skued.exponential

skued.exponential(time, tzero, amp, tconst, offset=0)

Exponential curve with onset. Equivalent to the following function:

\[\begin{split}I(t) = \begin{cases} I_0 + O &\text{if } t < t_0 \\ I_0 e^{-(t - t_0)/\tau} + O &\text{if } t \ge t_0 \end{cases}\end{split}\]

where \(\Theta(t - t_0)\) is the Heaviside step function.

This functions is expected to be used in conjunction with scipy.optimize.curve_fit or similar fitting routines.

Parameters:

time (~numpy.ndarray, shape(N,)) – Time values array [ps].
tzero (float) – Time-zero \(t_0\) [ps]. Exponential behavior happens for \(t > t_0\).
amp (float) – Initial amplitude \(I_0\).
tconst (float) – Decay time-constant \(\tau\) [ps].
offset (float, optional) – Constant amplitude offset \(O\).

Returns:

exp – Exponential curve.

Return type:

~numpy.ndarray, shape (N,)