Pléiades

Pléiades multispectral EO data products are calibrated using the Optical Products Calibration (OPT-Calib) service.

Figure 1 - True Color composite derived from calibrated Pléiades PMS ORTHO data acquired on 09/02/2023 over Sekeroba, Kahramanmaras, Turkey. Credits: Airbus DS, CNES.

Input

The input is an ingested Pléiades dataset. Find details here.

DN to Radiance

The Pléiades user guide¹ provides the formula below to convert the DN into radiance:

\[ L_{(b)} = {DN_{(b)} \over rescale gain_{(b)}} + rescale bias_{(b)} \]

For the conversion from \(DN\) (for Digital Numbers) to spectral radiance (or ‘TOA radiance’) \(L \), the following formula is used :

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

As such, the calibration uses:

\[ gain_{(b)} = {1 \over rescale gain_{(b)}} \]

and

\[ offset_{(b)} = rescale bias_{(b)} \]

\(L \) 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 acquisition metadata.

Output

The output is a STAC item GeoJSON[^6] including single band and overview assets in COG format. Below is given an example of assets included in the STAC item of a Pléiades ORTHO calibrated dataset.

  "assets": {
    "blue": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/blue.tif",
      "eo:bands": [
        {
          "name": "blue",
          "description": "Raw radiometric count (DN) to TOA Radiance (L). Formulae L=DN/GAIN+BIAS",
          "common_name": "blue",
          "solar_illumination": 1915
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.5,
          "statistics": {
            "minimum": 0,
            "maximum": 10000,
            "mean": 1099.1586831026,
            "stddev": 890.26671808737,
            "valid_percent": 100
          },
      "file:size": 796455776
    },
    "green": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/green.tif",
      "eo:bands": [
        {
          "name": "green",
          "description": "Raw radiometric count (DN) to TOA Radiance (L). Formulae L=DN/GAIN+BIAS",
          "common_name": "green",
          "solar_illumination": 1831
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.5,
          "statistics": {
            "minimum": 0,
            "maximum": 10000,
            "mean": 972.10462845682,
            "stddev": 851.7691225341,
            "valid_percent": 100
          },
      "file:size": 775575364
    },
    "red": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/red.tif",
      "eo:bands": [
        {
          "name": "red",
          "description": "Raw radiometric count (DN) to TOA Radiance (L). Formulae L=DN/GAIN+BIAS",
          "common_name": "red",
          "solar_illumination": 1594
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.5,
          "statistics": {
            "minimum": 0,
            "maximum": 10000,
            "mean": 845.9111852015,
            "stddev": 838.77620859596,
            "valid_percent": 100
          },
      "file:size": 760806521
    },
    "nir": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "data",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/nir.tif",
      "eo:bands": [
        {
          "name": "nir",
          "description": "Raw radiometric count (DN) to TOA Radiance (L). Formulae L=DN/GAIN+BIAS",
          "common_name": "nir",
          "solar_illumination": 1060
        }
      ],
      "raster:bands": [
        {
          "spatial_resolution": 0.5,
          "statistics": {
            "minimum": 0,
            "maximum": 10000,
            "mean": 1716.1581221858,
            "stddev": 1363.4867454117,
            "valid_percent": 100
          },
      "file:size": 921686021
    },
    "overview-trc": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "composite",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/overview-trc.tif",
      "file:size": 1275368027
    },
    "overview-civ": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "composite",
        "reflectance",
        "visual"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/overview-civ.tif",
      "file:size": 1330749445
    },
    "overview-trc-low-res": {
      "type": "image/tiff; application=geotiff; profile=cloud-optimized",
      "roles": [
        "composite",
        "overview",
        "reflectance"
      ],
      "href": "https://.../DS_PHR1A_202302090834089_FR1_PX_E036N37_1007_01591-calibrated/overview-trc-low-res.tif",
      "file:size": 1997776
    }
  }

Airbus Defence and Space, Pléiades User Guide, available at https://www.intelligence-airbusds.com ↩