Real And Positive Filter Based On Circular Harmonic Expansion

A real and positive filter for pattern recognition is presented. The filter, based on the circular harmonic (CH) expansion of a real function, is partially rotation invariant. As it is real and positive, the filter can be recorded on a transparency as an amplitude filter. Computer simulations of character recognition show a partial rotation invariance of about 40°. Optical experiments agree with these results and with acceptable discrimination between different characters. Nevertheless, due to experimental difficulties, the method is onerous for use in general pattern recognition problems.

Application Of Anamorphic Systems To Directional Pseudocolor Encoding

An optical nonsymmetrical imaging system composed of two anamorphic spectrum analyzers in cascade is implemented. This system can provide an undistorted final image in spite of the geometrical distortion effects in the intermediate Fourier plane. The introduction of chromatic sector filters in this plane provides a real-time technique to pseudocolor encode the spatial frequency information of a black-and-white transparency. In this way, greater discrimination is achieved in the angular orientation of object details that generate the same spatial frequencies. Experimental pseudocolored images, obtained with a symmetrical system and a nonsymmetrical system, of a black-and-white transparency a…

Phase Fourier vector model for scale invariant three-dimensional image detection.

A scale invariant 3D object detection method based on phase Fourier transform (PhFT) is addressed. Three-dimensionality is expressed in terms of range images. The PhFT of a range image gives information about the orientations of the surfaces in the 3D object. When the object is scaled, the PhFT becomes a distribution multiplied by a constant factor which is related to the scale factor. Then 3D scale invariant detection can be solved as illumination invariant detection process. Several correlation operations based on vector space representation are applied. Results show the tolerance of detection method to scale besides discrimination against false objects.

Anamorphic fractional Fourier transform: optical implementation and applications

An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. A laboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains are briefly suggested.

Contribución a un futuro sostenible. Una dimensión necesaria y posible en toda acción e investigación educativa

El estudio de los errores conceptuales, preconcepciones, concepciones alternativas, etc., ha constituido posiblemente la línea de investigación más desarrollada en didáctica de las ciencias. Miles de artículos publicados lo atestiguan (Duit, 2004). Sin embargo, la inmensa mayoría de estos trabajos se centra en conceptos concretos de los distintos campos de la ciencia y, en cambio, apenas si se ha prestado atención a otras concepciones, tanto del alumnado como del profesorado, con notable influencia en el proceso de enseñanza/ aprendizaje, como las referidas a la naturaleza de la ciencia y, más particularmente, a las relaciones CTSA. Para ver en qué medida este reduccionismo persiste hoy en …

Space–bandwidth product of optical signals and systems

The space–bandwidth product (SW) is fundamental for judging the performance of an optical system. Often the SW of a system is defined only as a pure number that counts the degrees of freedom of the system. We claim that a quasi-geometrical representation of the SW in the Wigner domain is more useful. We also represent the input signal as a SW in the Wigner domain. For perfect signal processing it is necessary that the system SW fully embrace the signal SW.

Recognition of unsegmented targets invariant under transformations of intensity.

Images taken in noncooperative environments do not always have targets under the same illumination conditions. There is a need for methods to detect targets independently of the illumination. We propose a technique that yields correlation peaks that are invariant under a linear intensity transformation of object intensity. The new locally adaptive contrast-invariant filter accomplishes this by combining three correlations in a nonlinear way. This method is not only intensity invariant but also has good discrimination and resistance to noise. We present simulation results for various intensity transformations with and without random and correlated noise. When the noise is high enough to thre…

Three-Dimensional Mapping and Ranging of Objects Using Speckle Pattern Analysis

In this chapter, we present two novel approaches for 3-D object shape measurement and range estimation based on digital image processing of speckle patterns. In the first one, 3-D mapping and range measurement are retrieved by projecting, through a ground glass diffuser, random speckle patterns on the object or on the camera for a transmissive and reflective configuration, respectively. Thus, the camera sensor records in time sequence different speckle patterns at different distances, and by using correlation operation between them, it is possible to achieve 3-D mapping and range finding. In the second one, the 3-D mapping and ranging are performed by sensing the visibility associated with …

Spatial information transmission using orthogonal mutual coherence coding.

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable c…

Spatially multiplexed interferometric microscopy with partially coherent illumination

We have recently reported on a simple, low cost, and highly stable way to convert a standard microscope into a holographic one [Opt. Express 22, 14929 (2014)]. The method, named spatially multiplexed interferometric microscopy (SMIM), proposes an off-axis holographic architecture implemented onto a regular (nonholographic) microscope with minimum modifications: the use of coherent illumination and a properly placed and selected one-dimensional diffraction grating. In this contribution, we report on the implementation of partially (temporally reduced) coherent illumination in SMIM as a way to improve quantitative phase imaging. The use of low coherence sources forces the application of phase…

Rank-order and morphological enhancement of image details with an optoelectronic processor.

In all-optical processors, enhancement of image details is the result of high-pass filtering. We describe an optoelectronic processor in which detail enhancement results from the digitally calculated difference between an original input image and its low-pass filtered version. The low-pass filtering is realized through the rank-order median and the morphological opening and closing operations calculated by use of the optical convolver. It is shown that the normalized difference between the morphological white and black top hats enhances bright and dark image details analogously to the rank-order unsharp masking.

Superesolution in digital holographic microscopy

In this contribution, we address with the possibility to overcome the limited resolving power of imaging systems beyond the limit imposed by Abbe's diffraction theory. We first review the mathematical foundations underlying superresolution (SR) from an information theory point of view and then we focus on two multiplexing approaches in digital holographic microscopy (DHM) for achieving SR by synthetic aperture (SA) generation.

Ray matrix analysis of anamorphic fractional Fourier systems

In this work we extend the application of the ray matrix approach to analyse anamorphic fractional Fourier systems, i.e., fractional Fourier optical systems where the fractional power is different for two orthogonal directions. The application of the ray matrix approach allows for easily obtaining the properties of the optical system, and it is therefore a powerful tool to design and simplify complicated systems. For simplicity we consider fractional Fourier systems with real orders and systems without apertures. We start by presenting the analysis of some previously reported anamorphic Fourier and fractional Fourier systems, and we end by proposing a simple optical system with tunable anam…

Superresolved imaging based on wavelength multiplexing of projected unknown speckle patterns

We propose a method for resolution enhancement of a diffraction limited optical system based on the capture of a set of low resolution images. These images are obtained after projection of an ensemble of unknown speckle patterns on top of the high resolution object that is to be imaged. Each speckle pattern is generated by the same thin (and unknown) diffuser, but illuminated with a slightly different wavelength. From the ensemble of low resolution images, we obtain a system of equations that can be solved in an iterative manner that enables reconstruction of the high resolution object. As a result, we also achieve the projected high resolution speckle patterns used for the encoding.

Spherical nonlinear correlations for global invariant three-dimensional object recognition

We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D fil…

Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter

A shift-and-scale-invariant elliptic coordinate-transformed phase-only filter in proposed. The filter is built in three steps: the complex conjugate of a basic-size target spectrum is calculated, its phase-only part is taken, and then the elliptic coordinate transformation is made. In the extreme case the scale ratio of recognizable objects equals 1:1.5, permitting good recognition of object sizes S within the range 0.83/= S/= 1.25. Discrimination abilities and relative Horner efficiencies of a few versions of the filter are calculated.

Recognition Of Polychromatic Test By Multi-Channel Correlation Filtering

A wavelength-multichannel correlation technique based on matched filtering is proposed to identify a colour object with a non uniform colour distribution. The filters are matched to the object which is illuminated with different wavelengths. This correlation gives the information of colour distribution in addition to other information usually obtained from image recognition. The theoretical study of this technique, numerical simulations and discussion are presented.

Experimental multichannel recognition capability of polychromatic objects using optical correlators

Polychromatic object recognition by multichannel correlation is experimentally achieved. Model objects whose shape changes with the wavelength of the illumination beam were used. Highpass matched filters were employed. The results confirm previous numerical simulations 1.

A Statistical Matrix Representation Using Sliced Orthogonal Nonlinear Correlations for Pattern Recognition

In pattern recognition, the choice of features to be detected is a critical factor to determine the success or failure of a method; much research has gone into finding the best features for particular tasks [1]. When images are detected by digital cameras, they are usually acquired as rectangular arrays of pixels, so the initial features are pixel values. Some methods use those pixel values directly for processing, for instance in normal matched filtering [2], whereas other methods execute some degree of pre-processing, such as binarizing the pixel values [3].

Two-dimensional optical wavelet decomposition with white-light illumination by wavelength multiplexing

We present a novel method for achieving in real time a two-dimensional optical wavelet decomposition with white-light illumination. The underlying idea of the suggested method is wavelength multiplexing. The information in the different wavelet components of an input object is transmitted simultaneously in different wavelengths and summed incoherently at the output plane. Experimental results show the utility of the new proposed method.

Recognition of polychromatic three-dimensional objects

We propose to use optical multichannel correlation in various chromatic systems to obtain a setup for recognition of polychromatic three-dimensional (3-D) objects based on Fourier-transform profilometry. Because red-green-blue color components are not able to split the luminance information of objects in a defined component, when the 3-D objects are brighter than the reference objects the correlation result gives false alarms. We demonstrate that it is possible to use different color spaces that can split luminance from chromatic information to yield adequate recognition of polychromatic 3-D objects. We show experimental results that prove the utility of the proposed method.

Fraunhofer diffraction patterns from apertures illuminated with nonparallel light in nonsymmetrical Fourier transformers.

In a recent paper, a 2-D axially nonsymmetrical Fourier transforming with an anamorphic system was presented. This work extends its performances with the use of spherical illumination. The results provide the conditions to obtain an exact Fourier transform and a greater angular magnification coefficient than with parallel illumination. Experimental results of the latter are shown.

Shift- and scale-invariant recognition of contour objects with logarithmic radial harmonic filters.

The phase-only logarithmic radial harmonic (LRH) filter has been shown to be suitable for scale-invariant block object recognition. However, an important set of objects is the collection of contour functions that results from a digital edge extraction of the original block objects. These contour functions have a constant width that is independent of the scale of the original object. Therefore, since the energy of the contour objects decreases more slowly with the scale factor than does the energy of the block objects, the phase-only LRH filter has difficulties in the recognition tasks when these contour objects are used. We propose a modified LRH filter that permits the realization of a shi…

Lensless object scanning holography for two-dimensional mirror-like and diffuse reflective objects

Recently proposed lensless object scanning holography (LOSH) [Opt. Express 20, 9382 (2012)] is a fully lensless method capable of improving the image quality in digital Fourier holography applied to one-dimensional (1D) reflective objects and it involves a very simplified experimental setup. LOSH is based on the recording and digital postprocessing of a set of digital lensless Fourier transform holograms, which finally results in a synthetic image with improved resolution, field-of-view (FOV), signal-to-noise ratio (SNR), and depth of field. In this paper, LOSH is extended to the cases of two-dimensional (2D) mirror-like and 1D diffuse-based objects. For 2D mirror-like objects, the experime…

Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes

We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.

Superresolution digital holographic microscopy for three-dimensional samples.

An approach that allows superresolution imaging of three-dimensional (3-D) samples by numerical refocusing is presented in the field of digital holographic microscopy. Based on the object's spectrum shift produced by tilted illumination, we present a time multiplexing superresolved approach to overcome the Abbe's diffraction limit. The proposed approach uses a microscope in a Mach-Zehnder interferometric architecture with the particularity that the output plane does not coincide with the image plane. Thus, a set of off-axis non-image plane holograms are sequentially recorded for every tilted beam used in the illumination stage. After that and by using simple digital post-processing and nume…

Method for determining the proper expansion center and order for Mellin radial harmonic filters

Abstract A method to improve the behaviour of the Mellin radial harmonic (MRH) filters in scale invariant pattern recognition is presented. An algorithm has been introduced to obtain the proper expansion center and order of the MRH development of any object. The procedure consists of the suspression of the non-discriminant uniform background in the energy function of the target. Computer simulations are presented.

Three-dimensional mapping and range measurement by means of projected speckle patterns.

We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.

Single-channel polychromatic pattern recognition by the use of a joint-transform correlator.

We present a single-channel system for color image recognition that is based on a joint-transform correlator setup. The color images are encoded as phase and amplitude functions, inspired from the Munsell color representation. A real-time implementation of the new codification method can be achieved by the use of a spatial light modulator operating in phase-only modulation mode. We determine the optimal codification for a linear color-phase code. Its performance is compared with a conventional multichannel correlator by means of computer simulations. Experimental results are also presented.

Two-dimensional temporal coherence coding for super resolved imaging

In this paper, we present an approach that can be used for transmission of 2D spatial information through space-limited systems capable of transmitting even only a single spatial pixel. The input 2D object is illuminated with temporally incoherent illumination. The axial coherence length is very short and it equals only a few microns. Attached to the input object spatial random phase mask generates different axial shift for every pixel of the input. The temporal delays of the encoding (axial shifts) of every pixel are longer than the coherence length of the illuminating source. Therefore no temporal correlation exists between the various pixels of the input. A lens combines all spatial pixe…

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.

Fractional Fourier Transforms and Geometrical Optics

Multiple Matched Spatial Filter Performed With Nonsymmetrical Fourier Transformers

MULTIPLE MATCHED SPATIAL FILTER PERFORMED WITH NONSYMMETRICAL FOURIER TRANSFORMERSCARLOS FERREIRA and CARMEN VAZQUEZDepartamento de Optica. Universitat de Valencia.C/ Dr. Moliner, 50. 46100 Burjassot, Spain.1. INTRODUCTIONClassical matched spatial filters (CMSF) have been successfully employed for optical pattern recog-nition. To detect different signals, multiple matched spatial filters can be synthesized and several me-thods to perform the filters have been developed. Based on the sensitivity to input orientation of CMSF,we proposed a filter [1] where the signals to be detected were rotated by different angles when recordingthe hologram. Thus, the recognition of a signal is only achieved …

Spatially-multiplexed interferometric microscopy (SMIM): converting a standard microscope into a holographic one

We report on an extremely simple, low cost and highly stable way to convert a standard microscope into a holographic one. The proposed architecture is based on a common-path interferometric layout where the input plane is spatially-multiplexed to allow reference beam transmission in a common light-path with the imaging branch. As consequence, the field of view provided by the layout is reduced. The use of coherent illumination (instead of the broadband one included in the microscope) and a properly placed one-dimensional diffraction grating (needed for the holographic recording) complete the experimental layout. The proposed update is experimentally validated in a regular Olympus BX-60 upri…

Color encoding for polychromatic single-channel optical pattern recognition

The common multichannel system for recognizing colored images is replaced by a color-encoded single-channel system. Amethod inspired by the Munsell color system is used for encoding the different colors as phase and amplitude functions. It is shown that for many practical cases the phase information part of the color code is sufficient for obtaining good results. An implementation based on a liquid-crystal television panel that works in a phase-modulation mode is suggested. Computer simulations that demonstrate the capabilities of the suggested method are given as well as a comparison with previously published multichannel performance.

Wavelength-multiplexing system for single-mode image transmission

The expanding use of optical communication by means of optical fibers and the situation of drastically increasing amounts of data to be transmitted urge the exploration of novel systems permitting the transmission of large amounts of spatial information by fiber with smaller spatial resolution. An optical encoding and decoding system is suggested for transmitting one- or two-dimensional images by means of a single-mode fiber. The superresolving system is based on wavelength multiplexing of the input spatial information, which is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the one- and two-dimensional c…

Teaching stable two-mirror resonators through the fractional Fourier transform

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…

Multi-channel chromatic transformations for nonlinear color pattern recognition

We present a new approach for color pattern recognition based on multi-channel nonlinear correlations. High discrimination capability is obtained in comparison with common linear multi-channel detection methods. We apply the nonlinear morphological correlation to different color channel decompositions as RGB and ATD channels. Moreover, in order to improve the discrimination we have introduced a new color transformation. When a high selectivity is required, the combination of the nonlinear correlation and the new color decomposition yields to detect the object using just a single channel. Simulation results are provided.

Fractional wavelet transform

The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform. Optical implementation of this transform is briefly discussed.

Teaching Fourier optics through ray matrices

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…

Improved rotation invariant pattern recognition using circular harmonics of binary gray level slices

We introduce a new rotation invariant pattern recognition method based on nonlinear correlation. The images are decomposed into disjoint binary slices and then correlated using the common linear correlation. This operation is very discriminant even when the target is embedded in strong noise. We extend our sliced orthogonal nonlinear generalized correlation method to rotation invariant pattern recognition by combining the information of a circular harmonic (CH) of each binary slice of the reference object with binary slices of the target. In addition to improved discrimination capability, the method avoids the time-consuming process of finding proper centers for the CHs. Results are present…

Real filter based on Mellin radial harmonics for scale-invariant pattern recognition.

Several theoretical and experimental studies are developed in order to simplify the construction of filters based on Mellin radial harmonics (MRH) for scale-invariant pattern recognition. A real filter based on MRH is designed. The impulse response of the filter is a hermitic function, obtained by a suitable modification of a MRH component. This real filter has the same scale invariance as the conventional complex MRH filters, with the main advantage of its simplicity. Both computer simulations and optical experiments are presented.

Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter.

A phase-only filter based on logarithmic harmonics for projection-invariant pattern recognition is presented. This logarithmic-harmonic-derived filter is directly calculated in the Fourier plane. With respect to normal logarithmic-harmonic filters it provides a smaller variation of the correlation intensity with the projection factor of the target. Computer and optical experiments are presented.

Resolution improvement by single-exposure superresolved interferometric microscopy with a monochrome sensor

Single-exposure superresolved interferometric microscopy (SESRIM) by RGB multiplexing has recently been proposed as a way to achieve one-dimensional superresolved imaging in digital holographic microscopy by a single-color CCD snapshot [Opt. Lett. 36, 885 (2011)]. Here we provide the mathematical basis for the operating principle of SESRIM, while we also present a different experimental configuration where the color CCD camera is replaced by a monochrome (B&W) CCD camera. To maintain the single-exposure working principle, the object field of view (FOV) is restricted and the holographic recording is based on image-plane wavelength-dispersion spatial multiplexing to separately record the thre…

Shift and scale-invariant correlator using a radially stretched phase-only filter

A radial stretching of the phase only filter depending on the energy angular distribution of the target spectrum is used to perform shift and scale invariant pattern recognition. The complex conjugate of a basic size target Fourier transform and the cumulative energy angular distribution are calculated. Then the radially stretched filter providing the same energy contribution to the correlation peak independent on the target size is prepared and used in a conventional correlator, with spherical-wave illumination. The maximum scale ratio of recognizable objects equals 1:1.5. Computer simulations and experimental results, showing the performance of the filter are presented.

Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display.

Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has b…

Different strategies in optical recognition of polychromatic images.

We treat two different problems in the recognition of polychromatic images: (1) recognition of an object with a given shape and color combination; (2) recognition of an object regardless of its color combination. To solve each problem we propose different strategies. The number of filters and the objects to which the filters are matched vary with the strategy. Phase-only filters have been used to achieve recognition of both problems. Computer results are given for different targets and scenes to show the behavior of the proposed strategies.

Weighted nonlinear correlation for controlled discrimination capability

We recently demonstrated the high discrimination capability as well as the high sensitivity to small intensity variations of the sliced orthogonal nonlinear generalized (SONG) correlation. This nonlinear correlation has a correlation matrix representation. Previous papers considered only the principal diagonal elements of the correlation matrix. We propose using the off-diagonal non-zero elements of the SONG correlation matrix in order to achieve variable discrimination performance and controlled detection adapted to the gray-scale variations. Moreover, we introduce negative coefficients in order to improve the discrimination properties of the SONG correlation. To control the degree of reco…

Invariant pattern recognition based on 1-D Wavelet functions and the polynomial decomposition

Abstract A new filter, consisting of 1-D Wavelet functions is suggested for achieving optical invariant pattern recognition. The formed filter is actually a real function, hence, it is theoretically possible to be implemented under both spatially coherent and spatially incoherent illuminations. The filter is based on the polynomial expansion, and is constructed out of a scaled bank of filters multiplied by 1-D Wavelet weight functions. The obtained output is shown to be invariant to 2-D scaling even when different scaling factors are applied on the different axes. The computer simulations and the experimental results demonstrate the potential hidden in this technique.

Pattern recognition using sequential matched filtering of wavelet coefficients

Abstract A bank of wavelets is used for pattern recognition by means of sequential filtering. Each element of the bank is matched to a different wavelet coefficient of the target. A sequential process leads to a set of correlation outputs. Post-processing by means of a fast blending method provides the final output correlation. Both computer simulations and optical experiments are presented, showing the discrimination capability for this implementation.

Nonlinear morphological correlation: optoelectronic implementation

An optoelectronic implementation of the nonlinear morphological correlation by use of a threshold-decomposition technique and a joint transform correlator architecture is presented. This nonlinear morphological correlation provides improved image detection compared with standard linear optical pattern-recognition correlation methods. It also offers a more robust detection of low-intensity images in the presence of high-intensity patterns to be rejected.

New key based on tilted lenses for optical encryption

A novel concept based on tilted spherical lenses for optical encryption using Lohmann’s type I systems is presented. The tilt angle of the spherical lenses is used as an encrypted key and the decryption performance is studied both qualitatively (visual image degradation) and quantitatively (mean squared error analysis) by numerical simulations. The paper presents a general mathematical framework in virtue of the dioptric power matrix formalism and oblique central refraction used in the optometry field. Computer simulations show that image information cannot be retrieved after a few degrees of tilt on both spherical lenses in the encryption system. In addition, a preliminary experiment is pr…

Superresolved imaging of remote moving targets.

We present a superresolving approach that allows one to exceed the diffraction limit and recover highly resolved contours of moving targets from a sequence of low-resolution images. The presented approach is suitable for remote sensing applications. The resolution decoding algorithm that is used to recover the high-resolution features of the target can be run partially via optical means and that way can be used to reduce the required computational complexity.

Fast algorithms for free-space diffraction patterns calculation

Here we present a fast algorithm for Fresnel integral calculation. Some fast algorithms using the fast Fourier transform are analysed and their performance has been checked. These methods are of easy implementation, but are only valid for a specific range of distances. Fast algorithms based on the Fractional Fourier transform allow accurate evaluation of the Fresnel integral from object to Fraunhofer domain in a single step.

Optoelectronic morphological image processor.

A morphological optoelectronic image processor based on the threshold decomposition concept is described and demonstrated. Binary slices of a gray-scale input image are optically convolved with a binary structuring element of arbitrary size and shape in a noncoherent convolver. The slices are displayed on a liquid-crystal spatial light modulator of 320 × 264 pixels. The kernels are implemented as modifications of the system impulse response. The processor’s convolution patterns are recorded with a CCD camera and fed into a PC by a frame grabber. Subsequent elementary morphological operations are looped. Examples of processing an input image of 256 × 256 pixels and 16 gray levels with kernel…

Joint transform correlator with spatial code division multiplexing.

A joint transform correlator may suffer from overlapping of the zero diffraction order of the output, which does not contain relevant information, and the correlation peaks that appear in the first diffraction orders if objects are not sufficiently separated. Such overlapping significantly reduces the signal-to-noise ratio of the identification process. We propose a novel approach based on code division multiplexing technique in which the contrast of the identification peaks is significantly enhanced. The approach does not include placing the two objects side by side but rather includes code multiplexing them. Moreover, the code division multiplexing technique allows the space-bandwidth pro…

Optical nonlinear correlation based on nonuniform subband decomposition

We present a nonlinear correlation to improve the selectivity for optical pattern recognition. The approach is based on morphological correlation which involves a threshold decomposition concept. Hereby, we propose a subband decomposition in the Fourier domain to perform the threshold decomposition operation. We consider two frequency bands that give rise to two separate channels. We apply the morphological correlation to each channel using a localized threshold decomposition. Then, we define a two-channel morphological correlation. The final detection decision is made as a combination of both correlation outputs. The two-channel morphological correlation yields improved discrimination capa…

Surpassing digital holography limits by lensless object scanning holography.

We present lensless object scanning holography (LOSH) as a fully lensless method, capable of improving image quality in reflective digital Fourier holography, by means of an extremely simplified experimental setup. LOSH is based on the recording and digital post-processing of a set of digital lensless holograms and results in a synthetic image with improved resolution, field of view (FOV), signal-to-noise ratio (SNR), and depth of field (DOF). The superresolution (SR) effect arises from the generation of a synthetic aperture (SA) based on the linear movement of the inspected object. The same scanning principle enlarges the object FOV. SNR enhancement is achieved by speckle suppression and c…

Extended scale-invariant pattern recognition with white-light illumination.

A previous method of obtaining scale-invariance detection with white-light illumination has been improved on. We were able to detect different scaled versions of the target up to a magnification factor equal to 2. We simultaneously detected several versions in the same scene, because each scale factor is codified in a different wavelength. Experimental results demonstrate the proposed technique and show the utility of the method.

A new criterion for determining the expansion center for circular-harmonic filters

A new criterion for locating the expansion center of circular harmonic filters is presented. The innovation consists in the use of the information provided by both the circular harmonic energy map and the peak to correlation energy map of the object to be detected. The choice of an expansion center with a high value of peak to correlation energy ensures a good discrimination capability of the filter. In addition, we choose a point which is a local maximum for the energy map. An improvement of the discrimination ability is obtained with respect to previous methods.

Nonsymmetric Fourier transforming with an anamorphic system

The idea of obtaining a nonsymmetric Fourier transform with crossed cylindrical lenses of different focal lengths is presented. The anamorphic rotation-variant system produces a scaled Fourier transform F(u,mv) of an object f(x,y), where m is a scaling constant. The system performs controlled angular magnification of an object spectrum. It is shown that the super resolution in one direction is gained by reducing the number of degrees of freedom of the optical message in the other. Experimental results are shown where the scaling constant m of up to 10 has been obtained.

Single-exposure super-resolved interferometric microscopy by RGB multiplexing in lensless configuration

Abstract Single-Exposure Super-Resolved Interferometric Microscopy (SESRIM) reports on a way to achieve one-dimensional (1-D) superresolved imaging in digital holographic microscopy (DHM) by a single illumination shot and digital recording. SESRIM provides color-coded angular multiplexing of the accessible sample׳s range of spatial frequencies and it allows their recording in a single CCD (color or monochrome) snapshot by adding 3 RGB coherent reference beams at the output plane. In this manuscript, we extend the applicability of SESRIM to the field of digital in-line holographic microscopy (DIHM), that is, working without lenses. As consequence of the in-line configuration, an additional r…

Graphical representation of non-absorbing polarization devices

A graphical representation of general non-absorbing polarization devices operating under normal plane-wave incidence is presented. The representation is based on a four-dimensional spherical parametrization of the Jones matrix of this kind of polarization devices. The graphical representation takes the form of a solid cylinder. The projection of the point representing the device over the base of the cylinder gives the corresponding polarization eigenvectors represented in the complex plane, while the height of the point in the cylinder is the phase of its eigenvalue. Some simple examples like wave-plates and rotators are discussed. The representation may represent a useful tool to identify …

Maximum likelihood for target location in the presence of substitutive noise .

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly…

Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering

Abstract Recently, in the field of fractional Fourier transforms (FRT) an operation coined “fractional correlation” has been proposed and investigated experimentally. In this paper we propose a new setup for obtaining the fractional correlation, which presents several advantages from the experimental point of view. The fractional filter plane can be adjusted accurately with the help of converging beam illumination and using an adjusting device consisting of a combination of Fresnel zone plates. Moreover the scaling factor between the input pattern and the filter can be adjusted at will. This degree of freedom is of special interest when using SLMs. In addition we present a configuration, ba…

Twist angle determination in liquid crystal displays by location of local adiabatic points

In this work we present a method for the determination of the twist angle of an arbitrary twisted nematic liquid crystal spatial light modulator. The method is based on the location of local adiabatic points, i.e., situations in which the liquid crystal SLM acts only as a rotation device. For these cases, the rotation induced on the polarization of the incident beam is equal to the twist angle. Consequently, the twist angle can be determined with high precision. We show that local adiabatic regime may be achieved in two ways, either by changing the incident beam wavelength, or by applying a voltage to the electrodes of the display. However, the simple model that describes the SLM in the off…

Optical implementation of the weighted sliced orthogonal nonlinear generalized correlation for nonuniform illumination conditions.

Optical pattern recognition under variations of illumination is an important issue. The sliced orthogonal nonlinear generalized (SONG) correlation has been proposed as an optical pattern recognition tool to discriminate with high efficiency between objects. But, at the same time, the SONG correlation is very sensitive to gray-scale image variations. In a previous work, we expanded the definition of the SONG correlation to the Weighted SONG (WSONG) correlation to modify the discrimination capability in a controlled way. Here, we propose to use the WSONG when pattern recognition is obtained by means of optical correlation under nonuniform illumination. The calculation of the WSONG correlation…

Projection of speckle patterns for 3D sensing

In this communication we present the use of projected speckle patterns coming from a phase random mask for sensing depths and thicknesses. The sensing is based on the change of the speckle pattern with propagation and the lack of correlation between speckle patterns recorded at different depths or lateral locations. The principle is used for mapping thickness of transparent media, for depth ranging and for 3D mapping of diffuse objects.

Rotation-invariant optical recognition of three-dimensional objects.

An automatic method for rotation-invariant three-dimensional (3-D) object recognition is proposed. The method is based on the use of 3-D information contained in the deformed fringe pattern obtained when a grating is projected onto an object’s surface. The proposed method was optically implemented by means of a two-cycle joint transform correlator. The rotation invariance is achieved by means of encoding with the fringe pattern a single component of the circular-harmonic expansion derived from the target. Thus the method is invariant for rotations around the line of sight. The whole experimental setup can be constructed with simple equipment. Experimental results show the utility of the pro…

Dietary inflammatory index and all-cause mortality in large cohorts: The SUN and PREDIMED studies

[Background]: Inflammation is known to be related to the leading causes of death including cardiovascular disease, several types of cancer, obesity, type 2 diabetes, depression-suicide and other chronic diseases. In the context of whole dietary patterns, the Dietary Inflammatory Index (DII®) was developed to appraise the inflammatory potential of the diet. [Objective]: We prospectively assessed the association between DII scores and all-cause mortality in two large Spanish cohorts and valuated the consistency of findings across these two cohorts and results published based on other cohorts.

Lensless Object Scanning Holography

Lensless object scanning holography (LOSH), a method for improving image quality in digital holography by combination of a set of digital holograms for different object positions is presented.

Overcoming the oblivion of technology in physics education

Technology is generally viewed as ‘applied science’, that is to say, as something that comes ‘after’ science. This conception justifies the lack of attention paid to technology in science education, especially where physics education is concerned. In this chapter we question this simplistic view of the science-technology relationship, historically rooted in the unequal appreciation of intellectual and manual work, and we try to show how the absence of the technological dimension in science education contributes to a naïve and distorted view of science which deeply affects the necessary scientific and technological literacy of all citizens, as well as the preparation of the future scientists…

Target localization in the three-dimensional space by wavelength multiplexing.

A method to localize a target in the three-dimensional space is presented. Each different position of the target on the depth axis produces, when captured with a CCD camera, an image of a different size on its sensor plane. The size of this image depends only on the distance between the target and the camera. The use of a white light optical correlator that gives us a different response depending on the scale of the input image permits us to know the depth position of the particular target. The obtained results demonstrate the utility of the newly proposed method.

Spatial information transmission using axial temporal coherence coding

We present an approach that can be used for transmission of information through space-limited systems or for superresolution. The spatial information is coded with different axial temporal coherence by interfering every spatial region in the input with the same region, but with a certain known delay in the longitudinal axis. Every spatial region has different delay. After mixing all of the spatial information, it is transmitted through the space-limited system. At the detection the information is passed through a similar interference setup containing certain axial delay. By temporally scanning along the longitudinal axis, each time a different spatial region that was coded with the correspo…