# Vision-1

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