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Updated documentation, descriptions for v1.0 release.
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@@ -3,6 +3,7 @@ import numpy as np
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from scipy import integrate
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import os
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from .ciddorModel import Observatory
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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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@@ -17,19 +18,99 @@ from .ciddorModel import Observatory
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'''
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class dispersion(Observatory):
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'''
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Class that sets the observer location.
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These location attributes are then used to calculate the
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appropriate atmospheric dispersion.
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See also:
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Observatory()
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refraction()
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...
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Attributes
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-----------
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lat : float
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Latitude of the observer in degrees
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h : float
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Altitude above mean sea level of the observer in meters
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Other Observatory() attributes
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Methods
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-------
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setReducedHeight(p, rho)
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Sets the reduced atmospheric height.
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planeParallel(n1, n2, zenith)
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Returns the atmospheric dispersion assuming a plane parallel
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atmosphere
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cassini(n1, n2, zenith, reduced_height=None)
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Returns the atmospheric dispersion asusming Cassini's homegeneous
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atmosphere model
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tan5(n1, n2, zenith, reduced_height=None)
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Returns the atmospheric dispersion following Oriani's theorem,
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including a fifth order term in the expansion.
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oriani(n1, n2, zenith, reduced_height=None)
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Returns the atmospheric dispersion following the classic version
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of Oriani's theorem.
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corbard(n1, n2, zenith, reduced_height=None)
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Returns the atmospheric dispersion following the method described
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in Corbard et al., 2019.
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refractionIntegral(n1, n2, z0, R0=None, useStandardAtmosphere=True, heightData=None, rhoData=None)
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Returns the atmospheric dispersion following the refraction integral.
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psi(x)
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Submethod for corbard()
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set_rc()
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Sets the local radius of curvature of the Earth at the observer.
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set_H(p, rho)
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Sets the reduced height for the conditions at the observer, assuming
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an adiabatic atmosphere.
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H_isotherm(T)
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Sets the reduced height for the conditions at the observer, assuming
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an isothermal atmosphere.
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cassiniError(z, l1, l2, T, p, RH, xc, dl1=0, dl2=0, dT=0.2, dP=20,
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dRH=0.02, dCO2=20, dz=0, lat=None, h=None)
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Returns the uncertainty in the atmospheric dispersion, assuming
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Cassini's homegeneous atmosphere model and the given parameters.
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Other Observatory() methods
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'''
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def __init__(self, lat, h):
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Observatory.__init__(self)
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self.h = h # height above sea level in meters
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self.lat = lat # Latitude of the observer in degrees
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self.rc = self.set_rc() * 1000 # Radius of curvature of the earth at the observer
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def setReducedHeight(self, P, rho):
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self.H = self.set_H(P, rho) # Reduced height of the atmosphere assuming ideal gas law
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def setReducedHeight(self, p, rho):
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'''
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Sets the reduced atmospheric height.
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Parameters
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----------
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p : float
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Atmospheric pressure in Pascal
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rho : float
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Density of the atmospheric air at the observer
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'''
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self.H = self.set_H(p, rho) # Reduced height of the atmosphere assuming ideal gas law
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def planeParallel(self, n1, n2, zenith):
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'''
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Refraction based on a flat atmosphere, easily derived from Snell's law.
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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zenith : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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_R1 = np.arcsin(n1 * np.sin( np.deg2rad(zenith) )) - np.deg2rad(zenith)
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_R2 = np.arcsin(n2 * np.sin( np.deg2rad(zenith) )) - np.deg2rad(zenith)
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@@ -40,6 +121,24 @@ class dispersion(Observatory):
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def cassini(self, n1, n2, zenith, reduced_height=None):
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'''
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Refraction of spherical atmosphere, derived from geometry using Sine law
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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zenith : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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reduced_height : float (optional)
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Reduced height of the atmosphere. Default value is calculated
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from the object attributes.
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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if reduced_height:
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H = reduced_height
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@@ -56,6 +155,24 @@ class dispersion(Observatory):
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'''
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Same as oriani's theorem, but including a higher order term.
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Found in Corbard et al., 2019.
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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zenith : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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reduced_height : float (optional)
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Reduced height of the atmosphere. Default value is calculated
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from the object attributes.
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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if reduced_height:
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H = reduced_height
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@@ -74,8 +191,27 @@ class dispersion(Observatory):
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def oriani(self, n1, n2, zenith, reduced_height=None):
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'''
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Classic refraction formula with two tan(z) terms. This does not assume any
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information about the structure of the atmosphere. Found with Oriani's theorem.
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Classic refraction formula with two tan(z) terms.
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This does not assume any information about the structure
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of the atmosphere. Found with Oriani's theorem.
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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zenith : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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reduced_height : float (optional)
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Reduced height of the atmosphere. Default value is calculated
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from the object attributes.
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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if reduced_height:
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H = reduced_height
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@@ -94,9 +230,28 @@ class dispersion(Observatory):
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def corbard(self, n1, n2, zenith, reduced_height=None):
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'''
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Corbard et al., 2019, mention an additional formula based on the error function.
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Oriani's theorem can be derived from this equation by 'keeping only the three first
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terms of its asymptotic expansion'.
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Corbard et al., 2019, mention an additional formula based on
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the error function. Oriani's theorem can be derived from this
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equation by 'keeping only the three first terms of its
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asymptotic expansion'.
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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zenith : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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reduced_height : float (optional)
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Reduced height of the atmosphere. Default value is calculated
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from the object attributes.
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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if reduced_height:
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H = reduced_height
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@@ -113,15 +268,46 @@ class dispersion(Observatory):
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def refractionIntegral(self, n1, n2, z0, R0=None, useStandardAtmosphere=True, heightData=None, rhoData=None):
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def refractionIntegral(self, n1, n2, z0, R0=None, useStandardAtmosphere=True,
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heightData=None, rhoData=None):
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'''
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Using data that gives temperature, pressure and density as a function of height,
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the gladstone-dale relation is invoked to calculate the path of a light ray
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along the atmosphere. This is allows us to also include atmospheric activity in
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Using data that gives temperature, pressure and density as a
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function of height, the gladstone-dale relation is invoked to
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calculate the path of a light ray along the atmosphere.
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This is allows us to also include atmospheric activity in
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different atmosphere layers.
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Recommended use with the US Standard Atmosphere from 1976.
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USSA1976 data generated from code supplied by http://www.pdas.com/atmos.html
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The method described in eq. 3 in Auer & Standish (2000) is used for the calculation.
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The method described in eq. 3 in Auer & Standish (2000) is used for the
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calculation.
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Parameters
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----------
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n1 : float
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Refractive index at the shortest wavelength of interest
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n2 : float
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Refractive index at the longest wavelength of interest
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z0 : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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R0 : float (optional)
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Local radius of curvature of the Earth in km.
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useStandardAtmosphere : bool
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Flag to use the included USSA1976 data
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heightData : 1D Array
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If "useStandardAtmosphere" is False, the function will ask
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for alternative atmospheric data to integrate over. This
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gives the altitudinal points
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rhoData : 1D Array
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If useStandardAtmosphere is False, the function will ask
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for alternative atmospheric data to integrate over. This
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gives the atmospheric density at the points defined by
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"heightData".
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Returns
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-------
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dR : float
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Atmospheric dispersion in degrees
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'''
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if not R0:
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R0 = self.rc
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@@ -163,6 +349,19 @@ class dispersion(Observatory):
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def psi(self, x):
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'''
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Submethod for corbard(). Described explicitly in Corbard et al.,2019.
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Parameters
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----------
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x : float
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Input of the function
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Returns
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-------
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y : float
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Output of the function
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'''
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_f = lambda a: np.exp(-a**2)
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_int = integrate.quad(_f, x, np.inf)
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return np.exp(x**2) * _int[0]
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@@ -173,6 +372,11 @@ class dispersion(Observatory):
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Returns the radius of the curvature at the observer in km,
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taking into account the latitude of the observer and the corresponding
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ellipsoidality of the earth.
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Returns
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-------
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rc : float
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Local radius of curvature of the Earth in kilometers.
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'''
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_A = 6378.137 # km
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_B = 6356.752 # km
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@@ -182,9 +386,21 @@ class dispersion(Observatory):
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return _rc0 + self.h/1000
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def set_H(self, P, rho):
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def set_H(self, p, rho):
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'''
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Calculates the reduced height of the atmosphere, assuming ideal gas law.
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Parameters
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----------
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p : float
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Atmospheric pressure in Pascal
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rho : float
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Density of the atmospheric air at the observer
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Returns
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-------
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H : float
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Reduced height of the atmosphere in meters
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'''
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_phi = np.deg2rad(self.lat)
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_c1 = 5.2790414e-3
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@@ -194,11 +410,22 @@ class dispersion(Observatory):
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_g0 = 9.780327 # m/s^2
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_g0_local = _g0 * (1 + _c1 * np.sin(_phi)**2 + _c2 * np.sin(_phi)**4 + _c3 * np.sin(_phi)**6 + _c4 * np.sin(_phi)**8)
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_g = _g0_local - (3.0877e-6 - 4.3e-9 * np.sin(_phi)**2) * self.h + 7.2e-13 * self.h**2
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return P / (rho * _g)
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return p / (rho * _g)
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def H_isotherm(self, T):
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'''
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Calculates the reduced height of the atmosphere, assuming an isotherm distribution.
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Calculates the reduced height of the atmosphere,
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assuming an isotherm distribution.
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Parameters
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----------
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T : float
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Atmospheric temperature in Kelvin
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Returns
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-------
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H : float
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Reduced height of the atmosphere in meters
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'''
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_kb = 1.38064852e-23 # kg m2 s-2 K-1
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_m = 4.809651698e-26 # kg (weight per molecule of air, assuming dry air)
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@@ -213,32 +440,63 @@ class dispersion(Observatory):
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return (_kb*T) / (_m * _g0_local)
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def cassiniError(self, z, l1, l2, T, p, RH, xc, dl1=0, dl2=0, dT=0.2, dP=20, dRH=0.02, dCO2=20, dz=0, lat=None, h=None):
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def cassiniError(self, z, l1, l2, T, p, RH, xc, dl1=0, dl2=0, dT=0.2, dP=20,
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dRH=0.02, dCO2=20, dz=0, lat=None, h=None):
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'''
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Calculates the uncertainty in the atmospheric dispersion, following the Cassini model,
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by using fully propagated error analysis.
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This involves almost endless use of the chain rule and evaluation of both the moist
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air and dry air components. Note: dry air does not contain any water, i.e. H=0, x_w=0, etc.
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Calculates the uncertainty in the atmospheric dispersion,
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following the Cassini model, by using fully propagated error analysis.
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This involves almost endless use of the chain rule and evaluation
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of both the moist air and dry air components.
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Note: dry air does not contain any water, i.e. H=0, x_w=0, etc.
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Not taken into account is the errror propagation in the scale height of the atmosphere or
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the zenith error, from my results this should give a small or even negligible difference.
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Not taken into account is the errror propagation in the scale height
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of the atmosphere, from my results this should give a small or even
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negligible difference.
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Parameters:
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z - Zenith angle in degrees
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l1 - Bluest wavelength in micron (0.4 - 2.5 micron)
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l2 - Reddest wavelength in micron (0.4 - 2.5 micron)
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T - Temperature in Kelvin
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p - Pressure in Pascals
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RH - Relative humidity (no units, don't use percentage but value 0<x<1)
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xc - CO2 density in ppm
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dl1 - Uncertainty in the blue wavelength
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dl2 - Uncertainty in the red wavelength
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dT - Uncertainty in the temperature, default: 0.2 K
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dP - Uncertainty in the pressure, default: 20 Pa
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dRH - Uncertainty in the relative humidity, default: 0.02
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dCO2- Uncertainty in the CO2 density, default: 20
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lat - [Optional] Latitude of the observatory in degrees
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h - [Optional] Height in m of the observatory
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Parameters
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----------
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z : float
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Angle of observation in degrees.
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zenith = 0 means the observation is directly overhead.
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l1 : float
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Wavelength of light in microns, at the shortest wavelength
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of interest
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l2 : float
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Wavelength of light in microns, at the longest wavelength
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of interest
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T : float
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Atmospheric temperature in Kelvin
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p : float
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Atmospheric pressure in Pascal
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RH : float
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Atmospheric relative humidity (0<=RH<=1)
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xc : float
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CO2 density in parts per million
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dl1 : float
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Uncertainty in the wavelength in microns, at the shortest
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wavelength of interest
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dl2 : float
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Uncertainty in the wavelength in microns, at the longest
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wavelength of interest
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dT : float (default: 0.2)
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Uncertainty in the atmospheric temperature in Kelvin
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dP : float (default: 20)
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Uncertainty in the atmospheric pressure in Pascal
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dRH : float (default: 0.02)
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Uncertainty in the atmospheric relative humidity
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dCO2: float (default: 20)
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Uncertainty in the atmospheric CO2 density in parts per million
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dz : float (default: 0)
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Uncertainty in the zenith angle, in degrees.
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lat : float (default: None)
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If entered, overrides the latitude attribute of the class.
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h : float (default=None)
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If entered, overrides the altitude attribute of the class.
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Returns
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-------
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dRR : float
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Uncertainty in the atmospheric dispersion in degrees.
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'''
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if lat == None:
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lat = self.lat
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