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7.1.4.2 Sky value misconceptions ¶

As defined in Sky value, the sky value is only accurately defined when the detection algorithm is not significantly reliant on the sky value. In particular its detection threshold. However, most signal-based detection tools¹⁹⁷ use the sky value as a reference to define the detection threshold. These older techniques therefore had to rely on approximations based on other assumptions about the data. A review of those other techniques can be seen in Appendix A of Akhlaghi and Ichikawa 2015.

These methods were extensively used in astronomical data analysis for several decades, therefore they have given rise to a lot of misconceptions, ambiguities and disagreements about the sky value and how to measure it. As a summary, the major methods used until now were an approximation of the mode of the image pixel distribution and \(\sigma\)-clipping.

• To find the mode of a distribution those methods would either have to assume (or find) a certain probability density function (PDF) or use the histogram. But astronomical datasets can have any distribution, making it almost impossible to define a generic function. Also, histogram-based results are very inaccurate (there is a large dispersion) and it depends on the histogram bin-widths. Generally, the mode of a distribution also shifts as signal is added. Therefore, even if it is accurately measured, the mode is a biased measure for the Sky value.
• Another approach was to iteratively clip the brightest pixels in the image (which is known as \(\sigma\)-clipping). See Sigma clipping for a complete explanation. \(\sigma\)-clipping is useful when there are clear outliers (an object with a sharp edge in an image for example). However, real astronomical objects have diffuse and faint wings that penetrate deeply into the noise, see Figure 1 in Akhlaghi and Ichikawa 2015.

As discussed in Sky value, the sky value can only be correctly defined as the average of undetected pixels. Therefore all such approaches that try to approximate the sky value prior to detection are ultimately poor approximations.