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Relative Flux Calibration

Using Reference Stars to

Correct Your Spectrum

S. Donnell

AAVSO Spectroscopy Special Interest Group Lead

Version 1.0, Jan 2025

Astronomical Spectroscopy

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Factors Affecting the Quality of a Spectrum

The atmosphere you’re looking through.�
The instrument used to obtain the spectrum (telescope and spectrograph).

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Effect on the Spectrum

Both atmosphere and instrument introduce differences between the 1D profile you obtain and the ideal 1D profile obtained from a perfect instrument located outside of Earth’s atmosphere.�

Overall shape of the continuum.
Relative depths of absorption lines.
Signal to noise at blue and red ends of the spectrum.

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Difference Between Corrected and Uncorrected Spectrum

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Atmosphere - Extinction

Wavelength-dependent reduction in the intensity of light (flux) due to absorption and scattering.
Atmosphere absorbs/scatters blue the most and red the least.
Effect is more pronounced at higher zenith angles

Zenith Angle = 80 deg

Zenith Angle = 60 deg

Zenith Angle = 40 deg

Zenith Angle = 0 deg

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Atmosphere - Extinction

Spectrum is affected:

Flux is reduced overall, but with blue the most and red the least.
The continuum shape will differ from the ideal exoatmospheric shape.

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Atmosphere - Dispersion

Wavelength-dependent differential refraction
Star is spread into a tiny spectrum perpendicular to the horizon with blue at higher elevation than red
Orientation of the slit relative to the ideal “perpendicular to the horizon” affects the amount of light passing through the blue and red ends of the spectrum
Contributes to the continuum shape differing from the ideal exoatmospheric shape

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Atmosphere - Dispersion

The amount of dispersion is comparable to the width of a slit in a typical spectrometer
A slit oriented perpendicular to the horizon will pass most or all of the light across the spectrum.
A slit oriented horizontal to the horizon will have a decrease in intensity in the blue and red ends.
Mostly affects slit spectrometers with broad spectral ranges and narrow slits.

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Instrument - Telescope

Optical coatings do not absorb or reflect all wavelengths equally�
Chromatic aberrations result in a different focus of wavelengths and can affect how much light of a given wavelength passes through the slit

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Instrument - Spectrograph

Diffraction gratings do not reflect/transmit all wavelengths equally.
Optical coatings on collimator and focusing lenses do not absorb or reflect all wavelengths equally.
Blue and red ends of dispersed spectrum may hit near edges of spectrograph optical components resulting in vignetting (reduced intensity) at these wavelengths.

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Instrument - Camera

Non-uniform spectral response of the sensor across the spectral range

The human eye has a sensitivity to visible light peaking in the green

Variations in pixel sensitivity

Small but unavoidable variations introduced in the manufacturing process

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Instrument - Camera

The sensitivity of the sensor to incident light (AKA response or quantum efficiency) varies by wavelength

Sensors tend to be less responsive in the blue and red ends of the visible spectrum

Different sensors have different spectral response curves

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Instrument Effects Corrected With Flat Field Images

A flat image using a halogen lamp ahead of the spectrograph slit produces a spectrum of the flat lamp on the camera sensor.
The flat correction during processing may compensate for the spectral response of all of the components after the lamp:

Grating
Camera sensor
Telescope optics (if the flat lamp is placed in front of the telescope)

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Relative Flux Calibration Overview

Preferably:

Record a spectrum of a star with a reliable known published spectrum, i.e. a “reference “star.
Divide this measured spectrum by the published spectrum for that star to produce a response function representing the difference between observed and ideal spectral profiles.
Record the spectrum of the target under the same conditions and divide it by the response function to produce the corrected spectrum of the target.

Alternately:

Record the spectrum of a target and divide this measured spectrum by a synthesized library spectrum of the same spectral type and class to produce a response function.
Apply this response function to the measured target spectrum to produce the corrected spectrum of the target.

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Relative Flux Calibration - The Reference Star

A star selected from a library of professionally calibrated stars corrected for atmospheric effects.
Used to correct a target spectrum for the effects of atmosphere and instrument response effects.
Commonly used library is the “Miles” library of stellar spectra.

Contains ~1000 calibrated reference stars across all spectral types and classes
Some stars have two variations:

Corrected for interstellar extinction (don’t use these)
Not corrected for interstellar extinction (use these)

Another library is the “Pickles” library

Not stars but instead synthesized spectra representative of the range of spectral types and classes.

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Two Methods for Performing the Correction

Create a response profile from a Pickles synthesized spectrum.

Requires the reference star spectrum be of the same spectral type and luminosity class as the target star (so you have to know that).
Does not account for any differences between the observed target star profile and the Pickles reference profile (e.g. photospheric temperature, pressure).

Create a response profile from an observed Miles reference star .

The reference star does not have to be of the same spectral type as the target.
Uses the difference between an observed reference star and the same star in the Miles database to create the response profile.
Observed reference star spectrum obtained under same conditions as target star.

The first method is easiest and doesn’t require acquiring and processing a spectrum of a reference star.

The second method requires more effort, but can provide a better correction based on the difference between the observed reference star and Miles library profile.

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Differences Between Pickles and Miles and Between Two Miles Stars of the Same Spectral Type

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Need to Correct by Instrument Type

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Spectrograph Type	Reference Star Correction Needed?	Reason
Slitless	Yes	Full spectrum image affected primarily by camera spectral response.
Broad Spectrum	Yes	Full spectrum image subject to atmospheric and instrument effects.
Narrow Spectrum	Maybe	Narrow wavelength range limits effect of atmospheric extinction and differential refraction. Sensor response may be nearly constant over narrow wavelength range. Vignetting may be negligible within the spectrograph.
Echelle	Yes	Full spectrum image subject to atmospheric and instrument effects.

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Method 1:

Relative Flux Calibration Using Synthesized Spectra

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Selecting the Reference Profile

Selected from a reference spectrum library typically included in the software used for processing spectra.

Pickles library for RSpec, Demetra, BassProject, ISIS, and others

Ideally the reference spectrum should be of spectral type and luminosity class matching the reference star.

The Pickles library does not include all spectral types and luminosity classes, so the one you need may not be there.
Variable stars exhibit changes in temperature/spectral type throughout their cycle, making it uncertain as to which Pickles profile to use
The Pickles library does not account for any temperature differences between stars of the same spectral type (~a few hundred to a thousand degrees K or more)

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del Aql (F1 IV) - No Reference Star Correction

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Pickles F0 V Reference Profile

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del Aql and Pickles A0V Reference Profiles

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del Aql Profile Divided by Pickles Profile (Raw IR Curve)

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Create Smoothed Response Curve

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Create Smoothed Response Curve

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Apply Response Correction to del Aql Profile

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Apply Response Correction to del Aql Profile

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del Aql Before and After Response Correction

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Method 1 Summary

A reference spectrum is selected from a reference library, such as the Pickle’s library, that is typically included in the software used for processing spectra.
The selected reference spectrum should be of spectral type and luminosity class matching the target star for the best correction.

Generating a reliable response curve for late spectral types may be problematic.

The Pickles library does not include all spectral types and luminosity classes, so the one you need may not be there.
Variable stars exhibit changes in temperature/spectral type throughout their cycle, making it uncertain as to which Pickles profile to use.
The Pickles library does not account for any temperature differences between stars of the same spectral type (but these differences are small).
Use a separate Pickle’s reference spectrum for each target (unless of they are of the same spectral type and observed at the same zenith angle).

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Method 2:

Relative Flux Calibration using Reference Star Observation

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Selecting a Reference Star

Reference star is selected from a reference star finder tool

Reference star spectra are obtained just before or after (or both) the target object spectrum.

Reference star zenith angle at its mid-exposure time should be within a degree or two of the target zenith angle at its mid-exposure time.
Slit orientation relative to the vertical must be the same for both target and reference stars (to minimize differential refraction effects)
Ideally the reference star should be of spectral type B or A and type V main sequence

Type A and B stars have well defined continuum with little clutter
Main sequence stars are generally not variable

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Reference Star Finder

Francois Teyssier

http://www.astronomie-amateur.fr/DocsSpectro/ReferenceStarFinder_V3_en.xlsm

Miles Search

Paolo Berardi

http://quasar.teoth.it/html/varie/MILES_SEARCH_V1_4.zip

Spectro StarFinder (on-line tool)

Serge Golovanow

https://spectro-starfinder.net

Reference Star Selection Tools

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Plotting Reference Stars in TheSky6

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Reference HD 13324 (A0 V) Observed Profile

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Reference HD 13324 (35 Aql A0 V) Observed Profile

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HD 183324 (Observed) and HD 183324 (Miles Reference) Profiles

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HD 183324 (Observed) Profile Divided by HD 183324 (Miles Reference) Profiles (Raw IR Curve)

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Create Smoothed Response Curve

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Create Smoothed Response Curve

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Apply Response Correction to HD 183324 (Observed) Profile

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Compare Corrected HD 183324 (Observed) Profile to HD 183324 (Miles) Profile

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Difference Between Observed and Corrected Reference Star Profiles

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Applying Response Curve to Target Star

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Flux Calibrated del Aql

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Method 2 Summary

Reference star is typically selected from a reference star finder tool and reference star spectra are obtained just before or after (or both) the target object spectrum.
Reference star zenith angle at its mid-exposure time should be within a degree or two of the target zenith angle at its mid-exposure time.
Slit orientation relative to the vertical must be the same for both target and reference stars
Ideally the reference star should be of spectral type B or A and type V main sequence since type A and B stars have well defined continuum with little clutter and main sequence stars are generally not variable
Use a separate Miles reference profile for each target unless the zenith angle is approximately the same for all observations and are close in azimuth

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Compare Both Methods

Planck Curve for 8000K

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Differences Between Pickles and Miles and Between Two Miles Stars of the Same Spectral Type

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Comparison of the Two Methods

Pickles Synthesized Spectrum	Observed Miles Reference Star
Requires Pickles spectrum to be same type and luminosity class as target star. This may not be known, especially for variable stars.	Reference star observed is selected from the Miles database, so the star observed is the same as the reference profile. Knowledge of spectral type of the target star is not necessary.
The pickles library does not include all spectral types and luminosity classes, so the one you need may not be there.	Reference star observed is selected from the Miles database, so the star observed is the same as the reference profile.

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Comparison of the Two Methods

Pickles Synthesized Spectrum	Observed Miles Reference Star
Creating a profile for spectral types G and later can be difficult and error prone due to cluttered continuum.	Reference stars are typically type A and B and a good response profile can be generated reliably.
Not a consideration for this method since no reference star is being observed.	Slit orientation for the observed reference star must be the same as for the target star to ensure consistency in the spectrum passed through the slit.

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Conclusions

Applying a correction for atmosphere and instrument response is a must for a properly calibrated 1D spectral profile

Method 1 - Create a response curve from a Pickles synthesized spectrum

Doesn’t require separate observation of a reference star
Works well only if you can match a Pickles spectral type to your target

Method 2 - Create a response curve from an observed Miles reference star

Works if you don’t know the spectral type of your target
Requires selection of a reference star close to your target
Requires attention to consistent slit angle between target and reference star observations

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For Either Method, Use a Separate Reference Profile for Each Observation

Do not use a Miles reference profile for multiple observations unless the airmass is approximately the same for all observations and are close in azimuth

Do not use a Pickle’s library profile for multiple observations as the airmass AND spectral types will be different

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Miles Reference Database

http://miles.iac.es/

No. Stars: 985

Spectral Range: 352.5 - 750.0 nm

Spectral Resolution: 0.25 nm (2.50 Å) FWHM

Spatial Coverage: -30 deg to +85 deg

Library at http://svocats.cab.inta-csic.es/miles/index.php?action=search

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Questions, Comments, Discussion