3 Treatment of systematic errors

As shown in the case of the visual Danjon astrolabe (Guinot 1958), the PHA I is not exempt of a spectral equation. For the PHA I, two photomultiplier tubes with cathodes of S-20 type are used to detect two images of starlight respectively, and multiple media layers with high reflection ($\gt 98\%$) and bandwidth of 260 nm (from 380 to 640 nm) were put on the surfaces of the combined prism. Each star for different spectral types has its own effective wavelength which causes different atmospheric refractions, so-called spectral equations (errors). The corrections for spectral equations at zenith distance $30^\circ$ could reach -0.15'' for early-type stars (O, B types), and 0.15'' for late-type stars (K, M types) (Yang Tinggao et al. 1980). These are much larger than those for the Danjon astrolabe. The first order of spectral corrections used here is derived from the values obtained earlier at zenith distance $30^\circ$, but multiplied by a factor of $1.732 (\tan45^\circ /\tan30^\circ$). The second order of spectral corrections was found from analysis of residuals of stars with different spectral types, shown in Table 3. After having used the second-order corrections, spectral equations could be eliminated quite well, better than 0.01'' (see residuals in Table 3). Table 4 does not provide magnitude equations, but does show that the observing precision is slightly lower for faint stars (around magnitude 9).

  

Table 3: Secondary corrections for spectrum and residuals

  

Table 4: Mean residual with magnitudes