Author: Matt Davis (SSB)
Date: 15 November 2011
Abstract
Pysynphot attempts to replicate much of the functionality of the Synphot bandpar utility but sometimes uses different formulae and algorithms. This TSR collects the calculations used in Pysynphot, Synphot, the formulae described in the Synphot Manual in Section 5.1 on page 42, and the formulae in the Synphot help files.
RMS width is added to image headers in the PHOTBW keyword.
Pysynphot
Synphot
The Synphot Manual section 5.1 gives the equation for RMS bandwidth as
where
The Synphot function rmslam does appear to implement this procedure for calculating the RMS width of the bandpass. The source code references the WF/PC-1 Instrument Handbook as the source of the equation for RMS width and references Schneider, Gunn and Hoessel (1983 ApJ 264,337) as the source for the equation for mean wavelength.
The bandpar help file gives the same equations as above for the RMS width but the Synphot Manual in section 7.1 gives different equations when describing bandpar. The equations in section 7.1 are the same as used by Pysynphot, shown below.
Pysynphot does not currently implement a FWHM calculation. See https://trac.assembla.com/astrolib/ticket/139.
Pysynphot
Synphot
Pysynphot calculates the equivalent width in the same manner as Synphot.
Pysynphot
Synphot
Synphot calculates the rectangular width at the same time it calculates the equivalent width by simply dividing the equivalent width by the maximum throughput of the passband:
This is equivalent to the formula given in section 5.1 of the Synphot Manual:
Pysynphot calculates the rectangular width in functionally the same way as Synphot but does not defer any calculation to the equivalent width method. Instead, Pysynphot directly calculates the integral of the throughput and divides by the maximum within the rectwidth method.
Unit response is added to image headers in the PHOTFLAM keyword.
Pysynphot
Synphot
where and
are the usual fundamental constants and
is the area of the telescope primary mirror.
Pysynphot calculates the unit response in the same way as Synphot.
Pivot wavelength is added to image headers in the PHOTPLAM keyword.
Pysynphot
Synphot
The pivot wavelength equation is recorded in sections 5.1 and 7.1 of the Synphot Manual and matches in both places.
Pysynphot calculates the pivot wavelength in the same way as Synphot.
Like the name implies, this is simply the wavelength at the point of peak throughput. Synphot finds it by looping over the throughput.
Pysynphot does not currently implement a peak wavelength calculation. See https://trac.assembla.com/astrolib/ticket/139.
This is simply the maximum throughput of the passband. Synphot finds it by looping over the throughput.
Pysynphot does not currently implement a peak throughput calculation. See https://trac.assembla.com/astrolib/ticket/139.
Pysynphot
Synphot
Pysynphot calculates the average wavelength in the same way as Synphot.
Pysynphot
Synphot
Pysynphot calculates the efficiency in the same way as Synphot.
This is simply the bandpass throughput at a reference wavelength. By default the reference wavelength is the average wavelength as defined above.
The throughput of a Pysynphot SpectralElement object can be sampled at any wavelength using the sample() method. There is no function specifically for retrieving the throughput at the average wavelength.
The equivalent monochromatic flux is a combination of unit response, rectangular width, peak throughput and throughput at the average wavelength:
Pysynphot does not currently implement an equivalent monochromatic flux calculation. See https://trac.assembla.com/astrolib/ticket/139.
See the section on average wavelength above.