Heterodyne instrument introduced
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esbo_etc/classes/sensor/Heterodyne.py
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281
esbo_etc/classes/sensor/Heterodyne.py
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from astropy import units as u
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from .ASensor import ASensor
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from ..IRadiant import IRadiant
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from ..Entry import Entry
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import numpy as np
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from astropy.constants import k_B
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from typing import Union
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from ...lib.logger import logger
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class Heterodyne(ASensor):
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"""
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A class for modelling the behaviour of a superheterodyne spectrometer.
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"""
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def __init__(self, parent: IRadiant, aperture_efficiency: float, main_beam_efficiency: float,
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receiver_temp: u.Quantity, eta_fss: float, lambda_line: u.Quantity, kappa: float, common_conf: Entry,
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n_on: float = None):
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"""
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Initialize a new heterodyne detector
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Parameters
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----------
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parent : IRadiant
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The parent element of the optical component from which the electromagnetic radiation is received.
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aperture_efficiency : float
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The aperture efficiency of the antenna.
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main_beam_efficiency : float
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The main beam efficiency of the telescope.
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receiver_temp : u.Quantity in Kelvins
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The intrinsic noise temperature of all receiver components.
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eta_fss : float
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The forward scattering efficiency of the antenna.
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lambda_line : u.Quantity
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The wavelength to be used for calculating the SNR.
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kappa : float
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The backend degradation factor.
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common_conf : Entry
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The common-Entry of the configuration.
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n_on : float
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The number of on source observations.
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"""
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self.aperture_efficiency = aperture_efficiency
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self.main_beam_efficiency = main_beam_efficiency
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self.receiver_temp = receiver_temp
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self.eta_fss = eta_fss
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self.lambda_line = lambda_line
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self.kappa = kappa
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self.common_conf = common_conf
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self.n_on = n_on
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super().__init__(parent)
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@u.quantity_input(exp_time="time")
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def getSNR(self, exp_time: u.Quantity) -> u.dimensionless_unscaled:
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"""
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Calculate the signal to background ratio (SNR) for the given exposure time using the CCD-equation.
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Parameters
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----------
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exp_time : time-Quantity
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The exposure time to calculate the SNR for.
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Returns
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-------
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snr : Quantity
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The calculated SNR as dimensionless quantity
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"""
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# Calculate the signal and background temperatures
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t_signal, t_background = self.calcTemperatures()
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t_sys = 2 * (t_background + self.receiver_temp)
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# Calculate the noise bandwidth
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delta_nu = self.lambda_line.to(u.Hz, equivalencies=u.spectral()) / (
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self.lambda_line / self.common_conf.wl_delta() + 1)
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# Calculate the RMS background temperature
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if self.n_on is None:
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t_rms = 2 * t_sys * self.kappa / np.sqrt(exp_time * delta_nu)
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else:
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t_rms = t_sys * self.kappa * np.sqrt(1 + 1 / np.sqrt(self.n_on)) / np.sqrt(exp_time * delta_nu)
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# Calculate the SNR
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snr = t_signal / t_rms
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# Print details
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if exp_time.size > 1:
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for i in range(exp_time.size):
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self.__printDetails(t_sys, delta_nu, t_rms[i], t_signal, "t_exp=%.2f s: " % exp_time[i].value)
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else:
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self.__printDetails(t_sys, delta_nu, t_rms, t_signal, "t_exp=%.2f s: " % exp_time.value)
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return snr
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@u.quantity_input(snr=u.dimensionless_unscaled)
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def getExpTime(self, snr: u.Quantity) -> u.s:
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"""
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Calculate the necessary exposure time in order to achieve the given SNR.
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Parameters
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----------
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snr : Quantity
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The SNR for which the necessary exposure time shall be calculated as dimensionless quantity.
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Returns
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-------
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exp_time : Quantity
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The necessary exposure time in seconds.
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"""
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# Calculate the signal and background temperatures
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t_signal, t_background = self.calcTemperatures()
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t_sys = 2 * (t_background + self.receiver_temp)
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# Calculate the noise bandwidth
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delta_nu = self.lambda_line.to(u.Hz, equivalencies=u.spectral()) / (
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self.lambda_line / self.common_conf.wl_delta() + 1)
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# Calculate the RMS background temperature
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t_rms = t_signal / snr
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# Calculate the exposure time
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if self.n_on is None:
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exp_time = ((2 * t_sys * self.kappa / t_rms) ** 2 / delta_nu).decompose()
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else:
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exp_time = ((t_sys * self.kappa / t_rms) ** 2 * (1 + 1 / np.sqrt(self.n_on)) / delta_nu).decompose()
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# Print details
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if snr.size > 1:
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for i in range(snr.size):
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self.__printDetails(t_sys, delta_nu, t_rms[i], t_signal, "SNR=%.2f: " % snr[i].value)
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else:
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self.__printDetails(t_sys, delta_nu, t_rms, t_signal, "SNR=%.2f: " % snr.value)
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return exp_time
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@u.quantity_input(exp_time="time", snr=u.dimensionless_unscaled, target_brightness=u.mag)
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def getSensitivity(self, exp_time: u.Quantity, snr: u.Quantity, target_brightness: u.Quantity) -> u.mag:
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"""
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Calculate the sensitivity of the telescope detector combination.
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Parameters
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----------
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exp_time : Quantity
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The exposure time in seconds.
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snr : Quantity
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The SNR for which the sensitivity time shall be calculated.
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target_brightness : Quantity
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The target brightness in magnitudes.
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Returns
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-------
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sensitivity: Quantity
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The sensitivity as limiting apparent star magnitude in mag.
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"""
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# Calculate the signal and background temperatures
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t_signal, t_background = self.calcTemperatures()
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t_sys = 2 * (t_background + self.receiver_temp)
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# Calculate the noise bandwidth
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delta_nu = self.lambda_line.to(u.Hz, equivalencies=u.spectral()) / (
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self.lambda_line / self.common_conf.wl_delta() + 1)
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# Calculate the RMS background temperature
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if self.n_on is None:
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t_rms = 2 * t_sys * self.kappa / np.sqrt(exp_time * delta_nu)
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else:
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t_rms = t_sys * self.kappa * np.sqrt(1 + 1 / np.sqrt(self.n_on)) / np.sqrt(exp_time * delta_nu)
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# Calculate the limiting signal temperature
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t_signal_lim = t_rms * snr
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# Print details
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if snr.size > 1:
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for i in range(snr.size):
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self.__printDetails(t_sys, delta_nu, t_rms[i], t_signal_lim[i],
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"SNR=%.2f t_exp=%.2f s: " % (snr[i].value, exp_time[i].value))
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else:
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self.__printDetails(t_sys, delta_nu, t_rms, t_signal_lim,
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"SNR=%.2f t_exp=%.2f s: " % (snr.value, exp_time.value))
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return target_brightness - 2.5 * np.log10(t_signal_lim / t_signal) * u.mag
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@u.quantity_input(t_sys=u.K, delta_nu=u.Hz, t_rms=u.K, t_signal=u.K)
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def __printDetails(self, t_sys: u.Quantity, delta_nu: u.Quantity, t_rms: u.Quantity,
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t_signal: u.Quantity, prefix: str = ""):
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"""
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Print details on the signal and noise composition.
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Parameters
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----------
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t_sys : Quantity
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The system temperature.
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delta_nu : Quantity
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The noise bandwidth.
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t_rms : Quantity
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The RMS antenna temperature.
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t_signal : Quantity
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The antenna temperature.
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prefix : str
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The prefix to be used for printing.
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Returns
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-------
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"""
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logger.info("-------------------------------------------------------------------------------------------------")
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logger.info(prefix + "System temperature: %1.2e K" % t_sys.value)
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logger.info(prefix + "Noise bandwidth: %1.2e K" % delta_nu.value)
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logger.info(prefix + "RMS antenna temperature: %1.2e K" % t_rms.value)
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logger.info(prefix + "Antenna temperature: %1.2e K" % t_signal.value)
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logger.info("-------------------------------------------------------------------------------------------------")
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def calcTemperatures(self):
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"""
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Calculate the noise temperatures of the signal and the background radiation.
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Returns
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-------
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t_signal : u.Quantity
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The signal temperature in Kelvins.
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t_background : u.Quantity
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The background temperature in Kelvins.
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"""
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logger.info("Calculating the system temperature.")
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t_background = (self._parent.calcBackground().rebin(self.lambda_line).qty.to(
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u.W / (u.m ** 2 * u.Hz * u.sr), equivalencies=u.spectral_density(self.lambda_line)) *
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self.lambda_line ** 2 / (2 * k_B) * u.sr).decompose()
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# Calculate the incoming photon current of the target
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logger.info("Calculating the signal temperature.")
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signal, obstruction = self._parent.calcSignal()
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size = "extended" if signal.qty.unit.is_equivalent(u.W / (u.m ** 2 * u.nm * u.sr)) else "point"
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if size == "point":
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signal = signal.rebin(self.lambda_line).qty.to(u.W / (u.m ** 2 * u.Hz),
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equivalencies=u.spectral_density(self.lambda_line))
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t_signal = (signal * self.aperture_efficiency * self.common_conf.d_aperture() ** 2 *
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np.pi / 4 / (2 * k_B) * self.eta_fss).decompose()
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else:
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signal = signal.rebin(self.lambda_line).qty.to(u.W / (u.m ** 2 * u.Hz * u.sr),
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equivalencies=u.spectral_density(self.lambda_line))
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t_signal = (signal * u.sr * self.main_beam_efficiency * self.lambda_line ** 2 / (
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2 * k_B) * self.eta_fss).decompose()
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logger.debug("Signal temperature: %1.2e K" % t_signal.value)
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logger.debug("Target size: " + size)
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logger.debug("Obstruction: %.2f" % obstruction)
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logger.debug("Background temperature: %1.2e K" % t_background.value)
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return t_signal, t_background
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@staticmethod
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def check_config(sensor: Entry, conf: Entry) -> Union[None, str]:
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"""
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Check the configuration for this class
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Parameters
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----------
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sensor : Entry
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The configuration entry to be checked.
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conf: Entry
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The complete configuration.
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Returns
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-------
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mes : Union[None, str]
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The error message of the check. This will be None if the check was successful.
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"""
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if not hasattr(sensor, "aperture_efficiency"):
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return "Missing container 'aperture_efficiency'."
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mes = sensor.aperture_efficiency.check_float("val")
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if mes is not None:
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return "aperture_efficiency: " + mes
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if not hasattr(sensor, "main_beam_efficiency"):
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return "Missing container 'main_beam_efficiency'."
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mes = sensor.main_beam_efficiency.check_float("val")
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if mes is not None:
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return "main_beam_efficiency: " + mes
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if not hasattr(sensor, "receiver_temp"):
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return "Missing container 'receiver_temp'."
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mes = sensor.receiver_temp.check_quantity("val", u.K)
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if mes is not None:
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return "receiver_temp: " + mes
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if not hasattr(sensor, "eta_fss"):
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return "Missing container 'eta_fss'."
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mes = sensor.eta_fss.check_float("val")
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if mes is not None:
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return "eta_fss: " + mes
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if not hasattr(sensor, "lambda_line"):
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return "Missing container 'lambda_line'."
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mes = sensor.lambda_line.check_quantity("val", u.nm)
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if mes is not None:
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return "lambda_line: " + mes
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if not hasattr(sensor, "kappa"):
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return "Missing container 'kappa'."
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mes = sensor.kappa.check_float("val")
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if mes is not None:
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return "kappa: " + mes
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if hasattr(sensor, "n_on") and isinstance(sensor.n_on, Entry):
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mes = sensor.n_on.check_float("val")
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if mes is not None:
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return "n_on: " + mes
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@ -2,6 +2,7 @@ from ..IRadiant import IRadiant
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from ..Entry import Entry
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from .ASensor import ASensor
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from .Imager import Imager
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from .Heterodyne import Heterodyne
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from ...lib.logger import logger
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@ -49,5 +50,14 @@ class SensorFactory:
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options.photometric_aperture.contained_pixels, Entry):
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args["contained_pixels"] = options.photometric_aperture.contained_pixels()
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return Imager(**args)
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elif options.type == "Heterodyne":
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args = dict(parent=self.__parent, aperture_efficiency=options.aperture_efficiency(),
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main_beam_efficiency=options.main_beam_efficiency(), receiver_temp=options.receiver_temp(),
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eta_fss=options.eta_fss(), lambda_line=options.lambda_line(), kappa=options.kappa(),
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common_conf=self.__common_conf)
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if hasattr(options, "n_on"):
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# noinspection PyCallingNonCallable
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args["n_on"] = options.n_on()
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return Heterodyne(**args)
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else:
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logger.error("Wrong sensor type: " + options.type)
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from .ASensor import *
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from .Imager import *
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from .Heterodyne import *
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from .SensorFactory import *
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50
tests/sensor/test_Heterodyne.py
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50
tests/sensor/test_Heterodyne.py
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from unittest import TestCase
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import astropy.units as u
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import numpy as np
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from esbo_etc.classes.Config import Configuration
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from esbo_etc.classes.target.FileTarget import FileTarget
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from esbo_etc.classes.target.BlackBodyTarget import BlackBodyTarget
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from esbo_etc.classes.optical_component.Atmosphere import Atmosphere
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from esbo_etc.classes.optical_component.CosmicBackground import CosmicBackground
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from esbo_etc.classes.optical_component.Mirror import Mirror
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from esbo_etc.classes.sensor.Heterodyne import Heterodyne
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class TestHeterodyne(TestCase):
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def setUp(self):
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self.config = Configuration("data/esbo-etc_defaults_heterodyne.xml").conf
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self.heterodyne_args = dict(aperture_efficiency=0.55, main_beam_efficiency=0.67,
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receiver_temp=1050 * u.K, eta_fss=0.97, lambda_line=157.774 * u.um, kappa=1.0,
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common_conf=self.config.common)
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self.target = FileTarget("data/target/line.csv", self.config.common.wl_bins())
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self.atmosphere = Atmosphere(self.target, "data/atmosphere/transmittance_great.csv")
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self.cosmic = CosmicBackground(self.atmosphere, temp=220 * u.K, emissivity=0.14)
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self.mirror = Mirror(self.cosmic, reflectance="data/mirror/reflectance_great.csv", emissivity=0.08,
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temp=230 * u.K)
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self.heterodyne = Heterodyne(self.mirror, **self.heterodyne_args)
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def test_getSNR(self):
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snr = self.heterodyne.getSNR(1900 * u.s)
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self.assertAlmostEqual(snr.value, 10.059625717085497)
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def test_getExpTime(self):
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exp_time = 1900 * u.s
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snr = self.heterodyne.getSNR(exp_time)
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exp_time_ = self.heterodyne.getExpTime(snr)
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self.assertAlmostEqual(exp_time.value, exp_time_.value)
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def test_getSensitivity(self):
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exp_time = 1900 * u.s
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target = BlackBodyTarget(self.config.common.wl_bins(), mag=20 * u.mag)
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atmosphere = Atmosphere(target, "data/atmosphere/transmittance_great.csv")
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cosmic = CosmicBackground(atmosphere, temp=220 * u.K, emissivity=0.14)
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mirror = Mirror(cosmic, reflectance="data/mirror/reflectance_great.csv", emissivity=0.08, temp=230 * u.K)
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heterodyne = Heterodyne(mirror, **self.heterodyne_args)
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snr = heterodyne.getSNR(exp_time)
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target = BlackBodyTarget(self.config.common.wl_bins(), mag=10 * u.mag)
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atmosphere = Atmosphere(target, "data/atmosphere/transmittance_great.csv")
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cosmic = CosmicBackground(atmosphere, temp=220 * u.K, emissivity=0.14)
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mirror = Mirror(cosmic, reflectance="data/mirror/reflectance_great.csv", emissivity=0.08, temp=230 * u.K)
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heterodyne = Heterodyne(mirror, **self.heterodyne_args)
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sensitivity = heterodyne.getSensitivity(exp_time, snr, 10 * u.mag)
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self.assertAlmostEqual(sensitivity.value, 20)
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