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

Genetic Algorithm

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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P\left(X_n \notin Cost_{min}\right) \approx \left(\frac{K}{n}\right)^\alpha}

(1)

Where K and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} are problem specific constants and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T=\bar{\Delta C^{(|)}}\left(\ln \frac{m_2}{m_2\chi_0-(1-\chi_0)m_1}\right)^{-1}}

(3)

References