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Absolute radiometric calibration

Digital Numbers to Radiance

Top Of Atmosphere (TOA) Radiance in Wμm-1 m-2 sr-1 is derived from DN values using the following formula:

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

where: \(L_\lambda\) is TOA Radiance in Wμm-1 m-2 sr-1.

Radiance to TOA Reflectance

TOA reflectance \(\rho_\lambda\) in spectral band \(\lambda\) is then derived from:

\[ \rho_\lambda = \frac {L \times d^2_{E,S} \times \pi} {ESUN \times cos(θ_{S})} \]

where: \(L_\lambda\) is the radiance in spectral band \(\lambda\), \(d^2_{E,S}\) is the is the earth-Sun distance in AU at given time, \(ESUN\) is the band averaged Exo Atmospheric Solar Irradiance at 1AU in mW m^-2 nm^-1, and \(θ_{S}\) is the solar zenith angle, and \(L\) is TOA Radiance in Wμm-1 m-2 sr-1.

ESUN is derived from reference Solar Spectral Irradiance and depends on radiometric resolution and Filter Spectral Response Profiles for each band of the optical EO data.

This information is usually provided in the mission handbooks or manuals. For those missions where the ESUN values were not provided, these are derived from Thuillier 2002, over nominal band spectral ranges. ESUN values can be refined once Filter Spectral Response Profiles for VHRI 100 imager sensors are known.

Below table reports an example of ESUN for multiple assets made using Thuillier 2002 model for Vision-1.

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


graph TB c(cos2) --> d[Dataset] d --> i[input] subgraph Inputs i end subgraph Optical Calibration i --> dntor((DN<br>to<br>radiance)) dntor --> rtor((radiance<br>to<br>reflectance)) end subgraph Outputs rtor --> o1[Optical<br>calibrated<br>product] end