feat: generalize AR calculations, chi center, polarizations, reflections

[BijalBPatel]

Proposed changes:

1. Generalize Calculation beyond para, perp, and polarization framing. Allow parameters chi_1, chi_2 as optional parameters to choose where the chi wedges are centered. Default behavior will be chi_1 = 0, chi_2 = chi1 - 90, but allow users to override this. This enables more flexibility e.g., computing AR along a target chi aligned with a biaxial director, or sanity check of calculating AR aligned 45 degrees to uniaxial director. Goal is for default behavior to match current behavior.
2. Add a flag to integrate 4 chi wedges per image, instead of 2. Presently, AR is calculated from two chi-wedges, centered on 0 +- chi_width (para) and -90 +- chi_width (perp). The proposed change would allow incorporating the reflection (so I_para is calculated from the wedges centered on 0 and 180, and I_perp is from wedges centered on 90 and -90).

Possible QOL additions:

• Warn if chi_1 and chi_2 are not perpendicular
• Warn if any wedges are overlapping
• Add a flag to enable inferring chi_1 and chi_2 from polarization metadata

Possible Connections with existing issues:

• can advance feat: Multi-polarization anisotropy in RSoXS module #2 Add documentation on anisotropic ratio and other rsoxs features #96 , but should discuss with @pbeaucage abt. tutorial notebooks etc.

Existing Code for reference:

PyHyperScattering/src/PyHyperScattering/RSoXS.py

Lines 109 to 151 in 6603dd4

	def AR(self,calc2d=False,two_AR=False,chi_width=5,calc2d_norm_energy=None):
	'''
	Calculate the RSoXS Anisotropic Ratio (AR) of either a single RSoXS scan or a polarized pair of scans.
	AR is defined as (para-perp)/(para+perp) where para is the chi slice parallel to the polarization direction, and perp is the chi slice 90 deg offset from the polarization direction.
	Args:
	img (xarray): image to plot
	calc2d (bool): calculate the AR using both polarizations
	two_AR (bool): return both polarizations if calc2d = True. If two_AR = False, return the average AR between the two polarizations.
	calc2d_norm_energy (numeric): if set, normalizes each polarization's AR at a given energy. THIS EFFECTIVELY FORCES THE AR TO 0 AT THIS ENERGY.
	chi_width (int, default 5): the width of chi slices used in calculating AR.
	'''
	if(not calc2d):
	para = self.slice_chi(0,chi_width=chi_width)
	perp = self.slice_chi(-90,chi_width=chi_width)
	return ((para - perp) / (para+perp))
	elif(calc2d):
	para_pol = self.select_pol(0)
	perp_pol = self.select_pol(90)
	para_para = para_pol.rsoxs.slice_chi(0,chi_width=chi_width)
	para_perp = para_pol.rsoxs.slice_chi(-90,chi_width=chi_width)
	perp_perp = perp_pol.rsoxs.slice_chi(-90,chi_width=chi_width)
	perp_para = perp_pol.rsoxs.slice_chi(0,chi_width=chi_width)
	AR_para = ((para_para - para_perp)/(para_para+para_perp))
	AR_perp = ((perp_perp - perp_para)/(perp_perp+perp_para))
	if calc2d_norm_energy is not None:
	AR_para = AR_para / AR_para.sel(energy=calc2d_norm_energy)
	AR_perp = AR_perp / AR_perp.sel(energy=calc2d_norm_energy)
	if (AR_para < AR_perp).all() or (AR_perp < AR_para).all():
	warnings.warn('One polarization has a systematically higher/lower AR than the other. Typically this indicates bad intensity values.',stacklevel=2)
	if two_AR:
	return (AR_para,AR_perp)
	else:
	return (AR_para+AR_perp)/2
	else:
	raise NotImplementedError('Need either a single DataArray or a list of 2 dataarrays')

[BijalBPatel]

Branch is feature complete, but there are some additions I want to make before PR.

• Tutorial
• Aggressive Testing on meaningful uniaxial datasets
• Automated Tests
• Redoing the logic to pull integration wedges into a helper function. Right now the code logic is unnecessarily muddy and intelligent selection selection of chi,q wedges is a useful thing on its own. This change is unlikely to be visible to function users, but it will make testing easier/ more robust.

At the earliest, i'll work on it again next Tuesday, but its open to anyone to test.