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How is radiance calculated?

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Question:

How is radiance calculated?

Answer:

During Level-1 Radiometric (L1R) product rendering, image pixels are converted to units of absolute radiance using 32-bit floating point calculations. Pixel values are then multiplied by 100 and converted to 16-bit integers prior to media output, preserving two digits of decimal precision. To convert the L1R image data back to radiance units, divide by 100.

Image artifacts such as banding, striping, and scan-correlated shifting are removed prior to radiometric correction, and these corrections are not reversible.

The L1R product geometry is identical to the input for Level-0 reformatted (L0R) data.

During Level-1 Geometric (L1G-Systematic) product rendering, image pixels are converted to units of absolute radiance using 32-bit floating point calculations. Pixel values are then scaled to byte values prior to output.

The following general equation is used to convert Digital Numbers (DNs) in a L1T, L1Gt or L1G product back to radiance (L):

Lλ = "gain" * QCAL + "bias"

which is also expressed as:

Lλ = ((LMAXλ - LMINλ)/(QCALMAX-QCALMIN)) * (QCAL-QCALMIN) + LMINλ

Where: Lλ = Spectral Radiance at the sensor's aperture in watts/(meter squared * ster * µm)
  "gain" = Rescaled gain (the data product "gain" contained in the Level-1 product header or ancillary data record) in watts/(meter squared * ster * µm)
  "bias" = Rescaled bias (the data product "offset" contained in the Level-1 product header or ancillary data record ) in watts/(meter squared * ster * µm)
  QCAL = the quantized calibrated pixel value in DN
  LMINλ = the spectral radiance that is scaled to QCALMIN in watts/(meter squared * ster * µm)
  LMAXλ = the spectral radiance that is scaled to QCALMAX in watts/(meter squared * ster * µm)
  QCALMIN = the minimum quantized calibrated pixel value (corresponding to LMINλ) in DN
= 1 for LPGS products
= 1 for NLAPS products processed after 4/4/2004
= 0 for NLAPS products processed before 4/5/2004
  QCALMAX = the maximum quantized calibrated pixel value (corresponding to LMAXλ) in DN
= 255

For information on the processing system (LPGS or NLAPS) used to produce a particular image, refer to the metadata file (_MTL.txt) provided with the data. The LMIN, LMAX, QCALMIN, and QCALMAX values can also be found in the metadata file.

For more information on how to calculate radiance for Landsat 5 TM data, refer to the Landsat 5 Thematic Mapper Thermal Band Calibration Update.

For more information on how to calculate radiance for Landsat 7 ETM+ data, refer to Section 11.3.1 of the Landsat 7 Science Data User Handbook.

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