PSD (paos.classes.psd)

class PSD(pupil, A=10.0, B=0.0, C=0.0, f=None, fknee=1.0, fmin=None, fmax=None, SR=0.0, units=Unit('m'))[source]

Bases: object

Generates a surface error field (SFE) with a given power spectral density (PSD) and surface roughness (SR).

The PSD is given by the following expression:

\(\displaystyle PSD(f) = \frac{A}{B + (f/f_{knee})^C}\)

Parameters:

  • pupil (array like) – The pupil for which the SFE is generated.

  • A (float) – The amplitude of the PSD.

  • B (float) – PSD parameter. If B = 0, the PSD is a power law.

  • C (float) – PSD parameter. It sets the slope of the PSD.

  • f (array like) – The frequency grid.

  • fknee (float) – The knee frequency of the PSD.

  • fmin (float) – The minimum frequency of the PSD.

  • fmax (float) – The maximum frequency of the PSD.

  • SR (float) – The rms of the surface roughness.

  • units (astropy.units) – The units of the SFE. Default is meters.

Returns:

wfe – The generated surface error field.

Return type:

array like

Example

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import astropy.units as u

>>> phi_x = 110.0  # mm
>>> phi_y = 73.0  # mm
>>> zoom = 4
>>> wl = 0.550
>>> D = zoom * np.max([phi_x, phi_y])
>>> grid = 1024
>>> delta = D / grid

>>> A, B, C, fknee, fmin, fmax = 7.0, 0.0, 1.5, 1.0, 1 / 20, 1 / 2
>>> SR = 0.0

>>> x = y = np.arange(-grid // 2, grid // 2) * delta
>>> xx, yy = np.meshgrid(x, y)
>>> pupil = np.zeros((grid, grid))

>>> mask = (2 * xx / phi_x) ** 2 + (2 * yy / phi_y) ** 2 <= 1
>>> pupil[mask] = 1.0
>>> wfo = np.ma.masked_array(pupil, mask=~mask)

>>> fx = np.fft.fftfreq(wfo.shape[0], delta)
>>> fxx, fyy = np.meshgrid(fx, fx)
>>> f = np.sqrt(fxx**2 + fyy**2)
>>> f[f == 0] = 1e-100

>>> wfo_ = PSD(wfo, A, B, C, f, fknee, fmin, fmax, SR, units=u.nm)

>>> plt.figure()
>>> plt.imshow(wfo_(), cmap="jet", origin="lower")
>>> plt.xlim(grid // 2 - grid // (2 * zoom), grid // 2 + grid // (2 * zoom))
>>> plt.ylim(grid // 2 - grid // (2 * zoom), grid // 2 + grid // (2 * zoom))
>>> plt.colorbar()
>>> plt.show()
static sfe_rms(A, B, C, f_knee, f_min, f_max)[source]

Method to compute the rms of the surface error field (SFE) from the power spectral density (PSD). It uses sympy to evaluate the integral of the PSD.