from astropy import units as u from .ASensor import ASensor from ..IRadiant import IRadiant from ..Entry import Entry import numpy as np from typing import Union, Tuple from ..psf.Airy import Airy from ..psf.Zemax import Zemax from ..SpectralQty import SpectralQty from .PixelMask import PixelMask import astropy.constants as const from logging import info, warning class Imager(ASensor): """ A class for modelling a Image-sensor """ __encircled_energy: Union[str, float, u.Quantity] @u.quantity_input(pixel_size="length", read_noise=u.electron ** 0.5 / u.pix, center_offset=u.pix, dark_current=u.electron / u.pix / u.second, well_capacity=u.electron, pixel_geometry=u.pix) def __init__(self, parent: IRadiant, quantum_efficiency: Union[str, u.Quantity], pixel_geometry: u.Quantity, pixel_size: u.Quantity, read_noise: u.Quantity, dark_current: u.Quantity, well_capacity: u.Quantity, f_number: Union[int, float], common_conf: Entry, center_offset: u.Quantity = np.array([0, 0]) << u.nm, shape: str = None, contained_energy: Union[str, int, float] = "FWHM", contained_pixels: u.Quantity = None): """ Initialize a new Image-sensor model. Initialize a new Image-sensor model. Parameters ---------- parent : IRadiant The parent element of the optical component from which the electromagnetic radiation is received. quantum_efficiency : Union[str, u.Quantity] The quantum efficiency of the detector. This can be either the path to the file containing the values of the spectral quantum efficiency or the overall quantum efficiency as int, float or astropy quantity. pixel_geometry : u.Quantity The geometry of the pixel array as Quantity in pixels with two entries: [number of pixels in x-direction, number of pixels in y-direction] pixel_size : length-Quantity The edge length of a pixel (assumed to be square). read_noise : Quantity The RMS-read noise per detector pixel in electrons^0.5 / pixel. dark_current : Quantity The dark current of a detector pixel in electrons / (pixels * s). well_capacity : Quantity The pixel's well capacity in electrons. f_number : Union[int, float] The f-number of the optical system. common_conf : Entry The common-Entry of the configuration. center_offset : u.Quantity The offset of the PSF-center relative to the center of the detector array as length-quantity with two entries: [offset in x-direction, offset in y-direction] shape : str The shape of the photometric aperture. Can be either square or circle contained_energy : Union[str, int, float] The energy contained within the photometric aperture. contained_pixels : u.Quantity The pixels contained within the photometric aperture. """ super().__init__(parent) if type(quantum_efficiency == str): self.__quantum_efficiency = SpectralQty.fromFile(quantum_efficiency, u.nm, u.electron / u.photon) elif type(quantum_efficiency) == u.Quantity: self.__quantum_efficiency = quantum_efficiency self.__pixel_geometry = pixel_geometry self.__array = np.zeros((int(pixel_geometry.value[0]), int(pixel_geometry.value[1]))) self.__pixel_size = pixel_size self.__read_noise = read_noise self.__dark_current = dark_current self.__well_capacity = well_capacity self.__f_number = f_number self.__center_offset = center_offset self.__shape = shape self.__contained_energy = contained_energy self.__contained_pixels = contained_pixels self.__common_conf = common_conf # Calculate central wavelength self.__central_wl = self.__common_conf.wl_min() + ( self.__common_conf.wl_max() - self.__common_conf.wl_min()) / 2 # Parse PSF if hasattr(common_conf, "psf") and common_conf.psf().lower() == "airy": # Use an airy disk as PSF self.__psf = Airy(self.__f_number, self.__central_wl, common_conf.d_aperture(), common_conf.psf.osf, pixel_size) else: # Read PSF from Zemax file self.__psf = Zemax(common_conf.psf(), self.__f_number, self.__central_wl, common_conf.d_aperture(), common_conf.psf.osf, pixel_size) @u.quantity_input(exp_time="time") def getSNR(self, exp_time: u.Quantity) -> u.dimensionless_unscaled: """ Calculate the signal to background ratio (SNR) for the given exposure time using the CCD-equation. Parameters ---------- exp_time : time-Quantity The exposure time to calculate the SNR for. Returns ------- snr : Quantity The calculated SNR as dimensionless quantity """ # Calculate the electron currents signal_current, background_current, read_noise, dark_current = self.__exposePixels() # Calculate the number of collected electrons signal = signal_current * exp_time background = background_current * exp_time dark = dark_current * exp_time return self.__calcSNR(signal, background, read_noise, dark) @u.quantity_input(snr=u.dimensionless_unscaled) def getExpTime(self, snr: u.Quantity) -> u.s: """ Calculate the necessary exposure time in order to achieve the given SNR. Parameters ---------- snr : Quantity The SNR for which the necessary exposure time shall be calculated as dimensionless quantity. Returns ------- exp_time : Quantity The necessary exposure time in seconds. """ # Calculate the electron currents signal_current, background_current, read_noise, dark_current = self.__exposePixels() # Calculate the electron currents for all pixels signal_current_tot = signal_current.sum() background_current_tot = background_current.sum() read_noise_tot = read_noise.sum() dark_current_tot = dark_current.sum() # Fix the physical units of the SNR snr = snr * u.electron**0.5 # Calculate the ratio of the background- and dark-current to the signal current as auxiliary variable current_ratio = (background_current_tot + dark_current_tot) / signal_current_tot # Calculate the necessary exposure time as inverse of the CCD-equation exp_time = snr ** 2 * ( 1 + current_ratio + np.sqrt((1 + current_ratio) ** 2 + 4 * read_noise_tot ** 2 / snr ** 2)) / ( 2 * signal_current_tot) # Calculate the SNR in order to check for overexposed pixels self.__calcSNR(signal_current * exp_time, background_current * exp_time, read_noise, dark_current * exp_time) return exp_time @u.quantity_input(exp_time="time", snr=u.dimensionless_unscaled, target_brightness=u.mag) def getSensitivity(self, exp_time: u.Quantity, snr: u.Quantity, target_brightness: u.Quantity) -> u.mag: """ Calculate the sensitivity of the telescope detector combination. Parameters ---------- exp_time : Quantity The exposure time in seconds. snr : Quantity The SNR for which the sensitivity time shall be calculated. target_brightness : Quantity The target brightness in magnitudes. Returns ------- sensitivity: Quantity The sensitivity as limiting apparent star magnitude in mag. """ # Calculate the electron currents signal_current, background_current, read_noise, dark_current = self.__exposePixels() # Fix the physical units of the SNR snr = snr * u.electron ** 0.5 signal_current_lim = snr * (snr + np.sqrt( snr ** 2 + 4 * (exp_time * (background_current.sum() + dark_current.sum()) + (read_noise ** 2).sum()))) / ( 2 * exp_time) return target_brightness - 2.5 * np.log10(signal_current_lim / signal_current.sum()) * u.mag @u.quantity_input(signal=u.electron, background=u.electron, read_noise=u.electron ** 0.5, dark=u.electron) def __calcSNR(self, signal: u.Quantity, background: u.Quantity, read_noise: u.Quantity, dark: u.Quantity) -> u.dimensionless_unscaled: """ Calculate the signal to noise ratio (SNR) of the given electron counts. Parameters ---------- signal : Quantity The collected electrons from the target in electrons. background : Quantity The collected electrons from the background in electrons. read_noise : Quantity The read noise in electrons. dark : Quantity The electrons from the dark current in electrons. Returns ------- snr : Quantity The signal to noise ration as dimensionless quantity """ # Calculate the total collected electrons per pixel total = signal + background + dark # Check for overexposed pixels overexposed = total > self.__well_capacity if np.any(overexposed): # Show a warning for the overexposed pixels warning(str(np.count_nonzero(overexposed)) + " pixels are overexposed.") info("Collected electrons from target: %1.2e electrons" % signal.sum().value) info("Collected electrons from background: %1.2e electrons" % background.sum().value) info("Electrons from dark current: %1.2e electrons" % dark.sum().value) info("Read noise: %1.2e electrons" % (read_noise ** 2).sum().value) info("Total collected electrons: %1.2e electrons" % total.sum().value) # Calculate the SNR using the CCD-equation snr = signal.sum() / np.sqrt(total.sum() + (read_noise ** 2).sum()) # Return the value of the SNR, ignoring the physical units (electrons^0.5) return snr.value * u.dimensionless_unscaled def __exposePixels(self) -> Tuple[u.Quantity, u.Quantity, u.Quantity, u.Quantity]: """ Expose the pixels and calculate the signal and noise electron currents per pixel. Returns ------- signal_current : Quantity The electron current from the target as PixelMask in electrons / s background_current : Quantity The electron current from the background as PixelMask in electrons / s read_noise : Quantity The read noise per pixel in electrons dark_current : Quantity The electron current from the dark noise as PixelMask in electrons / s """ # Calculate the total incoming electron current signal_current, size, obstruction, background_current = self.__calcIncomingElectronCurrent() # Initialize a new PixelMask mask = PixelMask(self.__pixel_geometry, self.__pixel_size, self.__center_offset) if size.lower() == "extended": # Target is extended, a diameter of 0 pixels results in a mask with one pixel marked d_photometric_ap = 0 * u.pix # Mask the pixels to be exposed mask.createPhotometricAperture("circle", d_photometric_ap / 2, np.array([0, 0]) << u.pix) else: # Target is a point source if self.__contained_pixels is not None: # Calculate the diameter of the photometric aperture as square root of the contained pixels d_photometric_ap = np.sqrt(self.__contained_pixels.value) * u.pix # Mask the pixels to be exposed mask.createPhotometricAperture("square", d_photometric_ap / 2, np.array([0, 0]) << u.pix) else: # Calculate the diameter of the photometric aperture from the given contained energy d_photometric_ap = self.__calcPhotometricAperture(obstruction) # Mask the pixels to be exposed mask.createPhotometricAperture(self.__shape, d_photometric_ap / 2) # Calculate the background current PixelMask background_current = mask * background_current * u.pix # Calculate the read noise PixelMask read_noise = mask * self.__read_noise * u.pix # Calculate the dark current PixelMask dark_current = mask * self.__dark_current * u.pix if self.__contained_pixels is None and size.lower() != "extended": if type(self.__contained_energy) == str: if self.__contained_energy.lower() == "peak": info("The radius of the photometric aperture is %.2f pixels. This equals the peak value" % ( d_photometric_ap.value / 2)) elif self.__contained_energy.lower() == "fwhm": info("The radius of the photometric aperture is %.2f pixels. This equals the FWHM" % ( d_photometric_ap.value / 2)) elif self.__contained_energy.lower() == "min": info("The radius of the photometric aperture is %.2f pixels. This equals the first minimum" % ( d_photometric_ap.value / 2)) else: info("The radius of the photometric aperture is %.2f pixels. This equals %.0f%% encircled energy" % (d_photometric_ap.value / 2, self.__contained_energy)) info("The photometric aperture contains " + str(np.count_nonzero(mask)) + " pixels.") if size.lower() != "extended": # Map the PSF onto the pixel mask in order to get the relative irradiance of each pixel mask = self.__psf.mapToPixelMask(mask, getattr(getattr(self.__common_conf, "jitter_sigma", None), "val", None), obstruction) # Calculate the signal current PixelMask signal_current = mask * signal_current return signal_current, background_current, read_noise, dark_current def __calcPhotometricAperture(self, obstruction: float) -> u.Quantity: """ Calculate the diameter of the photometric aperture Parameters ---------- obstruction : float The obstruction factor as A_ob / A_ap. Returns ------- d_photometric_ap : Quantity The diameter of the photometric aperture in pixels. """ # Calculate the reduced observation angle jitter_sigma = getattr(getattr(self.__common_conf, "jitter_sigma", None), "val", None) reduced_observation_angle = self.__psf.calcReducedObservationAngle(self.__contained_energy, jitter_sigma, obstruction) # Calculate angular width of PSF observation_angle = (reduced_observation_angle * self.__central_wl / self.__common_conf.d_aperture() * 180.0 / np.pi * 3600).decompose() * u.arcsec # Calculate FOV of a single pixel pixel_fov = (self.__pixel_size / (self.__f_number * self.__common_conf.d_aperture()) * 180.0 / np.pi * 3600).decompose() * u.arcsec # Calculate the radius of the photometric aperture in pixels d_photometric_ap = observation_angle / pixel_fov return d_photometric_ap * u.pix def __calcIncomingElectronCurrent(self) -> Tuple[u.Quantity, str, float, u.Quantity]: """ Calculate the detected electron current of the signal and the background. Returns ------- signal_current : Quantity The electron current on the detector caused by the target in electrons / s. size : str The size of the target. obstruction : float The obstruction factor as A_ob / A_ap. background_current : Quantity The electron current on the detector caused by the background in electrons / (s * pix). """ # Calculate the photon current of the background background_photon_current = self._parent.calcBackground() * np.pi * ( self.__pixel_size.to(u.m) ** 2 / u.pix) / (4 * self.__f_number ** 2 + 1) * (1 * u.sr) # Calculate the incoming photon current of the target signal, size, obstruction = self._parent.calcSignal() signal_photon_current = signal * np.pi * self.__common_conf.d_aperture() ** 2 # Calculate the electron current of the background and thereby handling the photon energy as lambda-function background_current = ( background_photon_current / (lambda wl: (const.h * const.c / wl).to(u.W * u.s) / u.photon) * self.__quantum_efficiency).integrate() # Calculate the electron current of the signal and thereby handling the photon energy as lambda-function signal_current = (signal_photon_current / (lambda wl: (const.h * const.c / wl).to(u.W * u.s) / u.photon) * self.__quantum_efficiency).integrate() return signal_current, size, obstruction, background_current @staticmethod def check_config(sensor: Entry, conf: Entry) -> Union[None, str]: """ Check the configuration for this class Parameters ---------- sensor : Entry The configuration entry to be checked. conf: Entry The complete configuration. Returns ------- mes : Union[None, str] The error message of the check. This will be None if the check was successful. """ if not hasattr(sensor, "f_number"): return "Missing container 'f_number'." mes = sensor.f_number.check_float("val") if mes is not None: return "f_number: " + mes if not hasattr(sensor, "pixel_geometry"): return "Missing container 'pixel_geometry'." mes = sensor.pixel_geometry.check_quantity("val", u.pix) if mes is not None: return "pixel_geometry: " + mes if hasattr(sensor, "center_offset") and isinstance(sensor.center_offset, Entry): mes = sensor.center_offset.check_quantity("val", u.pix) if mes is not None: return "center_offset: " + mes # Check pixel if not hasattr(sensor, "pixel"): return "Missing container 'pixel'." if not hasattr(sensor.pixel, "quantum_efficiency"): return "Missing container 'quantum_efficiency'." mes = sensor.pixel.quantum_efficiency.check_float("val") if mes is not None: mes = sensor.pixel.quantum_efficiency.check_file("val") if mes is not None: return "pixel -> quantum_efficiency: " + mes if not hasattr(sensor.pixel, "pixel_size"): return "Missing container 'pixel_size'." mes = sensor.pixel.pixel_size.check_quantity("val", u.m) if mes is not None: return "pixel -> pixel_size: " + mes if not hasattr(sensor.pixel, "dark_current"): return "Missing container 'dark_current'." mes = sensor.pixel.dark_current.check_quantity("val", u.electron / (u.pix * u.s)) if mes is not None: return "pixel -> dark_current: " + mes if not hasattr(sensor.pixel, "sigma_read_out"): return "Missing container 'sigma_read_out'." mes = sensor.pixel.sigma_read_out.check_quantity("val", u.electron ** 0.5 / u.pix) if mes is not None: return "pixel -> sigma_read_out: " + mes if not hasattr(sensor.pixel, "well_capacity"): return "Missing container 'well_capacity'." mes = sensor.pixel.well_capacity.check_quantity("val", u.electron) if mes is not None: return "pixel -> well_capacity: " + mes # Check photometric aperture if conf.astroscene.target.size == "point": if not hasattr(sensor, "photometric_aperture"): return "Missing container 'photometric_aperture'." if hasattr(sensor.photometric_aperture, "contained_pixels"): mes = sensor.photometric_aperture.contained_pixels.check_quantity("val", u.pix) if mes is not None: return "photometric_aperture -> contained_pixels: " + mes else: if not hasattr(sensor.photometric_aperture, "shape"): return "Missing container 'shape'." mes = sensor.photometric_aperture.shape.check_selection("val", ["square", "circle"]) if mes is not None: return "photometric_aperture -> shape: " + mes if not hasattr(sensor.photometric_aperture, "contained_energy"): return "Missing container 'contained_energy'." mes = sensor.photometric_aperture.contained_energy.check_float("val") if mes is not None: if conf.common.psf().lower() == "airy": mes = sensor.photometric_aperture.contained_energy.check_selection("val", ["peak", "FWHM", "fwhm", "min"]) if mes is not None: return "photometric_aperture -> contained_energy: " + mes else: mes = sensor.photometric_aperture.contained_energy.check_selection("val", ["FWHM", "fwhm"]) if mes is not None: return "photometric_aperture -> contained_energy: " + mes