Focus measurements are obatined by three different methods:
- Encircled Energy (NIC1 & NIC2)
- Phase retrieval (NIC1, NIC2, NIC3)
- Plate scale (NIC2 & NIC3)
The continuing difference, apparent after day 350, between the phase retrieval/Encircled Energy and plate scale results for camera 3 seems to indicate that the focus change was induced by a process not related to detector motion with respect to the Field Divider Assembly (FDA) because the part of the focus change caused by that motion is well tracked by plate scale changes. The main reason for plate scale varations is believed to be the changing distance between the detectors and the FDA.
Encircled Energy provides a direct measurement of the focus position and absolute variations in focus position. In this method, Encircled Energy is measured for approximately 40 stars in each image. The total photon counts were measured inside an aperture of fixed radius for each of the stars at each of the PAM positions in the focus sweep. The peak energy in PAM space was found for each of the stars by fitting the ~8 points nearest best focus to with a parabola. The best focus (per epoch) was taken to be the average value of all best focus measurments (for that epoch), translated to the center of the detector. This method was not applied to NIC3 since the focus sweeps did not pass through best focus.
Phase Retrieval Method
Phase retrieval provides a direct measurement of the focus position and absolute variations in focus position. The method was first developed by Krist & Burrows in 1995 and expanded in 1997 by Krist & Hook to include the NICMOS cameras.
The measured PSF is determined by the amplitude and phase of the incoming wavefront; if the wavefront is perfectly focussed, it has a phase error of zero. Phase retrieval is the process of retrieving the phase error from (out of focus) observations via PSF fitting, given knowledge of the instrument's optics.
Plate Scale Method
Plate scale gives an indirect measure of focus variations but the interpretation of these focus varations are dependent on the mechanisms causing the plate scale variations.
The change in plate-scale between epochs is proportional to the motion of the cold-well. The scale changes are related to absolute PAM space by scaling them to measures from phase-retrieval at a few of the epochs.
Note that the neither secondary mirror move nor the focus change induced by the use of a new Field Offset Mirror (FOM) position for the January 1998 NIC3 campaign change the plate scale, and hence the "plate scale method" continued to track only the internal dewar motions after that date. From that date onward, it no longer gave, in an absolute sense, the correct value of the focus position. The new FOM position gives a shift in focus position by approximately 1.5 mm, although the exact value is rather uncertain.