Module skytools.unit_conversion
This module computes unit conversion and color correction factors for CMB observations based on Planck 2013 IX: HFI Spectral Response. This is meant to be a python equivalent to the Planck UC_CC IDL codes.
Expand source code
#######################################################################
# This file is a part of SkyTools
#
# Sky Tools
# Copyright (C) 2023 Shamik Ghosh
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
# For more information about SkyTools please visit
# <https://github.com/1cosmologist/skytools> or contact Shamik Ghosh
# at shamik@lbl.gov
#
#########################################################################
########################################################
#
# UNIT CONVERSION CODE
#
# Cross checked for HFI with few percent error.
#
# Reference: Planck 2013 IX: HFI Spectral Response
#
# version 5: Shamik Ghosh, 2023-03-29
#
##########################################################
"""
This module computes unit conversion and color correction factors for CMB observations
based on Planck 2013 IX: HFI Spectral Response. This is meant to be a python equivalent
to the Planck UC_CC IDL codes.
"""
import numpy as np
import scipy.constants as con
from . import em_law as el
__pdoc__ = {}
T_CMB = 2.7255 # K
def MJysr_to_Kb(nuc_in_GHz):
"""
Gives conversion factor from MJy/sr to brightness temperature Kb (K_RJ).
Parameters
----------
nuc_in_GHz: float
A float denoting the central frequency of the band. No bandpass information needed.
Notes
-----
No bandpass is required only central frequency is assumed.
Returns
-------
float
A float value to convert MJy/sr to Kb.
"""
return con.c**2. / 2. / (nuc_in_GHz * con.giga)**2. / con.k / 1.e20 # 1e20 is conversion factor from SI unit of emissivity to MJy 1e-6 x 1e26 = 1e20
def KCMB_to_MJysr(nus_in_GHz, nuc_in_GHz=None, transmission=None):
"""
Gives conversion factor from K_CMB to MJy/sr.
MJy/sr assumes nu^-1 (IRAS) reference spectrum following Planck.
Parameters
----------
nus_in_GHz: float or np.ndarray
If single float value is provided, assumed to be delta transmission.
If np.ndarray is provided without transmission, assume tophat transmission.
nuc_in_GHz: float, default=None
If nus_in_GHz is a single number, then nuc_in_GHz is ignored, and is assumed to be the same.
If nus_in_GHz is a np.ndarray, and nuc_in_GHz is not provided, we assume transmission weighted
average of nus_in_GHz.
transmission: np.ndarray, default=None
Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition
of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of
MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing.
Returns
-------
float
A float value to convert K_CMB to MJy/sr.
"""
if not isinstance(nus_in_GHz, (list, np.ndarray)):
return el.B_prime_nu_T(nus_in_GHz) * 1.e20 # 1.e20 factor converts W/m2/Hz to MJy.
if isinstance(transmission, (list,np.ndarray)):
if len(transmission) != len(nus_in_GHz):
raise Exception("ERROR: transmission and frequency arrays are not of same size.")
else:
transmission = np.ones(nus_in_GHz.shape)
weights = transmission / np.trapz(transmission, x=nus_in_GHz * con.giga)
if nuc_in_GHz == None:
nuc_in_GHz = np.trapz(nus_in_GHz*weights, x=nus_in_GHz * con.giga)
band_integrated_CMB = np.trapz(weights*el.B_prime_nu_T(nus_in_GHz), x=nus_in_GHz * con.giga)
band_integrated_nucbynu = np.trapz(weights*(nuc_in_GHz / nus_in_GHz), x=nus_in_GHz * con.giga)
return (band_integrated_CMB / band_integrated_nucbynu) * 1.e20 # 1.e20 factor converts W/m2/Hz to MJy.
def KCMB_to_ySZ(nus_in_GHz, transmission=None):
"""
Computes conversion factor from K_CMB to y SZ (Compton parameter).
Parameters
----------
nus_in_GHz: float or np.ndarray
If single float value is provided, assumed to be delta transmission.
If np.ndarray is provided without transmission, assume tophat transmission.
transmission: np.ndarray, default=None
Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition
of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of
MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing.
Returns
-------
float
A float value that is the conversion factor from K_CMB to y SZ.
"""
if not isinstance(nus_in_GHz, (list, np.ndarray)):
return el.B_prime_nu_T(nus_in_GHz) / el.ysz_spectral_law(nus_in_GHz) # 1.e20 factor converts W/m2/Hz to MJy.
if isinstance(transmission, (list,np.ndarray)):
if len(transmission) != len(nus_in_GHz):
raise Exception("ERROR: transmission and frequency arrays are not of same size.")
else:
transmission = np.ones(nus_in_GHz.shape)
weights = transmission / np.trapz(transmission, x=nus_in_GHz * con.giga)
band_integrated_CMB = np.trapz(weights*el.B_prime_nu_T(nus_in_GHz), x=nus_in_GHz * con.giga)
band_integrated_ysz = np.trapz(weights*el.ysz_spectral_law(nus_in_GHz), x=nus_in_GHz * con.giga)
# Referenece: Eq 33 from Planck 2013 XI HFI spectral response
return band_integrated_CMB/band_integrated_ysz # returns in K_CMB^(-1) Functions
def KCMB_to_MJysr(nus_in_GHz, nuc_in_GHz=None, transmission=None)-
Gives conversion factor from K_CMB to MJy/sr. MJy/sr assumes nu^-1 (IRAS) reference spectrum following Planck.
Parameters
nus_in_GHz:floatornp.ndarray- If single float value is provided, assumed to be delta transmission. If np.ndarray is provided without transmission, assume tophat transmission.
nuc_in_GHz:float, default=None- If nus_in_GHz is a single number, then nuc_in_GHz is ignored, and is assumed to be the same. If nus_in_GHz is a np.ndarray, and nuc_in_GHz is not provided, we assume transmission weighted average of nus_in_GHz.
transmission:np.ndarray, default=None- Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing.
Returns
float- A float value to convert K_CMB to MJy/sr.
Expand source code
def KCMB_to_MJysr(nus_in_GHz, nuc_in_GHz=None, transmission=None): """ Gives conversion factor from K_CMB to MJy/sr. MJy/sr assumes nu^-1 (IRAS) reference spectrum following Planck. Parameters ---------- nus_in_GHz: float or np.ndarray If single float value is provided, assumed to be delta transmission. If np.ndarray is provided without transmission, assume tophat transmission. nuc_in_GHz: float, default=None If nus_in_GHz is a single number, then nuc_in_GHz is ignored, and is assumed to be the same. If nus_in_GHz is a np.ndarray, and nuc_in_GHz is not provided, we assume transmission weighted average of nus_in_GHz. transmission: np.ndarray, default=None Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing. Returns ------- float A float value to convert K_CMB to MJy/sr. """ if not isinstance(nus_in_GHz, (list, np.ndarray)): return el.B_prime_nu_T(nus_in_GHz) * 1.e20 # 1.e20 factor converts W/m2/Hz to MJy. if isinstance(transmission, (list,np.ndarray)): if len(transmission) != len(nus_in_GHz): raise Exception("ERROR: transmission and frequency arrays are not of same size.") else: transmission = np.ones(nus_in_GHz.shape) weights = transmission / np.trapz(transmission, x=nus_in_GHz * con.giga) if nuc_in_GHz == None: nuc_in_GHz = np.trapz(nus_in_GHz*weights, x=nus_in_GHz * con.giga) band_integrated_CMB = np.trapz(weights*el.B_prime_nu_T(nus_in_GHz), x=nus_in_GHz * con.giga) band_integrated_nucbynu = np.trapz(weights*(nuc_in_GHz / nus_in_GHz), x=nus_in_GHz * con.giga) return (band_integrated_CMB / band_integrated_nucbynu) * 1.e20 # 1.e20 factor converts W/m2/Hz to MJy. def KCMB_to_ySZ(nus_in_GHz, transmission=None)-
Computes conversion factor from K_CMB to y SZ (Compton parameter).
Parameters
nus_in_GHz:floatornp.ndarray- If single float value is provided, assumed to be delta transmission. If np.ndarray is provided without transmission, assume tophat transmission.
transmission:np.ndarray, default=None- Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing.
Returns
float- A float value that is the conversion factor from K_CMB to y SZ.
Expand source code
def KCMB_to_ySZ(nus_in_GHz, transmission=None): """ Computes conversion factor from K_CMB to y SZ (Compton parameter). Parameters ---------- nus_in_GHz: float or np.ndarray If single float value is provided, assumed to be delta transmission. If np.ndarray is provided without transmission, assume tophat transmission. transmission: np.ndarray, default=None Must be the same size as nus_in_GHz. Need not be normalized to one. Assume HFI/LFI definition of transmission, assuming \lambda^2 factor is multipled and the transmission is in units of MJy/sr. If your bandpass is in K_b unit then the \lambda^2 factor is missing. Returns ------- float A float value that is the conversion factor from K_CMB to y SZ. """ if not isinstance(nus_in_GHz, (list, np.ndarray)): return el.B_prime_nu_T(nus_in_GHz) / el.ysz_spectral_law(nus_in_GHz) # 1.e20 factor converts W/m2/Hz to MJy. if isinstance(transmission, (list,np.ndarray)): if len(transmission) != len(nus_in_GHz): raise Exception("ERROR: transmission and frequency arrays are not of same size.") else: transmission = np.ones(nus_in_GHz.shape) weights = transmission / np.trapz(transmission, x=nus_in_GHz * con.giga) band_integrated_CMB = np.trapz(weights*el.B_prime_nu_T(nus_in_GHz), x=nus_in_GHz * con.giga) band_integrated_ysz = np.trapz(weights*el.ysz_spectral_law(nus_in_GHz), x=nus_in_GHz * con.giga) # Referenece: Eq 33 from Planck 2013 XI HFI spectral response return band_integrated_CMB/band_integrated_ysz # returns in K_CMB^(-1) def MJysr_to_Kb(nuc_in_GHz)-
Gives conversion factor from MJy/sr to brightness temperature Kb (K_RJ).
Parameters
nuc_in_GHz:float- A float denoting the central frequency of the band. No bandpass information needed.
Notes
No bandpass is required only central frequency is assumed.
Returns
float- A float value to convert MJy/sr to Kb.
Expand source code
def MJysr_to_Kb(nuc_in_GHz): """ Gives conversion factor from MJy/sr to brightness temperature Kb (K_RJ). Parameters ---------- nuc_in_GHz: float A float denoting the central frequency of the band. No bandpass information needed. Notes ----- No bandpass is required only central frequency is assumed. Returns ------- float A float value to convert MJy/sr to Kb. """ return con.c**2. / 2. / (nuc_in_GHz * con.giga)**2. / con.k / 1.e20 # 1e20 is conversion factor from SI unit of emissivity to MJy 1e-6 x 1e26 = 1e20