5,010 research outputs found
Interferometry-based modal analysis with finite aperture effects
We analyze the effects of aperture finiteness on interferograms recorded to
unveil the modal content of optical beams in arbitrary basis using generalized
interferometry. We develop a scheme for modal reconstruction from
interferometric measurements that accounts for the ensuing clipping effects.
Clipping-cognizant reconstruction is shown to yield significant performance
gains over traditional schemes that overlook such effects that do arise in
practice. Our work can inspire further research on reconstruction schemes and
algorithms that account for practical hardware limitations in a variety of
contexts
Signal representation and recovery under partial information, redundancy, and generalized finite extent constraints
Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 143-150.We study a number of fundamental issues and problems associated with linear
canonical transforms (LCTs) and fractional Fourier transforms (FRTs). First,
we study signal representation under generalized finite extent constraints. Then
we turn our attention to signal recovery problems under partial and redundant
information in multiple transform domains. In the signal representation part,
we focus on sampling issues, the number of degrees of freedom, and the timefrequency
support of the set of signals which are confined to finite intervals in two
arbitrary linear canonical domains. We develop the notion of bicanonical width
product, which is the generalization of the ordinary time-bandwidth product, to
refer to the number of degrees of freedom of this set of signals. The bicanonical
width product is shown to be the area of the time-frequency support of this set of
signals, which is simply given by a parallelogram. Furthermore, these signals can
be represented in these two LCT domains with the minimum number of samples
given by the bicanonical width product. We prove that with these samples the
discrete LCT provides a good approximation to the continuous LCT due to the
underlying exact relation between them. In addition, the problem of finding the
minimum number of samples to represent arbitrary signals is addressed based on
the LCT sampling theorem. We show that this problem reduces to a simple geometrical
problem, which aims to find the smallest parallelogram enclosing a given
time-frequency support. By using this equivalence, we see that the bicanonical
width product provides a better fit to the actual number of degrees of freedom
of a signal as compared to the time-bandwidth product. We give theoretical
bounds on the representational efficiency of this approach. In the process, we
accomplish to relate LCT domains to the time-frequency plane. We show that
each LCT domain is essentially a scaled FRT domain, and thus any LCT domain
can be labeled by the associated fractional order, instead of its three parameters.
We apply these concepts knowledge to the analysis of optical systems with arbitrary
numbers of apertures. We propose a method to find the largest number
of degrees of freedom that can pass through the system. Besides, we investigate
the minimum number of samples to represent the wave at any plane in the system.
In the signal recovery part of this thesis, we study a class of signal recovery
problems where partial information in two or more fractional Fourier domains
are available. We propose a novel linear algebraic approach to these problems
and use the condition number as a measure of redundant information in given
samples. By analyzing the effect of the number of known samples and their distributions
on the condition number, we explore the redundancy and information
relations between the given data under different partial information conditions.Öktem, Sevinç FigenM.S
Roadmap on optical security
Postprint (author's final draft
Sampling and Super-resolution of Sparse Signals Beyond the Fourier Domain
Recovering a sparse signal from its low-pass projections in the Fourier
domain is a problem of broad interest in science and engineering and is
commonly referred to as super-resolution. In many cases, however, Fourier
domain may not be the natural choice. For example, in holography, low-pass
projections of sparse signals are obtained in the Fresnel domain. Similarly,
time-varying system identification relies on low-pass projections on the space
of linear frequency modulated signals. In this paper, we study the recovery of
sparse signals from low-pass projections in the Special Affine Fourier
Transform domain (SAFT). The SAFT parametrically generalizes a number of well
known unitary transformations that are used in signal processing and optics. In
analogy to the Shannon's sampling framework, we specify sampling theorems for
recovery of sparse signals considering three specific cases: (1) sampling with
arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels
and, (3) recovery from Gabor transform measurements linked with the SAFT
domain. Our work offers a unifying perspective on the sparse sampling problem
which is compatible with the Fourier, Fresnel and Fractional Fourier domain
based results. In deriving our results, we introduce the SAFT series (analogous
to the Fourier series) and the short time SAFT, and study convolution theorems
that establish a convolution--multiplication property in the SAFT domain.Comment: 42 pages, 3 figures, manuscript under revie
Linear canonical domains and degrees of freedom of signals and systems
We discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, we show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled by LCTs. We then study the number of degrees of freedom of optical systems and signals based on these concepts. We first discuss the bicanonical width product (BWP), which is the number of degrees of freedom of LCT-limited signals. The BWP generalizes the space-bandwidth product and often provides a tighter measure of the actual number of degrees of freedom of signals. We illustrate the usefulness of the notion of BWP in two applications: efficient signal representation and efficient system simulation. In the first application we provide a sub-Nyquist sampling approach to represent and reconstruct signals with arbitrary space-frequency support. In the second application we provide a fast discrete LCT (DLCT) computation method which can accurately compute a (continuous) LCT with the minimum number of samples given by the BWP. Finally, we focus on the degrees of freedom of first-order optical systems with multiple apertures. We show how to explicitly quantify the degrees of freedom of such systems, state conditions for lossless transfer through the system and analyze the effects of lossy transfer. © Springer International Publishing Switzerland 2016
Degrees of freedom of optical systems and signals with applications to sampling and system simulation
We study the degrees of freedom of optical systems and signals based on space-frequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed. © 2013 Optical Society of America
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