On what physical principles the measurement of intensity of light is based? As far as I understand, theoretically intensity of light is defined using the Poynting vector of the corresponding EM field.
How is the intensity of light measured in practice? On what physical principles such a measurement is based? Is it related to the Poynting vector?
 A: Intensity is basically the power per unit area transmitted by the light. A measurement would assume conservation of energy. Measurement might be based on a heating effect, but I suspect that most instruments measure a current which is proportional to the number of electrons being excited by incoming photons.  The problem with this is that the photon energy depends on frequency.  A photographers light meter might assume an average photon energy in sunlight.
A: As you may have expected, and as was pointed out in the comments, a photodetector based on the photoelectric effect really measures photon flux rather than optical power. Some assumption must be made about the wavelength (or spectrum) of the incident light to to determine the optical intensity.
For a direct measurement of the intensity, you can use a bolometer instead of a photoelectric detector. Since the bolometer measures the heating effect of the light, it measures the optical intensity directly. There may be some correction needed, for example if the target's reflectivity varies with wavelength, but these corrections can be made smaller than those required for photoelectric detectors.
