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KelSolaar/barten.py

Created Jan 31, 2019
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Contrast Sensitivity Function - Barten (1999)
# https://pure.tue.nl/ws/files/1613279/9901043.pdf
#http://car.france3.mars.free.fr/Formation%20INA%20HD/HDTV/HDTV%20%202007%20v35/SMPTE%20normes%20et%20confs/Contrastm.pdf
# %%
from __future__ import division
import matplotlib.pyplot as plt
import numpy as np
from colour.utilities import as_float_array
from colour.plotting import colour_style, plot_single_function
colour_style()
def photon_conversion_factor():
"""
Mmmh, tasty stuff to be done.
"""
pass
def optical_MTF_Barten1999(u, sigma=0.5):
"""
Parameters
----------
u : numeric or array_like
Spatial frequency :math:`u`.
sigma : numeric or array_like, optional
Standard deviation :math:`\sigma` of the line-spread function resulting
from the convolution of the different elements of the convolution
process.
"""
u = as_float_array(u)
sigma = as_float_array(sigma)
return np.exp(-2 * np.pi**2 * sigma**2 * u**2)
def pupil_diameter_Barten1999(L, X_0):
"""
Parameters
----------
L : numeric or array_like
Average luminance :math:`L` in :math:`cd/m^2`.
X_0 : numeric or array_like
Angular size of the object :math:`X_0` in degrees.
"""
return 5 - 3 * np.tanh(0.4 * np.log(L * X_0**2 / 40**2))
def sigma_Barten1999(sigma_0=0.5 / 60, C_ab=0.08 / 60, d=2.5):
"""
Parameters
----------
sigma_0 : numeric or array_like, optional
Constant :math:`\sigma_{0}` in degrees.
C_ab : numeric or array_like, optional
Spherical aberration of the eye :math:`C_{ab}` in degrees.
d : numeric or array_like, optional
Pupil diameter :math:`d` in millimeters.
Returns
-------
ndarray
Standard deviation :math:`\sigma` of the line-spread function resulting
from the convolution of the different elements of the convolution
process.
"""
sigma_0 = as_float_array(sigma_0)
C_ab = as_float_array(C_ab)
return np.sqrt((sigma_0)**2 + (C_ab * d)**2)
def retinal_illuminance_Barten1999(L, d=2.5, stiles_crawford_correction=True):
"""
Parameters
----------
d : numeric or array_like
Pupil diameter :math:`d` in millimeters.
L : numeric or array_like
Average luminance :math:`L` in :math:`cd/m^2`.
Returns
-------
ndarray
Retinal illuminance :math:`E` in Trolands.
Notes
-----
- This definition is for use with photopic viewing conditions and thus
corrects for the Stiles-Crawford effect by default, i.e. directional
sensitivity of the cone cells with lower response of cone cells
receiving light from the edge of the pupil.
"""
d = as_float_array(d)
L = as_float_array(L)
E = (np.pi * d**2) / 4 * L
if stiles_crawford_correction:
E *= (1 - (d / 9.7)**2 + (d / 12.4)**4)
return E
# %%
def function_contrast_sensitivity_Barten1999(u,
sigma=sigma_Barten1999(
0.5 / 60, 0.08 / 60, 3.0),
k=3.0,
T=0.1,
X_0=60,
X_max=12,
N_max=15,
n=0.03,
p=1.2 * 10**6,
E=retinal_illuminance_Barten1999(
20, 3),
phi_0=3 * 10**-8,
u_0=7):
"""
Parameters
----------
u : numeric
Spatial frequency :math:`u`.
sigma : numeric or array_like, optional
Standard deviation :math:`\sigma` of the line-spread function resulting
from the convolution of the different elements of the convolution
process.
k : numeric or array_like, optional
Signal-to-noise (SNR) ratio :math:`k`.
T : numeric or array_like, optional
Integration time :math:`T` in seconds of the eye .
X_0 : numeric or array_like, optional
Angular size :math:`X_0` in degrees of the object.
X_max : numeric or array_like, optional
Maximum angular size :math:`X_{max}` in degrees of the integration
area.
N_max : numeric or array_like, optional
Maximum number of cycles :math:`N_{max}` over which the eye can
integrate the information.
n : numeric or array_like, optional
Quantum efficiency of the eye :math:`n`.
p : numeric or array_like, optional
Photon conversion factor :math:`p` in
:math:`photons\div seconds\div degrees^2\div Trollands` that
depends on the light source.
E : numeric or array_like, optional
Retinal illuminance :math:`E` in Troland.
phi_0 : numeric or array_like, optional
Spectral density :math:`\phi_0` in :math:`seconds degrees^2` of the
neural noise.
u_0 : numeric or array_like, optional
Spatial frequency :math:`u_0` in :math:`cycles\div degrees` above which
the lateral inhibition ceases
Returns
-------
ndarray
Contrast sensitivity function :math:`S`.
Notes
-----
- This formula holds for the situation that the object dimensions in x
and y directions are equal. For non-equal dimensions, the factor
between the brackets that contains the object size has to be replaced
by :math:`1 / XY` where :math`X` and :math`Y` are given by ...
respectively.
"""
u = as_float_array(u)
k = as_float_array(k)
T = as_float_array(T)
X_0 = as_float_array(X_0)
X_max = as_float_array(X_max)
N_max = as_float_array(N_max)
n = as_float_array(n)
p = as_float_array(p)
E = as_float_array(E)
phi_0 = as_float_array(phi_0)
u_0 = as_float_array(u_0)
M_opt = optical_MTF_Barten1999(u, sigma)
S = (M_opt / k) / np.sqrt(
2 / T * (1 / X_0**2 + 1 / X_max**2 + u**2 / N_max**2) *
(1 / (n * p * E) + phi_0 / (1 - np.exp(-(u / u_0)**2))))
return S
# %%
L = np.linspace(0.01, 100, 10000)
# L = 500
X_0 = 60
d = pupil_diameter_Barten1999(L, X_0)
# d = 5 - 3 * np.tanh(0.4 * np.log(L))
sigma = sigma_Barten1999(0.5 / 60, 0.08 / 60, d)
E = retinal_illuminance_Barten1999(L, d, True)
# E = 14.7 * L**0.83
# u = np.linspace(0.1, 100, 10000)
u = X_0 / 15
y = lambda x: 1 / function_contrast_sensitivity_Barten1999(
u=u,
sigma=sigma,
k=3.0,
T=0.1,
X_0=X_0,
X_max=12,
N_max=15,
n=0.03,
p=1.2274*10**6,
E=E,
phi_0=3*10**-8,
u_0=7) * 2 * (1/ 1.27)
# plt.semilogx(u, optical_MTF_Barten1999(u, sigma))
# plt.semilogx(u, np.exp(-0.0016 * u**2 * (1 + 100 / L)**0.08))
# plt.show()
plot_single_function(
y,
samples=L,
log_x=10,
# log_y=10,
bounding_box=[0.1, 100, 0.001, 0.03],
**{'axes.grid.which': 'both'})
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@KelSolaar KelSolaar commented Jan 31, 2019

barten

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