Jerome Knopp

Measurement of the complex transmittance of the Epson liquid crystal television

The complex transmittance of an Epson liquid crystal television (LCTV) is determined as a function of the video drive signal. Several different operating configurations of the LCTV are established, and their usefulness as operating modes for spatial light modulators in the input and filter planes of a hybrid correlator is discussed. A high-stability phase measurement scheme is developed to determine the operating curves, and this system is presented. This measurement scheme is designed so that a fully characterized LCTV could be assuredly moved into the optical correlator. This allows filters to be calculated for the correlator using the exact physical action of the modulators. The transient response of the LCTV to field-rate changes in the video signal is also presented. It is observed that the switching speed of the liquid crystal molecules is a fundamental limitation on the operating speed of these devices.

Complex characterization of the Epson liquid crystal television

The complex transmittance of an Epson liquid crystal television was determined, as a function of the video drive signal. Several different operating configurations of the LCTVs were established, and their usefulness as operating modes for spatial light modulators in the input- and-filter-planes of a hybrid correlator is discussed. A high-stability phase measurement scheme was developed to determine the operating curves, and this system is presented. The transient response of the liquid crystal television to field-rate changes in the video signal is also presented. It is observed that the switching speed of the liquid crystal molecules presents an obstacle to the operating speed of these devices.

Live-input live-filter liquid-crystal correlator

We have constructed a correlator using a gray scale amplitude modulator for an input device and a gray scale phase modulator in the filter plane. The spatial light modulators used in the correlator are two of the three liquid crystal cells from a commercially available color projection television. The cells (twisted nematic liquid crystals) may be operated in an amplitude mostly or phase mostly mode by selecting the polarization of the light and the operating bias voltage. We show the Jones matrix analysis of the laboratory measurements and the corresponding operating curves. Signal to noise ratios on the order of 100:1 have been observed for some test objects using simple phase mostly filters.

HOLOMED: an algorithm for computer-generated holograms

We use a liquid crystal spatial light modulator to construct a computed wave that would have emanated from a hypothetical object that we mathematically specify. The method uses optimal filter theory and realistic devices. We show laboratory results. The method applies to video holograms and small head-up displays. The method was inspired by work using binary reflective SLMs, and we adapted it to a continuously variable and highly coupled operating curve.

Optical Joint Transform Correlation On The DMD

We report initial experimental investigation of the Texas Instruments deformable mirror device (DMD) in a joint optical transform correlator. We used the inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

Geometric approach for designing optical binary amplitude and binary phase-only filters

An analytic solution for real optimal filters is known, and the special case of optimal binary phase-only filters can be solved by a fast binning algorithm but no analytic solution is known. We establish a geometric solution for the design of optimal binary amplitude filters (OBAFs) and optimal binary phase-only filters (OBPOFs) for any object. The optimal filter is found in terms of maximizing the field strength at the origin in the correlation plane. We found that it is possible to construct a unique convex polygon by using an ordered set of phasors from the filter objects Fourier transform. This process leads eventually to an exact solution for the filter-design problem. We show that the maximum distance across the polygon divides the phasors into two groups: For the OBAF, it determines the group that is passed or blocked; for the OBPOF, it determines which group is passed with a zero or a pi phase shift. The shape of the convex polygon gives qualitative information on the criticalness and the tightness needed in the design process. It provides good insight into the binning-process algorithm and permits us to bound the error in the binning process. Design examples through computer simulation and applications in fingerprint identification are presented.

Pixel-level complex control of an Epson LCTV SLM

In order to implement computer generated holograms (CGHs) and correlation plane filters (CPFs) on an LCTV SLM, the pixel-level complex-amplitude properties of the modulator must be accurately known. These properties must then be incorporated into algorithms for achieving the pixel-level control via a frame grabber (FG) and NTSC video signal. Within this investigation we present techniques for measuring the properties of FG-to-video-to-LCTV system, and then develop an algorithm to allow pixel-level control of the LCTV.

Time-varying spectral analysis of non-stationary signals based on combined wavelet and Fourier transforms

The wavelet transform (WT) has received attention in recent years in the analysis of non-stationary signals. Studies have shown that the WT provides very good resolution in the time direction and comparatively poor resolution in the frequency direction for broadband signals. On the other hand, the Fourier transform (FT) provides better resolution in the frequency direction, but it is not suitable for the analysis of transients. A new algorithm is presented to analyse non-stationary signals efficiently. It is based on combined wavelet and Fourier transforms. This algorithm makes use of the WT to display the time domain signal components and the FT to display their spectral components. Further a new method is suggested to eliminate the interference terms between the different scales in wavelet analysis. The algorithm is applied to computer simulation and real data examples. Results suggest that it provides comparable temporal and frequency resolution of transients.

Optical calculation of correlation filters

A method is presented for designing optical correlation filters based on measuring intensity patterns in the Fourier plane. The method can be used in general to design any type of frequency plane filter but is especially attractive in the case of a binary phase only filter (BPOF). The method can produce a filter that is well matched to both the object, its transforming optical system and the spatial light modulator used in the correlator input plane. A working filter was produced using the technique, but the filter response was weak. The suspected causes of the weak output are imprecise Fourier plane positioning, nonlinearities in the recording process, and/or aliasing effects.

Partial rotation invariance in retinal pattern recognition

We desire to have a joint transform correlator track features in the image of a human retina. Previous binarized digital methods indicated unacceptable limitations in tracking through torsion motions of the eye. To create an extended range of response to eyeball rotation we tried several methods of processing the reference image. We compared laboratory measurements with digital simulations. Based on small statistics and our noiseless models, the results disagree; the digital method has less range, and the optical method has sufficient range (+/- 5 degree(s)) for our purpose.