# GeoEye-1 L1B

GeoEye-1 L1B panchromatic and multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service. The process applied is the same for PAN and MS acquisitions.

## Input

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

The GeoEye-1 product handbook1,2 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:

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

Table 1 - Gain and offset for the Geoeye-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.

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 Bandwidth Thuillier 2003
pan 0.3074 1610.73
blue 0.0584 1993.18
green 0.0646 1828.83
red 0.0316 1491.49
nir 0.1012 1022.58

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

## Output

The output is a STAC item GeoJSON3 including the assets shown below

  "assets": {
"green": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../green.tif",
"eo:bands": [
{
"name": "green",
"common_name": "green",
"center_wavelength": 0.545,
"solar_illumination": 1828.83,
"full_width_half_max": 0.03
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "6489",
"mean": "863.56089417308",
"stddev": "886.24396805544",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -12.723529411764705,
"max": 6501.7235294117645,
}
}
],
"file:size": 21813124
},
"nir08": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../nir08.tif",
"eo:bands": [
{
"name": "nir08",
"common_name": "nir08",
"center_wavelength": 0.85,
"solar_illumination": 1022.58,
"full_width_half_max": 0.03
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "6427",
"mean": "1886.247575313",
"stddev": "1620.4647902937",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -12.601960784313725,
"max": 6439.601960784314,
}
}
],
"file:size": 27161474
},
"blue": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../blue.tif",
"eo:bands": [
{
"name": "blue",
"common_name": "blue",
"center_wavelength": 0.48,
"solar_illumination": 1993.18,
"full_width_half_max": 0.03
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "5444",
"mean": "882.13915505924",
"stddev": "878.21414854936",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -10.674509803921568,
"max": 5454.674509803922,
}
}
],
"file:size": 20748394
},
"red": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"data",
"reflectance",
"visual"
],
"href": "https://.../red.tif",
"eo:bands": [
{
"name": "red",
"common_name": "red",
"center_wavelength": 0.673,
"solar_illumination": 1491.49,
"full_width_half_max": 0.03
}
],
"raster:bands": [
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "7533",
"mean": "669.12548358611",
"stddev": "833.3870434736",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -14.770588235294118,
"max": 7547.770588235294,
}
}
],
"file:size": 21817073
},
"overview-trc": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"composite",
"reflectance",
"visual"
],
"href": "https://.../overview-trc.tif",
"raster:bands": [
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "253",
"mean": "44.113735557357",
"stddev": "53.367084044392",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "252",
"mean": "59.218777275141",
"stddev": "58.264231030447",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "248",
"mean": "60.933859268563",
"stddev": "58.460926022744",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0000141800457472,
"statistics": {
"minimum": "0",
"maximum": "255",
"mean": "156.34194277981",
"stddev": "124.19497709926",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
}
],
"file:size": 33974844
},
"overview-trc-low-res": {
"type": "image/tiff; profile=cloud-optimized; application=geotiff",
"roles": [
"composite",
"overview",
"reflectance"
],
"href": "https://.../overview-trc-low-res.tif",
"raster:bands": [
{
"spatial_resolution": 0.0001445976930592,
"statistics": {
"minimum": "0",
"maximum": "253",
"mean": "44.10063457489",
"stddev": "53.378320324808",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0001445976930592,
"statistics": {
"minimum": "0",
"maximum": "252",
"mean": "59.193407058716",
"stddev": "58.26799239793",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0001445976930592,
"statistics": {
"minimum": "0",
"maximum": "248",
"mean": "60.905345916748",
"stddev": "58.462711737198",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
},
{
"spatial_resolution": 0.0001445976930592,
"statistics": {
"minimum": "0",
"maximum": "255",
"mean": "156.28141880035",
"stddev": "124.20901711164",
"valid_percent": "100"
},
"histogram": {
"count": 256,
"min": -0.5,
"max": 255.5,
}
}
],
"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. Podger, N.E., Colwell, W.B. and Taylor, M.H. (2011) GeoEye-1 Radiance at Aperture and Planetary Reflectance.

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