[Requirement] Implement multiplicated reflection collapsing (BEER)

[celinedurniak]

Executive summary

Implement multiplicated reflection collapsing (BEER)

Context and background knowledge

• This is a requirement for BEER
• BEER has pulse-shaping and pulse-modulation choppers.

For this requirement, we'll use this configuration "M2: Medium resolution, modulation, strain scanning"

The chopper settings are

Mode description: modulation (MR) 8X - M2
Number of choppers: 3
Nominal wavelength: 2.1 Å
FC1A: freq: 28 Hz; dist: 8.283 m

MCA: freq: 140 Hz; dist: 9.300 m

FC2A: freq: 14 Hz; dist: 79.975 m

Follow-up: implement methods of other chopper settings.

Inputs

• choppers' settings
• 1 or 2D spectrum

Methodology

See Rouijaa_NuclInstMethPhysRes2018.pdf for details

Outputs

Stitched 1D and 2D profiles

See enclosed example of input and output 1D profiles

Which interfaces are required?

Integrated into reduction workflow, Python module / function

Test cases

McStas NeXus files using duplex or Si powder as samples are stored at https://project.esss.dk/nextcloud/index.php/s/D6TWsGbk65kxkE8
Note that the 2 detector panels at +/- 90 degrees simulated in McStas only have one layer (compared to 12 layers in reality).

Comments

No response

[jokasimr]

I took a look at the 2D density over scattering angle and time of arrival and it looks to me like the lines are overlapping in some regions. Is that expected?

Si

Duplex

[jokasimr]

After reading the linked article, here's how I understand the procedure for doing the stitching:

For all events belonging to the same Bragg peak we have

$$ \lambda = 2 d_{hkl} sin(\theta) $$

where $\lambda = c t_{tof}/ z_{mc}$ and $z_{mc}$ is the travel distance from the modulating chopper and $t_{tof}$ is the travel time from MC to the detector pixel, $c$ is a constant.

Then

$$ c \frac{t_{tof}}{z_{mc}} = 2 d_{hkl} sin(\theta) $$ $$ \iff t_{tof} = 2\frac{z_{mc}}{c} d_{hkl} sin(\theta) $$ $$ \implies \frac{d t_{tof}}{d\theta} = \frac{2 d_{hkl}}{c} (\cos(\theta)z_{mc}+ sin(\theta)\frac{dz_{mc}}{d\theta}) = t_{tof} (\cot(\theta)+ \frac{1}{z_{mc}}\frac{dz_{mc}}{d\theta}) $$

and since $t_d$ (the time at the detector) is $t_d = t_{tof} + t_0$, assuming $t_0$ is constant with respect to $\theta$, $\frac{d t_d}{d\theta} = \frac{d t_{tof}}{d\theta}$.

Finally we have:

$$ \frac{d t_{d}}{d\theta} = t_{tof} (\cot(\theta)+ \frac{1}{z_{mc}}\frac{dz_{mc}}{d\theta}) $$ or $$ t_{tof} = \frac{d t_{d}}{d\theta} \frac{1}{(\cot(\theta)+ \frac{1}{z_{mc}}\frac{dz_{mc}}{d\theta})}. $$

In the above expression $\frac{d t_{d}}{d\theta}$ can be estimated as $\frac{d t_{d}}{d\theta} \approx Cov[t_{d}, \theta]/Var[\theta]$ within a cluster of events that belong to the same Bragg peak. The other terms, $\theta, z_{mc}, \frac{dz_{mc}}{d\theta}$ are known.

Procedure:

1. Cluster the events by the Bragg peak they belong to. This can be done by doing a coarse frame unwrapping ignoring the modulating chopper, getting an approximate $\lambda$ and computing an approximate $d_{hkl}$ from that.
2. Within each cluster, approximate $\frac{d t_{d}}{d\theta}$ as a function of $\theta$. Probably by computing $Cov[t_{d}, \theta]/Var[\theta]$ within each cluster, within short intervals of $\theta$.
3. Now $t_{tof}$ can be evaluated for each event, and we can compute the exact wavelength, $d_{hkl}$ etc.

This was a bit schematic, but maybe it's enough for someone more knowledgeable to say if it is roughly correct or not, and if anything should be done differently.

[celinedurniak]

Update: 2 nexus files containing the wavelength are available on NextCloud
(same mode of operation for the choppers and Si or duplex samples)

[jokasimr]

There's still work to be done here. But it looks similar to the spectrum in the issue.

Limiting the $\theta$ range makes the spectrum a bit sharper.

Quadratic fit instead of linear when estimating $\frac{dt_{tof}}{d\theta}$ makes the result significantly better:

[jokasimr]

How was the spectrum graph in the issue produced?

It would be useful to take a look at the code that created it.

[celinedurniak]

The 1D plot with the curves "processed as usual" and "with modulation correction" was made by the BEER instrument team.
For more details, here is this pdf from the minutes of meeting:

BEER-multiplexing.pdf

@jokasimr Did you apply any time offset? I noticed that for other choppers settings and with scippneutron.load_with_mantid to load the data, I had to withdraw delta_t, which for the mode of operation used for the shared NeXus files should be equal to m_n.value / h.value * 2.1 * 0.5 * 9.3* 1e-4 * sc.Unit('us').

[nvaytet]

This being mcstas data: can you also compare to the true wavelengths/d-spacing?

[jokasimr]

Did you apply any time offset?

Yes, but I'm not sure if it is the same you are referring to. I applied a "time offset" that was subtracted from the t variable in the McStas data to produce the initial estimate of d (the blue curve in the figure), there I used the value 6.5ms, it is essentially the center of the time window when the beam passes the first chopper.

[celinedurniak]

@jokasimr Note on the value of the time offset
In the NeXus files, there is a spectrum in d-spacing (from npi_tof_dhkl component).
After applying the value of the time offset I mentioned above, converting to d-spacing and histogramming, I get the plots below for Si and duplex sample to compare the spectra from Monitor_nD and npi_tof_dhkl component (note that I had to apply some scaling to one of the spectra)

[jokasimr]

@celinedurniak I'm not sure what you mean, maybe it's better if we have a chat in slack or in person.

The spectrum in the npi_tof_dhkl component does not correspond to the true d_hkl spectrum.
The component has the ability to output the true spectrum, but that is not turned on by default, and it seems to be turned off in this simulation. (This is what I understand from reading the documentation on the component: http://www.mcstas.com/download/components/3.5.27_current/contrib/NPI_tof_dhkl_detector.html )