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Updated documentation, descriptions for v1.0 release.
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#!/usr/bin/env Python
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import numpy as np
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import matplotlib.pyplot as plt
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from mpl_toolkits.axes_grid1 import host_subplot
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from AstroAtmosphere import *
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from pyslalib import slalib
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'''
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@ Author: Joost van den Born
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@ Contact: born@astron.nl
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@ Description: This script was used to compare the impact of using the old
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B&S equations, and the particular implementation of SLALIB.
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The rest of the script is almost a one-to-one copy of other
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script that compared the atmospheric models.
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Modeling the atmospheric refraction using multiple models of
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the atmosphere and then comparing them.
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Models included:
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- Full integration method
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- Plane-parallel atmosphere
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- Cassini's model
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- Tan5 model (A*tan(z) + B*tan^3(z) + C*tan^5(z))
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- Oriani's theorem (A*tan(z) + B*tan^3(z))
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- Erf model (from Corbard et al., 2019)
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- SLALIB
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'''
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class atmosphereSLALIB:
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def __init__(self, T=279.65, P=712, H=0.22):
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self.name = 'SLALIB atmosphere'
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self.T = T
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self.P = P
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self.H = H
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self.h = 3064
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self.lat = -24.5983
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self.TLR = 0.0065
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self.prec = 1e-8
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def atmModel(self, A, B, zenith):
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zenith = np.radians(zenith)
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return A * np.tan(zenith) + B * (np.tan(zenith)**3)
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def dispersion(self, l1, l2, z):
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A1, B1 = slalib.sla_refco(self.h, self.T, self.P, self.H, l1, np.deg2rad(self.lat), self.TLR, self.prec)
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A2, B2 = slalib.sla_atmdsp(self.T, self.P, self.H, l1, A1, B1, l2)
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D1 = np.degrees(self.atmModel(A1, B1, z)) * 3600
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D2 = np.degrees(self.atmModel(A2, B2, z)) * 3600
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dispersionValue = ((D1 - D2) * 1000)
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return dispersionValue
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def refractivity(self, l=None):
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'''
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SLALIB uses the same atmospheric model as ZEMAX
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based on the works of Hohenkerk & Sinclair and Seidelmann.
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They take the B&S refraction formula as a basis.
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'''
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zObs = np.deg2rad(45.06563)
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h = 0
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T = self.T
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P = self.P
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H = self.H
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lat = 24
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tlr = 0.0065
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eps = 1e-10
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if not l:
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l = self.lrange
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R = []
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if type(l) == float:
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l = [l]
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for wl in l:
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R.append(slalib.sla_refro(zObs, h, T, P, H, wl, lat, tlr, eps)+1)
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return np.asarray(R)
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if __name__ == '__main__':
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plt.rc('font', family='serif')
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# plt.rc('xtick', labelsize='x-small')
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# plt.rc('ytick', labelsize='x-small')
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plt.rc('axes', labelsize='large')
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# Standard atmospheric conditions
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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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T = 288.15 # k
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P = 101325 # Pa
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H = 0.0
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xc = 314 # 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 = 30 # degrees
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# Calculate the index of refraction
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at = Observatory()
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n1 = at.n_tph(l=l1, T=T, p=P, RH=H, xc=xc)
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n2 = at.n_tph(l=l2, T=T, p=P, RH=H, xc=xc)
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rho = at.rho(p=P, T=T, RH=H, xc=xc)
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#######################################################
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# DIRECT COMPARISON
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ref = dispersion(lat, h)
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ref.setReducedHeight(P, rho)
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print('Ciddor refractivity: ', n1, n2)
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print ('Cassini dispersion: %s mas' %(ref.cassini(n1, n2, zenith) * 3.6e6))
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n1c = n1
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n2c = n2
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refraction = refraction(lat, h)
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refraction.setReducedHeight(P, rho)
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refractionValueCiddor = refraction.cassini(n1c, zenith) * 3.6e6 # in mas
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# SLALIB
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atSLALIB = atmosphereSLALIB(T, P/100, H)
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n1 = atSLALIB.refractivity(l1)
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n2 = atSLALIB.refractivity(l2)
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print('B&S refractivity: ', n1, n2)
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print ('SLALIB model: %s mas' %(atSLALIB.dispersion(l1, l2, zenith) ) )
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# SLALIB refraction:
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A1, B1 = slalib.sla_refco(atSLALIB.h, atSLALIB.T, atSLALIB.P, atSLALIB.H, l1, np.deg2rad(atSLALIB.lat), atSLALIB.TLR, atSLALIB.prec)
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refractionValueSLALIB = np.degrees(atSLALIB.atmModel(A1, B1, zenith)) * 3.6e6 # in mas
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print('Differential dispersion = {} mas'.format(atSLALIB.dispersion(l1, l2, zenith) - ref.cassini(n1c, n2c, zenith) * 3.6e6) )
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print('Differential refraction = {} mas'.format( refractionValueSLALIB - refractionValueCiddor ) )
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#######################################################
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refractionAnalysis = True
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dispersionAnalysis = True
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tableCompare = True
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if dispersionAnalysis:
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# Initiate the refraction class
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ref = dispersion(lat, h)
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ref.setReducedHeight(P, rho)
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# Compare the refraction models to check if the output is okay
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print ('Plane - parallel atmosphere dispersion: %s mas' %(ref.planeParallel(n1, n2, zenith) * 3.6e6))
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print ('Cassini dispersion: %s mas' %(ref.cassini(n1, n2, zenith) * 3.6e6))
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print ('Tan5 dispersion: %s mas' %(ref.tan5(n1, n2, zenith) * 3.6e6))
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print ('Oriani dispersion: %s mas' %(ref.oriani(n1, n2, zenith) * 3.6e6))
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print ('Corbard dispersion: %s mas' %(ref.corbard(n1, n2, zenith)*3.6e6))
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print ('Full integration: %s mas' %(ref.refractionIntegral(n1, n2, zenith)*3.6e6))
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print ('SLALIB model: %s mas' %(atSLALIB.dispersion(l1, l2, zenith) ) )
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# Now we calculate the dispersion over a wide range of zenith angles
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# for ideal gas atmosphere
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zenithRange = np.linspace(30, 85, 1000)
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ppList = ref.planeParallel(n1, n2, zenithRange) * 3.6e6
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cassiniList = ref.cassini(n1, n2, zenithRange) * 3.6e6
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tan5List = ref.tan5(n1, n2, zenithRange) * 3.6e6
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orianiList = ref.oriani(n1, n2, zenithRange) * 3.6e6
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corbardList = [ref.corbard(n1, n2, z)[0] * 3.6e6 for z in zenithRange]
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fullIntegrationList = np.asarray([ref.refractionIntegral(n1, n2, z) * 3.6e6 for z in zenithRange])
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slalibList = atSLALIB.dispersion(l1, l2, zenithRange)
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# for isothermal atmosphere
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cassiniList_isotherm = ref.cassini(n1, n2, zenithRange, reduced_height=ref.H_isotherm(T)) * 3.6e6
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tan5List_isotherm = ref.tan5(n1, n2, zenithRange, reduced_height=ref.H_isotherm(T)) * 3.6e6
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orianiList_isotherm = ref.oriani(n1, n2, zenithRange, reduced_height=ref.H_isotherm(T)) * 3.6e6
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corbardList_isotherm = [ref.corbard(n1, n2, z, reduced_height=ref.H_isotherm(T))[0] * 3.6e6 for z in zenithRange]
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# check when the variation between the different models pass different values
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dispersionWidth = []
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widthList = []
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for z in range(len(zenithRange)):
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compList = [cassiniList[z], tan5List[z], orianiList[z], corbardList[z], cassiniList_isotherm[z], tan5List_isotherm[z], orianiList_isotherm[z], corbardList_isotherm[z], slalibList[z]]#, fullIntegrationList[z]]
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width = np.max(compList) - np.min(compList)
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widthList.append(width)
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dispersionWidth.append((zenithRange[z], width))
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masBorder = np.argmax(np.asarray(widthList)>1)
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p1masBorder = np.argmax(np.asarray(widthList)>0.1)
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p01masBorder = np.argmax(np.asarray(widthList)>0.01)
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p001masBorder = np.argmax(np.asarray(widthList)>0.001)
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plotAbsolute = 1
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if plotAbsolute:
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# Plotting it all, with vertical lines where the variation between the models exceed 1, 0.1, 0.01 and 0.001 mas.
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fig = plt.figure(figsize=(9,5))
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ax = fig.add_subplot(111)
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ax.set_xlim([30,85])
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ax.set_xlabel('Zenith (degrees)')
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ax.set_ylabel('Dispersion (mas)')
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ax.grid(True, alpha=0.3)
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ax.axvline(dispersionWidth[masBorder][0], linestyle='--', color='k', linewidth=0.5)
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ax.text(dispersionWidth[masBorder][0]-0.5, 402, '1 mas', ha='center', va='bottom', rotation='vertical')
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ax.axvline(dispersionWidth[p1masBorder][0], linestyle='--', color='k', linewidth=0.5)
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ax.text(dispersionWidth[p1masBorder][0]-0.5, 402, '0.1 mas', ha='center', va='bottom', rotation='vertical')
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ax.axvline(dispersionWidth[p01masBorder][0], linestyle='--', color='k', linewidth=0.5)
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ax.text(dispersionWidth[p01masBorder][0]-0.5, 402, '10 $\mu$as', ha='center', va='bottom', rotation='vertical')
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ax.axvline(dispersionWidth[p001masBorder][0], linestyle='--', color='k', linewidth=0.5)
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ax.text(dispersionWidth[p001masBorder][0]-0.5, 402, '1 $\mu$as', ha='center', va='bottom', rotation='vertical')
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ax.plot(zenithRange, ppList, 'k-', label='Plane-parallel', alpha=0.2)
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ax.plot(zenithRange, cassiniList, 'g-', label='Cassini')
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ax.plot(zenithRange, tan5List, 'b-', label='$Atan(z) - Btan^3(z) + Ctan^5(z)$')
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ax.plot(zenithRange, orianiList, 'y-', label='$Atan(z) - Btan^3(z)$')
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ax.plot(zenithRange, corbardList, 'r-', label='Error function')
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ax.plot(zenithRange, fullIntegrationList, 'c-', label='Full integration')
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ax.plot(zenithRange, cassiniList_isotherm, 'g--', label='Cassini (isotherm)')
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ax.plot(zenithRange, tan5List_isotherm, 'b--', label='$Atan(z) - Btan^3(z) + Ctan^5(z)$ (isotherm)')
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ax.plot(zenithRange, orianiList_isotherm, 'y--', label='$Atan(z) - Btan^3(z)$ (isotherm)')
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ax.plot(zenithRange, corbardList_isotherm, 'r--', label='Error function (isotherm)')
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ax.tick_params(axis ='both', direction='in')
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ax.legend()
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plt.tight_layout()
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plt.show()
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plotRelative = 1
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if plotRelative:
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# RELATIVE TO FULL INTEGRATION
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fig = plt.figure(figsize=(9,6))
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ax = fig.add_subplot(111)
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ax.set_xlim([30,85])
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ax.set_xlabel('Zenith (degrees)', fontsize=18)
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ax.set_ylabel(r'$\log_{10}(|(\Delta R - \Delta R_{int})|$ mas$^{-1})$', fontsize=18)
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ax.axhline(np.log10(0.4), linestyle='-', linewidth=1, color='red')
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ax.text(30.5, np.log10(0.4)+0.05, 'Residual dispersion requirement', fontsize=12)
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ax.grid(True, which='major', alpha=0.3)
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ax.grid(True, which='minor', alpha=0.2)
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ax.plot(zenithRange, np.log10(np.abs(ppList-fullIntegrationList)), color='k', linestyle='-', linewidth=2, label='Plane-parallel')
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ax.plot(zenithRange, np.log10(np.abs(cassiniList-fullIntegrationList)), color='g', linestyle=(0, (1, 1)), linewidth=2, label='Cassini')
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ax.plot(zenithRange, np.log10(np.abs(orianiList-fullIntegrationList)), color='y', linestyle='-.', linewidth=2, label='Oriani')
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ax.plot(zenithRange, np.log10(np.abs(tan5List-fullIntegrationList)), color='b', linestyle=(0, (5, 1)), linewidth=2, label='Oriani incl. fifth order')
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ax.plot(zenithRange, np.log10(np.abs(np.asarray(corbardList)-fullIntegrationList)), color='r', linestyle=(0, (3, 1, 1, 1, 1, 1)), linewidth=2, label='Error function')
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ax.plot(zenithRange, np.log10(np.abs(np.asarray(slalibList)-fullIntegrationList)), color='m', linewidth=2, label='SLALIB')
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ax.plot(zenithRange, np.log10(np.abs(cassiniList-fullIntegrationList)), color='g', linestyle=(0, (1, 1)), linewidth=2)
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ax.set_ylim(top=2.6, bottom=-7.2)
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ax.tick_params(axis ='both', direction='in', labelsize=16)
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ax.legend(fontsize=14, labelspacing=0.3, columnspacing=0.5, handletextpad=0.3, ncol=1, loc='lower right')
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plt.tight_layout()
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plt.show()
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