Hubble's Focus and PSF

HST's Cassegrain Optical Telescope Assembly (OTA) is a two mirror system, whose Primary and Secondary Mirrors are both tightly thermostatically controlled. The stable mirror temperatures, combined with a carefully designed and fabricated graphite epoxy optical truss result in a telescope that is quite stable, especially against non-axial element motions (tip, tilt, decenter).

The OTA does however experience noticeable changes in focal length as the separation between the Secondary and Primary Mirrors varies over timescales as short as an orbit and as long as the mission life (Lallo 20062007). Although the Point Spread Function (PSF) delivered to the Science Instruments (SIs) is obviously very stable compared with many other observatories, these variations in focus can be measurable in the images and are considerations in many types of science analyses (e.g. Makidon et al. 2006Sahu et al. 2007Suchkov & Casertano 1997).

To mitigate these effects, active corrections are occasionally performed to maintain long term focus stability, while for shorter term variations, focus and PSF models have evolved and are available to help characterize the science.

HST OTA Diagram

Monitoring & Refocusing

HST's focus has been monitored and adjusted throughout the mission's life. (e.g. Lallo et al. 20102001Casertano 1995).

The monitoring normally consists primarily of phase retrieval determinations of the amount of defocus aberration present in images taken with one or more SIs. (Krist & Burrows 1995Niemi et al. 2010Niemi & Lallo 2010).

Since deployment, the HST OTA has shrunk by ~150 microns (3x10-5 of its length), presumably due to desorption of moisture out of the truss. This has resulted in over twenty compensating Secondary Mirror (SM) adjustments away from the Primary Mirror (PM) to maintain good focus to the SIs.


On top of this long term trend, temperature fluctuations during normal science operations in low earth orbit produce additional significant focus changes that cannot be actively corrected. These thermal changes cause the SM to move axially (i.e. "piston" or "despace") about its nominal position by typically +/- 3 microns over an HST orbit, though excursions of up to +/- ~8 microns or more can be occasionally experienced.

1 micron of SM despace induces 6.1 nanometers of rms wavefront error in focus at the SIs. An observation made with the SM despaced 5 microns from optimal focus will experience a wavefront error of 30.5 nanometers, or ~lambda/16 at a wavelength of 0.5 micron.

When a new SI is installed, it is actively aligned to be as confocal as possible with the other operational SIs (e.g. Hartig et al. 20092002). To date, we have not needed to subsequently re-adjust an SI's optics, and phase retrieval measurements with the various imagers and channels indicate that we achieve confocality to within ~6 nanometers rms wavefront error. The small SI-specific offsets are given by Cox & Niemi 2011. Methods for assessing spectral sharpness indicate these approximate levels of confocality apply to COS and the STIS spectral plane as well.

Modeling & PSF Characterization

The OTA focus change as a function of temperature and secular terms affect all the SIs and have been modeled with increasing fidelity over the mission life. The focus models from the current to the earliest are described in detail by Cox & Lallo 2012Cox & Niemi 2011Di Nino et al. 2008Hershey 1998, & Bély et al. 1993.

A temperature-based model of focus is useful operationally by reducing scatter in monitoring data so that the OTA's long term shrinkage can be more accurately assessed, predicted, and compensated by refocusing when needed. It is also desired when attempting to establish confocality between a new and existing SI.

A model containing both the temperature terms as well as the best fitting secular function (Cox & Niemi 2011) is expected to be of use to HST observers by aiding in the creation of a simulated PSF that is more relevant to the specific time of a given science observation.

With this application in mind, we provide here a process for generating a model PSF, specific to a given SI channel, filter, pixel position, and focus state at the time of the observation:

At a basic level one can examine modeled focus changes in conjunction with observations to correlate possible variations in the image appearance. More analytically, science data can be analyzed by applying the focus results to the PSF simulator, Tiny Tim (Krist & Hook 2011, 2004Hook & Stoehr 2008), and then subtracting the simulated PSF from the observation.

Some applications include:

  • centroiding of stellar images.
  • small aperture photometry in which the fraction of light falling outside the measurement area needs to be known accurately.
  • subtraction of the stellar profile in coronagraphic studies.
  • deconvolution and/or interpretation of images of barely resolved objects.

Historically, model PSFs have proven less effective in characterizing the observed PSFs than more empirically-based methods such as the "ePSF" techniques prescribed by Anderson & King (2006), or "LOCI"-type PSF subtraction (Rajan et al. 2011). We identify these types of approaches for the GO to consider whenever practical.

In cases where model-based characterizations may be the only method possible or convenient, we hope that the focus model and PSF generator tools offered here will be of use. Both the models' specifics and their implementations are largely new for 2011, so we have limited experience with their current practical performance for science characterization.

We are very interested in feedback from the community, especially regarding any relative performance comparisons between the application of this model and earlier ones, or empirical methods such as described above. Please contact the Help Desk with any feedback.

Please Contact the HST Help Desk with any Questions