On Fourier's Phase and Gradient Index Optical Design

1994 ◽  
Vol 374 ◽  
Author(s):  
Peter D. Haaland
Keyword(s):  
Refractive Index ◽  
Fourier Transform ◽  
Constrained Optimization ◽  
Phase Modulation ◽  
Fourier Transforms ◽  
Optical Design ◽  
Optical Filters ◽  
Gradient Index ◽  
Design Objective ◽  
The Relationship

AbstractGradient index or rugate optical filters are continuous generalizations of the familiar quarterwave stack which find widespread applications in sensor hardening. In the design of a filter or mirror there are infinitely many refractive index profiles n(x) whose wavelength-dependent reflectance R(λ) is specified as a design objective. The relationship between R(λ) and n(x) is nearly that of a Fourier-transform pair. Exploiting this relationship, specifically the physically indeterminate phase of the Fourier transforms, permits constrained optimization of rugate designs. In this contribution we outline the approach of optimal phase modulation and indicate by examples its application to problems in optical limiting.

Optimal phase modulation for gradient-index optical filters

1993 ◽  
Vol 18 (19) ◽  
pp. 1583 ◽  
Author(s):  
Jeff Druessel ◽  
Peter Haaland ◽  
Jeff Grantham
Keyword(s):  
Phase Modulation ◽  
Optical Filters ◽  
Gradient Index

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

Identification of Static Unbalance Wheel of Passenger Car Carried out on a Road

2014 ◽  
Vol 214 ◽  
pp. 48-57 ◽  
Author(s):  
Krzysztof Prażnowski ◽  
Sebastian Brol ◽  
Andrzej Augustynowicz
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Constant Velocity ◽  
Fourier Transforms ◽  
Static Condition ◽  
Rotational Frequency ◽  
Acceleration Sensor ◽  
Short Time Fourier Transform ◽  
Road Roughness ◽  
Short Time

This paper presents a method of identification of non-homogeneity or static unbalance of the structure of a car wheel based on a simple road test. In particular a method the detection of single wheel unbalance is proposed which applies an acceleration sensor fixed on windscreen. It measures accelerations cause by wheel unbalance among other parameters. The location of the sensor is convenient for handling an autonomous device used for diagnostic purposes. Unfortunately, its mounting point is located away from wheels. Moreover, the unbalance forces created by wheels spin are dumped by suspension elements as well as the chassis itself. It indicates that unbalance acceleration will be weak in comparison to other signals coming from engine vibrations, road roughness and environmental effects. Therefore, the static unbalance detection in the standard way is considered problematic and difficult. The goal of the undertaken research is to select appropriate transformations and procedures in order to determine wheel unbalance in these conditions. In this investigation regular and short time Fourier transform were used as well as wavelet transform. It was found that the use of Fourier transforms is appropriate for static condition (constant velocity) but the results proves that the wavelet transform is more suitable for diagnostic purposes because of its ability of producing clearer output even if car is in the state of acceleration or deceleration. Moreover it was proved that in the acceleration spectrum of acceleration measured on the windscreen a significant peak can be found when car runs with an unbalanced wheel. Moreover its frequency depends on wheel rotational frequency. For that reason the diagnostic of single wheel unbalance can be made by applying this method.

Optimal refractive index changes for cross-gain and cross-phase modulation

1998 ◽  
Author(s):  
Thomas Keating ◽  
Jeffrey R. Minch ◽  
Seoung-Hwan Park ◽  
Shun-Lien Chuang ◽  
Tawee Tanbun-Ek
Keyword(s):  
Refractive Index ◽  
Phase Modulation ◽  
Cross Phase Modulation ◽  
Index Changes

Generalized signal-tuned Gabor approach for signal representation and analysis

2017 ◽  
Vol 28 (01) ◽  
pp. 1750001 ◽  
Author(s):  
José R. A. Torreão
Keyword(s):  
Fourier Transform ◽  
Visual Cortex ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Receptive Fields ◽  
Gabor Functions ◽  
Plausible Model ◽  
Spectral Signal ◽  
Potential Applications ◽  
Space Frequency

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

Wavelet packets associated with linear canonical transform on spectrum

2021 ◽  
pp. 2150030
Author(s):  
M. Younus Bhat ◽  
Aamir H. Dar
Keyword(s):  
Fourier Transform ◽  
Multiresolution Analysis ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Integral Transforms ◽  
Wavelet Packets ◽  
Linear Canonical Transform ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Vector Valued

The linear canonical transform (LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we, in this paper, constructed associated wavelet packets. First, we construct wavelet packets corresponding to nonuniform Multiresolution analysis (MRA) associated with LCT and then those corresponding to vector-valued nonuniform MRA associated with LCT. We investigate their various properties by means of LCT.

Nonlinear Refractive Index of Silicon Nanoparticles: A Short Review

2014 ◽  
Vol 1 (2) ◽  
pp. 87-97
Author(s):  
Sudakshina Prusty
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Phase Modulation ◽  
Silicon Nanoparticles ◽  
Nonlinear Coefficient ◽  
Short Review ◽  
Self Phase Modulation ◽  
Physical Mechanisms ◽  
Self Focusing ◽  
Physical Phenomena

This article discusses the nonlinear refractive index of silicon nanoparticles starting from the basic formalism to some of the consequent physical phenomena like self focusing and self phase modulation. Several experimental techniques mainly based on Z-scan are discussed to measure the nonlinear refractive index. Another less explored technique for silicon nanoparticles, which studies the far-field optical fringe pattern formed by spatial self-phase modulation, is also discussed. Computation of the nonlinear refractive index is shown in detail by employing these two techniques. While Z-scan can estimate the nonlinear coefficient of a medium in a chosen time scale, the optical fringe method can predict the overall nonlinear refractive index due to all possible physical mechanisms. Some of the recent results for silicon nanoparticles using these two techniques are also discussed.

IMPLEMENTING FAST FOURIER TRANSFORMS ON DISTRIBUTED-MEMORY MULTIPROCESSSORS USING DATA REDISTRIBUTIONS

1994 ◽  
Vol 04 (04) ◽  
pp. 477-488 ◽  
Author(s):  
S.K.S. GUPTA ◽  
C.-H. HUANG ◽  
P. SADAYAPPAN ◽  
R.W. JOHNSON
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Distributed Memory ◽  
Fourier Transforms ◽  
Experimental Performance ◽  
Minimum Number ◽  
Data Redistribution ◽  
Using Data ◽  
Performance Results ◽  
Fft Algorithms

Implementations of various fast Fourier transform (FFT) algorithms are presented for distributed-memory multiprocessors. These algorithms use data redistribution to localize the computation. The goal is to optimize communication cost by using a minimum number of redistribution steps. Both analytical and experimental performance results on the Intel iPSC/860 system are presented.

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