prysm.otf

A base optical transfer function interface.

class prysm.otf.MTF(data, x, y=None)

Bases: prysm._basicdata.BasicData

Modulation Transfer Function.

tan

Retrieve the tangential MTF.

Notes

Assumes the object is extended in y. If the object is extended along a different azimuth, this will not return the tangential MTF.

Returns

  • self.x (numpy.ndarray) – ordinate

  • self.data (numpy.ndarray) – coordiante

sag

Retrieve the sagittal MTF.

Notes

Assumes the object is extended in y. If the object is extended along a different azimuth, this will not return the sagittal MTF.

Returns

  • self.x (numpy.ndarray) – ordinate

  • self.data (numpy.ndarray) – coordiante

exact_polar(freqs, azimuths=None)

Retrieve the MTF at the specified frequency-azimuth pairs.

Parameters

  • freqs (iterable) – radial frequencies to retrieve MTF for

  • azimuths (iterable) – corresponding azimuths to retrieve MTF for

Returns

MTF at the given points

Return type

list

exact_xy(x, y=None)

Retrieve the MTF at the specified X-Y frequency pairs.

Parameters

  • x (iterable) – X frequencies to retrieve the MTF at

  • y (iterable) – Y frequencies to retrieve the MTF at

Returns

MTF at the given points

Return type

list

exact_tan(freq)

Return data at an exact x coordinate along the y=0 axis.

Parameters

freq (number or numpy.ndarray) – frequency or frequencies to return

Returns

ndarray of MTF values

Return type

numpy.ndarray

exact_sag(freq)

Return data at an exact y coordinate along the x=0 axis.

Parameters

freq (number or numpy.ndarray) – frequency or frequencies to return

Returns

ndarray of MTF values

Return type

numpy.ndarray

azimuthal_average()

Return the azimuthally averaged MTF.

Returns

  • nu (numpy.ndarray) – spatial frequencies

  • mtf (numpy.ndarray) – mtf values

plot2d(max_freq=200, power=1, cmap='Greys_r', fig=None, ax=None)

Create a 2D plot of the MTF.

Parameters

  • max_freq (float) – Maximum frequency to plot to. Axis limits will be ((-max_freq, max_freq), (-max_freq, max_freq)).

  • power (float) – inverse of power to stretch the MTF to/by, e.g. power=2 will plot MTF^(1/2)

  • fig (matplotlib.figure.Figure, optional:) – Figure to draw plot in

  • ax (matplotlib.axes.Axis, optional:) – Axis to draw plot in

Returns

  • fig (matplotlib.figure.Figure) – Figure to draw plot in

  • ax (matplotlib.axes.Axis) – Axis to draw plot in

plot_tan_sag(max_freq=200, lw=3, zorder=3, fig=None, ax=None, labels=('Tangential', 'Sagittal'))

Create a plot of the tangential and sagittal MTF.

Parameters

  • max_freq (float) – Maximum frequency to plot to. Axis limits will be ((-max_freq, max_freq), (-max_freq, max_freq))

  • lw (float, optional) – line width

  • zorder (int) – zorder

  • fig (matplotlib.figure.Figure, optional:) – Figure to draw plot in

  • ax (matplotlib.axes.Axis, optional:) – Axis to draw plot in

  • labels (iterable) – set of labels for the two lines that will be plotted

Returns

  • fig (matplotlib.figure.Figure) – Figure to draw plot in

  • ax (matplotlib.axes.Axis) – Axis to draw plot in

plot_azimuthal_average(max_freq=200, lw=3, zorder=3, fig=None, ax=None)

Create a plot of the azimuthally averaged MTF.

Parameters

  • max_freq (float) – Maximum frequency to plot to. Axis limits will be ((-max_freq, max_freq), (-max_freq, max_freq))

  • lw (float, optional) – line width

  • zorder (int, optional) –

  • fig (matplotlib.figure.Figure, optional:) – Figure to draw plot in

  • ax (matplotlib.axes.Axis, optional:) – Axis to draw plot in

  • labels (iterable) – set of labels for the two lines that will be plotted

Returns

  • fig (matplotlib.figure.Figure) – Figure to draw plot in

  • ax (matplotlib.axes.Axis) – Axis to draw plot in

static from_psf(psf)

Generate an MTF from a PSF.

Parameters

psf (PSF) – PSF to compute an MTF from

Returns

A new MTF instance

Return type

MTF

static from_pupil(pupil, efl, Q=2)

Generate an MTF from a pupil, given a focal length (propagation distance).

Parameters

  • pupil (Pupil) – A pupil to propagate to a PSF, and convert to an MTF

  • efl (float) – Effective focal length or propagation distance of the wavefunction

  • Q (number) – ratio of pupil sample count to PSF sample count. Q > 2 satisfies nyquist

Returns

A new MTF instance

Return type

MTF

center_x

Center “pixel” in x.

center_y

Center “pixel” in y.

copy()

Return a (deep) copy of this instance.

sample_spacing

center-to-center sample spacing.

samples_x

Number of samples in the x dimension.

samples_y

Number of samples in the y dimension.

shape

Proxy to phase or data shape.

size

Proxy to phase or data size.

slice_x

Retrieve a slice through the X axis of the phase.

Returns

  • self.unit (numpy.ndarray) – ordinate axis

  • slice of self.phase or self.data (numpy.ndarray)

slice_y

Retrieve a slice through the Y axis of the phase.

Returns

  • self.unit (numpy.ndarray) – ordinate axis

  • slice of self.phase or self.data (numpy.ndarray)

prysm.otf.diffraction_limited_mtf(fno, wavelength, frequencies=None, samples=128)

Give the diffraction limited MTF for a circular pupil and the given parameters.

Parameters

  • fno (float) – f/# of the lens.

  • wavelength (float) – wavelength of light, in microns.

  • frequencies (numpy.ndarray) – spatial frequencies of interest, in cy/mm if frequencies are given, samples is ignored.

  • samples (int) – number of points in the output array, if frequencies not given.

Returns

  • if frequencies not given –

    frequenciesnumpy.ndarray

    array of ordinate data

    mtfnumpy.ndarray

    array of coordinate data

  • else –

    mtfnumpy.ndarray

    array of MTF data

Notes

If frequencies are given, just returns the MTF. If frequencies are not given, returns both the frequencies and the MTF.

prysm.otf.longexposure_otf(nu, Cn, z, f, lambdabar, h_z_by_r=2.91)

Compute the long exposure OTF for given parameters.

Parameters

  • nu (numpy.ndarray) – spatial frequencies, cy/mm

  • Cn (float) – atmospheric structure constant of refractive index, ranges ~ 10^-13 - 10^-17

  • z (float) – propagation distance through atmosphere, m

  • f (float) – effective focal length of the optical system, mm

  • lambdabar (float) – mean wavelength, microns

  • h_z_by_r (float, optional) – constant for h[z/r] – see Eq. 8.5-37 & 8.5-38 in Statistical Optics, J. Goodman, 2nd ed.

Returns

the OTF

Return type

numpy.ndarray

prysm.otf.estimate_Cn(P=1013, T=273.15, Ct=0.0001)

Use Weng et al to estimate Cn from meteorological data.

Parameters

  • P (float) – atmospheric pressure in hPa

  • T (float) – temperature in Kelvin

  • Ct (float) – atmospheric struction constant of temperature, typically 10^-5 - 10^-2 near the surface

Returns

Cn

Return type

float