This PDF file contains the editorial “Editorial: Special Issues, Special Sections, and Related Topics” for OE Vol. 31 Issue 09

This PDF file contains the editorial “Guest Editorial: Wavelet Transforms” for OE Vol. 31 Issue 09

The causal analytical wavelet transform employs exponentially decaying nonsinusoidal wideband transient bases of compact support. The basis set h_ab(t) = h[(t- b)/a]√a is called daughter wavelets, which are constructed from a causal analytical mother wavelet h(t) by means of the dilation parameter a and the translation parameter b. We show that a causal (i.e., zero valued before signal arrives) and analytical mother wavelet still guarantees completeness. This permits the selection of mother wavelets that better match causal analytical input signals. An optical architecture is described for real-time implementation.

A new wavelet transform normalization procedure is proposed for the construction of a weighted bank of correlation filters. The standard normalization results in lower input frequencies producing larger wavelet transform magnitudes for equal-amplitude frequencies, while the new normalization produces equal responses as desired. This is illustrated with examples of Gibbs overshooting phenomenon and a cocktail party effect. A derivation is given to show that an inverse transform still exists when using the new normalization.

We consider theoretically the optical implementations of both discrete and continuous wavelet transforms. Discrete wavelet transforms (DWTs) require sums (or integrals) of the product of the input function with multiple stored functions (wavelets with various shifts and scales). The inverse DWT requires the same, exceptthe given function is replaced by the wavelet coefficients determined by the DWT. We show that we can store and utilize in parallel large banks of wavelets. This should allow "instantaneous" DWT of functions of a single variable and (relatively) fast DWTs of two-dimensional functions. Of course, the same applies to the inverse DWTs. A true continuous wavelet transform (CWT) must be continuous in both shift and scale. By means of a continuous anamorphic transformation of a one-dimensional signal and a suitable choice of kernel or filter, we can allow a normal two-dimensional optical Fourier transform image processor to perform a CWT.

The wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet transform filters. This approach provides a shift-invariant wavelet transform with continuous translation and discrete dilation parameters. The wavelet transform filters can be in many cases simply optical transmittance masks. Experimental results show detection of the frequency transition of the input signal by the optical wavelet transform.

Two architectures in space and frequency domains are given to optically implement wavelet transforms (WT) in real time and in 2-D parallel, which in principle can circumvent the 4-D display requirement for 2-D WT. Specifically, we have experimentally performed the 2-D Haar WT of binary images directly in the space domain by means of a shadow-casting system using 2-D lenslet arrays and micropolarizers. Shadowing is natural for scale changes, and polarization encoding is necessary to realize the bipolar nature of Haar wavelets. Haar wavelets have two elementary types in 2-D, a corner mother wavelet and an edge mother wavelet. Both are useful for the real-time feature extraction for multiple-resolution image processing and pattern recognition. Moreover, a holographic processor that implements the 2-D Haar WT through filtering operations in the frequency domain is numerically simulated. The feasibility of both architectures is demonstrated and compared by computer simulations and experiments.

An optical Haar mother wavelet is created with a Semetex 128 x 128 magneto-optic spatial light modulator. Two techniques for dilating the mother wavelet are explored: (1) aperture stopping and (2) operating the SLM in ternary phase-amplitude mode. Discrete resolution levels of a continuous wavelet transform are obtained by optically correlating a binarized image with multiple dilations ofthe mother wavelet. Frequency-plane masks for the correlation process are generated using thermoplastic holography. Experimental results are compared with a digital simulation of the wavelet transform.

A two-dimensional wavelet transform is implemented by a bank of wavelet transform filters in the Fourier domain. An optical N₄ multichannel correlator architecture is proposed to perform parallel optical 2-D wavelet transforms. A holographic recording scheme is proposed to implement such a wavelet transform filter array. The optical experimental results are presented using the computer-generated transmittance masks as the wavelet transform filters.

Recent development in vision and image understanding related study reveals that a signal decomposition before processing may provide an enormous amount of useful information aboutthe signal. Various signal decomposition models such as the Gabor and wavelet expansions have been proposed. While the Gabor signal expansion creates a fixed resolution space-frequency signal representation, the wavelet transform provides a multiresolution signal space-scale decomposition. Digital implementation of these expansions are computationally intensive both because of the nature of the coordinate-doubling of the transforms and because ofthe large quantity of convolution/correlation operations to be performed. Optics with its inherent parallel-processing capability has been applied to many useful linear signal and image transformations for feature analysis and extraction. We studied the suitability of using optical processing techniques for the signal Gabor and wavelet analysis. Gabor and wavelet expansions of both 1- and 2-D signals and images are discussed. System parameters and limitations are analyzed. Preliminary experimental results are presented.

We describe an optoelectronic system to extract gray-scale texture features. These systems utilize a nonlinear resistive grid to perform a 2-D pseudowavelet transform of the optical input image. Texture features are computed using first- and second-order variance estimates of the transform coefficients. Some preliminary results are presented that demonstrate the natural segmentation that the nonlinearity provides at the boundary of two dissimilar textures and the utility of the extracted features for texture discrimination.

We consider wavelet and Gabor transforms for detection of candidate regions of interest in a 2-D scene. We generate wavelet and Gabor coefficients for each spatial region of a scene using new linear combination optical filters to reduce the output dimensionality and to simplify postprocessing. We use two sets of wavelet coefficients as indicators of edge activity to suppress background clutter. The Gabor coefficients are found to be excellent for object detection and robust to object distortions and contrast differences. We provide insight into the selection of the Gabor parameters.

1-D scan that follows the Peano curve to a desired resolution is demonstrated to preserve a 2-D proximity relationship and is shown to be efficient for wavelet transform (WT) processing and artificial neural network pattern recognition. This deterministic fractal sampling method can be implemented in real time using optoelectronic scanning. For example, 2-D texture patterns are analyzed by using 1 -D wavelet transformation. Those WT coefficients can be fed into a standard back-propagation neural network for pattern recognition.

Methods are presented for adaptively generating wavelet templates for signal representation and classification using neural networks. Different network structures and energy functions are necessary and are given for representation and classification. The idea is introduced of a "super-wavelet," a linear combination of wavelets that itself is treated as a wavelet. The super-wavelet allows the shape of the wavelet to adapt to a particular problem, which goes beyond adapting parameters of a fixed-shape wavelet. Simulations are given for 1-D signals, with the concepts extendable to imagery. Ideas are discussed for applying the concepts in the paper to phoneme and speaker recognition.

Benign prostatic hyperplasia (BPH) is a common disease affecting past middle-aged males. Surgical treatment has been successfully used since the early 1900s. Currently, nonsurgical treatment modalities are under intensive study in BPH patients who have relative contraindications to surgery. Transurethral microwave hyperthermia (TUHT) is one of these modalities under study. TUHT has been applied in five to ten treatment sessions. The treatments were well tolerated with no major toxicity being reported. In BPH patients with predominance of median lobe or median bar enlargement the treatment efficacy was reduced to 30%. The effectiveness of TUHT was of particular importance in patients who had urinary retention. In this group 72% had normal voiding for 12 months or longer. A strong correlation between applied temperature and response to treatment was demonstrated. Current efforts are directed toward optimization of technique and treatment schedule. A phase III prospective randomized trial is required to define the role of TUHT in the management of BPH patients.

The need for storage, transmission, and archiving of medical images has led researchers to develop adaptive and efficient data compression techniques. Among medical images, x-ray radiographs of the breast are especially difficult to process because of their particularly low contrast and very fine structures. A block adaptive coding algorithm based on the discrete cosine transform to compress digitized mammograms is described. A homogeneous repartition of the degradation in the decoded images is obtained using a spatially adaptive threshold. This threshold depends on the coding error associated with each block of the image. The proposed method is tested on a limited number of pathological mammograms including opacities and microcalcifications. A comparative visual analysis is performed between the original and the decoded images. Finally, it is shown that data compression with rather high compression rates (11 to 26) is possible in the mammography field.

We determined the performance of an optical correlator as the filter SLM was reduced in resolution by a factor of M in a linear dimension. Our configuration allowed a constant reduction, by a factor of M², in the amount of data used to describe the filter when compared to using a filter at full resolution. Reducing the resolution of the filter is shown to primarily affect its impulse response by the addition of copies of the filter image. We provide both general expressions for performance measures and guidelines for minimizing the distortion induced as the resolution of a filter is decreased. Furthermore, we show the effect of reducing the resolution of a binary phase-only filter on autocorrelation experiments and cross-correlation experiments containing competing objects. We obtained experimental results with an optical correlator with a magneto-optic SLM of 128 x 128 pixels in the input plane and a filter of 64 x 64 pixels. The results showed that our arrangement can provide comparable results to a full-resolution filter when the resolution is decreased by a factor of M and the object within the filter images is less than N/M x N/M pixels in size.

A simple optoelectronic system for high-speed determination of binary phase-only filters for use in an optical correlator is described. Filters determined using the system were implemented using a liquid crystal spatial light modulator in the Fourier plane of an optical correlator. Results demonstrating the operation of the system are presented.

A new method for continuous recording of holographic information, "streak holography," is proposed. This kind of record can be useful for velocity and acceleration measurement as well as for observing a moving object whose trajectory cannot be predicted in advance. A very high speed camera system has been designed and constructed for streak holography. A ring-shaped 100-mm-diam film has been cut out from the high-resolution sheet film and mounted on a thin duralmin disk, which has been driven to rotate directly by an air-turbine spindle. Attainable streak velocity is 0.3 mm/μs. A direct film drive mechanism makes it possible to use a relay lens system of extremely small F number. The feasibility of the camera system has been demonstrated by observing several transient events, such as the forced oscillation of a wire and the free fall of small glass particles, using an argon-ion laser as a light source.

We present a study of the effects of a layer of water ice on the transmission of an infrared bandpass filter/window in the 10.5- to 12.5-μm spectral band. Computed spectral transmission is presented for a model consisting of water ice thicknesses of 20, 200, 2000, and 20,000 nm on the blocking stack side of a bandpass filter design. A ray angle of 20 deg is used to simulate the conditions at a filter situated in front of a cooled detector, where water ice might accumulate. The results show severe degradation in transmission for water ice thicknesses greater than 200 nm.

A method is presented for thermal noise reduction in a near room-temperature intrinsic IR photodetector. The method is based on suppression of the Auger generation-recombination processes using the electro-magnetic carrier depletion (EMCD) of a narrow gap semiconductor. The device is a lightly doped narrow gap semiconductor flake with a high backside surface recombination velocity, supplied with electrical contact band and placed in a magnetic field. Due to the action of the Lorentz force most of the device depletes charge carriers, which results in suppression of the Auger generation and recombination processes. As a result, the I-V characteristic becomes nonlinear, exhibiting regions of high positive and negative resistance. Thermal noise can be dramatically reduced, leading to a substantial improvement in performance. The ultimate detection may be determined either by background radiation or by Shockley-Read generation, depending on the ratio of the background photon flux to the recombination center concentration. Near-BLIP performance is predicted for 10.6-μm (Hg, Cd) Te devices, prepared from high-quality materials and operated at 225-250 K.

The radius of curvature is a fundamental parameter of optical surfaces. Improving the measurement tolerance is critical for an increasing number of applications. Interferometry is potentially a very accurate technique, but careful implementation is critical to achieving full potential. To this end, the error budget for radius of curvature measurement by interferometry is examined. The goal is to achieve 0.001% (10 ppm) measurement tolerance. The major errors, Abbé errors, are typically 10 to 100 μm, and can be virtually eliminated using a distance-measuring interferometer. The remaining major errors are cavity null errors and axial alignment errors. These are quantified and corrections are described. Other errors including environmental and tooling errors are also cataloged.

An orthogonally polarizing 180-deg rotational shearing interferometer was constructed and was used to measure the eccentricity of the lens and its coefficients of primary coma and distortion with great precision and in quantitative measure.

The relative effectiveness of using the unipolar and bipolar binaries is compared and the concept of hamming distance used for information storage and retrieval in neural network models is described. It is shown that the use of the bipolar retrieval key has the effect of doubling the length of the probe and stored vectors. This suggests useful modifications for improved performance and shows necessary conditions for a proper convergence when an unknown and erroneous unipolar or bipolar probe vector is used for retrieval. A new measure of distance defined over a field of real numbers is described.

The products of molecular susceptibilities and molecular dipole moments of nine organic nonlinear optical materials were evaluated by suggesting an expression using the solvatochromism procedure. The data were plotted versus the frequency factor F(ω). Another 51 pairs of data abstracted from separate literature were treated in a similar way. A fairly good linear relationship and, more interestingly, a rather small slope variation were observed in spite of the wide difference in chemical constitution and different measurement methods used.

The chemical, mechanical, and optical properties of the first two members of a new family of fluoroplastic materials are examined. These new materials have the unique properties of being optically transparent in the visible and near IR and also chemically inert. Comparison of the optical properties to other transparent materials is also presented.

We present a method of using a liquid crystal television (LCTV) as a spatial light modulator (SLM) in an optical computing experiment. Using LCTVs as SLMs to modulate an image optically and combining this process with a digital computer has allowed implementation of various image-processing algorithms that have only been demonstrated in the digital domain. In particular, we are using an LCTV as an SLM for the hybrid optical implementation of a homomorphic filter to remove image shading.

An optical associative processor that employs variable nonlinearity in the filter plane of the conventional-filter-based optical associative memory is described. It is shown that for severe compression types of nonlinearity, the performance of the associative processor in the areas of retrieval quality, convergence rate, and light efficiency is improved significantly. The nonlinearity in the filter plane is implemented using a nonlinearly transformed filter to store the associative images such that nonlinear correlations between the input image and the stored images are obtained. Two methods are described to construct the nonlinearly transformed filter. One method applies uniform nonlinear transformations to the filter function containing all associative signals. The second method applies controlled nonlinear operations on the filter function. Analysis and computer simulations are presented to illustrate the importance of applying nonlinear transformations in the filter plane of the optical associative processor.

A two-dimensional acousto-optic signal processor is shown to be useful for providing simultaneous spectrum analysis and direction finding of radar signals over an instantaneous field of view of 360 deg. A system analysis with emphasis on the direction-finding aspect of this new architecture is presented. The peak location of the optical pattern provides a direct measure of bearing, independent of signal frequency. In addition, the sidelobe levels of the pattern can be effectively reduced using amplitude weighting. Performance parameters, such as mainlobe beamwidth, peak-sidelobe level, and pointing error, are analyzed as a function of the Gaussian laser illumination profile and the number of channels. Finally, a comparison with a linear antenna array architecture is also discussed.

Thickness variations that are associated with the vacuum chuck were observed in wet-chemical-derived dielectric films applied by the spin-coating technique. These thickness variations are controlled by factors such as the thermal properties of the substrate material, the evaporation behavior of the coating solution, and the physical design of the vacuum chuck. Atechnique is described for evaluating the magnitude ofthis effect.

This PDF file contains the editorial “Book Rvw: Optical Shop Testing," by Daniel Malacara for OE Vol. 31 Issue 09

This PDF file contains the editorial “Book Rvw: Optical Signal Processing," by Anthony VanderLugt for OE Vol. 31 Issue 09