# UK-DMC-2

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

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:

$gain_{(b)} = { 1 \over rescale gain_{(b)} }$

and

$offset_{(b)} = rescale bias_{(b)}$

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

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

## Input

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

## Output

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

## References

RW01 - OTB Optical calibration