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GeoEye-1

GeoEye-1 acquisitions are calibrated using the Orfeo Toolbox.

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

DN to Radiance

The GeoEye-1 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 0.970 -1.926
blue 1.053 -4.537
green 0.994 -4.175
red 0.998 -3.754
nir 0.994 -3.870

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 1610.73
blue 1993.18
green 1828.83
red 1491.49
nir 1022.58

Input

The input is an ingested GeoEye-1, see details here.

Output

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