Normalization

The theoretical RV precision (only due to photon noise) is inversely dependent on the spectral flux. That is as the flux increases the error on the RV measurement decreases.

The flux of a observed spectra is dependant on a number of factors e.g.

  • Star luminosity
  • Integration time
  • Telescope area
  • Instrument efficiency

The photon flux can be scaled by multiplicative constant which affects the photon SNR and the radial velocity precision.

To compare the relative theoretical precision between different synthetic spectra they are normalized consistently.

This is achieved by normalizing to a specific SNR per resolution element at a particular location.

By default this is a SNR of 100 at the center of the “J” band. Other band centers or wavelengths as well as other SNR values can be chosen.

The following functions are used to determine the normalization constant to divide a spectrum by to achieve the desired normalization.

eniric.snr_normalization.snr_constant_wav(wav: numpy.ndarray, flux: numpy.ndarray, wav_ref: float, snr: Union[int, float] = 100, sampling: Union[int, float] = 3.0, verbose: bool = False) → float[source]

Determine the normalization constant to achieve a SNR at given wavelength.

SNR estimated by the square root of the number of photons in a resolution element.

Parameters:
  • wav (ndarray) – Wavelength array.
  • flux (ndarray) – Photon flux array (photons/s/cm**2).
  • wav_ref (float) – Wavelength to set the SNR per resolution element.
  • snr (int, float) – SNR per resolution element to achieve. Default is 100.
  • sampling (int or float) – Number of pixels per resolution element. Default is 3.
  • verbose (bool) – Enable verbose. Default is False.
Returns:

norm_value – Normalization value to divide the flux by to achieve the desired SNR “SNR” in resolution element (defined by “sampling”) around the wavelength “wav_ref”.
Return type:

float

Note

If sampling is a float it will rounded to the nearest integer for indexing.

eniric.snr_normalization.snr_constant_band(wav: numpy.ndarray, flux: numpy.ndarray, snr: Union[int, float] = 100, band: str = 'J', sampling: Union[int, float] = 3.0, verbose: bool = False) → float[source]

Determine the normalization constant to achieve a SNR in the middle of a given band.

SNR estimated by the square root of the number of photons in a resolution element.

Parameters:
  • wav (ndarray) – Wavelength array in microns.
  • flux (ndarray) – Photon flux array (photons/s/cm**2).
  • snr (int or float) – SNR per resolution element to achieve. Default is 100.
  • band (str) – Band to use for normalization. Default is “J”.
  • sampling (int or float) – Number of pixels per resolution element. Default is 3.
  • verbose (bool) – Enable verbose. Default is False.
Returns:

norm_value – Normalization value to divide spectrum by to achieve a signal-to-noise level of snr within an resolution element in the middle of the band.
Return type:

float

Note

This is a wrapper around snr_constant_wav, using the band center.

Warning

Wavelength is expected in microns!

eniric.snr_normalization.sampling_index(index: int, sampling: int = 3, array_length: Optional[int] = None) → numpy.ndarray[source]

Get a small number of index values around the given index value.

Parameters:
  • index (int) – The index value which to select values around.
  • sampling (int) – Number of index values to return (sampling per resolution element). Must be an integer. Default is 3.
  • array_length (int or None) – Length of array the indexes will be used in. To not exceed array length. Default is None.
Returns:

indexes – The index values.
Return type:

ndarray