Wavelength conversion (air and vacuum)¶

PyA provides tools to convert wavelengths from air into vacuum conditions and vice versa:

airtovac2

vactoair2

These functions allow to use the conversions specified by:

Edlen 1953, J. Opt. Soc. Am 43 no. 5
Peck and Reeder 1972, J. Opt. Soc. 62 no. 8
Ciddor 1996, Applied Optics 35 no. 9

Warning

The function airtovac and vactoair are based on the formula by Edlen 1953. It seems that air wavelengths (or wavenumbers) are used, where vacuum wavenumbers should be used.

airtovac
vactoair

Moreover, you can use:

specAirVacConvert

to convert from vacuum into air conditions or vice versa, but retain the input wavelength axis.

Usage examples for airtovac2 and vactoair2¶

Example: From air to vacuum and back¶

from __future__ import print_function, division
from PyAstronomy import pyasl
import numpy as np

# Define wavelength array
wvl = np.arange(10) + 5000.0
print("Input wavelengths: ", wvl)

# Convert wavelength in air to wavelength
# in vacuum. By default, the conversion
# specified by Ciddor 1996 are used.
wvlVac = pyasl.airtovac2(wvl)
print("Wavelength in vacuum: ", wvlVac)

# Convert wavelength from vacuum to air
wvlAir = pyasl.vactoair2(wvlVac)
print("Wavelength in air: ", wvlAir)

Example: Compare Edlen and Ciddor conversions¶

from PyAstronomy import pyasl
import numpy
import matplotlib.pylab as plt

# Compare the Edlen and Ciddor conversions
wvl = numpy.arange(3000, 10000, 1.0)
wvlVacCiddor = pyasl.airtovac2(wvl, mode="ciddor")
wvlVacEdlen = pyasl.airtovac2(wvl, mode="edlen53")

plt.subplot(2, 1, 1)
plt.title("Difference in air wavelength (Ciddor-Edlen)")
plt.ylabel("dWvl [A]")
plt.xlabel("Vacuum wvl [A]")
plt.plot(wvl, wvlVacCiddor-wvlVacEdlen, 'b.-')
plt.subplot(2, 1, 2)
plt.title("Difference in air wavelength (Ciddor-Edlen, in RV)")
plt.ylabel("dRV [m/s]")
plt.xlabel("Vacuum wvl [A]")
plt.plot(wvl, (wvlVacCiddor-wvlVacEdlen)/wvlVacCiddor*299792458., 'b.-')
plt.show()

API documentation: airtovac2 and vactoair2¶

PyAstronomy.pyasl.airtovac2(wvl, mode='ciddor', **kwargs)¶

Converts wavelength in air into wavelength in vacuum.

This function is a wrapper around the RefractiveIndexAV class.

Parameters

wvl :float or array: Wavelength in vacuum [A].
modestring, {edlen53, peckReeder, ciddor}, optional: The source for the wavelength conversion. The default is “ciddor”.
kwargsdict: Additional parameters handed to the airtovac method of RefractiveIndexAV.

Returns

wvlfloat or array: Wavelength in vacuum [A].

PyAstronomy.pyasl.vactoair2(wvl, mode='ciddor', **kwargs)¶

Converts wavelength in vacuum into wavelength in air.

This function is a wrapper around the RefractiveIndexAV class.

Parameters

wvl :float or array: Wavelength in vacuum [A].
modestring, {edlen53, peckReeder, ciddor}, optional: The source for the wavelength conversion. The default is “ciddor”.
kwargsdict: Additional parameters handed to the vactoair method of RefractiveIndexAV.

Returns

wvlfloat or array: Wavelength in air [A].

Obtaining the refractive index¶

Although the conversion of wavelength between air and vacuum conditions is the primary application targeted here, what is really needed to carry out the conversion is the refractive index.

class PyAstronomy.pyasl.RefractiveIndexAV(mode='ciddor')¶

Refractive index for conversion between air- and vacuum wavelengths.

The conversion is based on the formulae provided either by:

Edlen 1953, J. Opt. Soc. Am 43 no. 5
Peck and Reeder 1972, J. Opt. Soc. 62 no. 8
Ciddor 1996, Applied Optics 35 no. 9

This class provides the routine refractiveIndex, vactoair, and airtovac to convert between wavelengths in air and vacuum.

The method refractiveIndex points to either of _edlen53, _ciddor, or _peckReeder depending on the mode chosen.

To conversion from vacuum to air wavelengths is given by the respective formulae provided by the authors of the above papers, who all specify the refractive index of “standard air” as a function of vacuum wave number. The reverse conversion from air into vacuum is done by applying an iterative scheme. Standard air is at 15 degrees Celsius, dry, and at a pressure of 750 mmHg = 101325 Pa. Ciddor assumes a CO2 concentration of 450 ppm, while Edlen, and Peck and Reeder have assumed 300 ppm.

Parameters

modestring, {edlen53, peckReeder, ciddor}, optional: The source for the wavelength conversion. The default is “ciddor”.

Methods

`airtovac`(wvl[, precision, maxiter])	Convert air wavelength into wavelength in vacuum.
`vactoair`(wvl, **kwargs)	Convert vacuum wavelength into wavelength in air.

_ciddor(wvl, xc=None)¶

Refractive index given by Ciddor 1996.

Parameters

wvlfloat or array: Vacuum wavelength [A]
xcfloat, optional: Concentration of CO2 [ppm]

Returns

nfloat or array: Refractive index

_edlen53(wvl)¶

Refractive index according to Edlen 1953.

Parameters

wvlfloat or array: Vacuum wavelength [A]

Returns

nfloat or array: The refractive index.

_peckReeder(wvl)¶

Refractive index from Peck and Reeder 1972.

Parameters

wvlfloat or array: Vacuum wavelength [A]

Returns

nfloat or array: The refractive index.

airtovac(wvl, precision=1e-12, maxiter=30, **kwargs)¶

Convert air wavelength into wavelength in vacuum.

An iterative scheme is applied to invert the formula.

Parameters

wvlfloat or array: Wavelength in vacuum [A].
precisionfloat, optional: The target precision beyond which iteration should be stopped; default is 1e-12.
maxiterint, optional: Maximum number of iterations used to invert the conversion; default is 30.
kwargsdict: Additional keywords eventually needed in the call to the refractiveIndex function (depends on the specified ‘mode’).

Returns

wvlfloat or array: Wavelength in air.

vactoair(wvl, **kwargs)¶

Convert vacuum wavelength into wavelength in air.

Parameters

wvlfloat or array: Wavelength in vacuum [A].
kwargsdict: Additional keywords eventually needed in the call to the refractiveIndex function (depends on the specified ‘mode’).

Returns

wvlfloat or array: Wavelength in air.

Example: Obtain refractive index of standard air¶

from __future__ import print_function, division
from PyAstronomy import pyasl
import numpy as np

# Define wavelength array
wvl = np.arange(10) + 5000.0

# Obtain refractive index according to Ciddor 1996
ri = pyasl.RefractiveIndexAV(mode="ciddor")
n = ri.refractiveIndex(wvl)

print("Wavelength and 1.0 - Refractive index of 'standard air':")
for w, nc in zip(wvl, n):
    print("{0:5.1f}  {1:10.8e}".format(w, nc-1.0))

Transform spectrum, but retain wavelength axis¶

PyAstronomy.pyasl.specAirVacConvert(wvl, flux, direction, dontUse2=False)¶

Transform spectrum between air and vacuum wavelengths.

In contrast to airtovac() and vactoair(), which only transform the wavelength axis, this function converts the wavelength axis and interpolates the shifted spectrum to retain the input wavelength axis.

Due to the shift, a fraction of the spectrum is lost on one side, while there is no valid information on the other. Therefore, the function returns both a new flux array obtained by linear interpolation and an array of valid indices, i.e., those indices in the new spectrum, which are not NaN.

Warning

Linear interpolation of the spectrum can affect its noise properties. This function does nothing to prevent or correct for that effect.

Parameters

wvlarray: Input wavelength axis.
fluxarray: Input flux array.
directionstring, {“airtovac”,”vactoair”}: If the direction is “vactoair”, the input spectrum is assumed to be obtained in vacuum conditions. The opposite is true otherwise.
dontUse2boolean, optional: If True, the now deprecated function airtovac and vactoair will be used. Otherwise (default), airtovac2 and vactoair2 will be used with default settings.

Returns

New fluxarray: The shifted flux array, defined on the input wavelength axis.
Valid indicesarray: The array of valid, i.e., not NaN, indices.

Example: Convert spectrum from vacuum into air conditions¶

from PyAstronomy import pyasl
from PyAstronomy import funcFit as fuf
import numpy as np
import matplotlib.pylab as plt

g = fuf.GaussFit1d()
g["A"] = -0.1
g["sig"] = 0.03
g["mu"] = 5004.4752
g["off"] = 1.0

# Create a "spectrum" ...
wvl = np.linspace(5000., 5010., 1000)
flux = g.evaluate(wvl)
# ... and add some noise
flux += np.random.normal(0., 0.02, len(wvl))

# Assume that this spectrum is one observed
# or modeled in vacuum conditions. We want
# to convert it into a spectrum in air, but
# retain the old wavelength axis.
airflux, vind = pyasl.specAirVacConvert(wvl, flux,
                                        direction="vactoair")

# Plot the result
plt.plot(wvl, flux, "b.-")
plt.plot(wvl, airflux, "r.-")
plt.show()

API documentation: airtovac and vactoair¶

Note

These function are now considered deprecated.

Both functions have been ported from IDL’s astrolib.

PyAstronomy.pyasl.airtovac(wave, depWarn=True)¶

Convert air wavelengths to vacuum wavelengths

Warning

The conversion implemented here is based on the older formulae given by Edlen 1953. Furthermore, it seems that wave numbers in air are used, where vacuum wave numbers should be used, which, however, produces only a second-order deviation. Consider using airtovac2() instead.

Parameters

wavefloat, array: The wavelength in air [Angstrom]
depWarnboolean, optional: If True (default), a deprecation warning will be given.

Returns

Wavelengtharray: Wavelength in vacuum [Angstrom]

Notes

Note

This function was ported from the IDL Astronomy User’s Library.

IDL - Documentation

NAME:

AIRTOVAC

PURPOSE:

Convert air wavelengths to vacuum wavelengths

EXPLANATION:

Wavelengths are corrected for the index of refraction of air under standard conditions. Wavelength values below 2000 A will not be altered. Uses the IAU standard for conversion given in Morton (1991 Ap.J. Suppl. 77, 119)

CALLING SEQUENCE:

AIRTOVAC, WAVE

INPUT/OUTPUT:

WAVE - Wavelength in Angstroms, scalar or vector: WAVE should be input as air wavelength(s), it will be returned as vacuum wavelength(s). WAVE is always converted to double precision upon return.

EXAMPLE:

If the air wavelength is W = 6056.125 (a Krypton line), then AIRTOVAC, W yields an vacuum wavelength of W = 6057.8019

METHOD:

See Morton (Ap. J. Suppl. 77, 119) for the formula used

REVISION HISTORY

Written W. Landsman November 1991 Converted to IDL V5.0 W. Landsman September 1997

PyAstronomy.pyasl.vactoair(wave, depWarn=True)¶

Convert vacuum wavelengths to air wavelengths

Warning

The conversion implemented here is based on the older formulae given by Edlen 1953. Furthermore, it seems that wave numbers in air are used, where vacuum wave numbers should be used, which, however, produces only a second-order deviation. Consider using vactoair2() instead.

Parameters

wavefloat, array: The wavelength in vacuum [Angstrom]

Returns

Wavelengtharray,: Wavelength in air [Angstrom]
depWarnboolean, optional: If True (default), a deprecation warning will be given.

Notes

Note

This function was ported from the IDL Astronomy User’s Library.

IDL - Documentation

NAME:

VACTOAIR

PURPOSE:

Convert vacuum wavelengths to air wavelengths

EXPLANATION:

Corrects for the index of refraction of air under standard conditions. Wavelength values below 2000 A will not be altered. Accurate to about 0.005 A

CALLING SEQUENCE:

VACTOAIR, WAVE

INPUT/OUTPUT:

WAVE - Wavelength in Angstroms, scalar or vector: WAVE should be input as vacuum wavelength(s), it will be returned as air wavelength(s). WAVE is always converted to double precision

EXAMPLE:

If the vacuum wavelength is W = 2000, then

IDL> VACTOAIR, W

yields an air wavelength of W = 1999.353 Angstroms

METHOD:

An approximation to the 4th power of inverse wavenumber is used See IUE Image Processing Manual Page 6-15.

REVISION HISTORY

Written, D. Lindler 1982 Documentation W. Landsman Feb. 1989 Converted to IDL V5.0 W. Landsman September 1997

Wavelength conversion (air and vacuum)¶

Usage examples for airtovac2 and vactoair2¶

Example: From air to vacuum and back¶

Example: Compare Edlen and Ciddor conversions¶

API documentation: airtovac2 and vactoair2¶

Obtaining the refractive index¶

Example: Obtain refractive index of standard air¶

Transform spectrum, but retain wavelength axis¶

Example: Convert spectrum from vacuum into air conditions¶

API documentation: airtovac and vactoair¶

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