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”.

Variables:

  • index (float) – The refractive index of the material at 587.56 nm.

  • abbe (float) – The Abbe number of the material.

  • model_name (str) – The name of the model being used.

  • model (AbbeModel) – The underlying model instance.

property abbe#

The model’s live Abbe number in its reference-line convention.

classmethod from_dict(data)[source]#

Creates a material from a dictionary representation.

property index#

The model’s live reference-line refractive index.

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

model: AbbeModel#
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).

Variables:

  • index (float) – The refractive index of the material at 546.07 nm.

  • abbe (float) – The Abbe number of the material (V_e).

  • model (BuchdahlEModel) – The underlying model instance.

property abbe#

The model’s live Abbe number in its reference-line convention.

classmethod from_dict(data)[source]#

Creates a material from a dictionary representation.

property index#

The model’s live reference-line refractive index.

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

model: AbbeModel#
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.

abstractmethod predict_k(wavelength: float | be.ndarray) → float | be.ndarray[source]#

Predicts the extinction coefficient at a given wavelength.

abstractmethod 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, abbe)[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, abbe)[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, abbe)[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.