Publication

Phase estimation in digital holographic interferometry using cubic phase function based method

Pramod Rastogi, Sai Siva Gorthi
2010
Journal Articles

Abstract

The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reconstructed interference field in many segments and modeling signal data in each segment as a cubic phase signal. The polynomial coefficients in each segment are determined using cubic phase function algorithm. The phase is subsequently evaluated from the polynomial constructed using the obtained polynomial coefficients. The piecewise polynomial approximation approach is extended for all rows/columns and the overall phase is thus determined. The method's applicability is demonstrated using simulation and experimental results.

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Pramod Rastogi, Sai Siva Gorthi
2010
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e560b865-d6a7-4b6f-9d7b-1795fa2f6f5d

About this result

Related concepts (32)

Chebyshev polynomials

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as and . They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind are defined by Similarly, the Chebyshev polynomials of the second kind are defined by That these expressions define polynomials in may not be obvious at first sight, but follows by rewriting and using de Moivre's formula or by using the angle sum formulas for and repeatedly.

Polynomial

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. Polynomials appear in many areas of mathematics and science.

Polynomial ring

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers.

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