On 2020-04-08 15:17, Markus Neteler wrote:
..
I believe that you need to apply the formula along with the respective
band calibration values ABSCALFACTOR and  EFFECTIVEBANDWIDTH (the same
is also stored in the IMD files) from the XML metadata files:

grep 'ABSCALFACTOR\|EFFECTIVEBANDWIDTH'
058891334020_01_P001_MUL/18DEC03184338-M2AS-058891334020_01_P001.XML
            <ABSCALFACTOR>9.295654000000000e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>4.730000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>9.748051000000001e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>5.430000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>7.541495000000000e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>6.300000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>5.101088000000000e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>3.740000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>1.103623000000000e-02</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>5.740000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>4.539619000000000e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>3.930000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>1.224380000000000e-02</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>9.890000000000000e-02</EFFECTIVEBANDWIDTH>
            <ABSCALFACTOR>9.042234000000000e-03</ABSCALFACTOR>
<EFFECTIVEBANDWIDTH>9.959999999999999e-02</EFFECTIVEBANDWIDTH>

Citing from "Absolute Radiometric Calibration, Prepared By: Michele A. Kuester"
https://dg-cms-uploads-production.s3.amazonaws.com/uploads/document/file/209/ABSRADCAL_FLEET_2016v0_Rel20170606.pdf

  "The top-of-atmosphere radiance, L, in units of Wμm-1m-2sr-1, is
then found from the DigitalGlobe
    image product for each band by converting from digital numbers
(DN) using the equation,

    L = Gain * DN * (abscalfactor/effective bandwidth) + Offset

    The TDI specific "abscalfactor" and "effectiveBandwidth" are
delivered with the imagery in the metadata file.
    The digital number, DN, is the pixel value found in the imagery.
The Gain and Offset are the absolute
    radiometric calibration band dependent adjustment factors that are
given in Table 1. Note that these
are not necessarily stagnant values and they are revisited annually.
 "

(the "Table 1" is found in the same PDF file above. You may want to
check if a newer table version exists).

You can apply this formula with r.mapcalc, for each band to obtain TOA
data from DN.

See also https://gitlab.com/NikosAlexandris/i.worldview.toar or https://github.com/NikosAlexandris/i.worldview.toar.

Maybe useful (though ratehr badly programmed at the time).

Nikos
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