7 Isophotal radii

SExtractor can measure the areas of objects at 8 optimally selected thresholds (such information is often used to estimate object profiles). These thresholds are consequently different for each object. Traditionally this has not been the case and isophotal areas/radii have been measured at fixed magnitude intervals above the detection threshold. Consequently, for convenience and compatibility with existing data and analysis methods, the EXTRACTOR and Starlink SExtractor programs have been extended to provide a flexible configuration scheme that allows this traditional behaviour to be recovered and naturally extended.

The configuration options that control the chosen isophotal thresholds are:

RAD_TYPE can be either SB or INT, which indicate that the levels will be defined in terms of surface brightnesses or intensities (i.e. magnitudes and data counts), respectively.

The RAD_THRESH option can have up to three qualifying values, depending on the value of RAD_TYPE. If RAD_TYPE is SB then you should enter a line consisting of:

RAD_THRESH    step[,start,zp]

in your default.sex file. The value step being the required interval between levels, start being the value used as the first threshold and zp the data zero point, all in magnitudes per square arc-second. If only one value is given then the starting point is assumed to be the analysis threshold and the zero point is derived from the photometric value (MAG_ZEROPOINT).

If a RAD_THRESH value is not given then a default step of 0.75 magnitudes per square arcsec is used.

The actual formula used to generate the thresholds is:

Ii = A∗ 10−0.4∗(start+step∗i−zp), i = 0, 15

where Ii is the ith threshold, A is the area of an image pixel in arcseconds, start, step and zp are as described above.

If RAD_TYPE is INT then the correct RAD_THRESH format is:

RAD_THRESH     step[,start]

step being the interval between thresholds in magnitudes and start being the threshold used for the first level. If start is not given then the analysis threshold is used.

The formula used to generate these thresholds is:

Ii = start∗ 10−0.4∗step∗i, i = 0, 15

If no RAD_THRESH values are given this time then the APM/PISA (see SUN/109) analysis thresholds are used:

Ii = start∗ 2(i+2), i = 1, 15

This gives approx 0.75 magnitude steps (2.5 ∗log(2)). The first threshold is set to the analysis threshold.

Notes: before any measurements will be made at least one of the catalogue parameters RAD0 through RAD15 must be present in the default.param file. The minimum starting threshold that can be used is the analysis one — no information about values below this is available.

For completeness the existing ISO0-ISO7 areas in SExtractor are based on an optimal sampling of each object profile. Under this scheme each threshold is:

Ii = start∗ ( Ip start)i/8, i = 0, 7

where Ip = peak intensity. So you get a range of levels for each object spanning the range from its analysis threshold to just below the peak intensity.