1. Interferogram SimulationZernike 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
𝑍 𝑁
𝑚
(ρ,θ)=𝑁 𝑁
𝑚
𝑅|𝑚|
(𝜌) cos m𝜃; for m > 0
• -𝑁 𝑁
𝑚
𝑅|𝑚|
(𝜌) sin m𝜃; for m < 0
𝑅 𝑚
(ρ)=
(−1 𝑠
)(n − s)!
s!*0.5(n + |m|) − s+!*0.5(n − |m|) − s+!
(𝑛−|𝑚|)/2
𝑠=0
𝑁 𝑁
𝑚
= 2(𝑛+1)
1+𝛿 𝑚𝑜
δ is the Kronecker delta (= 1 for m = 0, 0 for m≠0).
g(x, y) = a(x, y) + b(x, y) cos[2𝒇 𝒐x + φ(x, y)]
φ(x, y) = 𝒕𝒂𝒏−𝟏 𝑰𝟒−𝑰𝟐
𝑰𝟏−𝑰𝟑