Glass#

class optika.materials.Glass(b1=0, b2=0, b3=0, c1=<Quantity 0. um2>, c2=<Quantity 0. um2>, c3=<Quantity 0. um2>)[source]#

Bases: AbstractMaterial

A transparent, refractive material whose index of refraction follows the three-term Sellmeier dispersion equation,

\[n^2(\lambda) = 1 + \frac{B_1 \lambda^2}{\lambda^2 - C_1} + \frac{B_2 \lambda^2}{\lambda^2 - C_2} + \frac{B_3 \lambda^2}{\lambda^2 - C_3},\]

where \(\lambda\) is the vacuum wavelength of the light, and \(B_i\) (dimensionless) and \(C_i\) (square length) are the Sellmeier coefficients of the glass.

Unlike Vacuum and Mirror, this material changes the index of refraction of a transmitted ray, so a curved surface made of it has optical power and bends light according to Snell’s law.

Examples

Plot the index of refraction of N-BK7 and F2 glass across the visible spectrum.

import matplotlib.pyplot as plt
import astropy.units as u
import named_arrays as na
import optika

wavelength = na.linspace(380, 750, axis="wavelength", num=101) * u.nm

glasses = {
    "N-BK7": optika.materials.Glass.n_bk7(),
    "F2": optika.materials.Glass.f2(),
}

fig, ax = plt.subplots(constrained_layout=True)
for name, glass in glasses.items():
    rays = optika.rays.RayVectorArray(wavelength=wavelength)
    na.plt.plot(
        wavelength,
        glass.index_refraction(rays),
        ax=ax,
        label=name,
    )
ax.set_xlabel(f"wavelength ({wavelength.unit:latex_inline})");
ax.set_ylabel("index of refraction");
ax.legend();

../_images/optika.materials.Glass_0_0.png

Attributes

`b1`	The first dimensionless Sellmeier coefficient.
`b2`	The second dimensionless Sellmeier coefficient.
`b3`	The third dimensionless Sellmeier coefficient.
`c1`	The first Sellmeier resonance (units of square length).
`c2`	The second Sellmeier resonance (units of square length).
`c3`	The third Sellmeier resonance (units of square length).
`is_mirror`	flag controlling whether this material reflects or transmits light
`shape`	The array shape of this object.
`transformation`	the coordinate transformation between the global coordinate system and this object's local coordinate system

Methods

`__init__`([b1, b2, b3, c1, c2, c3])
`attenuation`(rays)	the attenuation coefficient of the given rays
`efficiency`(rays, normal)	The fraction of light that passes through the interface.
`f2`()	SCHOTT F2 flint glass (\(n_d \approx 1.6200\), \(V_d \approx 36.4\)).
`index_refraction`(rays)	the index of refraction of this material for the given input rays
`n_bk7`()	SCHOTT N-BK7 borosilicate crown glass (\(n_d \approx 1.5168\), \(V_d \approx 64.2\)).
`to_string`([prefix])	Public-facing version of the `__repr__` method that allows for defining a prefix string, which can be used to calculate how much whitespace to add to the beginning of each line of the result.

Inheritance Diagram

Parameters:

classmethod f2()[source]#

SCHOTT F2 flint glass (\(n_d \approx 1.6200\), \(V_d \approx 36.4\)).

Return type:: Glass

classmethod n_bk7()[source]#

SCHOTT N-BK7 borosilicate crown glass (\(n_d \approx 1.5168\), \(V_d \approx 64.2\)).

Return type:: Glass

attenuation(rays)[source]#

the attenuation coefficient of the given rays

Parameters:: rays (RayVectorArray) – input rays to calculate the attenuation coefficient for
Return type:: int | float | complex | ndarray | Quantity | AbstractScalar

efficiency(rays, normal)[source]#

The fraction of light that passes through the interface.

Parameters:

rays (RayVectorArray) – the input rays to calculate the efficiency for
normal (AbstractCartesian3dVectorArray) – the vector perpendicular to the optical surface

Return type:

index_refraction(rays)[source]#

the index of refraction of this material for the given input rays

Parameters:: rays (RayVectorArray) – input rays used to evaluate the index of refraction
Return type:: int | float | complex | ndarray | Quantity | AbstractScalar

to_string(prefix=None)#

Public-facing version of the __repr__ method that allows for defining a prefix string, which can be used to calculate how much whitespace to add to the beginning of each line of the result.

Parameters:: prefix (None | str) – an optional string, the length of which is used to calculate how much whitespace to add to the result.
Return type:: str

b1: float | AbstractScalar = 0#: The first dimensionless Sellmeier coefficient.

b2: float | AbstractScalar = 0#: The second dimensionless Sellmeier coefficient.

b3: float | AbstractScalar = 0#: The third dimensionless Sellmeier coefficient.

c1: Quantity | AbstractScalar = <Quantity 0. um2>#: The first Sellmeier resonance (units of square length).

c2: Quantity | AbstractScalar = <Quantity 0. um2>#: The second Sellmeier resonance (units of square length).

c3: Quantity | AbstractScalar = <Quantity 0. um2>#: The third Sellmeier resonance (units of square length).

property is_mirror: bool#: flag controlling whether this material reflects or transmits light

property shape: dict[str, int]#: The array shape of this object.

property transformation: None#: the coordinate transformation between the global coordinate system and this object’s local coordinate system