Title: Detector sampling of optical/IR spectra: how many pixels per FWHM?,
Abstract: Most optical and IR spectra are now acquired using detectors with
finite-width pixels in a square array. This paper examines the effects of such
pixellation, using computed simulations to illustrate the effects which most
concern the astronomer end-user. Coarse sampling increases the random noise
errors in wavelength by typically 10 - 20% at 2 pixels/FWHM, but with wide
variation depending on the functional form of the instrumental Line Spread
Function (LSF) and on the pixel phase. Line widths are even more strongly
affected at low sampling frequencies. However, the noise in fitted peak
amplitudes is minimally affected. Pixellation has a substantial but complex
effect on the ability to see a relative minimum between two closely-spaced
peaks (or relative maximum between two absorption lines). The consistent scale
of resolving power presented by Robertson (2013) is extended to cover
pixellated spectra. The systematic bias errors in wavelength introduced by
pixellation are examined. While they may be negligible for smooth well-sampled
symmetric LSFs, they are very sensitive to asymmetry and high spatial frequency
substructure. The Modulation Transfer Function for sampled data is shown to
give a useful indication of the extent of improperly sampled signal in an LSF.
The common maxim that 2 pixels/FWHM is the Nyquist limit is incorrect and most
LSFs will exhibit some aliasing at this sample frequency. While 2 pixels/FWHM
is often an acceptable minimum for moderate signal/noise work, it is preferable
to carry out simulations for any actual or proposed LSF to find the effects of
sampling frequency. Where end-users have a choice of sampling frequencies,
through on-chip binning and/or spectrograph configurations, the instrument user
manual should include an examination of their effects. (Abridged)