PSF SUBTRACTION FOR WFPC2 IMAGES:

Purpose:

A common analysis problem for WFPC2 observations is the subtraction of the PSF from a much fainter background object. Common examples are searches for fuzz around QSO's and the search for circumstellar disks and planets around stars. This memo is designed to provide some basic advice, both during the observation planning stage and the analysis stage. More details, along with pictures, can be found in the article by John Krist in Calibrating Hubble Space Telescope: Post Servicing Mission.


Problems:

  • LARGE DYNAMIC RANGE REQUIRED: - The inherent difficulty is to see faint objects in the presence of very bright object. This requires having high S/N information about both the center and the wings of the PSF.

    Solutions:

    1. Take 2 or 3 images (e.g., a 1, 10, and 100 second exposure of a 
       10th magnitude star)
    
    2. Use the TINY TIM SOFTWARE
    
  • SPATIALLY DEPENDENT: - The PSF changes as a function of position on the chip.

    Solutions:

    1. Make PSF observations at the same location.
    
    2. Use the TINY TIM SOFTWARE
    
    3. Make observations near the center since most
       of the PSF's in the archives are there
    
    4. Consider an interactive acquisition so the
       PSF and target can be put very near the
       same position.
    
  • GHOSTS, RAYS, RINGS, and RIPPLES: - The PSF has several ghost images which can mimic nearby stars and galaxies, along with other features such as rays, Airy rings, diffraction spikes, ripples in the diffraction spieks etc. The ghosts in particular are very spatially dependent.

    Solutions:

    1. Make PSF observations at the same location.
    
    2. Make observations of your target at different
       roll angles so you can determine what is real.
    
  • UNDERSAMPLED PSF: - This is particularly important in the central regions and along the diffraction spikes when using the WF.

    Solutions:

    1. Take 2 or more images with subpixel dithering
    
    2. Use the TINY TIM SOFTWARE
    
  • FILTER AND SPECTRAL DEPENDENT: - The PSF depends on the filter used, and the spectrum (weakly) of the target.

    Solutions:

    1. Make PSF observations using the same filter,
       and using a star with a similar spectrum.
    
    2. Use the TINY TIM SOFTWARE
    
  • TIME DEPENDENT: - Changes in focus due both to desorption (slow change with focus adjustments roughly every 6 months) and due to "breathing" (orbital time scales) are present.

    Solutions:

    1. For desorption, take PSF observations as close 
        as possible in time to the target observations.
    
    2. In principle, it may also be possible to
       take PSF's at various phases of the breathing
       and use the one most appropriate to your
       target observations. I don't believe anyone
       has tried this in practice.
    

    Is there a PSF Library?:

    Yes! WFPC2 PSF Library Search Tool.


    Approaches:

    It is not possible to give specific advice that is relevant for all observers, since the scientific demands of programs vary. However, here are the 4 basic approaches people use, roughly in order of how stringent the scientific requirements are.

    1. Use TINY TIM. This is an excellent simulation software program written by John Krist. It is being constantly updated to better represent the true PSF. Advantages are that it provides very high S/N PSF's, allows you to subsample the image, allows you to define a wide variety of filters and spectral types, and allows you to determine the position on the chip. A disadvantage is that it does not handle internal reflections and scattered light (particularly important beyond a couple arcseconds).

    2. Use a nearby star from your own image. This is generally limited by the small chance of having a nicely exposed, well isolated star on your image.

    3. Search for a useable PSF star in the archives. As mentioned above, we plan on developing a list of such stars in the near future.

    4. Make the observations yourself, tailored to your own needs. This is still our advice for the proposals with very stringent requirements, especially those where a large amount of observing time is being spent already.


    Limiting Magnitudes:

    A common question is what is the limiting magnitude of a point like object near a bright star. Here is a a table providing some rough estimates. Observers with M(target) -- M(bright star) larger than the limiting values in the center column should be prepared to use PSF subtraction (i.e., using PSF from Tiny Tim, the archives, or their own observations). The right column shows typical limits after PSF subtraction has been performed.

    Distance from 	Limiting M(target)-M(bright) 	Limiting M(target)-M(bright) 
    bright star 	magnitude (3 sigma)        	mag (3 sigma) in 
    on PC CCD 	without PSF subtraction 	typical PSF subtraction 
    -------------	----------------------------	----------------------------
    
    0.1 ''         	2.0 mag     			3.5 mag 
    0.3		5.7				7.9
    1.0		8.9				10.7
    3.0		10.7				12.9
    

    Particularly Tough Observations:

    Detecting spherically symetric fuzz, as opposed to point like sources or disks, since the residuals from PSF subtraction will also be spherically symetric.

    The optimal wavelengths are around F555W. At shorter wavelengths, high frequency structure from the mirror zonal errors increases residuals. At longer wavelengths, the streaks increase in size and tend to move more with position changes.

    Narrow band filters give very sharp Airy rings which are very hard to remove.

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