Comparison of Synphot and Pysynphot Bandpar Functionality¶

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 - BANDW - PHOTBW¶

Summary¶

RMS width is added to image headers in the PHOTBW keyword.

Pysynphot

Function name: SpectralElement.rmswidth
Source code: spectrum.py
References: 3: page 836

Synphot

Bandpar name: BANDW
Function name: rmslam called by comppar called by bandpar.
Source code: rmslam.x
References: 1: sections 5.1,7.1, 2, 4: page 46

Synphot Equations¶

The Synphot Manual section 5.1 gives the equation for RMS bandwidth as

$\lambda_{rms}^2 = \bar{\lambda}^2 \frac{\int P_{\lambda} \ln(\lambda/\bar{\lambda})^2 \,d\lambda/\lambda}{\int P_{\lambda} \,d\lambda/\lambda}$

where

$\bar{\lambda} = \exp \left[ \frac{\int P_{\lambda} \ln(\lambda) \,d\lambda/\lambda} {\int P_{\lambda} \,d\lambda/\lambda} \right].$

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 Equations¶

The Pysynphot rmswidth source code references Koornneef et al 1987, page 836 as the source for its RMS width calculation, which is

$\lambda_{rms}^2 = \frac{\int P_{\lambda} (\lambda - \bar{\lambda})^2 \,d\lambda} {\int P_{\lambda} \,d\lambda}$

where

$\bar{\lambda} = \frac{\int \lambda P_{\lambda} \,d\lambda} {\int P_{\lambda} \,d\lambda}.$

Full Width Half-Max - FWHM¶

Summary¶

Pysynphot

Function name: SpectralElement.fwhm
Source code: spectrum.py
References:

Synphot

Bandpar name: FWHM
Function name: fwhmlam called by comppar called by bandpar.
Source code: fwhmlam.x
References: 1: section 5.1

Synphot Equations¶

The FWHM is simply defined relative to the RMS width above:

$fwhm = \sqrt{8\ln 2}\cdot rmswidth$

Pysynphot Equations¶

Pysynphot does not currently implement a FWHM calculation. See https://trac.assembla.com/astrolib/ticket/139.

Equivalent Width - EQUVW¶

Summary¶

Pysynphot

Function name: SpectralElement.equvwidth
Source code: spectrum.py
References:

Synphot

Bandpar name: EQUVW
Function name: widthlam called by comppar called by bandpar.
Source code: widthlam.x
References: 1: section 5.1

Synphot Equations¶

The equivalent width is simply the integral of the throughput:

$equvw = \int P_{\lambda}\,d\lambda$

Pysynphot Equations¶

Pysynphot calculates the equivalent width in the same manner as Synphot.

Rectangular Width - RECTW¶

Summary¶

Pysynphot

Function name: SpectralElement.rectwidth
Source code: spectrum.py
References:

Synphot

Bandpar name: RECTW
Function name: widthlam called by comppar called by bandpar.
Source code: widthlam.x
References: 1: section 5.1

Synphot Equations¶

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:

$rectw = \frac{equvw}{\max(P_{\lambda})}$

This is equivalent to the formula given in section 5.1 of the Synphot Manual:

$rectw = \frac{\int P_{\lambda}\,d\lambda}{\max(P_{\lambda})}$

Pysynphot Equations¶

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 - URESP - PHOTFLAM¶

Summary¶

Unit response is added to image headers in the PHOTFLAM keyword.

Pysynphot

Function name: SpectralElement.unit_response
Source code: spectrum.py
References:

Synphot

Bandpar name: URESP
Function name: funit called by comppar called by bandpar.
Source code: funit.x
References: 1: sections 5.1, 7.1

Synphot Equations¶

$U_{\lambda} = \frac{hc/A}{\int \lambda P_{\lambda}\,d\lambda}$

where $h$ and $c$ are the usual fundamental constants and $A$ is the area of the telescope primary mirror.

Pysynphot Equations¶

Pysynphot calculates the unit response in the same way as Synphot.

Pivot Wavelength - PIVWV - PHOTPLAM¶

Summary¶

Pivot wavelength is added to image headers in the PHOTPLAM keyword.

Pysynphot

Function name: SpectralElement.pivot
Source code: spectrum.py
References:

Synphot

Bandpar name: PIVWV
Function name: pivlam called by comppar called by bandpar.
Source code: pivlam.x
References: 1: sections 5.1, 7.1

Synphot Equations¶

The pivot wavelength equation is recorded in sections 5.1 and 7.1 of the Synphot Manual and matches in both places.

$\lambda_p = \sqrt{\frac{\int \lambda P_{\lambda}\,d\lambda} {\int P_{\lambda}\,d\lambda/\lambda}}$

Pysynphot Equations¶

Pysynphot calculates the pivot wavelength in the same way as Synphot.

Wavelength at Peak Throughput - WPEAK¶

Summary¶

Pysynphot

Function name:
Source code:
References:

Synphot

Bandpar name: WPEAK
Function name: peaklam2 called by comppar called by bandpar.
Source code: peaklam.x
References: 1: sections 5.1

Synphot Equations¶

Like the name implies, this is simply the wavelength at the point of peak throughput. Synphot finds it by looping over the throughput.

Pysynphot Equations¶

Pysynphot does not currently implement a peak wavelength calculation. See https://trac.assembla.com/astrolib/ticket/139.

Peak Throughput - TPEAK¶

Summary¶

Pysynphot

Function name:
Source code:
References:

Synphot

Bandpar name: TPEAK
Function name: peaklam2 called by comppar called by bandpar.
Source code: peaklam.x
References: 1: sections 5.1

Synphot Equations¶

This is simply the maximum throughput of the passband. Synphot finds it by looping over the throughput.

Pysynphot Equations¶

Pysynphot does not currently implement a peak throughput calculation. See https://trac.assembla.com/astrolib/ticket/139.

Average Wavelength - AVGWV¶

Summary¶

Pysynphot

Function name: SpectralElement.avgwave
Source code: spectrum.py
References: 3: page 836

Synphot

Bandpar name: AVGWV
Function name: avglam called by comppar called by bandpar.
Source code: avglam.x
References: 1: sections 5.1, 7.1

Synphot Equations¶

$\lambda_0 = \frac{\int \lambda P_{\lambda}\,d\lambda} {\int P_{\lambda}\,d\lambda}$

Pysynphot Equations¶

Pysynphot calculates the average wavelength in the same way as Synphot.

Dimensionless Efficiency - QTLAM¶

Summary¶

Pysynphot

Function name: SpectralElement.efficiency
Source code: spectrum.py
References:

Synphot

Bandpar name: QTLAM
Function name: qtlam called by comppar called by bandpar.
Source code: qtlam.x
References: 1: section 5.1, 5: page 152

Synphot Equations¶

$qtlam = \int P_{\lambda}\,d\lambda/\lambda$

Pysynphot Equations¶

Pysynphot calculates the efficiency in the same way as Synphot.

Throughput at Reference Wavelength - TLAMBDA¶

Summary¶

Pysynphot

Function name:
Source code:
References:

Synphot

Bandpar name: TLAMBDA
Function name: monolam called by comppar called by bandpar.
Source code: monolam.x
References: 1: sections 5.1

Synphot Equations¶

This is simply the bandpass throughput at a reference wavelength. By default the reference wavelength is the average wavelength as defined above.

Pysynphot Equations¶

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.

Equivalent Monochromatic Flux - EMFLX¶

Summary¶

Pysynphot

Function name:
Source code:
References:

Synphot

Bandpar name: EMFLX
Function name: monolam called by comppar called by bandpar.
Source code: monolam.x
References: 1: sections 5.1

Synphot Equations¶

The equivalent monochromatic flux is a combination of unit response, rectangular width, peak throughput and throughput at the average wavelength:

$emflx = uresp \cdot rectw \cdot \frac{tpeak}{tlambda}$

Pysynphot Equations¶

Pysynphot does not currently implement an equivalent monochromatic flux calculation. See https://trac.assembla.com/astrolib/ticket/139.

Reference Wavelength - REFWAVE¶

See the section on average wavelength above.

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Comparison of Synphot and Pysynphot Bandpar Functionality¶

RMS Width - BANDW - PHOTBW¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Full Width Half-Max - FWHM¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Equivalent Width - EQUVW¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Rectangular Width - RECTW¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Unit Response - URESP - PHOTFLAM¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Pivot Wavelength - PIVWV - PHOTPLAM¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Wavelength at Peak Throughput - WPEAK¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Peak Throughput - TPEAK¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Average Wavelength - AVGWV¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Dimensionless Efficiency - QTLAM¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Throughput at Reference Wavelength - TLAMBDA¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Equivalent Monochromatic Flux - EMFLX¶

Summary¶

Synphot Equations¶

Pysynphot Equations¶

Reference Wavelength - REFWAVE¶

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