The measurement of the topological charge of laser beams with orbital angular momentum (OAM) is key to many
applications like deciphering information encoded in several channels. Current techniques useful for that purpose are
interferometry, diffraction through different poligonal apertures like triangular or pentagonal and, azimuthal and radial
decomposition. A less explored issue is the diffraction of OAM beams through circular sectors. Jack et al. studied the
angular diffraction of Gaussian beams (whose OAM is null) through a circular sector.
By means of a Fourier transform of the truncated Gaussian beam they showed that the orbital angular momentum
spectrum of the transmitted beam has a sinc-shaped envelope centered at zero orbital angular momentum, the width of
which increases as the central angle of the circular sector decreases.
We analyze here the spectrum of a laser beam with integer OAM that has been diffracted by a circular sector. We
present results for circular sectors of different central angles. For circular π-sector, we also study the influence of the
transmittance in the OAM spectra of the transmitted beam, using straight borders of nanometric thin films of titanium
oxide with different thicknesses.
We use a spatial light modulator with a fork hologram placed on to generate the incoming OAM beam and measure the
evolution of the intensity profile of the diffracted beam as it propagates away from the circular sector. The spectra of the
diffracted OAM beams are shown numerically and experimentally to have a sinc shaped envelope centered at the OAM
value of the incoming OAM wave.
Different theories including Kolmogorov have been valid to explain and model physic phenomenal like vertical atmospheric turbulence. In horizontal path, we still have many questions, due to weather problems and consequences that it generates. To emulate some conditions of environment, we built an Optical Turbulence Generator (OTG) having spatial, humidity and temperature, measurements that were captured in the same time from optical synchronization. This development was made using digital modules as ADC (Analog to Digital Converters) and communications protocol as SPI. We all made from microcontrollers. On the other hand, to measure optical signal, we used a photomultiplier tube (PMT) where captured the intensity of fringes that shifted with a known frequency.
Outcomes show temporal shift and phase drive from dependent samples (in time domain) that correspond with frozen turbulence given by Taylor theory. Parameters studied were C2n, scintillation and inner scale in temporal patterns and analysis of their relationship with the physical associated variables. These patterns were taken from Young Interferometer in laboratory room scale. In the future, we hope with these studies, we will can implement an experiment to characterize atmospheric turbulence in a long distance, placed in the equatorial weather zone.
The Kolmogorov’s theory has been used to explain physical phenomena like the vertical turbulence in atmosphere, others recent works have made new advances and have improved K41 theory. In addition, this theory has been applied to studying different issues associated to measure atmospheric effects, and have special interest to find answers in optics to questions as e.g. at ground level, Could it find edges of two or more close objects, from a distant observer? (Classic resolution problem). Although this subject is still open, we did a model using the statistics of the centroid and the diameter of the laser beam propagated under horizontal turbulence at ground level until the object plane. The goal is to measure efficiently the turbulence effects in the long horizontal path propagation of electromagnetic wave. Natural movement of laser beam within the cavity needs be subtracted from the total transversal displacement in order to obtain a best approach. This simple proposed method is used to find the actual statistics of the centroid and beam diameter on the object plane where the turbulence introduces an additional transversal shift. And it has been tested for different values of horizontal distances under non-controlled environment in a synchronized acquisition scheme. Finally, we show test results in open very strong turbulence with high controlled temperature. This paper presents the implemented tests mainly into laboratory and discuss issues to resolve.
In this work we implemented a hybrid joint Fourier transform correlator (JTC optical/electronic) helpful in the pattern recognition when the scene is in movement. We have been use the standard architecture JTC, but in our case, the first step of the correlation process is carried out optically, using coherent illumination to obtain the joint power spectrum (JPS) of each frame display on a spatial light modulator, we used a liquid crystal display CRL XGA4 with 1024 x 768 pixels of resolution in gray scale. It display a video sequence where is include a mobile scene and the reference, then, the JPS of each frame will be obtain in real time with the quadratic sensor (camera CCD) that is located in the back focal plane of the lens. For the second step was use the tools of the Imaging Developer Kit TMS3206711 DSP (IDK) of Texas Instruments, in order to take advantage of the high speed arithmetic offers by the Digital Signal Proccessor (DSP) and the electronics versatility offers to take decisions. The IDK is a tool of hardware and software that allows capture, process and display images in real time. The DSP microprocessor makes a Fourier transform of the image captured by the CCD, in this way, we obtain the correlation of the scene in movement in quasi real time. Using an efficient computation of the digital Fourier transform of a 2N-point real sequence, the hybrid correlator achieve 15 correlations per second, if the final result is display on the monitor the rate fall to 13 frames per second, the correlation peak was use to determine in real time the target position in the mobile scene.
An iterative algorithm for computing holograms is presented: it is based on the fractional order Fourier transform. It allows us to generate diffraction patterns which are not in the Fourier plane. It also makes possible the design of computer generated holograms providing two beforehand given illumination patterns on two preselected planes. Holograms have been calculated according to the proposed method and have been engraved by photolithography. Experimental results are given. A speckle reduction technique is also explained.
Proc. SPIE. 5622, 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications
KEYWORDS: Signal to noise ratio, Energy efficiency, Sensors, Fourier transforms, Free space, Fractional fourier transform, Optical character recognition, Spherical lenses, Optical correlators, Binary data
Some properties of digital correlation based of the fractional Fourier transform are analyzed. We generalize the architecture of a VanderLugt correlator to achieve the VanderLugt fractional Fourier transform correlator such that fractional correlation can be obtained. In this situation the Fourier transform in the classical VanderLugt is replaced by the fractional Fourier transform, and four different VanderLugt fractional architectures can be implemented. The performances of such a correlator are analyzed according to the standard criteria of signal-to-noise ratio, correlation sharpness, peak-to-correlation energy, and Horner efficiency. Here the binary image of a character is used for the test.
Taking advantage of the high speed arithmetic offers by the parallelism of the digital signal processor DSP TMS320C6711 of TI, we implemented two algorithms to find the Fourier transform of fractional order of two dimensional signals ("The discrete fractional Fourier transform" and "Fractional Fourier Transform calculation through the fast-Fourier-transform algorithm"). As a result, we have two algorithms for calculate the fractional Fourier transform of images using a DSP, the images are captured using a camera CCD and the fractional Fourier transform is display in a monitor, both are connected to the DSP device directly. Finally, the work focuses in the evaluation of this algorithms, in order to find which is best performance related to four criteria determined from the properties of the Fourier transform of fractional order: The inverse transform, fractional Fourier transform of order one or standard Fourier transform, fractional Fourier transform of order zero or operator identity and order additivity.
In this work we proposed one optical setup for encryption based in the fractional Fourier Transform. The Fourier transform of fractional order add another degree of freedom, of course the degree fractional used, for the optical encryption realization. The inverse fractional Fourier transform is perform by phase conjugation. This technique allows use the optical setup for encryption and decryption simultaneously. Based in experimental results and numerical simulations we find that is not arbitrary the use of the keys for encryption and decryption operations. The optical fractional Fourier transform has been obtained using the Lohmann type I configuration and a photorefractive crystal BGO working as mirror phase conjugation has been used.
Proc. SPIE. 5622, 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications
KEYWORDS: Optical signal processing, Phase modulation, Laser applications, Fourier transforms, Signal processing, Fractional fourier transform, Convolution, Laser optics, Commercial off the shelf technology, Lead
The standard Fourier transform operator F is a particular case of the fractional order Fourier transform operator Fα (it is obtained for α = 1). In the same way that has been done for F, a sampling theorem for Fα is proposed for signals whose fractional Fourier transforms of order α have finite supports. An interpolation formula for fractional bandlimited functions is also deduced.
A new formulation of the classical scalar beam-propagation method is derived by use of the fractional order Fourier transform. The method relies on the fundamental fact that the coherence is transformed by a linear filter univocally connected to the filter acting on the electric field; building on this result, we solve exactly the problem of the passage of such fields through arbitrary lossless optical system characterized by their ABCD matrices.
In this paper we demonstrate that the propagation of a light wave into multi-element optical system can be treated in the framework of the fractional Fourier transform. This result provide new insight into wave propagation and multi-element resonators as well as the possibility of exploiting this result as a mathematical tool in analyzing such systems. This mathematical formulation gives the direct relationship between input and output of the light field, the confinement stability condition, the diameters of the beam at the mirrors and the diameter of the beam waist.
The ABCD matrix formalism, the Collins formula and the complex amplitude distributions on two spherical surfaces of given curvature and spacing are adapted to the mathematical expression of fractional order Fourier transform. This result provides a general expression as a tool for analyzing complicated systems involving several lenses and mirrors separated by arbitrary distances; for this class of system it is sufficient to specify the ray transfer matrix and the order of fractional Fourier transform to characterize the system completely.
One direct relation between the fractional Fourier transform and the Collins formula in space-domain has been derived. This result is applied to describe the behavior to many opticals system; this paper suggest a generalization of the fractional Fourier transform based on the Collins formula.
Optical correlation is a powerful tool for visual automatic inspection, because it offers high speed, non-destructive test and on-line inspection. W. Liu et al, proposed a hybrid optical/digital linear joint transform correlator for the detection of defects in optical fibers.
The TIA and the EIA have developed a set of standardized test procedures for optical loss of fiber, cables, connectors and splices under many varying environmental conditions called FOTPs. We have implemented the experimental setup corresponding to four of these FOTPs. The firs test allows to measure the change in optical transmittance for devices used in optical fiber systems, between an initial condition and a new condition induced by exposure of the device to physical or environmental changes. The second test determines the quality of the ends for both, bare and connectorized fiber using an interferometric microscope. The third one measures the cutoff wavelength for single-mode fibers. Finally, the capacity of a fiber cable to resist simultaneously torsion and traction are determined measuring the changes in optical transmittance when the cable is properly installed in a special tower. This work is considered as the first step towards the settlement of a regional center for fiber optic testing.
This communication introduces the Optics and Signal Processing Group from Universidad Industrial de Santander at Bucaramanga, Colombia. First, a brief description of how the group was formed, its strategic importance and also some of its more important achievements are presented. Then, the main scientific domains where the group carries out its research are described and finally, some guidelines about future research work in the group are given.
This paper presents a digital implementation of an out-of- plane target location system by means of a joint transform correlator (JTC). A sequence of images of the 3D scene is coded into a single performing an integration of each frame in the vertical sense. The coded sequence is used as the input plane of the JTC after binarization, Fourier transform is performed followed by removal of the DC term from joint power spectrum; finally correlation is evaluated.
This paper presents a segmentation technique for sandstone microscopic images. A sintetized image is obtained by means of operations with three images captured by a CCD camera at a specific wavelength and different polarization angles between polars and analyzer. Thus it is possible to obtain some characteristics to define size and shape of sandstone grains.
An image synthesis from images of a pilled fabric sample illuminated under different orientations is proposed to improve the input used for pilling evaluation by image analysis. The image synthesis is based on the Karhunen-Loeve transform.
Various techniques based on image processing are presented for the automatic quality control of textiles. General defects (shrinking, abrasion, etc.) are detected by using operations in the frequency domain. Local defects (broken threads, mispicks, double yarns, etc.) are detected using a method based on a multiscale and multiorientation Gabor scheme that imitates the visual coding in early human vision. Also pilling resistance is automatically evaluated in wear-and-tear fabrics by a new algorithm which combines operations in both the spatial and frequency domain.
Wear and tear generate fluffiness and pills that remain in the web surface spoiling the appearance of a fabric. In quality control of textiles it is necessary to have an objective method to measure pilling that improves current methods based on visual estimations of the degree of pilling. In this work we optimize a method for piling evaluation based on image analysis that we proposed recently. The method combined operations in both the frequency and the spatial domains in order to better segment pills from the textured web background. We considered a logarithmic in base two relationship between the area of pilling and the degree of pilling based on the human perception mechanisms.
High level image processing and pattern recognition tasks require multiple correlations. So multichannel correlators are of interest. Some architecture configurations have been presented for the Vander-Lugt architecture, but few have for the JTC. We present the experiments concerning two multichannel JTC architectures and compare some of their performances. One is based on the use of spatial light modulators with partially filled pixels, in the second Dammann gratings were used.