optmat.solid.models.formulas#

Published formulas of solids as models.

A curated source’s [[formulas]] entry for a solid becomes a model when it has a form this module knows; its coefficients are the printed strings, corrected by the entry’s corrections with the evidence for each (as for the gases):

n2_sellmeier: n^2 - 1 = A + sum_i B_i lambda^2 / (lambda^2 - C_i), lambda the vacuum wavelength in um, C_i in um^2 (terms A, optional, B, C);
n2_sellmeier_wavelength: the same with the poles printed as wavelengths, C_i = L_i^2 (terms B, L, in um);
n2_sellmeier_temperature: n^2 - 1 = sum_i S_i(T) lambda^2 / (lambda^2 - lambda_i(T)^2), with S_i(T) = sum_j S_ij T^j and lambda_i(T) = sum_j lambda_ij T^j (terms S1, S2, … and L1, L2, …, lambda in um, T in K), as Leviton & Frey fit fused silica; the model is evaluated at the entry’s reference_temperature_k, and FormulaModel.at_temperature() gives it at another temperature within temperature_range_k;
udm: Franta et al.’s universal dispersion model (optmat.solid.udm), with the values of its newAD2 parameter file as the terms: attributes (the file’s first line, he:ex=10:ut:ph=52) and each parameter in newAD2’s names and units.

A formula whose variable is the wavelength in standard air says so with wavelength_medium = "standard_air"; the model converts. A formula whose index is relative to the room air of the measurement, as minimum-deviation refractometry in air gives it, says so with index_medium = "air" and the air’s air_temperature_k and air_pressure_pa (101 325 Pa when the source states none); the model multiplies by the index of that air (Edlen’s dry air, optmat.conditions.air_refractivity()) to give the absolute index (TC-398). A formula whose index is relative to nitrogen, as Daimon & Masumura measure CaF2, says so with index_medium = "nitrogen" and nitrogen_temperature_k and nitrogen_pressure_pa; the model multiplies by the index of that nitrogen from optmat’s recommended N2 model at the ideal-gas density (TC-545). A Sellmeier formula is transparent (real epsilon) and meaningless near its poles; its range is the one its source states.

Module Attributes

FORMS

The formula forms solids use.

Functions

`published_model`(name)	Return one solid formula model, reading only its source's record.
`published_models`()	Return every solid formula model defined in the source records, by name.

Classes

`FormulaModel`(material, name, citation, ...)	A published Sellmeier formula of a solid.
`UdmModel`(material, name, citation, ...[, ...])	Franta et al.'s universal dispersion model of a solid, as a model.

optmat.solid.models.formulas.FORMS = frozenset({'n2_sellmeier', 'n2_sellmeier_temperature', 'n2_sellmeier_wavelength', 'udm'})#: The formula forms solids use.

class optmat.solid.models.formulas.FormulaModel(material, name, citation, wavelength_range, kind, axis='', form='', terms=<factory>, wavelength_medium='vacuum', air=None, reference_gas='air', temperature=None, temperature_range=None, *, status='user', status_reason='', modified=(), base='', intervals=())[source]#

Bases: Model

A published Sellmeier formula of a solid.

Attributes:

formstr: n2_sellmeier, n2_sellmeier_wavelength or n2_sellmeier_temperature.
termsdict of str to tuple of float: The coefficients, after corrections.
wavelength_mediumstr: vacuum, or standard_air for a formula whose variable is the wavelength in standard air (converted with Edlen’s formula).
airState or None: The state of the gas the formula’s index is relative to (room air, or nitrogen), or None for an absolute index.
reference_gasstr: air or nitrogen: the gas air is the state of.
temperaturefloat or None: The sample temperature in K of an n2_sellmeier_temperature formula.
temperature_rangetuple of float or None: The temperatures in K its source supports.

EVALUATES_THROUGH: ClassVar[tuple[str, ...]] = ('optmat.conditions',)#

EVALUATION_VERSION: ClassVar[int] = 2#

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

air: State | None = None#

at_temperature(temperature)[source]#

Return the model at another sample temperature.

Parameters:

temperaturefloat: The sample temperature, K, within the source’s temperature_range.

Returns:

FormulaModel: The same formula evaluated at temperature (typed as its base, for the runtime type checker).

Raises:

DataError: If the formula has no temperature dependence.

Warns:

ModelRangeWarning: If temperature is outside the range its source supports.

form: str = ''#

reference_gas: str = 'air'#

property reference_model: object[source]#

The gas model of a formula relative to nitrogen, bound once.

A solid formula relative to nitrogen needs the gas subpackage only when it is evaluated, or its identity asked for.

Returns:

optmat.gas.models.base.Model or None: The recommended model of N2, or None for a formula relative to air or absolute.

classmethod sellmeier(material, coefficients, wavelength_range, *, reference_medium='vacuum', citation='', name='')[source]#

Return a Sellmeier formula from its coefficients.

n^2 = 1 + A + sum_i B_i lambda^2 / (lambda^2 - C_i), lambda the vacuum wavelength in um and C_i in um^2.

Parameters:

materialstr: The material, the identity’s (a curated id or a caller’s name).
coefficientsMapping: B and C (equal lengths), and optionally A.
wavelength_rangetuple of float: The vacuum wavelengths the formula holds over, m.
reference_mediumstr or State, optional: "vacuum" for an absolute index, or the state of the room air the index is relative to.
citationstr, optional: Where the coefficients come from.
namestr, optional: The model’s name; user/<material> by default.

Returns:

FormulaModel: The model, status user.

Raises:

ValueError: If B and C differ in length or a term is missing.

Examples

>>> silica = FormulaModel.sellmeier(
...     "SiO2", {"B": (0.6961663, 0.4079426, 0.8974794),
...              "C": (0.0684043**2, 0.1162414**2, 9.896161**2)},
...     (210e-9, 3.71e-6), citation="Malitson (1965)")
>>> f"{float(silica.refractive_index(1e-6).real):.5f}"
'1.45042'

temperature: float | None = None#

temperature_range: tuple[float, float] | None = None#

terms: Mapping[str, tuple[float, ...]]#

wavelength_medium: str = 'vacuum'#

class optmat.solid.models.formulas.UdmModel(material, name, citation, wavelength_range, kind, axis='', udm=None, *, status='user', status_reason='', modified=(), base='', intervals=())[source]#

Bases: Model

Franta et al.’s universal dispersion model of a solid, as a model.

Attributes:

udmUniversalDispersionModel: The dielectric function in photon energy.

EVALUATION_VERSION: ClassVar[int] = 1#

udm: UniversalDispersionModel | None = None#

optmat.solid.models.formulas.published_model(name)[source]#

Return one solid formula model, reading only its source’s record.

published_models() reads every record with formulas, which takes seconds; a lookup by name needs one.

Parameters:

namestr: <source>/<formula>.

Returns:

Model: The model, the same as published_models() holds under that name.

Raises:

KeyError: If no solid formula has that name.

Examples

>>> published_model("malitson_1965/sellmeier").material
'SiO2'

optmat.solid.models.formulas.published_models()[source]#

Return every solid formula model defined in the source records, by name.

Returns:

dict of str to Model: The models, named <source>/<formula>.