Create PSF from airy disk

esbo_etc/classes/psf/Airy.py

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+from typing import Union
+import numpy as np
+from astropy import units as u
+from .IPSF import IPSF
+from scipy.optimize import newton
+from scipy.special import j0, j1
+from ...lib.helpers import error
+
+
+class Airy(IPSF):
+    """
+    A class for modelling the PSF using an airy disk.
+    """
+
+    @u.quantity_input(wl="length", d_aperture="length")
+    def __init__(self, wl: u.Quantity, d_aperture: u.Quantity):
+        self.__wl = wl
+        self.__d_aperture = d_aperture
+
+    def calcReducedObservationAngle(self, contained_energy: Union[str, int, float, u.Quantity]) -> u.Quantity:
+        """
+        Calculate the reduced observation angle in lambda / d_ap for the given contained energy.
+
+        Parameters
+        ----------
+        contained_energy : Union[str, int, float, u.Quantity]
+            The percentage of energy to be contained within a circle with the diameter reduced observation angle.
+
+        Returns
+        -------
+        reduced_observation_angle: Quantity
+            The reduced observation angle in lambda / d_ap
+        """
+        # Calculate the reduced observation angle in lambda / D for the given encircled energy
+        if type(contained_energy) == str:
+            # Encircled energy is of type string
+            if contained_energy.lower() == "peak":
+                # For the peak value of the PSF, the observation angle becomes zero which leads to one exposed
+                # pixel later in the code
+                reduced_observation_angle = 0
+            elif contained_energy.lower() == "fwhm":
+                # Width of the FWHM of the airy disk
+                reduced_observation_angle = 1.028
+            elif contained_energy.lower() == "min":
+                # Width of the first minimum of the airy disk
+                reduced_observation_angle = 1.22 * 2
+            else:
+                # Try to parse the encircled energy to float
+                reduced_observation_angle = 0
+                try:
+                    contained_energy = float(contained_energy) / 100.0 * u.dimensionless_unscaled
+                    # Calculate the width numerically from the integral of the airy disk
+                    # See also https://en.wikipedia.org/wiki/Airy_disk#Mathematical_formulation
+                    reduced_observation_angle = 2 * newton(lambda x: 1 - j0(np.pi * x) ** 2 - j1(np.pi * x) ** 2 -
+                                                           contained_energy, 1, tol=1e-6)
+
+                except ValueError:
+                    error("Could not convert encircled energy to float.")
+        else:
+            # Calculate the width numerically from the integral of the airy disk
+            reduced_observation_angle = 2 * newton(lambda x: 1 - j0(np.pi * x) ** 2 - j1(np.pi * x) ** 2 -
+                                                   contained_energy.value, 1, tol=1e-6)
+        return reduced_observation_angle * u.dimensionless_unscaled
+
+    def mapToGrid(self, grid: np.ndarray) -> np.ndarray:
+        """
+        Map the integrated PSF values to a sensor grid.
+
+        Parameters
+        ----------
+        grid : ndarray
+            The grid to map the values to. The values will only be mapped onto entries with the value 1.
+
+        Returns
+        -------
+        grid : ndarray
+            The grid with the mapped values.
+        """
+        pass

tests/psf/test_Airy.py

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+from unittest import TestCase
+from esbo_etc.classes.psf.Airy import Airy
+import astropy.units as u
+
+
+class TestAiry(TestCase):
+    def setUp(self):
+        self.airy = Airy(4 * u.um, 0.5 * u.m)
+
+    def test_calc_reduced_observation_angle(self):
+        self.assertAlmostEqual(self.airy.calcReducedObservationAngle("peak").value, 0.0)
+        self.assertAlmostEqual(self.airy.calcReducedObservationAngle("fwhm").value, 1.028)
+        self.assertAlmostEqual(self.airy.calcReducedObservationAngle("min").value, 2.44)
+        self.assertAlmostEqual(self.airy.calcReducedObservationAngle("80").value, 1.7938842051009245)