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Chapter 6: Calibration Using Synthetic Photometry
Once U(λ) is determined, the absolute flux distribution of any observed
source can be computed by simply multiplying the source’s count rate
spectrum, C(λ)/∆ t, by U(λ):
2
f λ ( λ ) = U ( λ ) ⋅ C ( λ )/ ∆t (ergs/sec/cm /Å)
Synthetic photometry permits a precise generalization of this procedure
from the narrow passbands of spectrophotometric pixels to a passband P(λ)
of arbitrary width and shape. For a broadband photometric mode the
analogous expression giving the detected count rate through passband P is:
A
C(P)
------------- = ------ ∫ P ( λ ) f λ ( λ )λ dλ
hc
∆t
The precise definition of mean flux density in a broad passband must
then be:
P ( λ ) f λ ( λ )λ dλ
f λ ( P ) = ∫-----------------------------------------∫ P ( λ )λ dλ
so the count rate to flux density conversion factor for a broad passband is:
f λ(P)
hc / A
U λ ( P ) = ---------------------= --------------------------C ( P ) ⁄ ∆t
∫ P ( λ )λ dλ
The calibration procedure for broadband photometry is now essentially
parallel to that for spectrophotometry. The only difference is that in the
spectrophotometric case the source’s flux distribution can be considered
constant across the narrow bandwidth of each spectroscopic pixel, whereas
in the photometric case the integral over wavelength must be performed
more carefully. So the normal method of calibrating photometric modes is
to first calculate the mean flux densities of spectrophotometric standard
stars in the broad bands, using the known flux spectra and passband shapes,
and then derive the flux conversion factors U(P) by comparing the mean
flux densities against the corresponding observed count rates.
Notice, however, that the last equation above shows us that, if we know
the passband function P(λ), we can derive U(P) directly, without the need
for standard star observations. This is the technique used by synphot (and
incorporated into the WFPC and FOC calibration pipelines) to calibrate
HST observing modes. The value of the PHOTFLAM header keyword that
appears in calibrated WFPC and FOC images is the flux conversion factor