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Updated documentation, descriptions for v1.0 release.
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#!/usr/bin/env Python
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from __future__ import division
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import numpy as np
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import matplotlib.pyplot as plt
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import AstroAtmosphere as atm
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import sys
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from ADC import *
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'''
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@author: Joost van den Born
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@Description: Calculates differential refraction (dispersion) between stars with a different
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effective temperature. Similar to Gubler & Tytler 1998
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'''
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def blackbody(l, T):
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'''
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Calculates the intensity output of a star with effective temperature T at wavelength l
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'''
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h = 6.626070150e-34 # J*s
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k = 1.38064852e-23 # J/K
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c = 299792458 # m/s
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return 2 * np.pi * h * c**2 / l**5 * 1 / (np.exp( h * c / (l * k * T)) - 1)
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def effectiveWavelength(T, lmin, lmax):
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'''
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Calculates effective wavelength of a star from the effective temperature.
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'''
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lmin = lmin/1e6
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lmax = lmax/1e6
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_l = np.linspace(lmin, lmax, 1000)
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_I = blackbody(_l, T)
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return np.sum(_I*_l)/np.sum(_I)*1e6
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if __name__ == '__main__':
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# Parameters at Cerro Armazones
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T = 279.65 # k
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P = 71200 # Pa
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H = 0.22
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xc = 450 # ppm
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lat = -24.5983 # degrees
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h = 3064 # m
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l1 = 1.49 # micron
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l2 = 1.78 # micron
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zenith = 60 # degrees
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offset = 0#.285/2 # degrees, ADC offset to simulate finite step size
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S2temps = [2500, 4000, 5500, 7000, 8500]
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S1temps = np.linspace(2500, 1e4, 100)
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########################################################################################
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########################################################################################
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# 1. We look at the differential refraction through the atmosphere, without an ADC
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# at = atm.dispersion(lat, h)
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at = atm.refraction(lat, h)
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at.setReducedHeight(P, at.rho(P, T, H, xc) )
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# Calculating the differential atmospheric refraction for stars of different temperatures
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data = []
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for T2 in S2temps:
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# Properties of star 2
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l_eff_2 = effectiveWavelength(T2, l1, l2)
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n2 = at.n_tph(l_eff_2, T, P, H, xc)
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R2 = at.cassini(n2, zenith)
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# Calculating the differences with star 1
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dataEntry = []
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for T1 in S1temps:
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l_eff_1 = effectiveWavelength(T1, l1, l2)
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n1 = at.n_tph(l_eff_1, T, P, H, xc)
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R1 = at.cassini(n1, zenith)
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diffRef = (R1 - R2) * 3.6e9
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dataEntry.append(diffRef)
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data.append(dataEntry)
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# Plotting the results
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plt.rc('font', family='serif')
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plt.rc('axes', labelsize='large')
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fig = plt.figure(figsize=(9,6))
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ax = fig.add_subplot(111)
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ax2 = ax.twiny()
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ax.grid(True, alpha=0.3)
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linestylesList = [':', '-.', '--', '-', (0, (3, 1, 1, 1, 1, 1))]
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for i in range(len(data)):
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ax.plot(S1temps, data[i], label=str(S2temps[i]) + ' K', linestyle=linestylesList[i], color='k', linewidth=2)
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S1temp_ticks = ax.get_xticks()
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S1temp_tick_loc = ax.get_xticks()
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l_eff_ticks = []
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for T1 in S1temp_ticks:
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l_eff_ticks.append(round( (effectiveWavelength(T1, l1, l2)*1000-1620),1))
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ax2.set_xticklabels(l_eff_ticks)
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ax2.set_xlim(np.min(S1temps), np.max(S1temps))
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ax2.set_xlabel('$\lambda_{eff} - 1620$ (nm) ', fontsize=18)
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ax2.tick_params(axis ='both', direction='in', labelsize=16)
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ax.set_xlabel('Temperature of Star 1 (K)', fontsize=18)
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ax.set_ylabel('$\Delta$R ($\mu$as)', fontsize=18)
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ax.legend(fontsize=16, labelspacing=0.3)
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ax.set_xlim(np.min(S1temps), np.max(S1temps))
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ax.tick_params(axis ='both', direction='in', labelsize=16)
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# plt.show()
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########################################################################################
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########################################################################################
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########################################################################################
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########################################################################################
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# 2. We look now at the differential refraction through the atmosphere, including an ADC
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at = atm.refraction(lat, h)
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at.setReducedHeight(P, at.rho(P, T, H, xc) )
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adc = ADC()
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# Conditions at the band cut-on and cut-off wavelength
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n_l1 = at.n_tph(l1, T, P, H, xc)
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n_l2 = at.n_tph(l2, T, P, H, xc)
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atd = atm.dispersion(lat, h)
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atd.setReducedHeight(P, at.rho(P, T, H, xc) )
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# Optimize ADC for broad band edges at zenith distance.
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atm_disp_full_band = atd.cassini(n_l1, n_l2, zenith)
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print(atm_disp_full_band*3.6e6)
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adcOptimumAngle = adc.optimize(atm_disp_full_band*3.6e6, l1, l2)
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adc.setOrientation(adcOptimumAngle+offset)
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# Calculating the differential atmospheric refraction for stars of different temperatures
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data = []
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for T2 in S2temps:
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# Properties of star 2
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l_eff_2 = effectiveWavelength(T2, l1, l2)
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n2 = at.n_tph(l_eff_2, T, P, H, xc)
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R2_atm = at.cassini(n2, zenith)
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R2_adc = adc.calculateDispersion(l_eff_2, l1, refraction=True)
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# Calculating the differences with star 1
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dataEntry = []
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for T1 in S1temps:
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l_eff_1 = effectiveWavelength(T1, l1, l2)
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n1 = at.n_tph(l_eff_1, T, P, H, xc)
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R1_atm = at.cassini(n1, zenith)
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R1_adc = adc.calculateDispersion(l_eff_1, l1, refraction=True)
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diffRef = ( (R1_adc[1] - R2_adc[1]) + ((R1_atm - R2_atm) * 3.6e6 ) ) * 1e3
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dataEntry.append(diffRef)
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data.append(dataEntry)
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# Plotting the results
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plt.rc('font', family='serif')
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plt.rc('axes', labelsize='large')
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fig = plt.figure(figsize=(9,6))
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ax = fig.add_subplot(111)
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ax2 = ax.twiny()
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ax.grid(True, alpha=0.3)
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linestylesList = [':', '-.', '--', '-', (0, (3, 1, 1, 1, 1, 1))]
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for i in range(len(data)):
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ax.plot(S1temps, data[i], label=str(S2temps[i]) + ' K', linestyle=linestylesList[i], color='k', linewidth=2)
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S1temp_ticks = ax.get_xticks()
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S1temp_tick_loc = ax.get_xticks()
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l_eff_ticks = []
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for T1 in S1temp_ticks:
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l_eff_ticks.append(round( (effectiveWavelength(T1, l1, l2)*1000-1620),1))
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ax2.set_xticklabels(l_eff_ticks)
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ax2.set_xlim(np.min(S1temps), np.max(S1temps))
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ax2.set_xlabel('$\lambda_{eff} - 1620$ (nm) ', fontsize=18)
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ax2.tick_params(axis ='both', direction='in', labelsize=16)
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ax.set_xlabel('Temperature of Star 1 (K)', fontsize=18)
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ax.set_ylabel('$\Delta$R ($\mu$as)', fontsize=18)
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ax.legend(fontsize=16, labelspacing=0.3, loc='lower right')
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ax.set_xlim(np.min(S1temps), np.max(S1temps))
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ax.tick_params(axis ='both', direction='in', labelsize=16)
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plt.show()
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########################################################################################
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########################################################################################
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########################################################################################
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########################################################################################
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# 3. Now we look at the differential dispersion, without an ADC
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at = atm.dispersion(lat, h)
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at.setReducedHeight(P, at.rho(P, T, H, xc) )
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# Conditions at the band cut-on and cut-off wavelength
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n_l1 = at.n_tph(l1, T, P, H, xc)
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n_l2 = at.n_tph(l2, T, P, H, xc)
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# Optimize ADC for broad band edges at zenith distance.
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atm_disp_full_band = at.cassini(n_l1, n_l2, zenith)
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print(atm_disp_full_band*3.6e6)
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# Check that we can use dispersion? If not, how to calculate refraction...?
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# We plot below the difference in atmospheric dispersion of the two stars, incl. an ADC.
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data = []
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for T2 in S2temps:
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l_eff_2 = effectiveWavelength(T2, l1, l2)
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n2 = at.n_tph(l_eff_2, T, P, H, xc)
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dataEntry = []
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for T1 in S1temps:
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l_eff_1 = effectiveWavelength(T1, l1, l2)
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n1 = at.n_tph(l_eff_1, T, P, H, xc)
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atm_disp = at.cassini(n1, n2, zenith) * 3.6e9
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dataEntry.append(atm_disp)
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data.append(dataEntry)
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plt.rc('font', family='serif')
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plt.rc('axes', labelsize='large')
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fig2 = plt.figure(figsize=(9,6))
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ax = fig2.add_subplot(111)
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ax2 = ax.twiny()
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ax.grid(True, alpha=0.3)
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linestylesList = [':', '-.', '--', '-', (0, (3, 1, 1, 1, 1, 1))]
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for i in range(len(data)):
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ax.plot(S1temps, data[i], label=str(S2temps[i]) + ' K', linestyle=linestylesList[i], color='k', linewidth=2)
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S1temp_ticks = ax.get_xticks()
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S1temp_tick_loc = ax.get_xticks()
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l_eff_ticks = []
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for T1 in S1temp_ticks:
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l_eff_ticks.append(round( (effectiveWavelength(T1, l1, l2)*1000-1620),1))
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# ax2.plot(S1temps, data[0], alpha=0)
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ax2.set_xticklabels(l_eff_ticks)
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ax2.set_xlim(np.min(S1temps), np.max(S1temps))
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ax2.set_xlabel('$\lambda_{eff} - 1620$ (nm) ', fontsize=18)
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ax2.tick_params(axis ='both', direction='in', labelsize=16)
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ax.set_xlabel('Temperature of Star 1 (K)', fontsize=18)
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ax.set_ylabel('$\Delta(\Delta$R) ($\mu$as), excl. ADC', fontsize=18)
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ax.legend(fontsize=16, labelspacing=0.3, loc='lower right')
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ax.set_xlim(np.min(S1temps), np.max(S1temps))
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ax.tick_params(axis ='both', direction='in', labelsize=16)
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# plt.show()
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########################################################################################
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########################################################################################
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########################################################################################
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########################################################################################
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########################################################################################
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# 4. Now we add the ADC and look again at the differential refraction, but on the detector
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at = atm.dispersion(lat, h)
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at.setReducedHeight(P, at.rho(P, T, H, xc) )
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adc = ADC()
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# Conditions at the band cut-on and cut-off wavelength
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n_l1 = at.n_tph(l1, T, P, H, xc)
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n_l2 = at.n_tph(l2, T, P, H, xc)
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# Optimize ADC for broad band edges at zenith distance.
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atm_disp_full_band = at.cassini(n_l1, n_l2, zenith)
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print(atm_disp_full_band*3.6e6)
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adcOptimumAngle = adc.optimize(atm_disp_full_band*3.6e6, l1, l2)
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adc.setOrientation(adcOptimumAngle+offset)
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# Check that we can use dispersion? If not, how to calculate refraction...?
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# We plot below the difference in atmospheric dispersion of the two stars, incl. an ADC.
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data = []
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for T2 in S2temps:
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l_eff_2 = effectiveWavelength(T2, l1, l2)
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n2 = at.n_tph(l_eff_2, T, P, H, xc)
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atm_disp2 = at.cassini(n_l1, n2, zenith) * 3.6e6
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adc_disp2 = adc.calculateDispersion(l1, l_eff_2)[1]
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dataEntry = []
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for T1 in S1temps:
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l_eff_1 = effectiveWavelength(T1, l1, l2)
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n1 = at.n_tph(l_eff_1, T, P, H, xc)
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atm_disp1 = at.cassini(n_l1, n1, zenith) * 3.6e6
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adc_disp1 = adc.calculateDispersion(l1,l_eff_1)[1]
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diffDisp = ((adc_disp1 - adc_disp2) - (atm_disp1 - atm_disp2)) * 1e3
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dataEntry.append(diffDisp)
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data.append(dataEntry)
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plt.rc('font', family='serif')
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plt.rc('axes', labelsize='large')
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fig2 = plt.figure(figsize=(9,6))
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ax = fig2.add_subplot(111)
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ax2 = ax.twiny()
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ax.grid(True, alpha=0.3)
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linestylesList = [':', '-.', '--', '-', (0, (3, 1, 1, 1, 1, 1))]
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for i in range(len(data)):
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ax.plot(S1temps, data[i], label=str(S2temps[i]) + ' K', linestyle=linestylesList[i], color='k', linewidth=2)
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S1temp_ticks = ax.get_xticks()
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S1temp_tick_loc = ax.get_xticks()
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l_eff_ticks = []
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for T in S1temp_ticks:
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l_eff_ticks.append(round( (effectiveWavelength(T, l1, l2)*1000-1620),1))
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# ax2.plot(S1temps, data[0], alpha=0)
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ax2.set_xticklabels(l_eff_ticks)
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ax2.set_xlim(np.min(S1temps), np.max(S1temps))
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ax2.set_xlabel('$\lambda_{eff} - 1620$ (nm) ', fontsize=18)
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ax2.tick_params(axis ='both', direction='in', labelsize=16)
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ax.set_xlabel('Temperature of Star 1 (K)', fontsize=18)
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ax.set_ylabel('$\Delta(\Delta$R) ($\mu$as), incl. ADC', fontsize=18)
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ax.legend(fontsize=16, labelspacing=0.3, loc='lower right')
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ax.set_xlim(np.min(S1temps), np.max(S1temps))
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ax.tick_params(axis ='both', direction='in', labelsize=16)
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plt.show()
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########################################################################################
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########################################################################################
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########################################################################################
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