Quadratic/cubic shear response

[rmjarvis]

I think the best way to look for a non-linear shear response would be to rotate the shear estimates to the frame where the true shear is in the +g1 direction. Then the estimated shear (g1hat, g2hat) would rotate to (g+hat, gxhat) in this coordinate system. Then g+hat could be fit as:

g+hat = c+ + m+ g_true + q+ g_true^3

It would be weird for gxhat to be inconsistent with zero from symmetry considerations, but you could fit that as well with a similar formula and see what you find.

I think Gary is right that it would be also be weird to have a g_true^2 term. I'm not completely convinced that it is entirely unphysical, but it would be non-analytic at the origin, so that would be a bit odd.

STEP1 only had applied shears in the +g1 direction, so they kind of did precisely this. And Gary suggested (in a conversation just now) that probably the quadratic term that was measured there was just fitting the cubic term and erroneously ascribing it to a quadratic. With as few points as they had, that's certainly plausible.

[rmandelb]

Hi Mike - thanks for posting. The quadratic/cubic stuff is something that is on my list to revisit once I'm back to work on this stuff (am in NJ visiting family right now) and indeed I had planned to bug you/Gary a bit about this!

During the discussion at the meeting, I totally forgot that the shears in STEP1 were not just aligned with the pixel direction, they were also strictly positive. In that case I suppose a cubic term could be mistaken for quadratic. My gut reaction when Gary suggested we should look for a cubic term was "our shears are <0.05, so a cubic term shouldn't be detectable." But if they were seeing signs of one in STEP1 then perhaps we should check for it here.

[rmandelb]

(And I think it'll be easy. We already have code to rotate into the frame defined by the PSF anisotropy, so rotating into the frame defined by the shear is a small change. And changing the fit from quadratic to cubic is trivial.)