calculate the spectral index of a body, in the case of non-thermal radiation. Calculating by frequency The brightness temperature of a source with known spectral radiance can be expressed as: When we can use the Rayleigh–Jeans law: For narrowband radiation with very low relative spectral linewidth and known radiance we can calculate the brightness temperature as: Calculating by wavelength Spectral radiance of black-body radiation is expressed by wavelength as: So, the brightness temperature can be calculated as: For long-wave radiation the brightness temperature is: For almost monochromatic radiation, the brightness temperature can be expressed by the radiance and the coherence length : References Temperature Radio astronomy Planetary science