Added optika.sensors.charge_diffusion() function, the CCD charge diffusion model given in Janesick (2001).

optika/sensors/__init__.py

@@ -4,6 +4,7 @@
 """
 
 from ._materials import (
+    charge_diffusion,
     energy_bandgap,
     energy_electron_hole,
     quantum_yield_ideal,
@@ -28,6 +29,7 @@
 )
 
 __all__ = [
+    "charge_diffusion",
     "energy_bandgap",
     "energy_electron_hole",
     "quantum_yield_ideal",

optika/sensors/_materials/__init__.py

@@ -1,3 +1,6 @@
+from ._diffusion import (
+    charge_diffusion,
+)
 from ._materials import (
     energy_bandgap,
     energy_electron_hole,
@@ -18,6 +21,7 @@
 from ._e2v_ccd_aia import E2VCCDAIAMaterial
 
 __all__ = [
+    "charge_diffusion",
     "energy_bandgap",
     "energy_electron_hole",
     "quantum_yield_ideal",

optika/sensors/_materials/_diffusion.py

@@ -0,0 +1,130 @@
+import astropy.units as u
+import numpy as np
+
+import named_arrays as na
+
+__all__ = [
+    "charge_diffusion",
+]
+
+
+def charge_diffusion(
+    absorption: u.Quantity | na.AbstractScalar,
+    thickness_implant: u.Quantity | na.AbstractScalar,
+    thickness_substrate: u.Quantity | na.AbstractScalar,
+    thickness_depletion: u.Quantity | na.AbstractScalar,
+) -> na.AbstractScalar:
+    r"""
+    The standard deviation of the charge diffusion in a backilluminated CCD
+    given by :cite:t:`Janesick2001`.
+
+    Parameters
+    ----------
+    absorption
+        The absorption coefficient of the light-sensitive layer for the
+        incident photon.
+    thickness_implant
+        The thickness of the partial-charge collection region of the imaging
+        sensor.
+    thickness_substrate
+        The thickness of the light-sensitive region of the imaging sensor.
+    thickness_depletion
+        The thickness of the depletion region of the imaging sensor.
+
+    Examples
+    --------
+
+    Plot the width of the charge diffusion kernel as a function of wavelength
+    and energy for the sensor parameters in :cite:t:`Heymes2020`.
+
+    .. jupyter-execute::
+
+        import matplotlib.pyplot as plt
+        import astropy.units as u
+        import astropy.visualization
+        import named_arrays as na
+        import optika
+
+        # Define a grid of wavelengths
+        wavelength = na.geomspace(1, 10000, axis="wavelength", num=1001) * u.AA
+
+        # Convert the grid to energies as well
+        energy = wavelength.to(u.eV, equivalencies=u.spectral())
+
+        # Load the optical properties of silicon
+        si = optika.chemicals.Chemical("Si")
+
+        # Retrieve the absorption coefficient of silicon
+        # for the given wavelenghts.
+        absorption = si.absorption(wavelength)
+
+        # Compute the charge diffusion
+        width_diffusion = optika.sensors.charge_diffusion(
+            absorption=absorption,
+            thickness_implant=40 * u.nm,
+            thickness_substrate=14 * u.um,
+            thickness_depletion=2.4 * u.um,
+        )
+
+        # Plot the charge diffusion as a function
+        # of wavelength and energy
+        with astropy.visualization.quantity_support():
+            fig, ax = plt.subplots()
+            ax2 = ax.twiny()
+            ax2.invert_xaxis()
+            na.plt.plot(
+                wavelength,
+                width_diffusion,
+                ax=ax,
+            )
+            na.plt.plot(
+                energy,
+                width_diffusion,
+                ax=ax2,
+                linestyle="None",
+            )
+            ax.set_xscale("log")
+            ax2.set_xscale("log")
+            ax.set_xlabel(f"wavelength ({ax.get_xlabel()})")
+            ax.set_ylabel(f"charge diffusion ({ax.get_ylabel()})")
+
+    Notes
+    -----
+
+    The standard deviation of the charge diffusion is given by
+    :cite:t:`Janesick2001` as
+
+    .. math::
+
+        \sigma_d = x_{ff} \left( 1 - \frac{L_A}{x_{ff}} \right)^{1/2}
+
+    where
+
+    .. math::
+
+        L_A &= \frac{\int_0^{x_s} x e^{-\alpha x} dx}{\int_0^{x_s} dx} \\
+            &= \frac{1 - (\alpha x_s + 1) e^{-\alpha x_s}}{\alpha^2 x_s}
+
+    is the average distance from the back surface at which to photon is absorbed,
+    :math:`\alpha` is the absorption coefficient of the light-sensitive layer,
+    :math:`x_s` is the total thickness of the light-sensitive layer,
+
+    .. math::
+
+        x_{ff} = x_s - x_p - x_d
+
+    is the thickness of the field-free region of the sensor,
+    :math:`x_p` is the thickness of the partial-charge collection region,
+    and :math:`x_d` is the thickness of the depletion region.
+    """
+    d = thickness_substrate
+
+    x_ff = d - thickness_implant - thickness_depletion
+
+    a = absorption
+
+    depth_avg = (1 - (a * d + 1) * np.exp(-a * d)) / (np.square(a) * d)
+
+    result = x_ff * np.sqrt(1 - depth_avg / x_ff)
+
+    return result

optika/sensors/_materials/_diffusion_test.py

@@ -0,0 +1,44 @@
+import pytest
+import astropy.units as u
+import named_arrays as na
+import optika
+
+
+@pytest.mark.parametrize(
+    argnames="absorption",
+    argvalues=[
+        1 / u.um,
+    ],
+)
+@pytest.mark.parametrize(
+    argnames="thickness_implant",
+    argvalues=[
+        100 * u.nm,
+    ],
+)
+@pytest.mark.parametrize(
+    argnames="thickness_substrate",
+    argvalues=[
+        15 * u.um,
+    ],
+)
+@pytest.mark.parametrize(
+    argnames="thickness_depletion",
+    argvalues=[
+        5 * u.um,
+    ],
+)
+def test_charge_diffusion(
+    absorption: u.Quantity | na.AbstractScalar,
+    thickness_implant: u.Quantity | na.AbstractScalar,
+    thickness_substrate: u.Quantity | na.AbstractScalar,
+    thickness_depletion: u.Quantity | na.AbstractScalar,
+):
+    result = optika.sensors.charge_diffusion(
+        absorption=absorption,
+        thickness_implant=thickness_implant,
+        thickness_substrate=thickness_substrate,
+        thickness_depletion=thickness_depletion,
+    )
+
+    assert result > 0 * u.um