Question

Homework 6-(Week 11, Lab) Submission deadline, 04/14/2019 at 9pm Problem 1: An interferometer is an instrument that uses the interference patterns formed by waves (usually light, radio, or sound waves) to measure certain characteristics of the waves themselves or of materials that reflect, refract, or transmit the waves. Interferometers can also be used to make precise measurements of distance. Depending on the path difference, it is possible to create constructive interference (where the strength of two waves are added), destructive interference (where to waves cancel each other), or any state in between. I- A B cos(p) where A and B are constants, l is the intensity and ф is the interferometer phase, that is related to the path difference (OPD) as ф--OPD, where n is the laser wavelength. In many systems, the path length is modulated by moving a mirror, so that a "well-known" phase shift & 2st is induced: LASER LASER Reconbined The Figure on the right shows a measurement of a series of intensities at different "well-known" phase shifts. The Data is stored in "HW6 Dataset1.mat". write a Matlab code that estimates ф and the OPD for h-385nm. Hint: simplify the expression for the intensity using cos(xty) cos(x) cos(y) - sin(x) sin(y)

Answer 1

warning off load("HN6Dataset1.mat" Assuming variable names are delta, intensity % Defining Fit type myfittype = fittype ('A + B*cos (phi+delta)', 'dependent ',ן'Intensity'}, 'independent',['delta', 'coefficients','A, 'B, 'phi'): % Fiting Data [myfit, gof] = fit (delta, intensity, myfittype); % myfit is cfit object which is our model % gof 13 a struct containing % values defining goodness of fit % like squared errors, rsquare, root mean sguare error % For getting value of phi phí = myfit.phí; For getting OPD 1am -385 ED- (1am/ (2.pǐ) ) .phí: % enter 'myfit, without qoutes in command window to get 95% confidence intervals of obtained % coefficients

Text :-

warning off
load("HW6Dataset1.mat")

% Assuming variable names are delta, intensity

% Defining Fit type
myfittype = fittype('A + B*cos(phi+delta)','dependent',{'Intensity'},...
                    'independent',{'delta'},'coefficients',{'A','B','phi'});

% Fiting Data
[myfit,gof] = fit(delta,intensity,myfittype);   % myfit is cfit object which is our model
                                                % gof is a struct containing
                                                % values defining goodness of fit
                                                % like Squared errors,
                                                % rsquare, root mean square error
% For getting value of phi
phi = myfit.phi;

% For getting OPD
lam = 385;
OPD = (lam/(2*pi))*phi;

% Plot using this to confirm if it fits data nearly
plot(myfit,delta,intensity)
% enter 'myfit' without qoutes in command window to get 95% confidence intervals of obtained
% coefficients

warning on