In this case, the function is the scattering amplitude and through the use of the optical theorem the imaginary part of the scattering amplitude is related to the total cross section which is a physically measurable quantity.
The function is the scattering amplitude. This is in this case. The imaginary part of the scattering amplitude is related to the total cross section. This was through the use of the optical theorem. This was in this case. This total cross section is a physically measurable quantity.