General n-dimensional quadrature transform and its application to interferogram demodulation
JOSA A, Vol. 20, Issue 5, pp. 925-934 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000925
Acrobat PDF (603 KB)
Abstract
Quadrature operators are useful for obtaining the modulating phase φ 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.
© 2003 Optical Society of America
[Optical Society of America ]
Citation
Manuel Servin, Juan Antonio Quiroga, and Jose Luis Marroquin, "General n-dimensional quadrature transform and its application to interferogram demodulation," J. Opt. Soc. Am. A 20, 925-934 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-925
You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
« Previous Article | Next Article »
OSA is a member of 