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Hubble Space Telescope
FOC Linearity

If two or more photon events overlap during a given frame, the VPU detection logic will only count one detected photon. This `undercounting', or non-linearity, sets a hard limit on the maximum allowable photon rate for the FOC. The linearity performance also depends on the image structure, with extended sources and point sources having unique behaviors. Regardless of the structure of the source, the size of the image determines the basic linearity performance characteristics. Therefore, by choosing a small format, the user can maximize the count rate that can be observed without suffering from non-linearity. Complete details can be found in either Section 6.2 of the FOC Instrument Handbook Version 5.0, or in one of the Instrument Science Reports written on linearity.

Extended Source (Flat-Field) Behavior

The flatfield nonlinearity was measured on-orbit during OV and SV using observations of the internal LED calibration lamps. The linearity curve was measured for several different formats to verify the format dependence of the saturation. The measured linearity relation for the 512 X 512 formats of the pre-COSTAR f/96 and pre-COSTAR f/48 detectors was fit by the relation:

[Linearity relation]

Values of a for the most commonly-used formats are given as:

[Table 9 from Handbook, pg 52]

The values refer to dezoomed data in the case of formats that were originally zoomed.

To ensure that non-linearity does not compromise the science data, users are advised to ensure that the count rate is kept below N(MAX), which is the count rate that would give 10% nonlinearity, as given in the third column of the table. Correct and quantifiable operation of the FOC at count rates exceeding N(MAX) cannot be guaranteed.

Point-Source Behavior

When the illumination comes from a star, the FOC is able to count at a much higher rate before saturation occurs. During OV and SV it became clear that for the FOC pre-COSTAR f/96 camera when used in the 512 X 512 format, the maximum obtainable count rate in the core of a star was approximately 3 counts/second/pixel. At count levels higher than this, the core of the star turns into a dark 'hole', and a bright crescent appears to one side of the core.

Comparison of PSF's taken with and without neutral density filters indicate that there is no noticeable deviation from linear behavior for core count rates up to 1 count/sec in the brightest pixel, as seen in this figure:

[Figure 27 from Handbook]

The use of either SYNPHOT or FOCSIM to calculate the count rate for the source can provide information on the expected linearity for the image. The simple guideline for observers should be keep the count rate in the central pixel below 1 count/sec. By following this guideline, any photometry method chosen will give results that are not biased by non-linearity effects.