qspec.inverse_doppler_d1  (  f_atom ,  f_lab ,  alpha ,  mode = 'raise-raise' ,  return_mask = False  )[source]

The first derivative $$\begin{aligned}\frac{\partial v}{\partial f_\mathrm{atom}} &= \frac{1}{sf_\mathrm{lab}}\left[\pm\left(\sqrt{s - 1} + \frac{(f_\mathrm{atom}/f_\mathrm{lab})^2}{\sqrt{s - 1}}\right) - 2\frac{v}{c}(f_\mathrm{atom}/f_\mathrm{lab})\right]\\[2ex] s &= (f_\mathrm{atom}/f_\mathrm{lab})^2 + \cos(\alpha)^2\end{aligned}.$$ For angles $-\pi/2 < \alpha < \pi/2$, there can be two solutions. Depending on the combination of f_atom, f_lab and alpha, the situation may be physically impossible. Specify mode to choose the desired behavior.

Parameters:

f_atomarray_like

The frequency of light $f_\mathrm{atom}$ in the atom's rest frame (arb. units).

f_labarray_like

The frequency of light $f_\mathrm{lab}$ in the laboratory frame ([f_atom]).

alphaarray_like

The angle $\alpha$ between the velocity- and the light-vector in the laboratory frame (rad).

modestr

The mode how to handle nan values and ambiguous velocities. Available options are:

• 'raise-raise': Raise an error if there are nan values or if the velocity is ambiguous.
• 'raise-small': Raise an error if there are nan values and return the smaller velocity.
• 'raise-large': Raise an error if there are nan values and return the larger velocity.
• 'isnan-raise': Ignore nan values and raise an error if the velocity is ambiguous.
• 'isnan-small': Ignore nan values and return the smaller velocity.
• 'isnan-large': Ignore nan values and return the larger velocity.

return_maskbool

Whether the mask where the velocity is ambiguous is returned as a second argument.

Returns:

out(ndarray, Optional[ndarray])

the first derivative $\partial v / \partial f_\mathrm{atom}$ of the velocity $v$ required to shift f_lab to f_atom. Optionally returns the mask where the velocity is ambiguous (m/(s MHz)).