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Observatory Support
HST Focus & PSF Resources

September 2014

This site discusses HST PSF variations: their monitoring, measurements, control, and modeling to facilitate science. It provides background information, a bibliography of related papers, and interfaces to a focus model and PSF generator. It is structured as follows:

  1. Overview
  2. Monitoring & Refocusing
  3. Modeling & PSF Characterization
  4. Documentation



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 2006, 2007). 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. 2006, Sahu et al. 2007, Suchkov & 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.



Monitoring & Refocusing
HST's focus has been monitored and adjusted throughout the mission's life. (e.g. Lallo et al. 2010, 2001, Casertano 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 1995, Niemi et al. 2010, Niemi & 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. 2009 & 2002). 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 2012, Cox & Niemi 2011, Di Nino et al. 2008, Hershey 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:

  1. Estimate the focus for your observation
  2. Generate the corresponding PSF

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 2011,2004, Hook & Stoehr 2008), and then subtracting the simulated PSF from the observation. See the WFPC2 PSF Subtraction Page for some relevant general discussion, and the WFPC2 PSF Page for resources specific to that camera.

Some applications include:

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.



The bibliography below lists in reverse chronological order, the majority of related reports, papers, and presentations produced by STScI. These supplement other papers from the scientific community on observed HST PSF variations and resulting attempts at calibration.

Experience with the Hubble Space Telescope: 20 years of an archetype
Optical Engineering paper describing the Hubble Mission, covering optical design and performance. Special emphasis is placed on the Space Telescope Science Institute's unique experience with Hubble's behavior as an astronomical telescope in the environment of low earth orbit for over two decades.
M. Lallo, Jan 2012

ISR 2012-01: COS FUV Focus Determination for the G140L Grating

Describes the procedures for determining the COS FUV fine-focus for the G140L grating.
P. Ghavamian 03 Oct 2012

ISR 2012-14: Breathing, Position Drift, and PSF Variations on the UVIS Detector
L. Dressel 13 Jul 2012

Keeping the Hubble Space Telescope in Focus
SPIE paper describing the focus model details and development.
C. Cox & M. Lallo, 1 Jun 2012

20 years of Hubble Space Telescope optical modeling using Tiny Tim
SPIE paper describing the evolution and applications of the Tiny Tim PSF Simulation software package.
J. E. Krist & R. N. Hook, 1 Oct 2011

ISR-WFC3-2011-07, High Contrast Imaging using WFC3/IR
Presents results of performing both classical and LOCI (Locally Optimized Combination of Images) PSF subtractions on WFC3/IR images of a bright (V=6.9) star with simulated companions.
A. Rajan et al., 10 Feb 2011

ISR-TEL-2011-01, Evaluation of the HST Focus Model
Describes the performance of the current focus model which includes a new secular formula and updates to SI-specific offsets.
C. Cox & S.-M. Niemi, 23 Feb 2011

ISR-TEL-2010-03, Phase Retrieval to Monitor HST Focus: II. Results Post-Servicing Mission 4
Discusses the results of focus monitoring since the last HST Secondary Mirror adjustment in July 2009, after Servicing Mission 4. Examines current focus of ACS & WFC3.
S.-M. Niemi & M. Lallo, 2 Dec 2010

ISR-TEL-2010-02, HST Focus in SMOV4: Strategy for OTA adjustment & SI Focus
Describes the observatory-level effort to produce optimal focus during Servicing Mission Observatory Verification 4.
M. Lallo et al., 1 Dec 2010

ISR-TEL-2010-01, Phase Retrieval to Monitor HST Focus: 1. WFC3 UVIS Software Implementation
Describes the adaptation and calibration of HST phase retrieval code to WFC3, and its subsequent use for focus and image monitoring.
S.-M. Niemi et al., 1 Aug 2010

ISR-WFC3-2009-45, WFC3 SMOV Programs 11424, 11434: UVIS Channel On-orbit Alignment
Describes the setting of the UVIS channel corrector mechanisms for optimal image quality and confocality with the other SIs.
G.F. Hartig et al., 14 Dec 2009

ISR-WFC3-2009-46, WFC3 SMOV Programs 11425, 11435: IR Channel On-orbit Alignment
Describes the setting of the IR channel corrector mechanisms for optimal image quality and confocality with the other SIs.
G.F. Hartig et al., 14 Dec 2009

ISR-WFC3-2009-38, WFC3 SMOV Programs 11436/8: UVIS On-orbit PSF Evaluation
Assessment of image quality in the WFC3 UVIS channel on orbit, following its optical alignment to the HST OTA.
G.F. Hartig, 10 Nov 2009

ISR-WFC3-2009-37, WFC3 SMOV Programs 11437/9: IR On-orbit PSF Evaluation
Assessment of image quality in the WFC3 IR channel on orbit, following its optical alignment to the HST OTA.
G.F. Hartig, 10 Nov 2009

ISR-WFC3-2008-41, WFC3 IR PSF Evaluation in Thermal-Vacuum Test #3
Assessment of image quality of the WFC3 IR channel in a flight-like thermal-vacuum environment.
G.F. Hartig, 16 Sep 2008

ISR-WFC3-2008-40, WFC3 UVIS PSF Evaluation in Thermal-Vacuum Test #3
Assessment of image quality in the WFC3 UVIS channel in a flight-like thermal-vacuum environment.
G.F. Hartig, 20 Aug 2008

ISR-WFC3-2008-014, WFC3 Support in Tiny Tim
Discusses the extension of the PSF simulator, Tiny Tim, to model WFC3 PSFs.
R. Hook & F. Stoehr, 27 Jun 2008

ISR-ACS-2008-03, HST Focus Variations with Temperature
Describes the temperature-based HST focus model that is the basis of our current (post-2002) modeling tool.
D. Di Nino et al., 7 May 2008

HST Focus & PSF Stability
Telescopes Group Talk Series, Talk #1
M. Lallo, 19 Sep 2007

ISR-ACS-2007-12, ACS PSF variations with temperatures
Describes observed PSF widths and their correlation with HST temperatures. Predates the temperature-based focus model detailed in Di Nino et al., (2008).
K. C. Sahu et al., 18 Sep 2007

ISR-TEL-2006-01, Modeling Aberrations in the Advanced Camera for Surveys
Investigates the plausibility of optical misalignments as the cause of apparent aberration changes implied by phase retrieval of HRC PSFs.
K. Houairi et al., 13 Oct 2006

Temporal Optical Behavior of HST: Impact on Science Observations
SPIE paper giving some discussion and examples that relate measurements of defocus wavefront error to characterizations more common to science data analysis (e.g. FWHM, and ellipticity).
R. B. Makidon et al., May 2006

Temporal Optical Behavior of HST: Focus, Coma & Astigmatism History
SPIE paper describing variations of HST aberrations as revealed by ongoing monitoring using phase retrieval techniques.
M. Lallo et al., May 2006

ISR-ACS-2006-01, PSFs, Photometry, and Astrometry for the ACS/WFC
Develops and provides a method for characterizing the HST PSF using the "effective PSF". A given observed ACS WFC PSF can be fit by interpolating between an array of fiducial PSFs over the detector, and by employing a "perturbation PSF" to capture the time-variability due mainly to focus changes. Effective PSF grids for 6 common WFC filters are provided, along with FORTRAN code for performing this analysis.
J. Anderson & I. R. King., Feb 2006

ISR-TEL-2005-03, HST Temporal Optical Behavior & Current Focus Status
Reviews the timescales, mechanisms, and importance of variations in aberrations (focus, coma, astigmatism). Presents focus status of the observatory.
M. Lallo et al., 27 Oct 2005

HST Temporal Optical Behavior: Models & Measurements with ACS
HST Calibration Workshop presentation describing apparent behavior of coma, astigmatism, and focus in ACS/HRC, and their effects on measured PSF characteristics.
R. B. Makidon et al., 30 Oct 2005

ISR-TEL-2005-02, Guiding Errors in 3-Gyro: Experience from WF/PC, WFPC2, STIS, NICMOS and ACS
This report summarizes typical behavior gleaned from several observations with ACS, WF/PC, WFPC2, STIS and NICMOS.
R. L. Gilliland, 20 Feb 2005

Telescope Image Modeling (Tiny Tim) Handbook
User's manual for "Tiny Tim". Software package for simulating HST PSFs. NOTE: this is the general User's Guide. It pre-dates WFC3 capability and the web-based user-input defocus values.
J. E. Krist, 1 Jun 2004

ISR-ACS-2003-06, ACS field-dependent PSF variations...
Examines PSF width and ellipticity variations over WFC and HRC field resulting from optical and charge diffusion effects.
J. E. Krist, 1 Jun 2003

OTA Focus Review Memo
Reviews focus history, mirror moves, and typical accuracies of measurements and commands.
M. Lallo, 25 Jun 2002

On-orbit alignment & imaging performance of HST ACS
SPIE paper documenting the on-orbit optical alignment of the ACS, with an assessment of residual aberrations and comparisons with models. Effects of HST OTA focus changes are also discussed.
G. F. Hartig et al., Jan 2002

ISR-OTA-2001-01, HST Focus in Year 2000 - A Review of the Cycle 9 Focus Monitor Program
Discusses the state of HST focus during the science cycle following an HST refocusing in June 2000.
M. Lallo, 1 Feb 2001

SESD-97-01, Modelling HST Focal-Length Variations
This report laid out the first attempt at a comprehensive temperature-based HST focus model. Though the specific model has since been replaced (Di Nino et al., 2008, & Cox 2011), the temperatures and temperature functions that most closely correlate with focus changes were first identified here. Also described was an attempt at a predictive model, expressing the focus function in terms of HST attitude parameters, rather than the resulting temperature changes.
J. Hershey, Jun 1998

ISR-WFPC2-1997-10, WFPC2 Photometry from Subtraction of Observed PSFs
Based on observed PSFs from WFPC2 calibration programs, a series of PSF subtraction tests were performed and the resulting photometry analyzed.
J. Surdej et al., 3 Oct 1997 (postscript)

WFPC2 Photometry from Subtraction of TinyTim PSFs
Describes a method for determining best fitting model PSFs for WFPC2/PC1 observations.
M. Rémy et al., Sept 1997 (postscript)

ISR-WFPC2-1997-01, Impact of Focus Drift on Aperture Photometry
Examines the impact of long term and short term focus variations on small aperture photometry performed on WF & PC channels of WFPC2.
A. Suchkov & S. Casertano, 31 Jan 1997

Phase-retrieval analysis of pre- and post-repair HST images
Applied Optics paper discussing phase retrieval techniques used for HST PSF monitoring and characterization.
J. E. Krist & C. J. Burrows, 1 Aug 1995

ISR-OTA-18, Focus Monitoring and Recommendation for Secondary Mirror Move
Focus monitoring and recommendation for secondary mirror move.
S. Casertano, 1 Jan 1995

SESD-1993-16, Orbital Focus Variations in the Hubble Space Telescope
This report first described the relationship between observed HST orbital focus changes and temperatures differences measured at HST's Light Shield just fore of the Secondary Mirror.
P. Y. Bély et al., Aug 1993