canted particles in radial geometry

[pkienzle]

In the radial geometry the beam travels through the Couette cell, scattering from both left-to-right and right-to-left flow, so the particle needs to be modeled by adding forward and reverse scattering in equal portion; this will be particularly evident for canted particles, leading to a twinned image on the detector.

We should be able to handle this after the model is calculated using I(qx, qy) + I(-qx, qy). This is pretty simple if the beam is centered on the detector because we can just add the computed image to its reverse. Any shift or rotation in the detector, though, makes it pretty messy. Easiest to just compute the pattern twice, once with +qx an again with -qx in that case, but this guarantees 2x cost. Otherwise we need to do a bunch of checks to select a set of qx-qy values to compute and interpolate within them for the qx,qy we need.

[richardh]

Would this not be up to the user to choose an orientation distribution function with the appropriate symmetry for a Couette cell? This would then shift the problem back to perhaps needing to add some more appropriate orientation distributions in sasview.

[pkienzle]

Yes, you could define a symmetric bimodal gaussian distribution with the position and width of one mode, with the other mode at the negative of position, but the GUI can't handle it since SasView? only allows us to set the distribution width (there should be a ticket for multi-parameter distributions). Should double the number of points in the distribution so each mode has enough calculation points, so you aren't saving anything compared to computing +qx and -qx for all qx. User also has to know to set it up, and that it applies to theta, phi and psi. I'm worried that it may push theta jitter to high angles where phi no longer works in the simple equirectangular projection we are using.

Better to do it as a sum of two models, with two different views on the model, one for forward and one for the back. With the correct set of constraints this doesn't introduce any additional fit parameters. It will be a little awkward to set up since you will have to create the sum model then set the constraints by hand, but the current system supports it.

Since the radial geometry is pretty common, it seems worthwhile to treat the data slightly differently, much as we do for sesans. We could hack it together with a flag in the data set, and update the resolution function so it automatically calculates -qx along with qx in the radial geometry.

[pkienzle]

Need to negate qz as well. Things tilting toward the beam on the front side of the cell will be tilting away from beam on the back side by the same amount, so return (I(qx, qy, qz) + I(-qx, qy, -qz)/2. Of course, since we are assuming qz=0 for SAS this doesn't make any difference.

[richardh]

Yes I suppose that really the mean orientation has two distinct directions, but the jitter (which we have in the frame of the particle) would be identical for both of them. So maybe there is much efficiency here to have a flag to "compute for Couette"(which could be done by introducing some special distribution choices in the drop down) But I suspect that in pure Couette flow you would need some other external influence to see the situation Paul K originally described??? This is where we need actual users to discuss their real life oriented SAS experiments with us.

[pkienzle]

This is a user request; we are seeing the splitting in our data here. For whatever reason on some samples the shear causes canting. We will try fitting it with a sum model, or perhaps using a script where we can insert the correction as part of the resolution calculation.

Given that the radial measurement will always have both the forward and backward flow, it is safer just to compute with it every time. In the case where there is no visible splitting a small amount of canting will look like a broadening of the distribution, and perhaps be inconsistent with orientation distributions measured tangentially and perpendicularly if you do not include the scattering from both directions.