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Vision-1 acquisitions are calibrated using the Orfeo Toolbox.

DN to Radiance

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

\[ L(b) = { DN_{(b)} \times gain_{(b)} } + bias_{(b)} \]

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

The gain and bias values are read from the acquisition metadata.

Radiance to TOA 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 \(ESUN_{(b)}\) values were derived from Thuillier 2002, over nominal band spectral ranges. These are:

Vision-1 (VHRI 100 imager)
Band λ(nm) ESUN (Thuillier 2002) mW m^-2 nm^-1
PAN 450-650 1830.15
Blue 440-510 2002.25
Green 510-590 1822.22
Red 600-670 1613.83
NIR 760-910 948.98