Filters for NIR astronomical photometry: comparison of commercial IRWG filters and designs using OpenFilters

Abstract

The photometric accuracy in the near-infrared (NIR) wavelength range (0.9–2.6 $\mu$m) is strongly affected by the variability of atmospheric transmission. The Infrared Working Group (IRWG) has recommended filters that help alleviate this issue and provide a common standard of NIR filtersets across different observatories. However, accurate implementation of these filters are yet to be available to astronomers. In the meantime, InGaAs based detectors have emerged as a viable option for small and medium telescopes. The present work explores the combination of IRWG filtersets with InGaAs detectors. A few commercially available filtersets that approximate the IRWG profile are compared. Design of more accurate IRWG filtersets suitable for the InGaAs sensitivity range is undertaken using an open-source filter design software – OpenFilters. Along with the photometric filters iZ, iJ and iH, design of a few useful narrow band filters is also presented. These filters present opportunities for small and medium telescopes for dedicated long-term observation of interesting infrared sources.

Appendices

Appendix A. Methods for SNR calculation

Collected flux in Watts from a star is specified as:

$$\begin{aligned} P_c =A_{\mathrm{eff}} \times F_{\mathrm{BW}} \times \Phi _{\mathrm{zero}} \times 10^{(m_{*}/-2.5)} \end{aligned},$$

(A1)

where $A_{\mathrm{eff}}$ is the effective collecting area of the telescope, $F_{\mathrm{BW}}$ is the filter bandwidth in nm, $\Phi _\mathrm{zero}$ is the flux from a zeroth magnitude star in W/$\hbox {m}^2$/nm and $m_{*}$ is the magnitude of the star.

$F_{\mathrm{BW}}$ and $m_{*}$ are known parameters and $\Phi _{\mathrm{zero}}$ is collected from Zombeck (2006). The effective collecting area, $A_{\mathrm{eff}}$ for a telescope is:

$$\begin{aligned} A_{\mathrm{eff}}= \pi \left( \frac{D}{2}\right) ^2\times a \times b \end{aligned},$$

(A2)

where D is the telescope diameter, a is a factor corresponding to secondary obstruction; nominally 0.85 and b is the throughput; nominally 0.2.

Using these parameters, the SNR for single pixel detectors can be calculated as:

$$\begin{aligned} {\mathrm{SNR}}=\frac{P_c}{{\mathrm{NEP}}\times \sqrt{1/T_{i}}}, \end{aligned}$$

(A3)

where $P_c$ is incident energy in Watts, NEP is noise equivalent power of the detector in Watts/$\sqrt{\mathrm{Hz}}$ and $T_{i}$ is the on-source integration time.

SNR for array based detectors:

$$\begin{aligned} {\mathrm{SNR}}=\frac{P_c \times T_{i}}{\sqrt{P_c \times T_{i}+ N_{\mathrm{dark}}\times p_n \times T_{i}+ N_{\mathrm{read}}^2\times p_n}}, \end{aligned}$$

(A4)

where $N_{\mathrm{dark}}$ is the dark current of the detector given in $\hbox {e}^-$/pixel/S, $N_{\mathrm{read}}$ is the read noise of the detector given in $\hbox {e}^-$/pixel, $p_n$ is the number of pixels used to sample the stellar disk; nominally 16 and $T_{i}$ is the on-source integration time.

Using these relations between the desired SNR and time of integration, minimum integration time for ${\mathrm{SNR}} = 100$ for various filter and detector combinations are given in Table 2.

Appendix B. Filter transform between IRWG and Johnson filters

For the present typical achievable photometric accuracies in NIR (Milone & Young 2007; Wing et al. 2011), i.e., 3–5%, filter transforms between different implementations of the IRWG filterset may not be required. For more accurate photometry, i.e., 1% or lower, just 57 bright standards may not be sufficient for an exact transformation. We have included the synthetic photometric data of all 57 MaunaKea primary stars in various filtersets considered, should there be interest for such transforms. The data are included in Table 5 as a list of magnitudes. A rudimentary transform fit between IRWG and the Johnson filterset derived from the 57 MaunaKea standards is also included in Figure 9. For various aspects of filter transforms of IRWG filtersets, the work done by Milone & Young (2005) is to be referred

Figure 8

In (a) the degradation of the filter profile due to introduction of random errors in layer thickness is shown. Errors within 0.5–1.5% maybe tolerated without significant degradation of transmission. In (b) the shortward shift of the profile is shown with increase in incidence angle. For incidence angles upto 8$^\circ$, the resulting change in transmission is minimal and within the allowable range. The atmospheric transmission window is shown in the background to demonstrate this. For large incidence angles (e.g., larger field of view) a slightly different approach to optimization may be taken (see text).

Figure 9

Using the synthetic photometry of the 57 MaunaKea primary standards, a rudimentary transform equations between IRWG filters iJ and iH can be constructed. A basic fit between J and iJ is shown in (a). A basic fit between H and iH is shown in (b). RMS error of 0.03 mag is seen in both the plots.

Table 5 Estimation of magintudes of MaunaKea primary standards in IRWG equivalent filters. Filters with prefix ‘i’ (as in iJ) are ideal IRWG profiles. Filters that have prefix ‘Ci’ are from Custom Scientific. Filters with prefix ‘Oi’ are from OmegaFilters. Filter that have prefix ‘Otsi’ are off-the-shelf approximations using short-pass and long-pass filters.