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In the SLC product, amplitude data is not explicitly provided by SLC Sentinel 1, only the real (i) and imaginary (q) bands of each polarization obtained, in addition to a band called “Intensity” for each polarization.

To get amplitude would have to do:

Amplitude = sqrt(i²+q²)

The intensity is obtained by:

Intensity= i²+q²

Now, then to get the amplitude on SLC Sentinel 1 I could simply calculate the square root of the Intensity band?:

Amplitude = sqrt(Intensity)

But in practice, physically, what do amplitude and intensity represent, what are their measurement units? Why does ESA use these two notations, theoretically for the same thing?

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You can think of amplitude as measuring a voltage (in units of Volts), which is proportional to energy, while intensity represents a power (in units of Watts). The images will look similar, but some features may stand out more in one view than the other. As in the link ycartwhelen shared, amplitude images have a narrower dynamic range than intensity images. People use both in radar because historically, electrical engineers have been interested in measuring responses of both "voltage" and "power."

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