2.9 Filters

The filters available for PHT-P and PHT-C are listed in Tables 2.2 and  2.7. Let $R({\lambda})$ be the actual bandpass, which is the filter transmission function convolved with the relative spectral detector response^2.1; then the central wavelength $\lambda_{\rm c}$, the filter width $\Delta \lambda$, and the average relative system response $R_{\rm mean}$ are defined as:

$$\lambda_c = \frac{\int^{\infty}_{0} \lambda R(\lambda) d\,\lambda} {\int^{\infty}_{0} R(\lambda) d \, \lambda }$$ (2.2)

$$\Delta \lambda = 2 \sqrt{ 3 \frac{\int_{0}^{\infty} (\lambda - \lambda_c)^2 R(\lambda) d\, \lambda} {\int_{0}^{\infty} R(\lambda) d\, \lambda} }$$ (2.3)

$$R_{mean} = \frac{ \int_{0}^{\infty} R(\lambda) d\, \lambda} {\Delta \lambda}$$ (2.4)

$\Delta \lambda$ is the width of a rectangular filter having the same integrated relative system response as the actual bandpass^2.2. The relative response curves of all bandpasses are shown in Appendix A.2. Note that due to the large wings of especially the long wavelength filters, the rectangular widths (given in Tables 2.2 and 2.7) are significantly different from the full width at half maximum. Some useful filter combinations, including comparisons with IRAS filters, are illustrated in Appendix A.2.