Poisson noise works wrong

What's wrong with that? Would you expect the background to be proportional to the incident beam intensity? That's not necessarily true in neutron experiments where there may also be a constant (beam-independent) noise.

I would expect signal-to-noise ratio to be sqrt(Intensity). Poisson noise is a thing caused by discreteness of probing particles (photons/neutrons). It grows with intensity, but slower than the intensity itself.

For 2D scattering it can be seen:

Intensity = 10^4:

Intensity = 10^6:

Intensity = 10^8:

That's not necessarily true in neutron experiments where there may also be a constant (beam-independent) noise.

Constant noise should have its own name in Background type combobox, if it is necessary.

Currently there are constant background and Poisson noise.

Sorry, I didn't mean constant noise. I meant Poisson noise with fixed parameter, as opposed to a Poisson parameter that is computed internally by multiplying the user-given parameter with the incident beam intensity. So you did not mean the latter anyway?

Under constant noise I also meant Poisson-like noise with fixed parameter.

But currently in BA this parameter is not given separately, by user.

The function

double PoissonBackground::addBackground(double intensity) const
{
    return Math::GeneratePoissonRandom(intensity);
}

uses intensity as average number of counts.

»I would expect signal-to-noise ratio to be sqrt(Intensity). Poisson noise is a thing caused by discreteness of probing particles (photons/neutrons). It grows with intensity, but slower than the intensity itself.«

For the Poisson distribution p(n|lambda), the expectation value is =lambda. Proportional to the Poisson-intensity parameter lambda, no square root here.

The square root only appears in the standard deviation, sigma=sqrt(lambda). If the Poisson background is the noise (as opposed to a scattering signal), then this standard deviation is a measure for the noise of the noise, so to say.

Agree, signal-to-noise ratio is lambda/sigma.

The problem is that now in specular mode the noise is calculated for already normalized curve. Moreover, for the wavelength distribution the noise is calculated for each sampled wavelength line and then all curves inside the distribution are averaged.

Example.

wavelength distribution, sampling=1:

wavelength distribution, sampling=10:

wavelength distribution, sampling=100:

This is definitely wrong. The noise should be calculated after averaging over the distribution, but before the normalization to beam intensity. But here both are done vice versa.