from .IPSF import IPSF
from ...lib.helpers import rasterizeCircle
from ..sensor.PixelMask import PixelMask
from ...lib.logger import logger
from abc import abstractmethod
import numpy as np
import astropy.units as u
from typing import Union
from scipy.optimize import bisect
from scipy.signal import fftconvolve
from scipy.interpolate import interp2d
[docs]class AGriddedPSF(IPSF):
"""
A class for modelling the PSF from a two dimensional grid
"""
@abstractmethod
@u.quantity_input(wl="length", d_aperture="length", pixel_size="length", grid_delta="length")
def __init__(self, psf: np.ndarray, f_number: float, wl: u.Quantity, d_aperture: u.Quantity, osf: float,
pixel_size: u.Quantity, grid_delta: u.Quantity, center_point: list):
"""
Initialize a new PSF from a 2D grid.
Parameters
----------
psf : ndarray
2D numpy array containing the parsed PSF values. The zero-point is in the top left corner.
f_number : float
The working focal number of the optical system
wl : Quantity
The central wavelength which is used for calculating the PSF
d_aperture : Quantity
The diameter of the telescope's aperture.
osf : float
The oversampling factor to be used for oversampling the PSF with regards to the pixel size.
pixel_size : Quantity
The size of a pixel as length-quantity.
grid_delta : Quantity
Size of a grid element as length-Quantity with a value for each grid dimension.
center_point : list
The center point coordinates as list with the zero point in the upper left corner.
"""
# Store parameters
self._f_number = f_number
self._wl = wl
self._d_aperture = d_aperture
self._osf = osf
self._pixel_size = pixel_size
self._psf = psf
self._grid_delta = grid_delta
self._center_point = center_point
self._center_point_os = None
self._psf_os = None
self._psf_osf = None
# @u.quantity_input(jitter_sigma=u.arcsec)
[docs] def calcReducedObservationAngle(self, contained_energy: Union[str, int, float, u.Quantity],
jitter_sigma: u.Quantity = None, obstruction: float = 0.0) -> 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.
jitter_sigma : Quantity
Sigma of the telescope's jitter in arcsec
obstruction : float
The central obstruction as ratio A_ob / A_ap
Returns
-------
reduced_observation_angle: Quantity
The reduced observation angle in lambda / d_ap
"""
# Parse the contained energy
if type(contained_energy) == str:
try:
contained_energy = float(contained_energy) / 100.0 * u.dimensionless_unscaled
except ValueError:
logger.error("Could not convert encircled energy to float.")
elif type(contained_energy) in [int, float]:
contained_energy = contained_energy / 100 * u.dimensionless_unscaled
center_point, psf, psf_osf = self._calcPSF(jitter_sigma)
# Calculate the maximum possible radius for the circle containing the photometric aperture
r_max = max(np.sqrt(center_point[0] ** 2 + center_point[1] ** 2),
np.sqrt((psf.shape[0] - center_point[0]) ** 2 + center_point[1] ** 2),
np.sqrt(center_point[0] ** 2 + (psf.shape[1] - center_point[1]) ** 2),
np.sqrt((psf.shape[0] - center_point[0]) ** 2 + (psf.shape[1] - center_point[1]) ** 2))
# Calculate the total contained energy of the PSF
total = np.sum(psf)
# Iterate the optimal radius for the contained energy
r = bisect(lambda r_c: contained_energy.value - np.sum(
psf * rasterizeCircle(np.zeros((psf.shape[0], psf.shape[1])), r_c, center_point[0],
center_point[1])) / total, 0, r_max, xtol=1e-1)
# Calculate the reduced observation angle in lambda / d_ap
# noinspection PyTypeChecker
reduced_observation_angle = r / psf_osf * self._grid_delta[0] / (
self._f_number * self._d_aperture) * self._d_aperture / self._wl
return 2 * reduced_observation_angle * u.dimensionless_unscaled
def _calcPSF(self, jitter_sigma: u.Quantity = None):
"""
Calculate the PSF from the grid. This includes oversampling the PSF and convolving with the
jitter-gaussian.
Parameters
----------
jitter_sigma : Quantity
Sigma of the telescope's jitter in arcsec.
Returns
-------
center_point : ndarray
The indices of the PSF's center point on the grid.
psf : ndarray
The PSF.
psf_osf : float
The oversampling factor of the returned PSF.
"""
# Calculate the psf oversampling factor for the PSF based on the current resolution of the PSF
psf_osf = np.ceil(max(self._grid_delta) / (self._pixel_size / self._osf)).value
if psf_osf == 1.0:
# No oversampling is necessary
psf = self._psf
center_point = self._center_point
else:
# Oversampling is necessary, oversample the PSF and calculate the new center point.
f = interp2d(x=np.arange(self._psf.shape[1]) - self._center_point[1],
y=np.arange(self._psf.shape[0]) - self._center_point[0], z=self._psf,
kind='cubic', copy=False, bounds_error=False, fill_value=None)
center_point = [(x + 0.5) * psf_osf - 0.5 for x in self._center_point]
psf = f((np.arange(self._psf.shape[1] * psf_osf) - center_point[1]) / psf_osf,
(np.arange(self._psf.shape[0] * psf_osf) - center_point[0]) / psf_osf)
if jitter_sigma is not None:
# Convert angular jitter to jitter on focal plane
jitter_sigma_um = (jitter_sigma.to(u.rad) * self._f_number * self._d_aperture / u.rad).to(u.um)
# Jitter is enabled. Calculate the corresponding gaussian bell and convolve it with the PSF
if min(self._grid_delta) / psf_osf < 6 * jitter_sigma_um:
# 6-sigma interval of the gaussian bell is larger than the grid width
# Calculate the necessary grid length for the 6-sigma interval of the gaussian bell
jitter_grid_length = np.ceil(6 * jitter_sigma_um / (min(self._grid_delta) / psf_osf)).value
# Make sure, the grid size is odd in order to have a defined kernel center
jitter_grid_length = int(jitter_grid_length if jitter_grid_length % 2 == 1 else jitter_grid_length + 1)
# Create a meshgrid containing the x and y coordinates of each point within the first quadrant of the
# gaussian kernel
xv, yv = np.meshgrid(range(-int((jitter_grid_length - 1) / 2), 1),
range(-int((jitter_grid_length - 1) / 2), 1))
# Calculate the gaussian kernel in the first quadrant
kernel = 1 / (2 * np.pi * jitter_sigma_um.value ** 2) * np.exp(
-((xv * min(self._grid_delta.value) / psf_osf) ** 2 +
(yv * min(self._grid_delta.value) / psf_osf) ** 2) / (2 * jitter_sigma_um.value ** 2))
# Mirror the kernel from the first quadrant to all other quadrants
kernel = np.concatenate((kernel, np.flip(kernel, axis=1)[:, 1:]), axis=1)
kernel = np.concatenate((kernel, np.flip(kernel, axis=0)[1:, :]), axis=0)
# Normalize kernel
kernel = kernel / np.sum(kernel)
# Convolve PSF with gaussian kernel
psf = fftconvolve(psf, kernel, mode="full")
# Calculate new center point
center_point = [x + int((jitter_grid_length - 1) / 2) for x in center_point]
# Save the values as object attribute
self._center_point_os = center_point
self._psf_os = psf
self._psf_osf = psf_osf
return center_point, psf, psf_osf
[docs] def mapToPixelMask(self, mask: PixelMask, jitter_sigma: u.Quantity = None, obstruction: float = 0.0) -> PixelMask:
"""
Map the integrated PSF values to a sensor grid.
Parameters
----------
obstruction
mask : PixelMask
The pixel mask to map the values to. The values will only be mapped onto entries with the value 1.
jitter_sigma : Quantity
Sigma of the telescope's jitter in arcsec
Returns
-------
mask : PixelMask
The pixel mask with the integrated PSF values mapped onto each pixel.
"""
# Calculate the indices of all non-zero elements of the mask
y_ind, x_ind = np.nonzero(mask)
# Extract a rectangle containing all non-zero values of the mask
mask_red = mask[y_ind.min():(y_ind.max() + 1), x_ind.min():(x_ind.max() + 1)]
# Calculate the new PSF-center indices of the reduced mask
psf_center_ind = [mask.psf_center_ind[0] - y_ind.min(), mask.psf_center_ind[1] - x_ind.min()]
# Oversample the reduced mask
mask_red_os = self._rebin(mask_red, self._osf).view(PixelMask)
# Calculate the new PSF-center indices of the reduced mask
psf_center_ind = [(x + 0.5) * self._osf - 0.5 for x in psf_center_ind]
# Get PSF values or calculate them if not available
if self._psf_os is not None and self._center_point_os is not None and self._psf_osf is not None:
center_point = self._center_point_os
psf = self._psf_os
psf_osf = self._psf_osf
else:
center_point, psf, psf_osf = self._calcPSF(jitter_sigma)
# Calculate the coordinates of each PSF value in microns
x = (np.arange(psf.shape[1]) - center_point[1]) * self._grid_delta[1].to(u.um).value / psf_osf
y = (np.arange(psf.shape[0]) - center_point[0]) * self._grid_delta[0].to(u.um).value / psf_osf
# Initialize a two-dimensional cubic interpolation function for the PSF
psf_interp = interp2d(x=x, y=y, z=psf, kind='cubic', copy=False, bounds_error=False, fill_value=None)
# Calculate the values of the PSF for all elements of the reduced mask
res = psf_interp((np.arange(mask_red_os.shape[1]) - psf_center_ind[1]) * mask_red_os.pixel_size.to(u.um).value,
(np.arange(mask_red_os.shape[0]) - psf_center_ind[0]) * mask_red_os.pixel_size.to(u.um).value)
# Bin the oversampled reduced mask to the original resolution and multiply with the reduced mask to select only
# the relevant values
res = mask_red * self._rebin(res, 1 / self._osf)
# Integrate the reduced mask and divide by the indefinite integral to get relative intensities
res = res * mask_red_os.pixel_size.to(u.um).value ** 2 / (
psf.sum() * (self._grid_delta[0].to(u.um).value / psf_osf) ** 2)
# reintegrate the reduced mask into the complete mask
mask[y_ind.min():(y_ind.max() + 1), x_ind.min():(x_ind.max() + 1)] = res
return mask