Working with MODIS L1B from scratch. 3. calibration, conversion to radiance at top-of-atmosphere

In the third part of this series we will calibrate the images to convert the pixel values to spectral radiance. The spectral radiance is a physical quantity expressing the amount of energy being radiated (in our case, back to space), and is measured in Watts (Joules per second, energy flux) per square meter (area) per micrometer (wavelength) per steradian (solid angle). The values that we will obtain here will not yet be corrected for illumination, topographic or atmospheric effects, and therefore correspond to what is measured by the satellite at the altitude of its orbit, as opposed to values on the ground that you can measure with a field spectrometer. The values we will obtain here are thus called "radiance at top-of-atmosphere", usually abbreviated "TOA". The conversion is based on a linear relationship between data counts (pixel values) and the radiance measured by the sensor (for the gory details have a look at the manuals in NASA's MODIS Characterization Support Team). The basic relationship is: radiance = (pixel_value - offset) x scale and has to be performed band-wise. We begin by extracting the scales and offset from bands 3-7, that is the 500 m bands (remind that we use the bands resampled to 1 km). We use the program read_sds_attributes that comes with the MODAT suite.