WFPC2 Instrument Handbook for Cycle 10

PSF Variations with Time / OTA Focus

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The shape and width of observed PSFs varies slightly over time, due to the change in focus of the telescope. The focus variation consists of two terms: a secular change due to the ongoing shrinkage of the Metering Truss Assembly at an estimated rate of 0.25 µm month^-1, and short-term variations, typically on an orbital time-scale (the so-called "breathing" of the telescope). The breathing is probably due to changes in the thermal environment as the telescope moves through its orbit, and has a typical peak-to-peak amplitude of 4 µm; larger variations are occasionally seen.

These small focus shifts will impact photometry performed with small (few pixel radius) apertures. Typical ±2 µm focus shifts will result in photometric variations in the PC1 of 6.8%, 4.5%, 2.0%, and 0.2% for aperture radii of 1, 2, 3, and 5 pixels, respectively, in F555W. This is based on the focus monitoring data taken over the period from July 1994 to January 1996. (See Figure 5.8). Hence, "breathing" is often one of the major sources of errors for small-aperture photometry. However, relative photometry (i.e. the difference in magnitudes of stars in the same image) is less affected by this variation, since all the stars in an image tend to be impacted by the defocusing in a similar way.

Figure 5.8: Measured OTA Focus Position (microns) as Function of Days since January 1, 1994. The focus position is defined as the difference between the optimal PC focus and the measured focus, in microns at the secondary mirror. Times and size of OTA focus adjustments are indicated along the bottom of the plot.
 
Figure 5.9: Measured Aperture Correction, V(r) - V(r=10 pix), in Magnitudes as Function of Shift from Optimal Focus. Data are given for aperture radii r=1, 2, 3, and 5 pixels for F555W filter on CCD PC1.
 

Systematic errors due to the secular focus drift can be corrected using aperture corrections as a function of focus change (see Figure 5.9). The aperture correction adjusted for focus change is hence:

ap_corr = ap_corr_nominal + a(r) x d

where ap_corr_nominal is the nominal aperture correction (mag) as derived from Table 2a in Holtzman et al. (1995a), a(r) is the flux variation per 1 µm of focus drift (mag per micron) using an aperture with radius r (pixels), and d (µm) is the focus shift from the nominal position. The monitoring data mentioned above yield for PC1 and F555W, the following values for a(r):

a(1 pix) = 0.0338 ± 0.0038 a(2 pix) = 0.0226 ± 0.0024 a(3 pix) = 0.0100 ± 0.0018 a(5 pix) = 0.00105 ± 0.0015

Suchkov and Casertano (1997) provide further information on aperture corrections. They find that the aperture correction varies with focus by up to 10% for a 1-pixel radius in the PC, and is generally well-fitted by a quadratic function of focus position (see Figure 5.10). A 10% change is measured only for 5 µm defocus, which is about the largest that can be expected during normal telescope operations.

It is important to note that WF cameras can also have significant variations in their aperture corrections as the focus varies. While one would naively expect the larger pixels on the WFC to produce weaker variations in the aperture corrections, in practice, the focus offsets between cameras, and the fact that the overall OTA focus is usually optimized for PC1, can lead to significant corrections in the WFC.

Suchkov and Casertano provide formulae that estimate the change in aperture correction due to defocus for a variety of circumstances.

Figure 5.10: Magnitude change for a 1 pixel radius aperture as function of focus position. Derived from quadratic fits to observed data. Note offset between optimal focus for PC1 (solid line) and WF3 (dashed lines). From Suchkov and Casertano (1997).
 

Large focus changes, with amplitudes up to 10µm, are seen occasionally (See Hasan and Bely, Restoration of HST Images and Spectra II, p. 157). On May 1, 1994, and February 27, 1995, a short-lived defocusing of the telescope of up to 10µm was seen, probably due to extreme thermal conditions after the telescope was at an almost exact anti-sun pointing for an extended time. Such a defocusing causes an increase of the PSF width by about 5-10% and a significant change in its shape. This is especially evident in the PC both because of its higher resolution and its astigmatism, which makes the out-of-focus image appear elongated. The change in the PSF appears to be modeled adequately by the TIM software. (See Hasan and Bely, Restoration of HST Images and Spectra II, p. 157. Also see the sample PSF subtraction in Figure 7.2).

For more information, see the HST focus web site at

http://www.stsci.edu/instruments/observatory/focus/focus2.html.