Quantum limit of error in energy measurement using Kerr's effect

In the earlier published papers, when calculating the error in wave energy measurement using Kerr's optical effect it was assumed that the error of measurement of $E^2$ ($E$ is the electric field intensity amplitude) in a nonlinear medium completely determined the error in the wave energy estimation. The fact that during the measurement the wave impedance of the medium became principally indeterminate and the indeterminacy was the greater the higher the accuracy of the $E^2$ measurement was not taken into account. Therefore in such measurements there exists a principal quantum limit of error equal to $(n/(\omega_2\tau))^{1/2}\hbar\omega_1$ (where $n$ is the average number of photons, $\omega_1$ and $\omega_2$ are the wave frequencies before and during the measurement, respectively, and $\tau$ is the measurement duration).