LSSTApplications  18.0.0+56,19.0.0+1,19.0.0+18,19.0.0+19,19.0.0+21,19.0.0+26,19.0.0+5,19.0.0-1-g20d9b18+12,19.0.0-1-g425ff20,19.0.0-1-g5549ca4,19.0.0-1-g580fafe+12,19.0.0-1-g6fe20d0+4,19.0.0-1-g8c57eb9+12,19.0.0-1-ga72da6b,19.0.0-1-gbfe0924+3,19.0.0-1-gdc0e4a7+17,19.0.0-1-ge272bc4+12,19.0.0-1-ge3aa853+3,19.0.0-16-g3a790c8c,19.0.0-18-g955d782+1,19.0.0-2-g0d9f9cd+19,19.0.0-2-g260436e+3,19.0.0-2-g9b11441+6,19.0.0-2-gd955cfd+25,19.0.0-3-g6513920+3,19.0.0-3-gc4f6e04+2,19.0.0-4-g41ffa1d+5,19.0.0-4-g725f80e+21,19.0.0-5-g0745e3f+3,19.0.0-6-g5a632bb5+1,19.0.0-6-gb6b8b0a+3,19.0.0-7-g686a884,19.0.0-7-gea0a0fe+8,19.0.0-9-gd2f60f3c3,w.2020.03
LSSTDataManagementBasePackage
Functions | Variables
lsst.afw.coord.refraction Namespace Reference

Functions

def refraction (wavelength, elevation, observatory, weather=None)
 
def differentialRefraction (wavelength, wavelengthRef, elevation, observatory, weather=None)
 
def deltaN (wavelength, weather)
 
def densityFactorDry (weather)
 
def densityFactorWater (weather)
 
def humidityToPressure (weather)
 
def extractTemperature (weather, useKelvin=False)
 
def defaultWeather (altitude)
 

Variables

float deltaRefractScale = 1.0E8
 

Function Documentation

◆ defaultWeather()

def lsst.afw.coord.refraction.defaultWeather (   altitude)
Set default local weather conditions if they are missing.

Parameters
----------
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation
altitude : `astropy.units.Quantity`
    The altitude of the observatory, in meters.

Returns
-------
default : `lsst.afw.coord.Weather`
    Updated Weather class with any `nan` values replaced by defaults.

Definition at line 294 of file refraction.py.

294 def defaultWeather(altitude):
295  """Set default local weather conditions if they are missing.
296 
297  Parameters
298  ----------
299  weather : `lsst.afw.coord.Weather`
300  Class containing the measured temperature, pressure, and humidity
301  at the observatory during an observation
302  altitude : `astropy.units.Quantity`
303  The altitude of the observatory, in meters.
304 
305  Returns
306  -------
307  default : `lsst.afw.coord.Weather`
308  Updated Weather class with any `nan` values replaced by defaults.
309  """
310  if isinstance(altitude, units.quantity.Quantity):
311  altitude2 = altitude
312  else:
313  altitude2 = altitude*units.meter
314  p0 = 101325.*units.pascal # sea level air pressure
315  g = 9.80665*units.meter/units.second**2 # typical gravitational acceleration at sea level
316  R0 = 8.31447*units.Joule/(units.mol*units.Kelvin) # gas constant
317  T0 = 19.*units.Celsius # Typical sea-level temperature
318  lapseRate = -6.5*units.Celsius/units.km # Typical rate of change of temperature with altitude
319  M = 0.0289644*units.kg/units.mol # molar mass of dry air
320 
321  temperature = T0 + lapseRate*altitude2
322  temperatureK = temperature.to(units.Kelvin, equivalencies=units.temperature())
323  pressure = p0*np.exp(-(g*M*altitude2)/(R0*temperatureK))
324  humidity = 40. # Typical humidity at many observatory sites.
325  weather = Weather((temperature/units.Celsius).value, (pressure/units.pascal).value, humidity)
326  return weather
327 
def defaultWeather(altitude)
Definition: refraction.py:294

◆ deltaN()

def lsst.afw.coord.refraction.deltaN (   wavelength,
  weather 
)
Calculate the differential refractive index of air.

Parameters
----------
wavelength : `float`
    wavelength is in nanometers
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation

Returns
-------
deltaN : `float`
    The difference of the refractive index of air from 1.,
    calculated as (n_air - 1)*10^8

Notes
-----
The differential refractive index is the difference of
the refractive index from 1., multiplied by 1E8 to simplify
the notation and equations. Calculated as (n_air - 1)*10^8

This replicates equation 14 of [1]_

References
----------
.. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
   Refraction," Publications of the Astronomical Society of the Pacific,
   vol. 108, p. 1051, 1996.

Definition at line 124 of file refraction.py.

124 def deltaN(wavelength, weather):
125  """Calculate the differential refractive index of air.
126 
127  Parameters
128  ----------
129  wavelength : `float`
130  wavelength is in nanometers
131  weather : `lsst.afw.coord.Weather`
132  Class containing the measured temperature, pressure, and humidity
133  at the observatory during an observation
134 
135  Returns
136  -------
137  deltaN : `float`
138  The difference of the refractive index of air from 1.,
139  calculated as (n_air - 1)*10^8
140 
141  Notes
142  -----
143  The differential refractive index is the difference of
144  the refractive index from 1., multiplied by 1E8 to simplify
145  the notation and equations. Calculated as (n_air - 1)*10^8
146 
147  This replicates equation 14 of [1]_
148 
149  References
150  ----------
151  .. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
152  Refraction," Publications of the Astronomical Society of the Pacific,
153  vol. 108, p. 1051, 1996.
154  """
155  waveNum = 1E3/wavelength # want wave number in units 1/micron
156  dryAirTerm = 2371.34 + (683939.7/(130. - waveNum**2.)) + (4547.3/(38.9 - waveNum**2.))
157  wetAirTerm = 6487.31 + 58.058*waveNum**2. - 0.71150*waveNum**4. + 0.08851*waveNum**6.
158  return (dryAirTerm*densityFactorDry(weather) + wetAirTerm*densityFactorWater(weather))
159 
160 
def densityFactorWater(weather)
Definition: refraction.py:196
def densityFactorDry(weather)
Definition: refraction.py:161
def deltaN(wavelength, weather)
Definition: refraction.py:124

◆ densityFactorDry()

def lsst.afw.coord.refraction.densityFactorDry (   weather)
Calculate dry air pressure term to refractive index calculation.

Parameters
----------
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation

Returns
-------
densityFactor : `float`
    Returns the relative density of dry air
    at the given pressure and temperature.

Notes
-----
This replicates equation 15 of [1]_

References
----------
.. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
   Refraction," Publications of the Astronomical Society of the Pacific,
   vol. 108, p. 1051, 1996.

Definition at line 161 of file refraction.py.

161 def densityFactorDry(weather):
162  """Calculate dry air pressure term to refractive index calculation.
163 
164  Parameters
165  ----------
166  weather : `lsst.afw.coord.Weather`
167  Class containing the measured temperature, pressure, and humidity
168  at the observatory during an observation
169 
170  Returns
171  -------
172  densityFactor : `float`
173  Returns the relative density of dry air
174  at the given pressure and temperature.
175 
176  Notes
177  -----
178  This replicates equation 15 of [1]_
179 
180  References
181  ----------
182  .. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
183  Refraction," Publications of the Astronomical Society of the Pacific,
184  vol. 108, p. 1051, 1996.
185  """
186  temperature = extractTemperature(weather, useKelvin=True)
187  waterVaporPressure = humidityToPressure(weather)
188  airPressure = weather.getAirPressure()*units.pascal
189  dryPressure = airPressure - waterVaporPressure
190  eqn = dryPressure.to_value(cds.mbar)*(57.90E-8 - 9.3250E-4/temperature.to_value(units.Kelvin)
191  + 0.25844/temperature.to_value(units.Kelvin)**2.)
192  densityFactor = (1. + eqn)*dryPressure.to_value(cds.mbar)/temperature.to_value(units.Kelvin)
193  return densityFactor
194 
195 
def humidityToPressure(weather)
Definition: refraction.py:233
def densityFactorDry(weather)
Definition: refraction.py:161
def extractTemperature(weather, useKelvin=False)
Definition: refraction.py:270

◆ densityFactorWater()

def lsst.afw.coord.refraction.densityFactorWater (   weather)
Calculate water vapor pressure term to refractive index calculation.

Parameters
----------
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation

Returns
-------
densityFactor : `float`
    Returns the relative density of water vapor
    at the given pressure and temperature.

Notes
-----
This replicates equation 16 of [1]_

References
----------
.. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
   Refraction," Publications of the Astronomical Society of the Pacific,
   vol. 108, p. 1051, 1996.

Definition at line 196 of file refraction.py.

196 def densityFactorWater(weather):
197  """Calculate water vapor pressure term to refractive index calculation.
198 
199  Parameters
200  ----------
201  weather : `lsst.afw.coord.Weather`
202  Class containing the measured temperature, pressure, and humidity
203  at the observatory during an observation
204 
205  Returns
206  -------
207  densityFactor : `float`
208  Returns the relative density of water vapor
209  at the given pressure and temperature.
210 
211  Notes
212  -----
213  This replicates equation 16 of [1]_
214 
215  References
216  ----------
217  .. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
218  Refraction," Publications of the Astronomical Society of the Pacific,
219  vol. 108, p. 1051, 1996.
220  """
221  temperature = extractTemperature(weather, useKelvin=True)
222  waterVaporPressure = humidityToPressure(weather)
223  densityEqn1 = (-2.37321E-3 + 2.23366/temperature.to_value(units.Kelvin)
224  - 710.792/temperature.to_value(units.Kelvin)**2.
225  + 7.75141E-4/temperature.to_value(units.Kelvin)**3.)
226  densityEqn2 = waterVaporPressure.to_value(cds.mbar)*(1. + 3.7E-4*waterVaporPressure.to_value(cds.mbar))
227  relativeDensity = waterVaporPressure.to_value(cds.mbar)/temperature.to_value(units.Kelvin)
228  densityFactor = (1 + densityEqn2*densityEqn1)*relativeDensity
229 
230  return densityFactor
231 
232 
def densityFactorWater(weather)
Definition: refraction.py:196
def humidityToPressure(weather)
Definition: refraction.py:233
def extractTemperature(weather, useKelvin=False)
Definition: refraction.py:270

◆ differentialRefraction()

def lsst.afw.coord.refraction.differentialRefraction (   wavelength,
  wavelengthRef,
  elevation,
  observatory,
  weather = None 
)
Calculate the differential refraction between two wavelengths.

Parameters
----------
wavelength : `float`
    wavelength is in nm (valid for 230.2 < wavelength < 2058.6)
wavelengthRef : `float`
    Reference wavelength, typically the effective wavelength of a filter.
elevation : `lsst.geom.Angle`
    Elevation of the observation, as an Angle.
observatory : `lsst.afw.coord.Observatory`
    Class containing the longitude, latitude,
    and altitude of the observatory.
weather : `lsst.afw.coord.Weather`, optional
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation
    If omitted, typical conditions for the observatory's elevation will be calculated.

Returns
-------
differentialRefraction : `lsst.geom.Angle`
    The refraction at `wavelength` minus the refraction at `wavelengthRef`.

Definition at line 95 of file refraction.py.

95 def differentialRefraction(wavelength, wavelengthRef, elevation, observatory, weather=None):
96  """Calculate the differential refraction between two wavelengths.
97 
98  Parameters
99  ----------
100  wavelength : `float`
101  wavelength is in nm (valid for 230.2 < wavelength < 2058.6)
102  wavelengthRef : `float`
103  Reference wavelength, typically the effective wavelength of a filter.
104  elevation : `lsst.geom.Angle`
105  Elevation of the observation, as an Angle.
106  observatory : `lsst.afw.coord.Observatory`
107  Class containing the longitude, latitude,
108  and altitude of the observatory.
109  weather : `lsst.afw.coord.Weather`, optional
110  Class containing the measured temperature, pressure, and humidity
111  at the observatory during an observation
112  If omitted, typical conditions for the observatory's elevation will be calculated.
113 
114  Returns
115  -------
116  differentialRefraction : `lsst.geom.Angle`
117  The refraction at `wavelength` minus the refraction at `wavelengthRef`.
118  """
119  refractionStart = refraction(wavelength, elevation, observatory, weather=weather)
120  refractionEnd = refraction(wavelengthRef, elevation, observatory, weather=weather)
121  return refractionStart - refractionEnd
122 
123 
def refraction(wavelength, elevation, observatory, weather=None)
Definition: refraction.py:37
def differentialRefraction(wavelength, wavelengthRef, elevation, observatory, weather=None)
Definition: refraction.py:95

◆ extractTemperature()

def lsst.afw.coord.refraction.extractTemperature (   weather,
  useKelvin = False 
)
Thin wrapper to return the measured temperature from an observation.

Parameters
----------
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation
useKelvin : bool, optional
    Set to True to return the temperature in Kelvin instead of Celsius
    This is needed because Astropy can't easily convert
    between Kelvin and Celsius.

Returns
-------
temperature : `astropy.units.Quantity`
    The temperature in Celsius, unless `useKelvin` is set.

Definition at line 270 of file refraction.py.

270 def extractTemperature(weather, useKelvin=False):
271  """Thin wrapper to return the measured temperature from an observation.
272 
273  Parameters
274  ----------
275  weather : `lsst.afw.coord.Weather`
276  Class containing the measured temperature, pressure, and humidity
277  at the observatory during an observation
278  useKelvin : bool, optional
279  Set to True to return the temperature in Kelvin instead of Celsius
280  This is needed because Astropy can't easily convert
281  between Kelvin and Celsius.
282 
283  Returns
284  -------
285  temperature : `astropy.units.Quantity`
286  The temperature in Celsius, unless `useKelvin` is set.
287  """
288  temperature = weather.getAirTemperature()*units.Celsius
289  if useKelvin:
290  temperature = temperature.to(units.Kelvin, equivalencies=units.temperature())
291  return temperature
292 
293 
def extractTemperature(weather, useKelvin=False)
Definition: refraction.py:270

◆ humidityToPressure()

def lsst.afw.coord.refraction.humidityToPressure (   weather)
Convert humidity and temperature to water vapor pressure.

Parameters
----------
weather : `lsst.afw.coord.Weather`
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation

Returns
-------
pressure : `astropy.units.Quantity`
    The water vapor pressure in Pascals
    calculated from the given humidity and temperature.

Notes
-----
This replicates equations 18 & 20 of [1]_

References
----------
.. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
   Refraction," Publications of the Astronomical Society of the Pacific,
   vol. 108, p. 1051, 1996.

Definition at line 233 of file refraction.py.

233 def humidityToPressure(weather):
234  """Convert humidity and temperature to water vapor pressure.
235 
236  Parameters
237  ----------
238  weather : `lsst.afw.coord.Weather`
239  Class containing the measured temperature, pressure, and humidity
240  at the observatory during an observation
241 
242  Returns
243  -------
244  pressure : `astropy.units.Quantity`
245  The water vapor pressure in Pascals
246  calculated from the given humidity and temperature.
247 
248  Notes
249  -----
250  This replicates equations 18 & 20 of [1]_
251 
252  References
253  ----------
254  .. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
255  Refraction," Publications of the Astronomical Society of the Pacific,
256  vol. 108, p. 1051, 1996.
257  """
258  humidity = weather.getHumidity()
259  x = np.log(humidity/100.0)
260  temperature = extractTemperature(weather)
261  temperatureEqn1 = (temperature + 238.3*units.Celsius)*x + 17.2694*temperature
262  temperatureEqn2 = (temperature + 238.3*units.Celsius)*(17.2694 - x) - 17.2694*temperature
263  dewPoint = 238.3*temperatureEqn1/temperatureEqn2
264  waterVaporPressure = (4.50874 + 0.341724*dewPoint + 0.0106778*dewPoint**2 + 0.184889E-3*dewPoint**3
265  + 0.238294E-5*dewPoint**4 + 0.203447E-7*dewPoint**5)*133.32239*units.pascal
266 
267  return waterVaporPressure
268 
269 
def humidityToPressure(weather)
Definition: refraction.py:233
def extractTemperature(weather, useKelvin=False)
Definition: refraction.py:270

◆ refraction()

def lsst.afw.coord.refraction.refraction (   wavelength,
  elevation,
  observatory,
  weather = None 
)
Calculate overall refraction under atmospheric and observing conditions.

Parameters
----------
wavelength : `float`
    wavelength is in nm (valid for 230.2 < wavelength < 2058.6)
elevation : `lsst.geom.Angle`
    Elevation of the observation, as an Angle.
observatory : `lsst.afw.coord.Observatory`
    Class containing the longitude, latitude,
    and altitude of the observatory.
weather : `lsst.afw.coord.Weather`, optional
    Class containing the measured temperature, pressure, and humidity
    at the observatory during an observation
    If omitted, typical conditions for the observatory's elevation will be calculated.

Returns
-------
refraction : `lsst.geom.Angle`
    The angular refraction for light of the given wavelength,
    under the given observing conditions.

Notes
-----
The calculation is taken from [1]_.

References
----------
.. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
   Refraction," Publications of the Astronomical Society of the Pacific,
   vol. 108, p. 1051, 1996.

Definition at line 37 of file refraction.py.

37 def refraction(wavelength, elevation, observatory, weather=None):
38  """Calculate overall refraction under atmospheric and observing conditions.
39 
40  Parameters
41  ----------
42  wavelength : `float`
43  wavelength is in nm (valid for 230.2 < wavelength < 2058.6)
44  elevation : `lsst.geom.Angle`
45  Elevation of the observation, as an Angle.
46  observatory : `lsst.afw.coord.Observatory`
47  Class containing the longitude, latitude,
48  and altitude of the observatory.
49  weather : `lsst.afw.coord.Weather`, optional
50  Class containing the measured temperature, pressure, and humidity
51  at the observatory during an observation
52  If omitted, typical conditions for the observatory's elevation will be calculated.
53 
54  Returns
55  -------
56  refraction : `lsst.geom.Angle`
57  The angular refraction for light of the given wavelength,
58  under the given observing conditions.
59 
60  Notes
61  -----
62  The calculation is taken from [1]_.
63 
64  References
65  ----------
66  .. [1] R. C. Stone, "An Accurate Method for Computing Atmospheric
67  Refraction," Publications of the Astronomical Society of the Pacific,
68  vol. 108, p. 1051, 1996.
69  """
70  if wavelength < 230.2:
71  raise ValueError("Refraction calculation is valid for wavelengths between 230.2 and 2058.6 nm.")
72  if wavelength > 2058.6:
73  raise ValueError("Refraction calculation is valid for wavelengths between 230.2 and 2058.6 nm.")
74  latitude = observatory.getLatitude()
75  altitude = observatory.getElevation()
76  if weather is None:
77  weather = defaultWeather(altitude*units.meter)
78  reducedN = deltaN(wavelength, weather)/deltaRefractScale
79  temperature = extractTemperature(weather, useKelvin=True)
80  atmosScaleheightRatio = 4.5908E-6*temperature.to_value(units.Kelvin)
81 
82  # Account for oblate Earth
83  # This replicates equation 10 of Stone 1996
84  relativeGravity = (1. + 0.005302*np.sin(latitude.asRadians())**2.
85  - 0.00000583*np.sin(2.*latitude.asRadians())**2. - 0.000000315*altitude)
86 
87  # Calculate the tangent of the zenith angle.
88  tanZ = np.tan(np.pi/2. - elevation.asRadians())
89  atmosTerm1 = reducedN*relativeGravity*(1. - atmosScaleheightRatio)
90  atmosTerm2 = reducedN*relativeGravity*(atmosScaleheightRatio - reducedN/2.)
91  result = float(atmosTerm1*tanZ + atmosTerm2*tanZ**3.)*lsst.geom.radians
92  return result
93 
94 
def defaultWeather(altitude)
Definition: refraction.py:294
def refraction(wavelength, elevation, observatory, weather=None)
Definition: refraction.py:37
def deltaN(wavelength, weather)
Definition: refraction.py:124
def extractTemperature(weather, useKelvin=False)
Definition: refraction.py:270

Variable Documentation

◆ deltaRefractScale

float lsst.afw.coord.refraction.deltaRefractScale = 1.0E8

Definition at line 34 of file refraction.py.