snompy.pdm.taylor_coef

pdm.taylor_coef(z_tip, j_taylor, A_tip, n, r_tip, alpha_tip, n_trapz)

Return the coefficient for the power of reflection coefficient used by the Taylor series representation of the bulk PDM.

Parameters:

z_tipfloat

Height of the tip above the sample.

j_taylorinteger

The corresponding power of the reflection coefficient in the Taylor series.

A_tipfloat

The tapping amplitude of the AFM tip.

nint

The harmonic of the AFM tip tapping frequency at which to demodulate.

r_tipfloat

Radius of curvature of the AFM tip.

alpha_tipcomplex

Polarizability of the conducting sphere used as a model for the AFM tip.

n_trapzint

The number of intervals used by snompy.demodulate.demod() for the trapezium-method integration.

Returns:

a_jcomplex

Coefficient for the power of reflection coefficient used by the Taylor series representation of the bulk FDM

See also

snompy.demodulate.demod

The function used here for demodulation.

Notes

This function implements

\[a_j = \hat{F_n}[f^j],\]

where \(\hat{F_n}[f(j)]\) is the \(n^{th}\) Fourier coefficient of the function \(f^j\), and \(f\) is implemented here as geom_func().