Cylinder absorp corr

[jokasimr]

Fixes scipp/essdiffraction#22

[jokasimr]

scipp/essdiffraction#22 will require additional changes in essdiffraction before it can be closed.

The results should be verified with Celine.

But while that's being done this part of the change can be reviewed.

[jokasimr]

There's now a verification of this through McStas simulation.

Setup

The total counts at a pixel are

$$I(p) = \Omega_{p} \int_{sample} S(x, p) T(x, p) \ dx$$

where $\Omega_p$ is the solid angle of the pixel as seen from the sample, $S$ is the scattering intensity from $x$ in the direction of $p$ and $T$ is the transmission probability through the sample if the neutron scattered at $x$.
If the sample is sufficiently far from the detector, or if we only consider inhomogeneous scattering then $S(x, p)$ is constant and

$$I(p) = \Omega_{p} S(p) \int_{sample} T(x, p) \ dx .$$

The term

$$C_{abs} = \int_{sample} T(x, p) \ dx = \int_{sample} exp(-c (l_1(x) + l_2(x, p))) \ dx$$

is what is computed in the absorption correction procedure, $c$ is the absorption coefficient and $l_1$ and $l_2$ is the distance the neutron traveled through the sample before scattering respectively the distance the neutron traveled through the sample after scattering.

Verifying the absorption correction

The intensity $I(p)$ depends on the absorption coefficient $c$. Taking the ratio of two $I(p)$ computed using different absorption coefficients $c_1$ and $c_2$ we get rid of the solid angle and get the ratio of $C_{abs}$ for the two different absorption coefficients:

$$I_{c_1}(p) / I_{c_2}(p) = C_{c_1, abs} / C_{c_2, abs}$$

$I_{c_1}(p)$ and $I_{c_2}(p)$ can be computed using McStas simulation, $C_{c_1, abs}$ and $C_{c_2, abs}$ are computed from the routine in this repo.

McStas

For one specific setup (cylinder height, radius, $c_1$, $c_2$ etc) this is $I_{c_1}(p) / I_{c_2}(p)$ computed py McStas:

This PR

And this is the corresponding $C_{c_1, abs} / C_{c_2, abs}$:

Relative Error

The maximum relative error is <2%. But it looks like much of the error is noise from the Monte Carlo simulation. The real error is probably closer to 1%.

Comment

The results are close. Strictly speaking this only verifies the relative magnitude of the correction for different pixels, but there is a test that verifies the absolute magnitude in one case at one pixel position.