Questions of gaussian distribution source

Dear Geant4 experts,

I tried to set a photon source with Gaussian distribution in position, the FWHM of source is 100um. Then I set the following command.

/gps/pos/type Beam
/gps/pos/sigma_r 42.462 um

May I ask if my settings are correct?

Besides, I have another question, is the meaning of sigma_r (or sigma_x, sigma_y) in ‘gps’ command consistent with the standard deviation igma in Gaussian distribution formulas?
3NP4QEDG)4@CI8LREO

If so, should the following formula be satisfied?
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Thank you so much for your attention!

SHZONG

Not an answer but maybe you could store the positions of the track passing a plane into a 2D histogram to check what you need, e.g., in your SteppingAction.cc

G4String preStepVol = step->GetPreStepPoint()->GetPhysicalVolume()->GetName();
G4String postStepVol =  step->GetPostStepPoint()->GetPhysicalVolume()->GetName();
G4String particleName = step->GetTrack()->GetParticleDefinition()->GetParticleName();
G4double trackWeight = step->GetTrack()->GetWeight();
if ((preStepVol == "World" && postStepVol == "Plane") && particleName == "gamma")
{
    G4ThreeVector vertex  =  step->GetTrack()->GetPosition();
    const G4AffineTransform transformation  =  step->GetTrack()->GetNextTouchable()->GetHistory()->GetTransform(1);
    G4ThreeVector localVetex  =  transformation.TransformPoint(vertex);
    G4double x  =  localVetex.x();
    G4double y  =  localVetex.y();         
    analysisManager->FillH2(1, x, y, trackWeight);
}