Interferograms

Prysm offers rich features for analysis of interferometric data. Interferogram objects are conceptually similar to Pupils and both inherit from the same base class, as they both have to do with optical phase. The construction of an Interferogram requires only a few parameters:

>>> import numpy as np
>>> from prysm import Interferogram
>>> x = y = np.arange(129)
>>> z = np.random.uniform((128,128))
>>> interf = Interferogram(phase=z, intensity=None, unit_x=x, unit_y=y, scale='mm', phase_unit='nm', meta={'wavelength': 632.8e-9})

Notable are the scale, and phase unit, which define the xy and z units, respectively. Any SI unit is accepted as well as angstroms. Imperial units not accepted. meta is a dictionary to store metadata. For several interferogram methods to work, the wavelength must be present in meters. This departure from prysm’s convention of preferred units is used to maintain compatability with Zygo dat files. Interferograms are usually created from such files:

>>> interf = Interferogram.from_zygo_dat(your_path_file_object_or_bytes)

and both the dat and datx format from Zygo are supported. Dat carries no dependencies, while datx requries the installation of h5py. In addition to properties inherited from the OpticalPhase class (pv, rms, Sa, std), Interferograms have a dropout_percentage property, which gives the percentage of NaN values within the phase array. These NaNs may be filled,

>>> interf.fill(_with=0)

with 0 as a default value; only constants are supported. The modification is done in-place and the method returns self. Piston, tip-tilt, and power may be removed:

>>> interf.fill()\
>>>     .remove_piston()\
>>>     .remove_tiptilt()\
>>>     .remove_power()

again done in-place and returning self, so methods can be chained. One line convenience wrappers exist:

>>> interf.remove_piston_tiptilt()
>>> interf.remove_piston_tiptilt_power()

spikes may also be clipped,

>>> interf.spike_clip(nsigma=3)  # default is 3

setting points with a value more than nsigma standard deviations from the mean to NaN. Masks may be applied:

>>> your_mask = np.ones(interf.phase.shape)
>>> interf.mask(your_mask)

the phase is deleted (replaced with NaN) wherever the mask is equal to zero. The same applies to the intensity.

Interferograms may be cropped, deleting empty (NaN) regions around a measurment;

>>> interf.crop()

Convenience properties are provided for data size,

>>> interf.shape, interf.diameter_x, interf.diameter_y, interf.diameter

shape mirrors the shape of the underlying ndarray. The x and y diameters are in units of interf.spatial_unit and diameter is the greater of the two.

The two dimensional Power Spectral Density (PSD) may be computed. The data may not contain NaNs, and piston tip and tilt should be removed prior. A 2D Welch window is used, so there is no need for concern about zero values creating a discontinuity at the edge of circular or other nonrectangular apertures.

>>> interf.crop().remove_piston_tiptilt_power().fill()
>>> ux, uy, psd = interf.psd()

x, y, and azimuthally averaged cuts of the PSD are also available

>>> psd_dict = interf.psd_xy_avg()
>>> ux, psd_x = psd_dict['x']
>>> uy, psd_y = psd_dict['y']
>>> ur, psd_r = psd_Dict['avg']

and the PSD may be plotted,

>>> interf.plot_psd2d(axlim=1, interp_method='lanczos', fig=None, ax=None)
>>> interf.plot_psd_xyavg(xlim=(1e0,1e3), ylim=(1e-7,1e2), fig=None, ax=None)

For the x/y and average plot, a Lorentzian model may be plotted alongside the data for e.g. visual verification of a requirement:

>>> interf.plot_psd_xyavg(a=1,b=1,c=1)

A bandlimited RMS value derived from the 2D PSD may also be evaluated,

>>> interf.bandlimited_rms(wllow=1, wlhigh=10, flow=1, fhigh=10)

only one of wavelength (wl; spatial period) or frequency (f) should be provided. f will overrule wavelength.

The complete API documentation is below.

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class prysm.interferogram.Interferogram(phase, intensity=None, x=None, y=None, scale='px', phase_unit='nm', meta=None)

Bases: prysm._phase.OpticalPhase

Class containing logic and data for working with interferometric data.

bandlimited_rms(wllow=None, wlhigh=None, flow=None, fhigh=None)

Calculate the bandlimited RMS of a signal from its PSD.

wllow : float

short spatial scale

wlhigh : float

long spatial scale

flow : float

low frequency

fhigh : float

high frequency

float

band-limited RMS value.

crop()

Crop data to rectangle bounding non-NaN region.

dropout_percentage

Percentage of pixels in the data that are invalid (NaN).

fill(_with=0)

Fill invalid (NaN) values.

_with : float, optional

value to fill with

Interferogram

self

static from_zygo_dat(path, multi_intensity_action='first', scale='um')

Create a new interferogram from a zygo dat file.

path : path_like

path to a zygo dat file

multi_intensity_action : str, optional

see io.read_zygo_dat

scale : str, optional, {‘um’, ‘mm’}

what xy scale to label the data with, microns or mm

Interferogram

new Interferogram instance

mask(mask)

Apply a mask to the data.

mask : numpy.ndarray

masking array; expects an array of zeros (remove) and ones (keep)

Interferogram

self

plot_psd2d(axlim=None, clim=(1e-09, 100.0), interp_method='lanczos', fig=None, ax=None)

Plot the two dimensional PSD.

axlim : float, optional

symmetrical axis limit

power : float, optional

inverse of power to stretch image by

interp_method : str, optional

method used to interpolate the image, passed directly to matplotlib imshow

fig : matplotlib.figure.Figure

Figure containing the plot

ax : matplotlib.axes.Axis

Axis containing the plot

fig : matplotlib.figure.Figure

Figure containing the plot

ax : matplotlib.axes.Axis

Axis containing the plot

plot_psd_xyavg(a=None, b=None, c=None, lw=3, xlim=None, ylim=None, fig=None, ax=None)

Plot the x, y, and average PSD on a linear x axis.

a : float, optional

a coefficient of Lorentzian PSD model plotted alongside data

b : float, optional

b coefficient of Lorentzian PSD model plotted alongside data

c : float, optional

c coefficient of Lorentzian PSD model plotted alongside data

lw : float, optional

linewidth provided directly to matplotlib

xlim : tuple, optional

len 2 tuple of low, high x axis limits

ylim : tuple, optional

len 2 tuple of low, high y axis limits

fig : matplotlib.figure.Figure

Figure containing the plot

ax : matplotlib.axes.Axis

Axis containing the plot

fig : matplotlib.figure.Figure

Figure containing the plot

ax : matplotlib.axes.Axis

Axis containing the plot

psd()

Power spectral density of the data., units (self.phase_unit^2)/((cy/self.spatial_unit)^2).

unit_x : numpy.ndarray

ordinate x frequency axis

unit_y : numpy.ndarray

ordinate y frequency axis

psd : numpy.ndarray

power spectral density

psd_xy_avg()

Power spectral density of the data., units (self.phase_unit^2)/((cy/self.spatial_unit)^2).

dict

with keys x, y, avg. Each containing a tuple of (unit, psd)

remove_piston()

Remove piston from the data by subtracting the mean value.

remove_piston_tiptilt()

Remove piston/tip/tilt from the data, see remove_tiptilt and remove_piston.

remove_piston_tiptilt_power()

Remove piston/tip/tilt/power from the data.

remove_power()

Remove power from the data by least squares fitting.

remove_tiptilt()

Remove tip/tilt from the data by least squares fitting and subtracting a plane.

spike_clip(nsigma=3)

Clip points in the data that exceed a certain multiple of the standard deviation.

nsigma : float

number of standard deviations to keep

self

this Interferogram instance.