skued.biexponential

skued.biexponential(time, tzero, amp1, amp2, tconst1, tconst2, offset=0)

Bi-exponential curve with onset. Equivalent to the following function:

\[\begin{split}I(t) = \begin{cases} I_1 + I_2 + O &\text{if } t < t_0 \\ I_1 e^{-(t - t_0)/\tau_1} + I_2 e^{-(t - t_0)/\tau_2} + O &\text{if } t \ge t_0 \end{cases}\end{split}\]

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 \(t > t_0\).
amp1 (float) – Initial amplitude \(I_1\).
amp2 (float) – Initial amplitude \(I_2\).
tconst1 (float) – Decay time-constant \(\tau_1\) [ps].
tconst2 (float) – Decay time-constant \(\tau_2\) [ps].
offset (float, optional) – Constant amplitude offset \(O\).

Returns:

biexp – Biexponential curve.

Return type:

~numpy.ndarray, shape (N,)