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# Measuring and recreating the sky value

## How Sky Values are Measured

It is quite clear what astronomers mean by `sky': the mean value of all pixels in an image which are not explicitly identified as part of any detected object. It is this quantity which, when multiplied by the effective number of pixels in an object, tells us how much of the measured flux is not in fact associated with the object of interest. Unfortunately, means are not very robust, and the identification of pixels not explicitly identified as part of any detected object is fraught with difficulties.

There are two main strategies employed to avoid these difficulties: the use of clipped means, and the use of rank statistics such as the median.

`Photo` performs two levels of sky subtraction; when first processing each frame it estimates a global sky level, and then, while searching for and measuring faint objects, it re-estimates the sky level locally (but not individually for every object).

The initial sky estimate is taken from the median value of every pixel in the image (more precisely, every fourth pixel in the image), clipped at 2.32634 sigma. This estimate of sky is corrected for the bias introduced by using a median, and a clipped one at that. The statistical error in this value is then estimated from the values of sky determined separately from the four quadrants of the image.

Using this initial sky estimation, `Photo` proceeds to find all the bright objects (typically those with more than 60 sigma detections). Among these are any saturated stars present on the frame, and `Photo` is designed to remove the scattering wings from at least the brighter of these --- this should include the scattering due to the atmosphere, and also that due to scattering within the CCD membrane, which is especially a problem in the i band. In fact, we have chosen not to aggressively subtract the wings of stars, partly because of the difficulty of handling the wings of stars that do not fall on the frame, and partly due to our lack of a robust understanding of the outer parts of the PSF . With the parameters employed, only the very cores of the stars (out to 20 pixels) are ever subtracted, and this has a negligible influence on the data. Information about star-subtraction is recorded in the `fpBIN` files, in HDU 4.

Once the `BRIGHT` detections have been processed, `Photo` proceeds with a more local sky estimate. This is carried out by finding the same clipped median, but now in 256x256 pixel boxes, centered every 128 pixels. These values are again debiased.

This estimate of the sky is then subtracted from the data, using linear interpolation between these values spaced 128 pixels apart; the interpolation is done using a variant of the well-known Bresenham algorithm usually employed to draw lines on pixellated displays.

This sky image, sampled every 128x128 pixels is written out to the `fpBIN` file in HDU 2; the estimated uncertainties in the sky (as estimated from the interquartile range and converted to a standard deviation taking due account of clipping) is stored in HDU 3. The value of sky in each band and its error, as interpolated to the center of the object, are written to the `fpObjc` files along with all other measured quantities.

After all objects have been detected and removed, `Photo` has the option of redetermining the sky using the same 256x256 pixel boxes; in practice this has not proved to significantly affect the photometry.

## Caveats

There is a slight and only recently recognized downward bias in the determination of the sky level in the photometry, at the level of roughly 0.1 DN per pixel. This is apparent if one compares large-aperture and PSF photometry of faint stars; the bias is of order 29 mag arcsec-2 in r. This, together with scattered light problems in the u band, can cause of order 10% errors in the u band Petrosian fluxes of large galaxies.