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

The artificial neural network approach utilizes the ability fo

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 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} 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.

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 \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)

Table of Proposed Runs

Clustering

SA Clustering Solver

Clustering Scheduler

• SA Aarts
• SA Easy Scheduler

Multiple Independent Runs (M.I.R.)

MIR_Solver

MIR_Scheduler

Use Combinations of the Different Solver/Scheduler Classes