Numerical Analysis of Interference Patterns

This page is currently a work in progress.

Phase Shifting Technique

• requires three phase shifted fringe patterns
• the phase shift must be known
• carefully controlled conditions must be maintained

Fourier Analysis Method

• requires carrier frequency, narrow frequency, low noise and open fringes
• estimates the phase wrapped (via arctan)

Phase-Locked Loop Algorithm

• computer simulated oscillator (VCO) needed
• phase error b/w the fringe pattern and the VCO vanishes

Artificial Neural Network Method

• requires carrier phase
• non-algorithmic (i.e. must have learning phase)
• types of learning include: supervised, unsupervised and reinforcement
• multi-layer: input, output, hidden neurons present

Simulated Annealing

ParSA

Here [1] is the link the the ParSA documentation.

The ParSA (Parallel Simulated Annealing) library is a set of classes written in C++ that can be used to solve optimization problems via a process know as simulated annealing.

The ParSA library contains many different types of

The Equation for convergence speed is:

$P\left(X_{n}\notin Cost_{min}\right)\approx \left({\frac {K}{n}}\right)^{\alpha }$

(1)

Where K and $\alpha$ are problem specific constants and $X_{n}$ is a solution of length n. Using equation (1) and test runs on smaller problems of lower order, K and $\alpha$ can be determined. Along with some suggestions provided in the ParSA documentation, progress can be made towards finding higher quality solutions at a much faster rate.

$\ln P=\alpha \left(\ln K-\ln n\right)$

(2)

The equation for warming temperature in the Aarts scheduler:

$T={\bar {\Delta C^{(|)}}}\left(\ln {\frac {m_{2}}{m_{2}\chi _{0}-(1-\chi _{0})m_{1}}}\right)^{-1}$

(3)