# WorldView-3

WorldView-3 L1B panchromatic and multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service.

Figure 1 - True Color composite derived from Worldview-3 L1B calibrated data acquired on 23/06/2023 over Spera District, Khost Province, Afghanistan. Credits: DigitalGlobe, USGS.

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

## Input

The input is an ingested WorldView-3, find details here.

## DN to Radiance

The WorldView-3 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 Table 1:

Common band name Gain Offset
pan 0.950 -3.629
coastal 0.905 -8.604
blue 0.940 -5.809
green 0.938 -4.996
yellow 0.962 -3.649
red 0.964 -3.021
rededge 1.000 -4.521
nir08 0.961 -5.522
nir09 0.978 -2.992
Table 1 - Gain and offset for the Worldview-3 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 values for the $$ESUN(b)$$ are provided in Table 2:

Common band name Thuillier 2003
pan 1574.41
coastal 1757.89
blue 2004.61
green 1830.18
yellow 1712.07
red 1535.33
rededge 1348.08
nir08 1055.94
nir09 858.77
Table 2 - ESUN value employed in the conversion of radiance to reflectance for Worldview-3 products.

## Output

The output is a STAC item GeoJSON2 including the assets shown below

"assets": {
"coastal": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/coastal.tif",
"eo:bands": [
{
"name": "coastal",
"common_name": "coastal",
"center_wavelength": 0.4274,
"solar_illumination": 1757.89,
"full_width_half_max": 0.02025
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "6347",
"mean": "854.39426479578",
"stddev": "551.85802604088",
"valid_percent": "100"
},
"file:size": 91755870
},
"red": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/red.tif",
"eo:bands": [
{
"name": "red",
"common_name": "red",
"center_wavelength": 0.6601,
"solar_illumination": 1535.33,
"full_width_half_max": 0.02925
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "9597",
"mean": "781.44649721892",
"stddev": "601.396273167",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -18.81764705882353,
"max": 9615.817647058824,
}
}
],
"file:size": 120220176
},
"blue": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/blue.tif",
"eo:bands": [
{
"name": "blue",
"common_name": "blue",
"center_wavelength": 0.4819,
"solar_illumination": 2004.61,
"full_width_half_max": 0.027
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "7645",
"mean": "787.38125030186",
"stddev": "537.64898625588",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -14.990196078431373,
"max": 7659.990196078431,
}
}
],
"file:size": 103085046
},
"yellow": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/yellow.tif",
"eo:bands": [
{
"name": "yellow",
"common_name": "yellow",
"center_wavelength": 0.6043,
"solar_illumination": 1712.07,
"full_width_half_max": 0.01905
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "6683",
"mean": "739.05154238735",
"stddev": "552.66287363469",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -13.10392156862745,
"max": 6696.103921568628,
}
}
],
"file:size": 118063652
},
"rededge": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/rededge.tif",
"eo:bands": [
{
"name": "rededge",
"common_name": "rededge",
"center_wavelength": 0.7227,
"solar_illumination": 1348.08,
"full_width_half_max": 0.01935
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "7853",
"mean": "887.91057425555",
"stddev": "627.02772123954",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -15.398039215686275,
"max": 7868.398039215686,
}
}
],
"file:size": 124186124
},
"green": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/green.tif",
"eo:bands": [
{
"name": "green",
"common_name": "green",
"center_wavelength": 0.5471,
"solar_illumination": 1830.18,
"full_width_half_max": 0.0309
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "7279",
"mean": "744.49282038834",
"stddev": "537.28707470685",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -14.272549019607844,
"max": 7293.272549019608,
}
}
],
"file:size": 119246699
},
"nir09": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/nir09.tif",
"eo:bands": [
{
"name": "nir09",
"common_name": "nir09",
"center_wavelength": 0.9136,
"solar_illumination": 858.77,
"full_width_half_max": 0.04445
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "6455",
"mean": "949.00748966677",
"stddev": "653.75464762957",
"valid_percent": "100"
},
"histogram": {
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"min": -12.656862745098039,
"max": 6467.656862745098,
}
}
],
"file:size": 125324505
},
"nir08": {
"type": "image/tiff; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/nir08.tif",
"eo:bands": [
{
"name": "nir08",
"common_name": "nir08",
"center_wavelength": 0.824,
"solar_illumination": 1055.94,
"full_width_half_max": 0.0502
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "9543",
"mean": "1135.7010306127",
"stddev": "787.44611040581",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -18.711764705882352,
"max": 9561.711764705882,
}
}
],
"file:size": 127019973
},
"overview-trc": {
"type": "image/tiff; application=geotiff",
"roles": [
"composite",
"reflectance",
"visual"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/overview-trc.tif",
"raster:bands": [
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "254",
"mean": "53.662709830289",
"stddev": "42.936631425032",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "253",
"mean": "50.487792319208",
"stddev": "37.664632349125",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0000147646949405,
"statistics": {
"minimum": "0",
"maximum": "253",
"mean": "53.685524163955",
"stddev": "37.257732058376",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
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}
},
{
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"statistics": {
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"mean": "188.48946167463",
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"valid_percent": "100"
},
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"min": -0.5,
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}
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],
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},
"type": "image/tiff; application=geotiff",
"roles": [
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"reflectance",
"visual"
],
"raster:bands": [
{
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"statistics": {
"minimum": "0",
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"stddev": "37.664632349125",
"valid_percent": "100"
},
"histogram": {
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"min": -0.5,
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}
},
{
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"statistics": {
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"stddev": "37.257732058376",
"valid_percent": "100"
},
"histogram": {
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}
},
{
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"statistics": {
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"mean": "59.08198349908",
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"valid_percent": "100"
},
"histogram": {
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"min": -0.5,
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}
},
{
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"statistics": {
"minimum": "0",
"maximum": "255",
"mean": "188.48946167463",
"stddev": "111.96667166902",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
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}
}
],
"file:size": 194843970
},
"overview-trc-low-res": {
"type": "image/tiff; application=geotiff",
"roles": [
"composite",
"overview",
"reflectance"
],
"href": "https://.../WV03N33_174861E069_5258332022062300000000MS00-calibrated/overview-trc-low-res.tif",
"raster:bands": [
{
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"statistics": {
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"maximum": "253",
"mean": "53.602964401245",
"stddev": "42.907030195412",
"valid_percent": "100"
},
"histogram": {
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"min": -0.5,
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}
},
{
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"statistics": {
"minimum": "0",
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"mean": "50.43909740448",
"stddev": "37.639390122484",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0001712070192611,
"statistics": {
"minimum": "0",
"maximum": "252",
"mean": "53.643088340759",
"stddev": "37.23933497564",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
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}
},
{
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"statistics": {
"minimum": "0",
"maximum": "255",
"mean": "188.43219280243",
"stddev": "111.99784765917",
"valid_percent": "100"
},
"histogram": {
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"min": -0.5,
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}
}
],
"file:size": 4197770
}
}

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