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WorldView-2

WorldView-2 acquisitions are calibrated using the Orfeo Toolbox.

The process applied is the same for PAN and MS acquisitions.

DN to Radiance

The WorldView-2 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 0.942 -2.704
coastal 1.151 -7.478
blue 0.988 -5.736
green 0.936 -3.546
yellow 0.949 -3.564
red 0.952 -2.512
rededge 0.974 -4.120
nir1 0.961 -3.300
nir2 1.002 -2.891

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 1571.36
coastal 1773.81
blue 2007.27
green 1829.62
yellow 1701.85
red 1538.85
rededge 1346.09
nir1 1053.21
nir2 856.599

Input

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

Output

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

References

RE01 - TODO add reference to slides about WorldView