Data

PyDIET relies largely on precomputed spectral data to feed its simulation engine.

This section illustrates their content and explains how they were obtained in the context of the CFHT configuration of the ETC.

Filter curves

The CFHT filter curves in PyDIET originate from the MegaCam and WIRCam instrument filter pages. They were converted to Synphot-compliant FITS throughput tables using the provided extract_filter.py Python script. Fig. 4, Fig. 5, Fig. 6, and Fig. 7 show the total throughput as a function of wavelength for all the supported filters.

Fig. 4 Total throughput at airmass 1.2, including atmosphere and instrument (in grey), as a function of wavelength for the MegaCam ugriz filters.

Fig. 5 Same as Fig. 4 for the other MegaCam filters.

Fig. 6 Total throughput at airmass 1.2, including atmosphere and instrument (in grey), as a function of wavelength for the WIRCam YJHKₛ filters.

Fig. 7 Same as Fig. 6 for the other WIRCam filters.

Mirror ageing

The mirror contribution to the instrumental response is represented by a wavelength-dependent throughput (reflectance) curve \(T_\mathrm{mir}(\lambda)\). PyDIET can use several throughput curves for \(T_\mathrm{mir}(\lambda)\), each representing a different mirror state, from "pristine" (the reference), to, e.g., different levels of surface degradation with time. This degradation is not computed inside PyDIET, but a stand-alone Python script, degrade_mirror.py, is provided that can be "applied" to a pristine mirror reflectance curve to generate degraded reflectance curves once for all.

The degradation model in degrade_mirror.py follows the two-factor description of Okita et al. (2019) [7], in which the loss of reflectance is described as the product of:

• an achromatic loss term, independent of wavelength;

• a wavelength-dependent scattering term caused by the growth of surface roughness.

If \(T_\mathrm{mir}^{(0)}(\lambda)\) is the pristine mirror reflectance/throughput, the aged mirror throughput after a time \(t\) since re-coating is written

(51)\[T_\mathrm{mir}(\lambda, t) = T_\mathrm{mir}^{(0)}(\lambda) D(\lambda, t),\]

where \(D(\lambda, t)\) is the relative degradation factor. The script uses

(52)\[D(\lambda, t) = \alpha(t)\exp\left[-\left<\cos^2\theta_i\right>\left({4\pi\sigma(t) \over \lambda}\right)^2\right],\]

where

(53)\[\alpha(t) = \exp(-At)\]

and

(54)\[\sigma(t) = \sigma_0 + S t.\]

Here \(A\) is the achromatic loss rate, \(\sigma_0\) is the initial RMS surface roughness just after coating, \(S\) is the rate at which the RMS roughness increases with time, and \(\theta_i\) is the angle of incidence on the mirror.

The achromatic factor \(\alpha(t)\) lowers the mirror reflectance by the same multiplicative amount at all wavelengths. It represents grey losses such as uniform contamination or coating ageing.

The exponential scattering term produces a chromatic loss. Since it depends on \((\sigma/\lambda)^2\), the effect is stronger at short wavelengths. As the surface roughness grows with time, the blue part of the mirror response therefore degrades faster than the red and near-infrared part.

The default parameters used by the PyDIET mirror-degradation utility are \(A = 0.023~\mathrm{yr}^{-1}\), \(\sigma_0 = 10~\mathrm{\AA}\), \(S = 40~\mathrm{\AA},\mathrm{yr}^{-1}\), and \(\left<\cos^2\theta_i\right> = 0.9974\).

The degraded mirror curve is produced by multiplying the tabulated pristine throughput by \(D(\lambda,t)\). The resulting curve is then used like any other mirror throughput curve in the instrumental response:

\[T_\mathrm{inst}(\lambda) = R(\lambda,t) T_\mathrm{optics}(\lambda) T_\mathrm{filter}(\lambda) T_\mathrm{detector}(\lambda).\]

Consequently, mirror ageing affects the magnitude zero-point through the reference-source count rate. A degraded mirror lowers the detected count rate from both astronomical sources and sky background. The zero-point becomes fainter because a source of a given magnitude produces fewer detected counts per second.

The chromatic part of the degradation also means that the zero-point change is filter-dependent. Blue filters are affected more strongly than red or near-infrared filters, because scattering losses scale approximately as \(\lambda^{-2}\) for a given roughness.