RT Journal Article
T1 General n-dimensional quadrature transform and its application to interferogram demodulation
A1 Quiroga Mellado, Juan Antonio
A1 Servín Guirado, Manuel
A1 Marroquín Zaleta, José Luis
AB Quadrature operators are useful for obtaining the modulating phase 0 in, interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these, cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(φ) into -sin(φ) regardless of the-frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of φ over all the domain of interest. Our quadrature operator is composed of-two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal: The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.
PB Optical Society of America
SN 0740-3232
YR 2003
FD 2003-05
LK https://hdl.handle.net/20.500.14352/50826
UL https://hdl.handle.net/20.500.14352/50826
LA eng
NO © 2003 Optical Society of America.J. L. Marroquín and M. Servín were partially supported by grants 34575A and 33429-E from Consejo Nacional de Ciencia y Tecnología, México.
NO Consejo Nacional de Ciencia y Tecnología, México
DS Docta Complutense
RD 8 abr 2025