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WorldView-1

WorldView-1 panchromatic EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service.

Image-001

DN to Radiance

The WorldView-1 product handbook1 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 1.016 -1.824

Table 1 - Gain and offset for the Worldview-1 DN to radiance conversion.

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 conversion from elevation angle to solar zenith angle \(θ\) (in degrees) is:

\[ θ = { 90 - elevation_angle } \]

The value for the \(ESUN(b)\) is provided in Table 2:

Common band name Thuillier 2003
pan 1478.62

Table 2 - ESUN value employed in the conversion of radiance to reflectance for Worldview-1 products.

Input

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

Output

The output is a STAC item GeoJSON2 having a similar structure to the Worldview-3 one available here.

References


  1. Kuester, M. Absolute Radiometric Calibration: 2016v0; updated on 6/6/2017 GE01 and CAVIS, DigitalGlobe: Westminster, CO, USA, 2017; pp. 1–8. 

  2. Radiant Earth Foundation, STAC item specifications, a single spatiotemporal asset as a GeoJSON feature plus datetime and links, available at:https://github.com