough surfaces. In many applications, absolute PSPFP measurements, capable of compensating for the lateral distortions in the measured object shape and providing an expression of the measured shape under a predefined reference system, are highly desired. In this paper, an absolute PSPFP technique combining the lateral calibration and the phase-to- depth calibration is proposed. The principles of the proposed absolute PSPFP measurement technique will be discussed together with the calibration and measurement methods based on a particular formalism of absolute PSPFP measurements.

Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator

Synthesis of a spatial-domain bipolar composite filter (SBCF) using simulated annealing algorithm is presented. Since a SBCF is a spatial-domain filter, it is very suitable for implementation in a joint transform correlator. To alleviate the stringent control requirement of a phase-modulated spatial light modulator (SLM), a position-encoding technique is used to generate the SBCF as well as the input objects. Experimental demonstrations are also provided, in which it is shown that the SBCF has a higher discrimination capability of extracting the target objects against the antitarget objects.

PATTERN CLASSIFICATION USING A JOINT TRANSFORM CORRELATOR BASED NEAREST NEIGHBOR CLASSIFIER

A JTC-based nearest neighbor classifier (JTC-NNC) is presented, by which shift-invariant pattern classification can be obtained. To efficiently utilize the spatial domain input plane, a non-zero-order JTC is introduced to remove the autocorrelation power spectra. In addition, a phase-transform technique is introduced into the JTC-NNC to improve the light efficiency and pattern discriminability. Finally, application of the JTC-NNC to optical character recognition is discussed, and computer simulation is provided to show the feasibility of the JTC-NNC.