Publication

Simultaneous estimation of phase and phase derivative using a difference equation representation of the interference field

Pramod Rastogi, Rishikesh Dilip Kulkarni
2014
Journal Articles

Abstract

A computationally efficient technique for fringe analysis in digital holographic interferometry using a difference equation representation of the interference field is presented. The spatially varying coefficient of the difference equation is estimated accurately by constraining it in the subspace spanned by the linearly independent basis functions. The coefficient estimated provides an accurate estimation of the interference phase derivative and enables the linear estimation of the interference field. Thereupon, the interference phase is estimated using a simple unwrapping algorithm. The performance of the proposed method is validated with the help of simulation and experimental results.

Official source

https://infoscience.epfl.ch/entities/publication/1d1d67cf-f585-4366-9144-17493620db76

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Pramod Rastogi, Rishikesh Dilip Kulkarni
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1d1d67cf-f585-4366-9144-17493620db76

About this result

Related concepts (32)

Linear subspace

In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. If V is a vector space over a field K and if W is a subset of V, then W is a linear subspace of V if under the operations of V, W is a vector space over K.

Linear span

In mathematics, the linear span (also called the linear hull or just span) of a set S of vectors (from a vector space), denoted span(S), is defined as the set of all linear combinations of the vectors in S. For example, two linearly independent vectors span a plane. The linear span can be characterized either as the intersection of all linear subspaces that contain S, or as the smallest subspace containing S. The linear span of a set of vectors is therefore a vector space itself. Spans can be generalized to matroids and modules.

Finite difference

A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted is the operator that maps a function f to the function defined by A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives.

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