slmsuite.holography.analysis.fitfunctions.sinc2d

sinc2d(xy, x0, y0, R, a=1, b=0, c=0, d=0, kx=0, ky=0)

For fitting a 2D rectangular \(\text{sinc}^2\) distribution, potentially with a sinusoidal modulation.

\[z(x,y) = d + \left(c + \frac{a}{2} \left[1+\cos(k_xx+k_yy-b) \right]\right) * \text{sinc}^2(\pi (x-x_0) / R) * \text{sinc}^2(\pi (y-y_0) / R).\]

where

\[\text{sinc}(x) = \frac{\sin(x)}{x}\]

Parameters:

• xy (numpy.ndarray) – Points to fit upon (x, y).

• x0 (float) – Vector offset.

• y0 (float) – Vector offset.

• R (float) – Square radius of the sinc (radius of the first zero).

• a (float) – Peak amplitude.

• b (float) – Phase offset.

• c (float) – Sinusoidal amplitude offset.

• d (float) – Global offset.

• kx (float) – Vector phase scale factor. Default is 0.

• ky (float) – Vector phase scale factor. Default is 0.

Returns:

z – Rectangular sinc fit evaluated at all (x,y) in xy.

Return type:

numpy.ndarray