Realizations of focus invariance in optical-digital systems with wave-front coding

We report experimental verification of an extended depth of focus (EDF) system with near-diffraction-limited performance capabilities. Dowski and Cathey [Appl. Opt. 34, 1859-1866 (1995)] described the theory of this system in detail. We can create an EDF system by modifying a standard incoherent optical system with a special cubic phase plate placed at the aperture stop. We briefly review the theory and present the first optical experimental verification of this EDF system. The phase plate codes the wave front, producing a modified optical transfer function. Once the image is transformed into digital form, a signal-processing step decodes the image and produces the final in-focus image. We have produced a number of images from various optical systems using the phase plate, thus demonstrating the success of this EDF system.     

Practical implementation of a high-speed multichannel correlator with fiber-optic delays

We discuss architecture, subsystems, and applications of a multichannel digital correlator we constructed by using a combination of optical and electrical delays. Our system is capable of a 1-ns bin width in normal operation, when a derandomizer is used at the input stage and a 0.25-ns bin width when the derandomizer is bypassed. When switchable delay lines are used, the 16 real-time channels can access a 160-ns delay range, providing up to 160 channels at 1-ns bin width or 640 channels at 0.25-ns bin width.     

Operating experience of optical-digital systems for measuring the capillary characteristics of materials

We analyzed the well-known optical-digital systems of optical nondestructive testing and measurement of the capillary characteristics of materials by the method of sessile drop. We show that the parameters and operating modes of such systems should be optimized. We consider a model and created a breadboard on its basis. By using the breadboard, we investigated optical and electronic noises of the system and the other sources of measurement errors of the geometric parameters of a drop image. The results allow one to optimize the parameters of the system in such a way that the measurement errors of the capillary characteristics should be minimum. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 5, pp. 81–87, September–October, 1997.     

Experimental verifications of a joint transform correlator using compressed reference images

Single-target and multiple-target detections by using a joint transform correlator (JTC) with compressed reference images are experimentally verified. Two high-contrast images with different spatial-frequency content are used as test scenes. Although an effect of the additive noise on detection performance of the proposed correlator is more severe than that of the compression, the experimental results confirm the feasibility of implementing the JTC with compressed reference images.     

Acousto-optical wideband correlator system: design, implementation, and evaluation

We describe the design and development of an acousto-optical wideband correlator that we integrated into a digital signal-processing system testbed. We report its measured performance and compare it with various theoretical performance measures, one of which compares the optical system with an equivalent efficient digital correlator. The measured performance of the optical system was 20 to 70 times that of a VAX 6410 computer using a fast-Fourier-transform correlation algorithm and a vector processor, even though the electronic interface system limited the performance of the optical system to less than 0.5% of its potential. We also compare the system with commercially available digital signal-processing boards.     

Security and encryption optical systems based on a correlator with significant output images

An improved optical security system based on two phase-only computer-generated masks is proposed. The two transparencies are placed together in a 4f correlator so that a known output image is received. In addition to simple verification, our security system is capable of identifying the type of input mask according to the corresponding output image it generates. The two phase masks are designed with an iterative optimization algorithm with constraints in the input and the output domains. A simulation is presented with the resultant images formed by the two phase-only elements. Various mask combinations are compared to show that a combination is unique and cannot be duplicated. This uniqueness is an advantage in security systems.     

Log-polar transform-based wavelet-modified maximum average correlation height filter for distortion invariance in a hybrid digital-optical correlator

We discuss and implement a log-polar transform-based distortion-invariant filter for automatic target recognition applications. The log-polar transform is a known space-invariant image representation used in several image vision systems to eliminate the effects of scale and rotation in an image. For in-plane rotation invariance and scale invariance, a log-polar transform-based filter was synthesized. In cases of in-plane rotation invariance, peaks shift horizontally, and in cases of scale invariance, peaks shift vertically. To achieve out-of-plane rotation invariance, log-polar images were used to train the wavelet-modified maximum average correlation height (WaveMACH) filter. The designed filters were implemented in the hybrid digital-optical correlation scheme. It was observed that, for a certain range of rotation and scale differences, the correlation signals merge with the strong dc. To solve this problem a shift was introduced in the log-polar image of the target. The use of a chirp function for dc removal has also been discussed. Correlation peak height and peak-to-sidelobe ratio have been calculated as metrics of goodness of the log-polar transform-based WaveMACH filter. Experimental results are presented.     

Hybrid optical-digital method for local-displacement analysis by use of a phase-space representation

A method for evaluating the local deformation or displacement of an object in speckle metrology is described. The local displacements of the object in one direction are digitally coded in a one-dimensional specklegram. By optically performing the local spectrum of this pattern, one simultaneously achieves information about the local displacement and its spatial position. The good performance of this technique is demonstrated with computer-generated test signals.     

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.     

High-efficiency hybrid joint transform correlator with pre-processed input image and replicated binary spectrum array

Abstract

The performance of a hybrid joint transform correlator (JTC) is improved by the input image pre-processing method and our proposed spectrum binarizing and replicating technique. The input image pre-processing can enhance the correlation discrimination ability of a JTC system, and the replication of the binary spectrum under an appropriate condition can further substantially increase the light efficiency, the maximum correlation peak intensity, the peak sharpness and the signal-to-noise ratio of the system at the same time by the mechanics of constructive interference. Theoretical analyses are presented. Both the computer simulation and optical experiment verifying the effectiveness of this technique are also given.     

Wavelet-modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital-optical correlator

We discuss and implement a wavelet-modified maximum average correlation height (MACH) filter for 0 degrees -360 degrees in-plane rotations in a hybrid digital-optical correlator. Use of a wavelet transform improves the performance of the MACH filter by reducing the number of filters that are required to identify a target rotated at any angle between 0 degrees and 360 degrees in-plane rotations and enhances the autocorrelation peak intensity significantly. The output of a hybrid digital-optical correlator contains two autocorrelation peaks and a strong dc. Using a chirp function with the wavelet-modified MACH filter, the correlation signals are focused in three different planes. Thus placing a peak-capturing CCD camera at a particular plane, only one autocorrelation peak is recorded, discarding the strong dc and other autocorrelation peaks. A signal-to-noise ratio has been calculated as a metric of goodness of the proposed wavelet-modified MACH filter.     

Two-dimensional shifting tolerance of a volume-holographic correlator

A simple method for simulating two-dimensional (2-D) distributions of the diffraction lights of a volume-holographic-type VanderLugt correlator is proposed and demonstrated. The simulation results are similar to those of the corresponding experiments, and only a few dozen points are sampled from both the input and the reading patterns. We show that the shifting tolerance to the reading pattern is a result of Bragg degeneracy and is not isotropic. The Bragg degeneracy generates different degrees of cross talk between the horizontal and the vertical directions. With the method we further simulate the 2-D shifting tolerance of the volume-holographic correlator. The simulation results offer a clear picture of the diffraction in a transmission volume hologram used as an optical spatial correlator.     

Aperture tapering in a coherent optical correlator

Sharp edges located in an optical correlator input beam cause unwanted edge effects. A 1-D analysis is used to demonstrate this effect and how edge tapers can reduce this effect. Then an aperture made on film approximating the best taper is used to reduce the spurious signals in a matched filter correlator.     

Quasi-periodic oscillations generated using a sign correlator

It is shown that a sign correlation of two harmonic oscillations with any irrational relationship of their frequencies gives rise to a quite regular process, the spectrum of which contains components possessing nonequidistant combination frequencies. The spectrum of such a signal is analytically determined and some features of this spectrum are discussed. The results confirm the conclusions made by Vladimirov [Usp. Fiz. Nauk 174, 217 (2004)] concerning the impossibility of generating a chaotic pulse sequence using a sign correlator of two periodic signals proposed by Evdokimov et al. [Usp. Fiz. Nauk 171, 775 (2001)].     

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.     

Image classification with a chirp-encoded joint transform correlator

We describe a method of performing image classification with a chirp-encoded joint transform correlator. In the proposed system the reference images and the input image that is to be classified are placed in different input planes of the joint transform correlator. As a result, different output planes of the correlator are associated with each reference image. The input image is classified on the basis of the intensity and the spatial position of the correlation peak. The reference images and the input image can be positioned in one input plane with glass blocks of different thicknesses placed on each reference image. This produces the same effect as having the reference images and the input image in different planes. Analytical expressions, computer simulations, and optical experiments are presented to investigate the performance of the chirp-encoded joint transform correlator for image classification.     

Joint transform correlator subtracting a modified Fourier spectrum

The optically generated joint Fourier transform (JFT) of a test image and a reference image is processed using a new method: the JFT is recorded twice. In the second recording the reference image is phase shifted by π with respect to the first recording. The two JFT's are subtracted and binarized with a threshold of zero. Strong correlation peaks are obtained, and correlations within the test image are suppressed. Some results of optical implementation are presented, using a ferroelectric liquid crystal display with 128 × 128 pixels for data input. The phase shift of the reference was implemented by the contrast-inverted reference input on the binary light-modulating device. Processing of the JFT is done by a CCD camera, a frame grabber, and a personal computer.