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UK-DMC-2 acquisitions are calibrated using the Orfeo Toolbox.

DN to Radiance

The UK-DMC-2 product handbook provides the formula below to convert the DN into radiance:

\[ L_{(b)} = { DN_{(b)} \over rescale gain_{(b)} } + rescale bias_{(b)} \]

For the conversion from \(DN\) (for Digital Numbers) to spectral radiance (or ‘TOA radiance’) \(L \), the following formula is used :

\[ L_\lambda = gain \times DN + offset \]

As such, the calibration uses:

\[ gain_{(b)} = { 1 \over rescale gain_{(b)} } \]


\[ offset_{(b)} = rescale bias_{(b)} \]

\(L \) in \(W/m^2/steradians/micrometers\) with \(b\) being a band ID.

Radiance to Reflectance

To convert TOA radiance to TOA reflectance, the following formula is used :

\[ R(b) = { {\pi \times L(b) \times d \times d} \over {ESUN(b) \times cos(θ)} } \]

where :

  • \(L(b)\) is the spectral radiance for band b

  • \(pi\) is the famous mathematical constant

  • \(d\) is the earth-sun distance (in astronomical units) and depends on the acquisition’s day and month

  • \(ESUN(b)\) is the mean TOA solar irradiance (or solar illumination) in \(W/m^2/micrometers\)

  • \(θ\) is the solar zenith angle in degrees.

The values for the \(ESUN(b)\) are provided in the table below:

Common band name Mean TOA solar irradiance
nir 1036
red 1561
green 1811


The input is an ingested UK-DMC-2, see details here.


The output is a STAC item geojson ... including the assets ...


RW01 - OTB Optical calibration