tokens: it is not objectively easy to determine the optimal deblending performance because it is not fundamentally trivial to determine if an object is actually composed of two galaxies or a single morphologically disturbed galaxy with two cores. This fundamental problem is unfortunately not unique to our morphological measures, but can occur in any qualitative or quantitative investigation of morphology. Fortunately, we only have two deblending statuses, i.e. ‘deblended’ or ‘blended’, therefore the effect of ‘deblending ability’ remains roughly constant down to a certain ‘deblending limit’, then it drops. Note also that this deblending limit is independent from a particular choice of desired morphological measure. Furthermore, this deblending ability can be roughly characterized only by the apparent size of an object (e.g. the number of pixels of a galaxy), because the average surface density of galaxies (or the inverse of average separation between two galaxies) is related to the apparent magnitude of galaxies, and this magnitude is approximately correlated to the number of pixels of a galaxy. Because of this simplicity, when we plot the mean value of each measure versus the number of pixels of an object inside the entire image, one can find that the mean value of any measure is approximately flat down to a certain number of pixels, then an object consists of smaller number of pixels starts to show much different (usually bigger) mean value. By monitoring the sudden change in the morphological measures, such as the concentration and the asymmetry of a galaxy, for various input npix values, we estimated that the optimal minimum number of pixels related to this deblending ability should be set around npix = 50 for the nominal setting related to ‘deblending’ of our extracting software, sextractor . Note that the minimum number of pixels related to a single object, explained earlier in this section, varies among various morphological measures. Therefore, the ‘overall’ minimum number of pixels should be determined by comparing the two types of minimum number of pixels (i.e. one type related to a single galaxy, and another related to ‘deblending’) on measure-by-measure bases, and that overall threshold, usually ranging between 20 and 100 pixels, should be applied to a different set of measures for various analyses. 3.3 Variation in detection fraction To investigate variations in the detection and measuring ability of sextractor , we performed a simulation through adding of galaxies into random positions of the each real cluster image. These added galaxies were randomly selected from a list of galaxies satisfying the specific selection conditions (e.g. magnitude and colour ranges) identical to each of the investigations in the next section. The list was constructed from the outer part (2 Mpc or more from the cluster centre) of the same cluster image. The exclusion of galaxies inside 2 Mpc radius was to ensure that added galaxies were free from any
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