Browsing by Subject "Fourier optics"

Now showing 1 - 20 of 28

Open Access
Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems
(Optical Society of America, 1997-09) Erden, M. F.; Özaktaş, Haldun M.
We define the accumulated Gouy phase shift as the on-axis phase accumulated by a Gaussian beam in passing through an optical system, in excess of the phase accumulated by a plane wave. We give an expression for the accumulated Gouy phase shift in terms of the parameters of the system through which the beam propagates. This quantity complements the beam diameter and the wave-front radius of curvature to constitute three parameters that uniquely characterize the beam with respect to a reference point in the system. Measurement of these parameters allows one to uniquely recover the parameters characterizing the first-order system through which the beam propagates.
Open Access
Chirp filtering in the fractional Fourier domain
(Optical Society of America, 1994-11-10) Dorsch, R. G.; Lohmann, A. W.; Bitran, Y.; Mendlovic, D.; Özaktaş, Haldun M.
In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved.
Open Access
Convolution and filtering in fractional fourier domains
(Springer-Verlag, 1994) Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D.
Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.
Open Access
Design of dynamically adjustable anamorphic fractional Fourier transformer
(Elsevier BV * North-Holland, 1997-03-01) Erden, M. F.; Özaktaş, Haldun M.; Sahin, A.; Mendlovic, D.
We form optical systems by using only free space portions and cylindrical lenses, and consider these systems as anamorphic fractional Fourier transformers. We dynamically adjust the transform order, scale factor and field curvature of both orthogonal dimensions of anamorphic fractional Fourier transformation by just changing the focal lengths of cylindrical lenses used in the proposed setups. Here, we also consider two approaches for implementing cylindrical lenses with dynamically adjustable focal lengths. There may also be some other methods to obtain cylindrical lenses having adjustable focal lengths which can successfully be used in these proposed setups.
Open Access
Evaluation of the validity of the scalar approximation in optical wave propagation using a systems approach and an accurate digital electromagnetic model
(Taylor and Francis Ltd., 2016) Kulce, O.; Onural, L.; Özaktaş, Haldun M.
The cause and amount of error arising from the use of the scalar approximation in monochromatic optical wave propagation are discussed using a signals and systems formulation. Based on Gauss’s Law, the longitudinal component of an electric field is computed from the transverse components by passing the latter through a two input single output linear shift-invariant system. The system is analytically characterized both in the space and frequency domains. For propagating waves, the large response for the frequencies near the limiting wave number indicates the small angle requirement for the validity of the scalar approximation. Also, a discrete simulator is developed to compute the longitudinal component from the transverse components for monochromatic propagating electric fields. The simulator output helps to evaluate the validity of the scalar approximation when the system output cannot be analytically calculated. © 2016 Informa UK Limited, trading as Taylor & Francis Group.
Open Access
Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering
(Optical Society of America, 1996-06-10) Özaktaş, Haldun M.; Mendlovic, D.
We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) consecutive filtering operations in several fractional Fourier domains and (ii) consecutive filtering operations alternately in the space and the frequency domains.
Open Access
Fast and accurate linear canonical transform algorithms
(IEEE, 2015) Özaktaş, Haldun M.; Koç, A.
Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform family. This family of transforms is especially important for the modelling of wave propagation. It has many applications such as noise removal, image encryption, and analysis of optical systems. Here we discuss algorithms for fast and accurate computation of these transforms. These algorithms can achieve the same accuracy and speed as fast Fourier transform algorithms, so that they can be viewed as optimal algorithms. Efficient sampling of signals plays an important part in the development of these algorithms.
Open Access
Fourier transforms of fractional order and their optical interpretation
(Elsevier, 1993) Özaktaş, Haldun M.; Mendlovic, D.
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a=1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Fractional Fourier transforms can extend the range of spatial filtering operations.
Open Access
Fractional correlation
(Optical Society of America, 1995) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.
Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads to some new applications for fractional correlation as shift-variant image detection. A bulk-optics implementation of fractional correlation is suggested and demonstrated with computer simulations.
Open Access
The fractional fourier transform
(IEEE, 2001) Özaktas, Haldun M.; Kutay, M. A.
A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.
Open Access
Fractional Fourier transform: simulations and experimental results
(Optical Society of America, 1995) Bitran, Y.; Mendlovic, D.; Dorsch, R. G.; Lohmann, A. W.; Özaktaş, Haldun M.
Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation 3J. Opt. Soc. Am. A 10, 2181 1199324 provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.
Open Access
Generalization of time-frequency signal representations to joint fractional Fourier domains
(IEEE, 2005-09) Durak, L.; Özdemir, A. K.; Arıkan, Orhan; Song, I.
The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose a joint fractional domain signal representation (JFSR) based on an intuitive understanding from a time-frequency distribution constructing a 2-D function which designates the joint time and frequency content of signals. The JFSR of a signal is so designed that its projections on to the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR including its relations to quadratic time-frequency representations and fractional Fourier transformations. We present a fast algorithm to compute radial slices of the JFSR.
Open Access
Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform
(Optical Society of America, 1994) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.
Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.
Embargo
High-precision laser focus positioning of rough surfaces by deep learning
(Elsevier Ltd, 2023-05-18) Polat, Can; Yapici, Gizem Nuran; Elahi, Sepehr; Elahi, Parviz
This work presents a precise positioning detection based on a convolutional neural network (CNN) to control the laser focus in laser material processing systems. The images of the diffraction patterns measured at different positions of the laser focus concerning the workpiece are classified in the range of the Rayleigh length of the focusing lens with an increment of about 7% of it. The experiment was carried out on different materials with different levels of surface roughness, such as copper, silicon, and steel, and over 99% accuracy in the positioning detection was achieved. Considering surface roughness and camera noise, a theoretical model is established, and the effects of these parameters on the accuracy of focus detection are also presented. The proposed method exhibits a noise-robust focus detection system and the potential for many precise positioning detection systems in industry and biology. © 2023 Elsevier Ltd.
Open Access
High-throughput, high-resolution interferometric light microscopy of biological nanoparticles
(American Chemical Society, 2020-01) Yurdakul, C.; Avcı, O.; Matlock, A.; Devaux, A. J.; Quintero, M. V.; Özbay, Ekmel; Davey, R. A.; Connor, J. H.; Karl, W. C.; Tian, L.; Ünlü, M. Selim
Label-free, visible light microscopy is an indispensable tool for studying biological nanoparticles (BNPs). However, conventional imaging techniques have two major challenges: (i) weak contrast due to low-refractive-index difference with the surrounding medium and exceptionally small size and (ii) limited spatial resolution. Advances in interferometric microscopy have overcome the weak contrast limitation and enabled direct detection of BNPs, yet lateral resolution remains as a challenge in studying BNP morphology. Here, we introduce a wide-field interferometric microscopy technique augmented by computational imaging to demonstrate a 2-fold lateral resolution improvement over a large field-of-view (>100 × 100 μm2 ), enabling simultaneous imaging of more than 104 BNPs at a resolution of ∼150 nm without any labels or sample preparation. We present a rigorous vectorial-optics-based forward model establishing the relationship between the intensity images captured under partially coherent asymmetric illumination and the complex permittivity distribution of nanoparticles. We demonstrate high-throughput morphological visualization of a diverse population of Ebola virus-like particles and a structurally distinct Ebola vaccine candidate. Our approach offers a low-cost and robust label-free imaging platform for high-throughput and high-resolution characterization of a broad size range of BNPs.
Open Access
Noise robust focal distance detection in laser material processing using CNNs and Gaussian processes
(S P I E - International Society for Optical Engineering, 2022-05-17) Elahi, Sepehr; Polat, Can; Safarzadeh, Omid; Elahi, Parviz
In this work, we investigate the effects of noise on real-time focal distance control for laser material processing by generating the images of a sample at different focal lengths using Fourier optics and then designing, training, and testing a deep learning model in order to detect the focal distances from the simulated images with varying standard deviations of added noise. We simulate both input noise, such as noise due to surface roughness, and output noise, such as detection camera noise, by adding zero-mean Gaussian noise to the source wave and the simulated image, respectively, for different focal distances. We then train a convolutional neural network combined with a Gaussian process classifier to predict focus distances of noisy images together with confidence ratings for the predictions.
Open Access
Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions
(Elsevier BV * North-Holland, 1995-10-15) Sahin, A.; Özaktaş, Haldun M.; Mendlovic, D.
Previous optical implementations of the two-dimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present general design formulae for optically implementing such transforms. This design formulae allows us to specify the two orders and the input, output scale parameters simultaneously.
Open Access
Optical information processing: A historical overview
(Academic Press, 2021-12) Özaktaş, Haldun Memduh; Kutay, Mehmet Alper
Optical information processing lies at the intersection of optics and signal processing. It involves the processing of optical information as well as the use of optical means to process information, the later being the main emphasis of this work. A historical review of various forms of optical signal processing and holography, optoelectronic and digital optical computing, and optical interconnections is given.
Open Access
Optimal image restoration with the fractional Fourier transform
(OSA - The Optical Society, 1998-04) Kutay, M. A.; Özaktaş, Haldun M.
The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for space-invariant degradation models and space-invariant signal and noise characteristics. For space-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. Optimal filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain Wiener filtering for certain types of degradation and noise while requiring only O(N log N) implementation time. The amount of reduction in error depends on the signal and noise statistics as well as on the degradation model. The largest improvements are typically obtained for chirplike degradations and noise, but other types of degradation and noise may also benefit substantially from the method (e.g., nonconstant velocity motion blur and degradation by inhomegeneous atmospheric turbulence). In any event, these reductions are achieved at no additional cost. © 1998 Optical Society of America.
Open Access
Optimal representation and processing of optical signals in quadratic-phase systems
(Elsevier, 2016) Arik, S. Ö.; Özaktaş, Haldun M.
Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs.