opcsim.mie.coef_pi_tau¶

opcsim.mie.coef_pi_tau(theta, x)¶

Compute the angle-dependant functions (pi and tau) using upward recurrence.

Per Bohren and Huffman (1983) eq. 4.47, the angle-dependant functions \(\pi_n\) and \(\tau_n\) can be computed using upward recurrance from the relations:

\[\pi_n=\frac{2n-1}{n-1}\mu\pi_{n-1}-\frac{n}{n-1}\pi_{n-2} \]

\[\tau_n=n\mu\pi_n - (n+1)\pi_{n-1}\]

Parameters

theta: float: The scattering angle in degrees.
x: float: The dimensionless size parameter, used to determine the number of elements to compute.

Returns

pi_n, tau_n: np.ndarray of floats