# -*- coding: utf-8 -*-
################################ Begin license #################################
# Copyright (C) Laboratory of Imaging technologies,
# Faculty of Electrical Engineering,
# University of Ljubljana.
#
# This file is part of PyXOpto.
#
# PyXOpto is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# PyXOpto is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with PyXOpto. If not, see <https://www.gnu.org/licenses/>.
################################# End license ##################################
import numpy as np
from .base import Scale, Normalize, Model
def _ri(params: np.ndarray, pp: Scale or Normalize,
wavelengths: np.ndarray, num_terms: int) -> np.ndarray:
'''
Compute the refractive index for the given model parameters
and wavelengths of light using the Sellmeier equation.
Parameters
----------
params: np.ndarray
Model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor.
wavelengths: np.ndarray
Wavelengths of light (m).
num_terms: int
Number of terms.
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
wn = pp(wavelengths)
inv_wn2 = 1.0/(wn)**2
result = None
for term in range(num_terms):
if term == 0:
result = params[2*term]/(1.0 - params[2*term + 1]*inv_wn2)
else:
result += params[2*term]/(1.0 - params[2*term + 1]*inv_wn2)
result += 1.0
return np.sqrt(result)
def _ri_ex(params: np.ndarray, pp: Scale or Normalize,
wavelengths: np.ndarray, num_terms: int) -> np.ndarray:
'''
Compute the refractive index for the given model parameters
and wavelengths of light using the extended Sellmeier equation.
Parameters
----------
params: np.ndarray
Model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor.
wavelengths: np.ndarray
Wavelengths of light (m).
num_terms: int
Number of terms.
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
wn = pp(wavelengths)
inv_wn2 = 1.0/(wn)**2
result = None
for term in range(num_terms):
if term == 0:
result = params[2*term + 1]/(1.0 - params[2*term + 2]*inv_wn2)
else:
result += params[2*term + 1]/(1.0 - params[2*term + 2]*inv_wn2)
result += params[0]
return np.sqrt(result)
[docs]class Sellmeier_1(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
One term Sellmeier model of the refractive index.
:math:`n^{2} = 1 + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = 1.0 + {:.8e}/(1.0 - {:.8e}/wn**2'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [0.0]*2
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri(params, self.pp, wavelengths, 1)
[docs]class SellmeierEx_1(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Extended one term Sellmeier model of the refractive index.
:math:`n^{2} = A + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = {:.8e} + {:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [1.0] + [0.0]*2
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri_ex(params, self.pp, wavelengths, 1)
[docs]class Sellmeier_2(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Two term Sellmeier model of the refractive index.
:math:`n^{2} = 1 + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = 1.0 + ' \
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [0.0]*4
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri(params, self.pp, wavelengths, 2)
[docs]class SellmeierEx_2(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Extended two term Sellmeier model of the refractive index.
:math:`n^{2} = A + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = {:.8e} + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [1.0] + [0.0]*4
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri_ex(params, self.pp, wavelengths, 2)
[docs]class Sellmeier_3(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Three term Sellmeier model of the refractive index.
:math:`n^{2} = 1 + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = 1.0 + ' \
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [0.0]*6
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri(params, self.pp, wavelengths, 3)
[docs]class SellmeierEx_3(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Extended three term Sellmeier model of the refractive index.
:math:`n^{2} = A + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = {:.8e} + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [1.0] + [0.0]*6
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri_ex(params, self.pp, wavelengths, 3)
[docs]class Sellmeier_4(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Four term Sellmeier model of the refractive index.
:math:`n^{2} = 1 + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3} + B_{4}\\lambda^{2}/(\\lambda^{2} - C_{4})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = 1.0 + ' \
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [0.0]*8
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri(params, self.pp, wavelengths, 4)
[docs]class SellmeierEx_4(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Four term Sellmeier model of the refractive index.
:math:`n^{2} = A + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3} + B_{4}\\lambda^{2}/(\\lambda^{2} - C_{4})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = {:.8e} + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [1.0] + [0.0]*8
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri_ex(params, self.pp, wavelengths, 4)
[docs]class Sellmeier_5(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Five term Sellmeier model of the refractive index.
:math:`n^{2} = 1 + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3} + B_{4}\\lambda^{2}/(\\lambda^{2} - C_{4} + B_{5}\\lambda^{2}/(\\lambda^{2} - C_{5})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = 1.0 + ' \
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [0.0]*10
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri(params, self.pp, wavelengths, 5)
[docs]class SellmeierEx_5(Model):
def __init__(self, params, pp: Scale or Normalize = None, **kwargs):
'''
Five term Sellmeier model of the refractive index.
:math:`n^{2} = A + B_{1}\\lambda^{2}/(\\lambda^2 - C_{1}) + B_{2}\\lambda^{2}/(\\lambda^{2} - C_{2}) + B_{3}\\lambda^{2}/(\\lambda^{2} - C_{3} + B_{4}\\lambda^{2}/(\\lambda^{2} - C_{4} + B_{5}\\lambda^{2}/(\\lambda^{2} - C_{5})`
Parameters
----------
params: np.ndarray
Default model parameters.
pp: xopto.materials.ri.util.model.base.Scale or xopto.materials.ri.util.model.base.Normalize
Wavelength preprocessor instance.
kwargs: dict
Parameters passed to the baseclass.
'''
formatstr = 'n*n = {:.8e} + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2) + '\
'{:.8e}/(1.0 - {:.8e}/wn**2)'
super().__init__(formatstr, params, pp, **kwargs)
[docs] def guess(self, wavelengths: np.ndarray, n: np.ndarray) -> list:
'''
Returns an initial guess of the model parameters for optimization/fit.
Parameters
----------
wavelengths: np.ndarray
The wavelengths of light at which the values of refractive index
are defined.
n: np.ndarray
The values of refractive index at the given wavelengths of light.
Returns
-------
params0: np.ndarray
Initial guess for the values of the model parameters
'''
return [1.0] + [0.0]*10
[docs] def ri(self, params: np.ndarray, wavelengths: np.ndarray):
'''
Compute the refractive index for the given model parameters
and wavelengths of light.
Parameters
----------
params: np.ndarray
Model parameters.
wavelengths: np.ndarray
Wavelengths of light (m).
Returns
-------
n: np.ndarray
Refractive index estimated for the given model parameters and
at the given wavelengths of light.
'''
return _ri_ex(params, self.pp, wavelengths, 5)