[FEAT]: Add wrapper functions for soft x-ray index of refraction.

[HarlanHeilman]

It would be nice if the popular index of refraction components $\delta$ and $\beta$ could be added as functions to the xsf module. They could be modeled from the index of refraction function.

Proposed addition:

def delta(compound, *, density=None, natural_density=None,
                        energy=None, wavelength=None):
    """
    Calculates the δ component of the index of refraction for a given compound
    ...
    """
    if energy is not None:
        wavelength = xray_wavelength(energy)
    assert wavelength is not None, "scattering calculation needs energy or wavelength"
    f1, f2 = xray_sld(compound,
                      density=density, natural_density=natural_density,
                      wavelength=wavelength)
    return wavelength**2/(2*pi)*(f1)*1e-6

def beta(compound, *, density=None, natural_density=None,
                        energy=None, wavelength=None):
    """
    Calculates the β component of the index of refraction for a given compound
    ...
    """
    if energy is not None:
        wavelength = xray_wavelength(energy)
    assert wavelength is not None, "scattering calculation needs energy or wavelength"
    f1, f2 = xray_sld(compound,
                      density=density, natural_density=natural_density,
                      wavelength=wavelength)
    return -wavelength**2/(2*pi)*(f2)*1e-6

Should I make a pr for this?

[pkienzle]

We already have xray.index_of_refraction(compound) which returns n = 1 - δ + iβ using your definition of δ and β above.

periodictable/periodictable/xsf.py

Lines 434 to 466 in 0b8ba54

	def index_of_refraction(compound, *, density=None, natural_density=None,
	energy=None, wavelength=None):
	"""
	Calculates the index of refraction for a given compound
	:Parameters:
	*compound* : Formula initializer
	Chemical formula.
	*density* : float | |g/cm^3|
	Mass density of the compound, or None for default.
	*natural_density* : float | |g/cm^3|
	Mass density of the compound at naturally occurring isotope abundance.
	*wavelength* : float or vector | |Ang|
	Wavelength of the X-ray.
	*energy* : float or vector | keV
	Energy of the X-ray, if *wavelength* is not specified.
	:Returns:
	*n* : float or vector | unitless
	index of refraction of the material at the given energy
	:Notes:
	Formula taken from http://xdb.lbl.gov (section 1.7) and checked
	against http://henke.lbl.gov/optical_constants/getdb2.html
	"""
	if energy is not None:
	wavelength = xray_wavelength(energy)
	assert wavelength is not None, "scattering calculation needs energy or wavelength"
	f1, f2 = xray_sld(compound,
	density=density, natural_density=natural_density,
	wavelength=wavelength)
	return 1 - wavelength**2/(2*pi)*(f1 + f2*1j)*1e-6

Do you ever need δ and β alone? Is it sufficient to use δ, β = 1 - n.real, n.imag in these cases?

Note that the sign convention on β seems to vary. CXRO gives n = 1 - δ - iβ here but most other sources say n = 1 - δ + iβ.

[HarlanHeilman]

It's very common to need β without δ when computing mass absorption, a critical step for the normalization of x-ray spectroscopy.

While delta, beta = 1-n.real, n.imag is straightforward, directly exposing δ, β, and ñ = n + ik would significantly improve the package's usability. This has become particularly apparent in two contexts:

1. Teaching X-ray science courses, where students newer to programming struggle with these conversions, creating an unnecessary barrier to getting started with the analysis workflow.

2. The ongoing transition of soft X-ray synchrotron beamlines from Igor Pro analysis toolkits to Python. Many beamline users are willing to make this transition but frequently ask why these standard tools don't already exist in the Python ecosystem. Having δ and β readily available would address a common pain point and help demonstrate that Python-based analysis can be as streamlined as the Igor workflows they're accustomed to.

Having these values available by default would reduce boilerplate and make the package more accessible to the broader X-ray science community, particularly those migrating from other analysis platforms.

[pkienzle]

Please create a PR.

I'm slightly bothered by the inefficiency – if δ, β and ñ are all used then it will parse and walk the formula three times – but this is unlikely to be a problem in practice. The beta casein example takes 600 μs on my M2 chip so I wouldn't want it on the inner loop of a fit, but the extra time would be invisible in a jupyter notebook tutorial or data reduction step:

from periodictable import xsf, fasta

%timeit xsf.xray_sld("aa:"+fasta.beta_casein, wavelength=4.7)