Principle of Derivative Algorithm
To obtain se(t)se(t — s)* from the beat signal, a controllable delay line is usually involved in nonlinearity correction algorithms. The delay line technique provides a controllable time delay sref of the original signal without changing its amplitude. Therefore, the nonlinear error phase can be calculated from Eq. 5.3.8 as
Meta et al.  proposed an estimation algorithm which is genetic to all nonlinearity models. This algorithm regards the difference of e(tr) in beat signal as the derivative of e(tr) in the case that the time delay sref is far smaller than PRI. Therefore, the nonlinear phase error can be approximated as
Thus, s(tr) can be estimated as
The algorithm in , referred to as derivative algorithm, is an efficient method with simple processing steps. If sref is far smaller than PRI, it will give an accurate estimation of transmitted nonlinearity. However, it is inherently a biased algorithm since it is based on the derivative approximation, which makes it inapplicable in high resolution imaging. Moreover, estimation performance decreases sharply as time delay increases.