# 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