optmat.solid.models.tabulated#

Stitched tables of optical constants as models: a metal’s complex index.

A metal has no single model from the ultraviolet to the far infrared: its optical constants are measured piecewise, each range by a different technique (electron energy-loss spectra, ellipsometry, reflectance with Kramers-Kronig analysis, far-infrared reflectance). A table model joins curated datasets, one per wavelength range, as its configuration data/solid/tables/<material>.toml chooses them, each range with its reason (TC-544):

material = "Ag"

[[segments]]
real = "babar_2015/eps1_Ag"          # refractive_index or permittivity_real
imaginary = "babar_2015/eps2_Ag"     # extinction_coefficient or ...imaginary
range_nm = [207.0, 12400.0]
reason = "..."

The model takes the wavelengths the two datasets of a segment share (an x-ray table may print n only to some energy and 1 - n above it, as refractive_index_decrement, while its k runs on). In the extreme ultraviolet and x-ray range a segment may instead be Henke et al.’s atomic scattering factors (henke = "<element>", CXRO’s file in data/external/henke/) with a curated atom_density dataset: n + ik = 1 - r_e lambda^2 N (f1 - i f2) / (2 pi) (Henke et al. 1993, Eq. 3; their n = 1 - delta - i beta is this package’s n + ik with k = beta), the independent-atom limit, which holds well above the valence excitations and away from absorption edges (TC-645):

[[segments]]
henke = "ag"
atom_density = "<source>/<atom_density dataset>"
range_nm = [1.0, 12.0]
reason = "..."

The model interpolates log n and log k against log omega with a monotone piecewise-cubic Hermite interpolant (PCHIP), which neither overshoots between points nor rings at a join between sources (a natural cubic spline does both); its first derivative is continuous and exact for the interpolant, so epsilon and d epsilon / d omega are consistent. Outside the tabulated range the constants are held at the end points, with a ModelRangeWarning.

Module Attributes

`TABLES_DIRECTORY`	The table models' configurations, one per material.
`HENKE_DIRECTORY`	CXRO's tables of Henke et al.'s atomic scattering factors, `<element>.nff`.

Functions

`load_table`(path)	Build a table model from its configuration.
`tabulated_models`()	Return every configured table model, named `table/<material>`.

Classes

`Segment`(real, imaginary, range_nm, reason[, ...])	One range of a table model and the datasets that supply it.
`TabulatedModel`(material, name, citation, ...)	A complex index interpolated from curated tables, joined by range.

optmat.solid.models.tabulated.HENKE_DIRECTORY = PosixPath('/home/docs/checkouts/optmat/checkouts/7/src/optmat/data/external/henke')#: CXRO’s tables of Henke et al.’s atomic scattering factors, <element>.nff.

class optmat.solid.models.tabulated.Segment(real, imaginary, range_nm, reason, henke='', atom_density='')[source]#

Bases: object

One range of a table model and the datasets that supply it.

Attributes:

realstr: The key of the dataset of n or epsilon_1 (empty for a Henke segment).
imaginarystr: The key of the dataset of k or epsilon_2, on the same abscissae (empty for a Henke segment).
range_nmtuple of float: The vacuum wavelengths taken from these datasets, nm.
reasonstr: Why these datasets supply this range.
henkestr: The element of a Henke segment (CXRO’s file name), or empty.
atom_densitystr: The key of the atom_density dataset of a Henke segment, or empty.

atom_density: str = ''#

property cited: tuple[str, ...]#

Return the sources the segment rests on.

Returns:

tuple of str: The source ids.

henke: str = ''#

imaginary: str#

property label: str#

Return what supplies the segment, for messages.

Returns:

str: henke/<element> or the key of the real dataset.

range_nm: tuple[float, float]#

real: str#

reason: str#

optmat.solid.models.tabulated.TABLES_DIRECTORY = PosixPath('/home/docs/checkouts/optmat/checkouts/7/src/optmat/data/solid/tables')#: The table models’ configurations, one per material.

class optmat.solid.models.tabulated.TabulatedModel(material, name, citation, wavelength_range, kind, axis='', segments=(), knots=<factory>, index=<factory>, *, status='user', status_reason='', modified=(), base='', intervals=(), out_of_range='hold')[source]#

Bases: Model

A complex index interpolated from curated tables, joined by range.

Attributes:

segmentstuple of Segment: The ranges, in increasing wavelength.
knotsnumpy.ndarray: The tabulated vacuum wavelengths, m, increasing.
indexnumpy.ndarray: The complex index n + ik at the knots.
out_of_range{“hold”, “raise”}: Outside the knots the table holds its end values, with a ModelRangeWarning ("hold", the default), or refuses with StateError ("raise"; with_out_of_range()).

DERIVED: ClassVar[tuple[str, ...]] = ('segments', 'wavelength_range')#: Fields derived from the inputs, which an override may not name.

EVALUATION_VERSION: ClassVar[int] = 1#

INPUTS: ClassVar[tuple[str, ...]] = ('index', 'intervals', 'knots')#: The parameters with_parameters() may change.

classmethod from_arrays(material, wavelength, n, k, *, citation='', name='')[source]#

Return a table model from a caller’s arrays.

Parameters:

materialstr: The material, the identity’s (a curated id or a caller’s name).
wavelengthnumpy.ndarray: Vacuum wavelengths, m, increasing; the range is their span.
nnumpy.ndarray: The real index at them, > 0.
knumpy.ndarray: The extinction coefficient, > 0 (the interpolation is in log k).
citationstr, optional: Where the table comes from.
namestr, optional: The model’s name; user/<material> by default.

Returns:

TabulatedModel: The model, status user.

Raises:

ValueError: If the arrays differ in length, the wavelengths do not increase, or n or k is not positive.

Examples

>>> import numpy as np
>>> table = TabulatedModel.from_arrays(
...     "Au", np.array([500e-9, 600e-9, 700e-9]), np.array([0.9, 0.25, 0.16]),
...     np.array([1.9, 3.0, 3.9]))
>>> table.wavelength_range, table.identity.status
((5e-07, 7e-07), 'user')

index: Complex[ndarray, 'n']#

knots: Float[ndarray, 'n']#

out_of_range: str = 'hold'#

segments: tuple[Segment, ...] = ()#

with_out_of_range(mode)[source]#

Return the table with another rule outside its knots, its status kept.

Not an override: within the table the numbers are the same.

Parameters:

mode{“hold”, “raise”}: Hold the end values (with a warning), or refuse.

Returns:

TabulatedModel: The model with that rule.

Examples

>>> from optmat.solid.models.registry import model
>>> strict = model("table/Ag").with_out_of_range("raise")
>>> strict.out_of_range, strict.status
('raise', 'validated')

optmat.solid.models.tabulated.load_table(path)[source]#

Build a table model from its configuration.

Parameters:

pathpathlib.Path: The configuration, data/solid/tables/<material>.toml.

Returns:

TabulatedModel: The model, named table/<material>.

Raises:

DataError: If the configuration is malformed, the ranges overlap or a dataset is unusable.

optmat.solid.models.tabulated.tabulated_models()[source]#

Return every configured table model, named table/<material>.

Returns:

dict of str to TabulatedModel: The models.