deerlab.distancerange¶

distancerange(t, nr=None)[source]¶

Empirical distance range given a dipolar EPR experiment time axis

This function calculates the empirical distance range for a DEER time axis. The distance range is determined by the time step and the Nyquist criterion for the minimum distance, and by the requirement that at least half an oscillation should be observable over the measured time window for the maximum distance. The function allows to specify the length of the output distance axis. If not given, only the minimum and maximum distances are returned.

Parameters:

tarray_like: Time axis, in microseconds. The time points at which the dipolar signal was measured.
nrscalar, integer: Length of output distance axis. If not given, only min and max distance are returned.

Returns:

rndarray or tuple: Distance axis, in nanometers, running between empirical lower and upper limits rmin and rmax. Either an ndarray r (if nr is given) or a tuple (rmin,rmax) (if nr is not given).

Notes

The minimal and maximal distances, rmin and rmax, are empirical values that determine the minimal and maximal distance for which the given time trace can provide reliable information.

The minimum distance is determined by the time step $\Delta t$ and the Nyquist criterion:

$r_\text{min} = \left( \frac{4\Delta t \nu_0}{0.85} \right)^{1/3}$

The maximum distance is determined by the requirement that at least half an oscillation should be observable over the measured time window from $t_\text{min}$ to $t_\text{max}$ .

$r_\text{max} = 6\left( \frac{t_\text{max}-t_\text{min}}{2} \right)^{1/3}$

where $\nu_0$ = 52.04 MHz nm^3.

See Jeschke et al, Appl. Magn. Reson. 30, 473-498 (2006), https://doi.org/10.1007/BF03166213