Wavelet transforms for optical pulse analysis

An exploration of wavelet transforms for ultrashort optical pulse characterization is given. Some of the most common wavelets are examined to determine the advantages of using the causal quasi-wavelet suggested in Proceedings of the LEOS 15th Annual Meeting (IEEE, 2002), Vol. 2, p. 592, in terms of pulse analysis and, in particular, chirp extraction. Owing to its ability to distinguish between past and future pulse information, the causal quasi-wavelet is found to be highly suitable for optical pulse characterization.     

Joint transform optical correlator designed and analyzed by use of two- and one-dimensional hilbert transforms

Novel real-time joint transform, Hilbert transform optical correlators are proposed in which only a half or a quarter of the Fourier plane is written onto an optically addressable spatial light modulator. A point source is used to recover the result for the whole plane. As a result, images with a two- or four-times larger space-bandwidth product can be matched in amplitude and phase. The effect of truncating the transform plane is explained with two- and one-dimensional Hilbert transform analysis. Results of computer simulation are shown.     

Nonlinear rotation-invariant pattern recognition by use of the optical morphological correlation

We introduce a modification of the nonlinear morphological correlation for optical rotation-invariant pattern recognition. The high selectivity of the morphological correlation is conserved compared with standard linear correlation. The operation performs the common morphological correlation by extraction of the information by means of a circular-harmonic component of a reference. In spite of some loss of information good discrimination is obtained, especially for detecting images with a high degree of resemblance. Computer simulations are presented, as well as optical experiments implemented with a joint transform correlator.     

Image magnification using families of fast orthogonal transforms

We outline a method if image magnification based on parametric families of fast orthogonal transforms which arise from the multiresolution/wavelet paradigm of Mallat and Meyer. The essential idea is to consider the original image as a low-frequency component of a family of potential enlargements, all of which are computable in real time. We sketch the underlying theory and pertinent algorithms. Several specific examples are detailed. © 1996 John Wiley & Sons, Inc.     

Finite volume distance field and its application to medial axis transforms

Accurate and efficient computation of the nearest wall distance d (or level set) is important for many areas of computational science/engineering. Differential equation‐based distance/level set algorithms, such as the hyperbolic‐natured Eikonal equation, have demonstrated valuable computational efficiency. Here, in the context, as an ‘auxiliary’ equation to the main flow equations, the Eikonal equation is solved efficiently with two different finite volume approaches (the cell‐vertex and cell‐centered). The application of the distance solution is studied for various geometries. Moreover, a procedure using the differential field to obtain the medial axis transform (MAT) for different geometries is presented. The latter provides a skeleton representation of geometric models that has many useful analysis properties. As an alternative to other methods, the current d‐MAT procedure bypasses difficulties that are usually encountered by pure geometric methods (e.g. the Voronoi approach), especially in three dimensions, and provides better accuracy than pure thinning methods. It is also shown that the d‐MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Copyright © 2009 John Wiley & Sons, Ltd.     

Laser-to-fiber optical coupling scheme with a long working distance by use of thermally overexpanded fiber

A laser-diode-optical-fiber coupling scheme that uses aspherically ended thermally overexpanded fiber is proposed. The scheme is verified by both an analytical formalism and a wide-angle beam-propagation method analysis in cylindrical coordinates.     

Two class minimax distance transform correlation filter

A new correlation filter formulation (that we refer to as the minimax distance transform correlation filter (MDTCF) is presented that minimizes the average squared distance from the filtered desired (or true-) class training images to a filtered reference image while maximizing the mean squared distance of the filtered undesired (or false-) class training images to this filtered reference image. This approach increases the separation between the false-class correlation outputs and the true-class correlation outputs. Classification can be performned using the squared distance of a filtered test image to the chosen filtered reference image. We show that the previously introduced distance classifier correlation filter (DCCF) is similar to a special case of MDTCF. We also examine the differences between the DCCF and the MDTCF, and show that MDTCF can offer increased discrimination performance. Also, MDTCF performance is evaluated on two different face databases.     

A robust correlation receiver for distance estimation

Many methods for distance estimation, such as the ultrasonic pulse-echo method, involve the estimation of a time-of-flight (TOF). In this paper, a signal model is developed that, apart from the TOF, accounts for an unknown, linear frequency dependent distortion as well as for additive noise. We derive a TOF estimator for this model based on the criteria of maximum likelihood. The resulting receiver can be seen as an extension or generalization of the well known cross-correlation, or “matched filter”, estimator described, e.g., by Nilsson. The novel receiver is found to be more robust against unknown pulse shape distortion than the cross-correlation estimator, giving less biased TOF estimates. Also, bias versus noise sensitivity can be controlled by proper model order selection     

Wavelet filter: pure-intensity spatial filters that implement wavelet transforms

Saloma [Opt. Lett. 20, 1943 (1995)] proposed the concept of mirrors with point-spread functions that exhibit wavelet-related characteristics. We propose novel filters with wavelet point-spread functions. The mirrors are suggested to reform not only the phases of optical waves, but also the filters for amplitude. The transmittance functions of the filters, which are real and positive under some conditions, are given. Optical wavelet transforms can easily be made with these filters, and computer simulations for edge and corner extractions are given.     

Characteristics of heat flow in optical fiber devices that use integrated thin-film heaters

We describe the analysis of heat flow in a type of tunable optical fiber grating that uses thin-film resistive heaters microfabricated on the surface of the fiber. The high rate of heat loss from these microstructures and the relatively low thermal diffusivity of the glass yield unusual thermal properties. Approximate one-dimensional analytical calculations capture important aspects of the thermal characteristics of these systems. Comparison with experimental results that we obtained from devices with established designs validates certain features of the computations. This modeling also establishes the suitability of integrated thin-film heaters for several new types of tunable fiber grating devices.     

Strain measurement by optical correlation

The application of optical correlation measurements to evaluating elastic strain and plastic strain in metals is discussed in this paper. A selected area of the metal surface is illuminated by coherent light. The optical correlation intensity is then measured by transmitting light scattered from the surface through a holographic filter, in which information about the topography of the surface at an earlier time is stored. Changes in surface topography arising from rigid-body displacement, elastic strain, or plastic strain, respectively, cause corresponding changes in optical correlation intensity. Correlation changes arising from surface translation or rotation can be compensated for. An analysis of the process of holographic reconstruction from an elastically strained surface gives good agreement with the experimental results. The correlation technique is sensitive to elastic strains of the order of 10^–5 and to monotonic plastic strains of the order of 10^–4; the change in correlation intensity is essentially linear with increasing plastic strain, up to a maximum strain of about 10^–3.     

High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser

A high-accuracy optical distance meter with a mode-locked femtosecond laser is proposed for distance measurements in a 310-m-long optical tunnel. We measured the phase shift of the optical beat component between longitudinal modes of a mode-locked laser. A high resolution of 50 mum at 240-m distance was obtained without cyclic error correction. The group refractive index of air is automatically extracted to an accuracy of 6 parts per million (ppm) by two-color measurement with the pulses of fundamental and second-harmonic wavelengths. Finally, an absolute mechanical distance of 240 m was obtained to within 8-ppm accuracy by use of a series of beat frequencies with the advantage of a wide range of intermode frequency, together with the results of the two-color measurement.     

Polynomial distance classifier correlation filter for pattern recognition

We introduce what is to our knowledge a new nonlinear shift-invariant classifier called the polynomial distance classifier correlation filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter [Appl. Opt. 35, 3127 (1996)] to include nonlinear functions of the input pattern. This new filter provides a framework (for combining different classification filters) that takes advantage of the individual filter strengths. In this new filter design, all filters are optimized jointly. We demonstrate the advantage of the new PDCCF method using simulated and real multi-class synthetic aperture radar images.     

Designs of optoelectronic trinary signed-digit multiplication by use of joint spatial encodings and optical correlation

Trinary signed-digit (TSD) symbolic-substitution-based (SS-based) optical adders, which were recently proposed, are used as the basic modules for designing highly parallel optical multiplications by use of cascaded optical correlators. The proposed multiplications perform carry-free generation of the multiplication partial products of two words in constant time. Also, three different multiplication designs are presented, and new joint spatial encodings for the TSD numbers are introduced. The proposed joint spatial encodings allow one to reduce the SS computation rules involved in optical multiplication. In addition, the proposed joint spatial encodings increase the space-bandwidth product of the spatial light modulators of the optical system. This increase is achieved by reduction of the numbers of pixels in the joint spatial encodings for the input TSD operands as well as reduction of the number of pixels used in the proposed matched spatial filters for the optical multipliers.     

Comparative study of face recognition techniques that use joint transform correlation and principal component analysis

Face recognition based on principal component analysis (PCA) that uses eigenfaces is popular in face recognition markets. We present a comparison between various optoelectronic face recognition techniques and a PCA-based technique for face recognition. Computer simulations are used to study the effectiveness of the PCA-based technique, especially for facial images with a high level of distortion. Results are then compared with various distortion-invariant optoelectronic face recognition algorithms such as synthetic discriminant functions (SDF), projection-slice SDF, optical-correlator-based neural networks, and pose-estimation-based correlation.     

Absolute distance measurement with an optical feedback interferometer

An important use of the self-mixing effect inside a frequency-modulated single-mode laser diode is in laser velocimetry and range-finding applications. The optical beam reflected by a target and injected into the laser diode cavity modulated by a reshaped current is mixed with the light inside the cavity, causing variations of the optical output power. A theoretical analysis of this effect is proposed, based on the determination of the beat frequencies of the optical power variations, to improve the accuracy of laser distance measurement. A resolution of ?1.5 mm from 50 cm to 2 m is obtained when thermal effects are taken into account.     

Novel optical distance sensor based on MSM technology

This paper describes a novel distance-sensor concept based on photodiodes in metal-semiconductor-metal technology (MSM). MSM photodiodes can be operated as electrooptical mixers functioning similar to the so-called photonic mixing device (PMD). This paper employs the correlation techniques previously used with the PMD to the MSM. First, experimental results obtained with the MSM inserted into the authors' standard laboratory setup are provided. Additionally, different configurations well suited for mixer operation of the MSM are pointed out. Throughout this paper, similarities between the PMD and MSM are pointed out, as well as key differences.     

Scale-tunable optical correlation with natural light

We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one's shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.     

Rotation-invariant and controllable space-variant optical correlation

We propose a method for designing a correlator for achieving rotation-invariant and controllable space-variant optical correlation. The design concept is based on a combination of fractional correlation and circular-harmonic decomposition of the reference object. The suggested method is described and analyzed in detail. Numerical simulations show that this new correlator might provide potential applications in practice.