Phase Unwrapping

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Interferogram Simulation Zernike polynomials are the quantized wave-front aberrations. Computationally producing zernike polynomials and using them to simulate an interferogram has been achieved. FFT methods and Phase shifting techniques were used to analyze the fringe pattern to obtain phase information. The phase so obtained is indeterminate to a factor of 2π. In most cases, a computer-generated function subroutine gives a principal value ranging from −π to π. An oset of phase has to be added to the discontinuous phase distribution to obtain the continuous phase map. This refers to the PHASE UNWRAPPING PROBLEM. FFT Analysis Phase Shifting Interferometry Wrapped Wavefront Phase Unwrapped Phase Map Phase Unwrapping of an Interferogram B.Santosh Kumar Department of Physics Sri Sathya Sai Institute Of Higher Learning Zernike polynomials simulation (ρ,θ)= || () cos m; for m > 0 - || () sin m; for m < 0 (ρ)= (−1 )(n − s)! s!*0.5(n + |m|) s+!*0.5(n |m|) s+! (−||)/2 =0 = 2(+1) 1+ δ is the Kronecker delta (= 1 for m = 0, 0 for m≠0). g(x, y) = a(x, y) + b(x, y) cos[2 x + φ(x, y)] φ(x, y) =

Transcript of Phase Unwrapping

Page 1: Phase Unwrapping

Interferogram Simulation Zernike polynomials are the quantized wave-front

aberrations. Computationally producing zernike polynomials

and using them to simulate an interferogram has been

achieved. FFT methods and Phase shifting techniques were

used to analyze the fringe pattern to obtain phase

information. The phase so obtained is indeterminate to a

factor of 2π. In most cases, a computer-generated function

subroutine gives a principal value ranging from −π to π. An

offset of phase has to be added to the discontinuous phase

distribution to obtain the continuous phase map. This refers

to the PHASE UNWRAPPING PROBLEM.

FFT Analysis

Phase Shifting Interferometry

Wrapped Wavefront Phase Unwrapped Phase Map

Phase Unwrapping of an Interferogram

B.Santosh Kumar

Department of Physics Sri Sathya Sai Institute Of Higher Learning

Zernike polynomials simulation

𝑍𝑁𝑚 (ρ,θ)=𝑁𝑁

𝑚𝑅|𝑚|(𝜌) cos m𝜃; for m > 0 • -𝑁𝑁

𝑚𝑅|𝑚|(𝜌) sin m𝜃; for m < 0

𝑅 𝑚 (ρ)= (−1𝑠)(n − s)!

s!*0.5(n + |m|) − s+!*0.5(n − |m|) − s+!(𝑛−|𝑚|)/2𝑠=0

𝑁𝑁𝑚= 2(𝑛+1)

1+𝛿𝑚𝑜 δ is the Kronecker delta (= 1 for m = 0, 0 for m≠0).

g(x, y) = a(x, y) + b(x, y) cos[2𝒇𝒐x + φ(x, y)]

φ(x, y) = 𝒕𝒂𝒏−𝟏𝑰𝟒−𝑰𝟐

𝑰𝟏−𝑰𝟑