optmat.conditions#

States (pressure and temperature) and air-to-vacuum wavelengths.

Measurements are reported at, or reduced to, a stated pressure and temperature (“0 degrees C and 760 Torr”, “15 degrees C and 1 atm”, “1 bar and 0 degrees C”); this module holds the state and the named states. What a state implies for a medium (the number density of a gas, optmat.gas.eos) belongs to that medium’s subpackage.

Pressures here are in pascals, like everything else in the package.

Much of the older literature (Leonard 1974, Cuthbertson) gives wavelengths in standard air (15 degrees C, 101 325 Pa); vacuum_wavelength_from_standard_air() converts them with Edlen’s 1966 dispersion formula for standard air. Solids measured by minimum deviation in room air give an index relative to that air; air_refractivity() gives its refractivity at the room’s temperature and pressure.

Module Attributes

`EVALUATION_VERSION`	The version of this module's evaluation code, in the identity of every model that evaluates through it; raised whenever the code changes its output (OEP 1, section 4.8).
`ONE_ATM_0C`	0 degrees C and 1 atm (760 Torr): the "STP" or "NTP" of most refractivity papers.
`ONE_BAR_0C`	0 degrees C and 1 bar: Borzsonyi et al. (2008) and Luna's normalisation.
`ONE_ATM_15C`	15 degrees C and 1 atm: the atmospheric-science convention (He et al. 2021).
`ONE_ATM_20C`	20 degrees C and 1 atm: the frequency-comb measurements (Zhang et al. 2008).

Functions

`air_refractivity`(vacuum_wavenumber, state)	Return `n - 1` of dry air at a temperature and pressure, from Edlen 1966.
`standard_air_refractivity`(vacuum_wavenumber)	Return `n - 1` of standard air from Edlen's 1966 formula.
`vacuum_wavelength_from_standard_air`(...)	Convert wavelengths measured in standard air to vacuum wavelengths.

Classes

State(pressure, temperature)

A thermodynamic state: a pressure and a temperature.

optmat.conditions.EVALUATION_VERSION: Final = 1#: The version of this module’s evaluation code, in the identity of every model that evaluates through it; raised whenever the code changes its output (OEP 1, section 4.8).

optmat.conditions.ONE_ATM_0C: Final = State(pressure=101325.0, temperature=273.15)#: 0 degrees C and 1 atm (760 Torr): the “STP” or “NTP” of most refractivity papers.

optmat.conditions.ONE_ATM_15C: Final = State(pressure=101325.0, temperature=288.15)#: 15 degrees C and 1 atm: the atmospheric-science convention (He et al. 2021).

optmat.conditions.ONE_ATM_20C: Final = State(pressure=101325.0, temperature=293.15)#: 20 degrees C and 1 atm: the frequency-comb measurements (Zhang et al. 2008).

optmat.conditions.ONE_BAR_0C: Final = State(pressure=100000.0, temperature=273.15)#: 0 degrees C and 1 bar: Borzsonyi et al. (2008) and Luna’s normalisation.

class optmat.conditions.State(pressure, temperature)[source]#

Bases: object

A thermodynamic state: a pressure and a temperature.

Attributes:

pressurefloat: Absolute pressure in Pa, > 0.
temperaturefloat: Temperature in K, > 0.

Raises:

StateError: If either value is not finite and positive.

Examples

>>> State(101325.0, 273.15).pressure
101325.0

pressure: float#

temperature: float#

optmat.conditions.air_refractivity(vacuum_wavenumber, state)[source]#

Return n - 1 of dry air at a temperature and pressure, from Edlen 1966.

Edlen’s Eq. (12) (Metrologia 2, 71 (1966), p. 78) scales the standard-air refractivity by the density factor of dry air, (n - 1)_tp = p (n - 1)_s / 720.775 * [1 + p (0.817 - 0.0133 t) 1e-6] / (1 + 0.0036610 t), with t in degrees C and p in torr, for 5 to 30 degrees C. It returns standard_air_refractivity() at 15 degrees C and 760 torr. Water vapour and a CO2 content other than 0.03 % are not included (Edlen’s corrections for them are some 1e-7 at room conditions).

Parameters:

vacuum_wavenumberarray_like or float: Vacuum wavenumber 1 / lambda_vac in m^-1 (roughly 200 nm to 2 um, the range of the standard-air formula).
stateState: The air’s pressure (Pa) and temperature (K); the formula is stated for 5 to 30 degrees C and laboratory pressures.

Returns:

numpy.ndarray: n - 1 of the air, the shape of the input.

Examples

>>> f"{float(air_refractivity(1 / 800e-9, ONE_ATM_20C)):.4e}"
'2.7033e-04'

optmat.conditions.standard_air_refractivity(vacuum_wavenumber)[source]#

Return n - 1 of standard air from Edlen’s 1966 formula.

Standard air is dry air with 0.03 % CO2 at 15 degrees C and 101 325 Pa. The formula is 1e8 (n - 1) = 8342.13 + 2406030 / (130 - s^2) + 15997 / (38.9 - s^2) with s the vacuum wavenumber in um^-1 (B. Edlen, Metrologia 2, 71 (1966)).

Parameters:

vacuum_wavenumberarray_like or float: Vacuum wavenumber 1 / lambda_vac in m^-1; the formula is fitted over roughly 200 nm to 2 um.

Returns:

numpy.ndarray: n - 1 of standard air, the shape of the input.

Examples

>>> f"{float(standard_air_refractivity(1 / 546.2e-9)):.4e}"
'2.7790e-04'

optmat.conditions.vacuum_wavelength_from_standard_air(air_wavelength)[source]#

Convert wavelengths measured in standard air to vacuum wavelengths.

Solves lambda_vac = n(lambda_vac) lambda_air with standard_air_refractivity() by fixed-point iteration; the refractivity changes by ~1e-10 per iteration after the first, so four iterations reach double precision.

Parameters:

air_wavelengtharray_like or float: Wavelength in standard air, m.

Returns:

numpy.ndarray: Vacuum wavelength, m, the shape of the input.

Examples

>>> f"{float(vacuum_wavelength_from_standard_air(546.0740e-9)) * 1e9:.4f}"
'546.2258'