Tag Archives: Error Function Fitting

Laser Beam Profile: Knife Edge Method Matlab Function for Error Function Fitting

Here is the Matlab function to calculate the beam profile of a Gaussian beam using error function fit.

Fitting function:

Transmission(x-x0) = 0.5(1+erf(sqrt(2).(x-x0)./w))

where x is the position of the knife edge (measured in mm usually), x0 is the beam center, w is the beam waist that we will calculate, erf is the error function.


Here is the Matlab Function:

function [w, x0, fitresult, gof] = knifEdge(x, TransmittedPower)
% knifEdge(x,NormalizedPower)
% Knife edge method: Calculation of beam waist and center of the beam
% Input :
% X Input : Knife position (eg. in mm)
% Y Output: Power for each of the x position.
% Output:
% w = beam waist
% x0 = center of the beam
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.

%% Fit: ‘Error Function Fitting’.
NormalizedPower = TransmittedPower./max(TransmittedPower); % Normalizing Power
x = x-min(x);
lincoeff = polyfit(x, NormalizedPower, 1);
a = lincoeff(1);

[xData, yData] = prepareCurveData( x, NormalizedPower );

% Fit Type
if a<0
ft = fittype( ‘0.5*(1-erf(sqrt(2).*(x-x0)./w))’, ‘independent’, ‘x’, ‘dependent’, ‘y’ );
ft = fittype( ‘0.5*(1+erf(sqrt(2).*(x-x0)./w))’, ‘independent’, ‘x’, ‘dependent’, ‘y’ );
opts = fitoptions( ‘Method’, ‘NonlinearLeastSquares’ );
opts.Display = ‘Off’;
opts.StartPoint = [0.913375856139019 0.63235924622541];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
figure( ‘Name’, ‘Error Function Fitting’ );
h = plot( fitresult, xData, yData );
legend( h, ‘x vs Normalized Power ‘, ‘Error Function Fitting’, ‘Location’, ‘NorthEast’ );
w = fitresult.w;
x0 = fitresult.x0;
% Label axes
xlabel x
ylabel NormalizedPower
grid on