Migrate offspec

[jokasimr]

Fixes #32

[jl-wynen]

Please make the monitor name a parameter. See, e.g., cell 5 in https://scipp.github.io/esssans/user-guide/isis/sans2d.html

[jl-wynen]

Missing the first line of the license header. Also in other files.

[jl-wynen]

Please update the year in all files.

[jl-wynen]

It looks like the workflow has changed. The old one normalised in wavelength and then converted to Q. This one converts to Q first and then normalises. Did you check with the scientists that this makes sense? This workflow was meant to replicate the ISIS workflow for OFFSPEC.

[jokasimr]

I didn't check with any scientist, but I'm sure it's not a problem, and I don't think we should bother them with this since it's a one-off workflow for an instrument at a different facility.

Maybe you want me to check with them anyway, but let me at least try to convince you that what we are doing here is fine.

This is how the measured intensities are modeled, $I_s$ is the sample measurement and $I_r$ is the reference measurement

$$I_s(\lambda )=D(\lambda )M_s(\lambda )R(Q(\lambda ))$$ $$I_r(\lambda )=D(\lambda )M_r(\lambda ).$$

To estimate $R(q_i)$, move the monitor term to the lhs and integrate over a small $Q$-bin ${\mathrm{\Delta }}_i=[q_{i-\frac{1}{2}},q_{i+\frac{1}{2}}]$

$${\int }_{Q\in {\mathrm{\Delta }}_i}\frac{I_s(\lambda )}{M_s(\lambda )}d\lambda \approx {\int }_{Q\in {\mathrm{\Delta }}_i}D(\lambda )d\lambda R(q_i)⟹R(q_i)\approx \frac{{\int }_{Q\in {\mathrm{\Delta }}_i}\frac{I_s(\lambda )}{M_s(\lambda )}d\lambda }{{\int }_{Q\in {\mathrm{\Delta }}_i}D(\lambda )d\lambda }$$ where the integral of $D$ is estimated using the reference measurement $${\int }_{Q\in {\mathrm{\Delta }}_i}\frac{I_r(\lambda )}{M_r(\lambda )}d\lambda ={\int }_{Q\in {\mathrm{\Delta }}_i}D(\lambda )d\lambda$$ so that $$R(q_i)\approx \frac{{\int }_{Q\in {\mathrm{\Delta }}_i}\frac{I_s(\lambda )}{M_s(\lambda )}d\lambda }{{\int }_{Q\in {\mathrm{\Delta }}_i}\frac{I_r(\lambda )}{M_r(\lambda )}d\lambda }.$$

In the above expression it's natural to think about it like we are integrating over $Q$-bins. But we could equally well think about it like we are integrating over $\lambda$-bins because $Q(\lambda )$ is bijective and

$$Q\in {\mathrm{\Delta }}_i⟺\lambda \in [\lambda (q_{i+\frac{1}{2}}),\lambda (q_{i-\frac{1}{2}})]$$

So doing the normalization in $Q$ and doing the normalization in $\lambda$ is equivalent, provided that you use equivalent grids.

[jl-wynen]

Please move this into workflow.py. There should be no definitions in __init__.py, only imports.