Título
Reformulation of the fresnel transform to introduce sampling and recovery region control and its acceleration
Autor
MODESTO GUADALUPE MEDINA MELENDREZ
Colaborador
MIGUEL OCTAVIO ARIAS ESTRADA (Asesor de tesis)
MARIA ALBERTINA CASTRO IBARRA (Asesor de tesis)
Nivel de Acceso
Acceso Abierto
Materias
Fast fourier transforms - (FAST FOURIER TRANSFORMS) Embedded systems - (SISTEMAS EMBEBIDOS) Fourier transforms computation - (FOURIER TRANSFORMS COMPUTATION) Wavefront numerical reconstruction - (WAVEFRONT NUMERICAL RECONSTRUCTION) Fresnel transform - (FRESNEL TRANSFORM) CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA - (CTI) MATEMÁTICAS - (CTI) CIENCIA DE LOS ORDENADORES - (CTI)
Resumen o descripción
The Fresnel transform has been used in several applications of digital holography to
recover wave fields from digital holograms. Three-dimensional (3D) reconstruction, 3D
recognition and particle tracking velocimetry can be found among these applications.
Depending on the application, the recovered wave fields should satisfy certain
requirements. Sampling rate control (availability to choose the distance between samples in
the recovered wave field) is a requirement for several digital holography applications;
furthermore, recovery region control (availability to choose the size and position of the
recovered wave fields) can be useful since in most applications only a small region of the
wave fields is required. Nevertheless, none of the actual formulations of the Fresnel
transform can be used to control the sampling rate and the recovery region in the same
formulation. There are a few proposals that completely control the sampling rate of the
wave fields to be recovered, but they use the computation of at least a couple of two dimensional
discrete Fourier transforms with dependency between them. This dependency
restricts the minimum execution time that can be achieved.
In this research, it is proved that implementations of the Fresnel transform with a single
two-dimensional discrete Fourier transform can be used to control the sampling rate and the
recovery region of the wave fields and, at the same time, to reduce the required execution
time. In a proposed software alternative, the use of a single two-dimensional discrete
Fourier transform can achieve shorter execution times for most of the practical applications
than the current alternatives if a small flexibility is permitted in the required sampling rate.
Furthermore, a parallel hardware architecture, where the flexibility is not required, is
proposed. The hardware architecture can achieve shorter execution times than any existing
alternative to compute the Fresnel transform.
The new formulation of the Fresnel transform can require computing only a few
coefficients of the two-dimensional discrete Fourier transform applied to an input array
padded with zeros. In order to reduce the execution time required by the new formulation of
the Fresnel transform, an input and/or output pruning method for composite length discrete
Fourier transforms was proposed. The pruning method avoids computing the
multiplications per zero and non required Fourier coefficients.
Editor
Instituto Nacional de Astrofísica, Óptica y Electrónica
Fecha de publicación
enero de 2010
Tipo de publicación
Tesis de doctorado
Versión de la publicación
Versión aceptada
Recurso de información
Formato
application/pdf
Idioma
Inglés
Audiencia
Estudiantes
Investigadores
Público en general
Sugerencia de citación
Medina-Melendrez M.G.
Repositorio Orígen
Repositorio Institucional del INAOE
Descargas
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