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Calibration Access and Data Handbook

Procedure

Colour transformations are supplied only for the three visual bandpass filter (U, B, V). Due to time constraints or due to bright source restrictions the normally used colour terms may not be available and non-standard colour transformations have to be used instead. For that purpose non-standard colour transformations are supported, which make use of the UV filters. Colour transformations making use of the UVM2 filter are not considered at all because of the strong dependence of the UVM2 brightness on interstellar absorption.
The accuracy achieved by a colour transformation differs between the various transformations. Therefore a priority is assigned to the various transformations, which should be followed by the calling task: if possible, the colour transformation with the highest priorities should be used first.
The following table shows the supported colour transformations sorted according to their priority (1 is highest). Only the listed combinations are possible.

FILTERID1	FILTERID2	priority
B	V	1
U	V	2
UVW1	V	3
UVW2	V	4
U	B	1
UVW1	B	2
UVW2	B	3
UVW1	U	1

The colour indices of the correction terms (mag$_1$-mag$_2$) are always defined as (shorter wavelength passband - longer wavelength passband), e.g. (u-b), (b-v) or (uvw1-u) etc.

A new keyword ALGOID is used in the CCF to associate parameters sets with different algorithm. An ALGOID keyword value of 1 corresponds to the transformation described in this version (2.0 or later) of the calibration handbook. An ALGOID keyword value of 0 corresponds to transformation as described in calibration handbook version 1.1 or earlier.

The CAL provides the following functionality (assuming the keyword ALGOID has a value of 1):

• verify that one of the input filter identifiers is either U, B or V.
• check whether the input is provided with filter1 being at a shorter wavelength than filter2.
• compute the colour term (mag1-mag2) in the instrumental system
• select the applicable colour transformation
  • the transformations of the correct colours are selected:
    match the input filter identifier filter1 and filter2 to the filter identifier in the CCF column FILTERID1 and FILTERID2
  • the correct branch of the colour transformation is selected:
    match the value of the optional parameter branch (if not set the default value 0 is used) to the value in the column BRANCH of the CCF COLOURMAG extension.
  • the correct interval of the colour transformation is selected:
    the parameters of the colour interval are selected so that the colour term (mag1-mag2) is within the validity range of the colour transformation (as defined in equation 31).
• transform colour term (mag1-mag2) into standard system according to equation 33
• transform magnitude mag2 into standard system according to equation 34

The colour transformation can only be applied when a transformation exists between the specified filters filter1 and filter2 with the colour (mag1-mag2) falling within the validity range of the colour transformation equation and if the specified transformation branch branch is listed in the COLORMAG extension of the CCF ColorTrans component.

The colour in the instrumental system (mag1-mag2) must fall within the validity range of the colour transformation:

$$r_0 \le {\tt (mag1-mag2)} < r1$$ (31)

where

$r_0, r_1$	defines the validity range of the colour transformation as defined in the column
	TRAFOLIMIT of the ColorTrans CCF component.
mag1-mag2	the colour index calculated from the two input magnitudes in the instrumental
	system.

and the parameters of the colour equation must be defined for the requested branch (specified by the optional input parameter branch) of the colour-colour diagram:

$${\tt branch} = branch$$ (32)

where

$branch$	value in column BRANCH in the COLORMAG extension of the CCF
	ColorTrans component.
branch	value of optional input parameter

The transformation of the colour term (mag1-mag2) into a standard system is described by the equation

$$(MAG1-MAG2) = \sum_{i=0,9} k_i \cdot ({\tt mag1-mag2})^i$$ (33)

where

$k_i$	are the parameters stored in the TRAFOP1 column of the ColorTrans CCF
	component.
mag1-mag2	the colour index calculated from the two input magnitudes in the instrumental
	system

The transformation of the instrumental magnitude mag2 into the magnitude MAG2 of a standard photometric system is described by the equation:

$$MAG2 = \sum_{i=0,n}(l_i \cdot ({\tt mag1-mag2})^i) + {\tt mag2}$$ (34)

where

$l_i$	are the parameters stored in the TRAFOP2 column of the
	ColorTrans CCF component.
mag1-mag2	the colour index calculated from the two input magnitudes
	in the instrumental system
mag2	brightness in the instrumental system of filter2
MAG2	brightness in the standard system of filter2