Spectrum¶

This module contains a few different routines for the manipulation of spectra.

Log lambda spacing¶

Throughout Starfish, we try to utilize log-lambda spaced spectra whenever possible. This is because this sampling preserves the Doppler content of the spectrum at the lowest possible sampling. A spectrum spaced linear in log lambda has equal-velocity pixels, meaning that

\[\frac{v}{c} = \frac{\Delta \lambda}{\lambda}\]

A log lambda spectrum is defined by the WCS keywords CDELT1, CRVAL1, and NAXIS1. They are related to the physical wavelengths by the following relationship

\[\lambda = 10^{{\rm CRVAL1} + {\rm CDELT1} \times i}\]

where \(i\) is the pixel index, with \(i = 0\) referring to the first pixel and \(i = ({\rm NAXIS1} - 1)\) referring to the last pixel.

The wavelength array and header keywords are often stored in a wl_dict dictionary, which looks like {"wl":wl, "CRVAL1":CRVAL1, "CDELT1":CDELT1, "NAXIS1":NAXIS1}.

These keywords are related to various wavelengths by

\[\frac{v}{c} = \frac{\Delta \lambda}{\lambda} = 10^{\rm CDELT1} - 1\]

\[{\rm CDELT1} = \log_{10} \left ( \frac{v}{c} + 1 \right )\]

\[{\rm CRVAL1} = \log_{10} ( \lambda_{\rm start})\]

Many spectral routines utilize a keyword dv, which stands for \(\Delta v\), or the velocity difference (measured in km/s) that corresponds to the width of one pixel.

\[\textrm{dv} = c \frac{\Delta \lambda}{\lambda}\]

When resampling wavelength grids that are not log-lambda spaced (e.g., the raw synthetic spectrum from the library) onto a log-lambda grid, the dv must be calculated. Generally, calculate_dv() works by measuring the velocity difference of every pixel and choosing the smallest, that way no spectral information will be lost.

Data Spectrum¶

The DataSpectrum holds the data spectrum that you wish to fit. You may read your data into this object in a few ways. First let’s introduce the object and then discuss the reading methods.

First, you can construct an instance using the traditional __init__ method:

# Read waves, fluxes, and sigmas from your dataset
# as numpy arrays using your own method.
waves, fluxes, sigmas = myownmethod()

myspec = DataSpectrum(waves, fluxes, sigmas)

Since myownmethod() may require a bunch of additional dependencies (e.g, IRAF), for convenience you may want to first read your data using your own custom method but then save it to a different format, like hdf5. Since HDF5 files are all the rage these days, you may want to use them to store your entire data set in a single binary file. If you store your spectra in an HDF5 file as (norders, npix) arrays:

/
/waves
/fluxes
/sigmas
/masks

Then can read your data in as:

myspec = DataSpectrum.load("myspec.HDF5")

When using HDF5 files, we highly recommended using a GUI program like HDF View to make it easer to see what’s going on.