MATLAB: Intensity-weighted centroid noise formula

Assumptions:

NumberOfPhotons = 40E3;
psfStandardDeviation = ( 0.84E-6 + 0.9E-6 ) * 0.34
pixelSize = 185E-9
objectArea = pi * 0.84e-6^2 / 4
numberOfPixels = round( objectArea / pixelSize^2 * 4 )
cameraNoiseVarianceOfOnePixel = 50
cameraNoiseVariance = numberOfPixels * cameraNoiseVarianceOfOnePixel

Feel free to substitute values that are closer to the ones you measured in lab.

Here is the code for evaluating the centroid uncertainty formula in the paper:

function [ MeanSquaredError, ImagingNoise, SpatialQuantizationNoise ] = WeightedCentroidError( NumberOfPhotons, PsfStandardDeviation, PixelSize, CameraNoiseStandardDeviation )

    SpatialQuantizationNoise = ( PsfStandardDeviation^2 + PixelSize^2 / 12 ) / NumberOfPhotons;
    ImagingNoise = 4 * pi^0.5 * PsfStandardDeviation^3 * CameraNoiseStandardDeviation^2 / ( PixelSize * NumberOfPhotons^2 );
    MeanSquaredError = SpatialQuantizationNoise + ImagingNoise;
    
end
</pre