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WorldView-3

WorldView-3 acquisitions are calibrated using the Orfeo Toolbox.

DN to Radiance

The WorldView-3 product handbook provides the formula below to convert the DN into radiance:

\[ L_{(b)} = gain_{(b)} \times DN_{(b)} \times { abscalfactor \over effectivebandwith } + offset_{(b)} \]

Where:

\(gain_{(b)}\) and \(offset_{(b)}\) are values taken from the table below:

Band Gain Offset
pan 0.950 -3.629
coastal 0.905 -8.604
blue 0.940 -5.809
green 0.938 -4.996
yellow 0.962 -3.649
red 0.964 -3.021
rededge 1.000 -4.521
nir1 0.961 -5.522
nir2 0.978 -2.992

And \(abscalfactor\) and \(effectivebandwith\) are extracted from the acquisition metadata.

The conversion from \(DN\) (for Digital Numbers) to spectral radiance (or ‘TOA radiance’) \(L \) is done with the formula below:

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

As such, the calibration uses:

\[ gain = gain_{(b)} \times { abscalfactor \over effectivebandwith } \]

and

\[ offset = offset_{(b)} \]

\(L \) 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:

Band

Thuillier 2003

pan 1574.41
coastal 1757.89
blue 2004.61
green 1830.18
yellow 1712.07
red 1535.33
rededge 1348.08
nir1 1055.94
nir2 858.77

Input

The input is an ingested WorldView-3, see details here.

Output

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

References

RE01 - TODO add reference to slides about WorldView