materials.abbe

Abbe Material

This module defines a material based on the refractive index and Abbe number. It provides support for both d-line (587.56 nm) and e-line (546.07 nm) definitions.

Models: 1. “polynomial”: A polynomial fit to glass data (Legacy, D-line only). 2. “buchdahl”: A Buchdahl 3-term model with LASSO-derived coefficients.

Kramer Harrison, 2024

Classes

`AbbeMaterial`(n, abbe[, model])	Represents a material based on the refractive index and Abbe number.
`AbbeMaterialE`(n, abbe)	Represents a material based on the refractive index and Abbe number at e-line.
`AbbeModel`()	Abstract base class for Abbe number based material models.
`AbbePolynomialModel`(index, abbe)	Legacy polynomial model for Abbe materials (d-line).
`BuchdahlDModel`(index, abbe)	Buchdahl model for d-line (587.56 nm) materials.
`BuchdahlEModel`(index, abbe)	Buchdahl model for e-line (546.07 nm) materials.
`BuchdahlModel`(index, abbe)	Base class for Buchdahl 3-term models.

class AbbeMaterial(n, abbe, model=None)[source]

Represents a material based on the refractive index and Abbe number.

This class serves as a wrapper around specific model implementations. Currently supported models: - ‘polynomial’: The legacy polynomial fit (Default, deprecated). - ‘buchdahl’: The new Buchdahl 3-term model (Recommended).

Parameters:

n (float) – The refractive index of the material at 587.56 nm (n_d).
abbe (float) – The Abbe number of the material (V_d).
model (str, optional) – The model to use. Defaults to “polynomial”. Valid options are “polynomial” and “buchdahl”.

index

The refractive index of the material at 587.56 nm.

Type:: float

abbe

The Abbe number of the material.

Type:: float

model_name

The name of the model being used.

Type:: str

model

The underlying model instance.

Type:: AbbeModel

abbe() → float

Calculate the Abbe number (Vd) of the material.

The Abbe number is a measure of the material’s dispersion, defined as Vd = (n_d - 1) / (n_F - n_C), where n_d, n_F, and n_C are the refractive indices at the Fraunhofer d (587.5618 nm), F (486.1327 nm), and C (656.2725 nm) spectral lines, respectively.

Returns:: The Abbe number of the material.
Return type:: float

classmethod from_dict(data)[source]: Creates a material from a dictionary representation.

k(wavelength: float | be.ndarray, **kwargs) → float | be.ndarray

Calculates the extinction coefficient at a given wavelength with caching.

Parameters:

wavelength (float | be.ndarray) – The wavelength(s) of light in microns. Can be a float, numpy array, or torch tensor.
**kwargs – Additional keyword arguments for calculation.

Returns:

The extinction coefficient at the given wavelength(s).

Return type:

float | be.ndarray

n(wavelength: float | be.ndarray, **kwargs) → float | be.ndarray

Calculates the refractive index at a given wavelength with caching.

Parameters:

wavelength (float | be.ndarray) – The wavelength(s) of light in microns. Can be a float, numpy array, or torch tensor.
**kwargs – Additional keyword arguments for calculation (e.g., temperature).

Returns:

The refractive index at the given wavelength(s).

Return type:

float | be.ndarray

to_dict()[source]: Returns a dictionary representation of the material.

class AbbeMaterialE(n, abbe)[source]

Represents a material based on the refractive index and Abbe number at e-line.

This class uses a Buchdahl 3-term model fitted to e-line (546.07 nm) data.

Parameters:

n (float) – The refractive index of the material at 546.07 nm (n_e).
abbe (float) – The Abbe number of the material (V_e).

index

The refractive index of the material at 546.07 nm.

Type:: float

abbe

The Abbe number of the material (V_e).

Type:: float

model

The underlying model instance.

Type:: BuchdahlEModel

abbe() → float

Calculate the Abbe number (Vd) of the material.

The Abbe number is a measure of the material’s dispersion, defined as Vd = (n_d - 1) / (n_F - n_C), where n_d, n_F, and n_C are the refractive indices at the Fraunhofer d (587.5618 nm), F (486.1327 nm), and C (656.2725 nm) spectral lines, respectively.

Returns:: The Abbe number of the material.
Return type:: float

classmethod from_dict(data)[source]: Creates a material from a dictionary representation.

k(wavelength: float | be.ndarray, **kwargs) → float | be.ndarray

Calculates the extinction coefficient at a given wavelength with caching.

Parameters:

wavelength (float | be.ndarray) – The wavelength(s) of light in microns. Can be a float, numpy array, or torch tensor.
**kwargs – Additional keyword arguments for calculation.

Returns:

The extinction coefficient at the given wavelength(s).

Return type:

float | be.ndarray

n(wavelength: float | be.ndarray, **kwargs) → float | be.ndarray

Calculates the refractive index at a given wavelength with caching.

Parameters:

wavelength (float | be.ndarray) – The wavelength(s) of light in microns. Can be a float, numpy array, or torch tensor.
**kwargs – Additional keyword arguments for calculation (e.g., temperature).

Returns:

The refractive index at the given wavelength(s).

Return type:

float | be.ndarray

to_dict()[source]: Returns a dictionary representation of the material.

class AbbeModel[source]

Abstract base class for Abbe number based material models.

abstract predict_k(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the extinction coefficient at a given wavelength.

abstract predict_n(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the refractive index at a given wavelength.

class AbbePolynomialModel(index: float, abbe: float)[source]

Legacy polynomial model for Abbe materials (d-line).

This model uses a polynomial fit to glass data from the Schott catalog. It corresponds to the original implementation of AbbeMaterial.

predict_k(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the extinction coefficient at a given wavelength.

predict_n(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the refractive index at a given wavelength.

class BuchdahlDModel(index: float, abbe: float)[source]

Buchdahl model for d-line (587.56 nm) materials.

ALPHA = 2.5

V1_COEFFS = [0.00416, 4.462559, 2.32666, 0.00233, -0.003697, -4.697604]

V2_COEFFS = [0.066434, -7.636396, 12.597434, -0.037014, 5.551013]

V3_COEFFS = [-0.032218, 2.230357, -103.318994, -0.009654, 1.934983]

WAVE_REF = 0.5875618

predict_k(wavelength: float | be.ndarray) → float | be.ndarray: Predicts the extinction coefficient at a given wavelength.

predict_n(wavelength: float | be.ndarray) → float | be.ndarray: Predicts the refractive index at a given wavelength.

class BuchdahlEModel(index: float, abbe: float)[source]

Buchdahl model for e-line (546.07 nm) materials.

ALPHA = 2.5

WAVE_REF = 0.546074

predict_k(wavelength: float | be.ndarray) → float | be.ndarray: Predicts the extinction coefficient at a given wavelength.

predict_n(wavelength: float | be.ndarray) → float | be.ndarray: Predicts the refractive index at a given wavelength.

class BuchdahlModel(index: float, abbe: float)[source]

Base class for Buchdahl 3-term models.

ALPHA = 2.5

abstract property WAVE_REF: float: Reference wavelength in microns.

predict_k(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the extinction coefficient at a given wavelength.

predict_n(wavelength: float | be.ndarray) → float | be.ndarray[source]: Predicts the refractive index at a given wavelength.