****
MTFs
****


Prysm models often include analysis of Modulation Transfer Function (MTF) data.  The MTF is formally defined as:

    the normalized magnitude of the Fourier transform of the point spread function

It is nothing more and nothing less.  It may not be negative, complex-valued, or equal to any value other than unity at the origin.

Initializing an MTF model should feel similar to a :doc:`PSF <./psfs>`,

>>> import numpy as np
>>> from prysm import MTF
>>> x = y = 1/np.linspace(-1,1,128)
>>> z = np.random.random((128,128))
>>> mt = MTF(data=z, unit_x=x, unit_y=y)

MTFs are usually created from a PSF instance

>>> mt = MTF.from_psf(your_psf_instance)

If modeling the MTF directly from a pupil plane, the intermediate PSF plane may be skipped;

>>> mt = MTF.from_pupil(your_pupil_instance, Q=2, efl=2)

Much like a PSF or other Convolvable, MTFs have quick-access slices

>>> print(mt.tan)
    (array([...]), array([...]))

>>> print(mt.sag)
    (array([...]), array([...]))

The tangential MTF is a slice through the x=0 axis, and assumes the usual optics sign convention of an object extended in y.  The sagittal MTF is a slice through the y=0 axis.

The MTF at exact frequencies may be queried through any of the following methods:  :code:`(MTF).exact_polar`, takes arguments of freqs and azimuths.  If there is a single frequency and multiple azimuths, the MTF at each azimuth and and the specified radial spatial frequency will be returned.  The reverse is true for a single azimuth and multiple frequencies.  :code:`(MTF).exact_xy` follows the same semantics, but with Cartesian coordinates instead of polar.  :code:`(MTF).exact_tan` and :code:`(MTF).exact_sag` both take a single argument of freq, which may be an int, float, or ndarray.

Finally, MTFs may be plotted:


>>> mt.plot_tan_sag(max_freq=200, fig=None, ax=None, labels=('Tangential', 'Sagittal'))
>>> mt.plot2d(max_freq=200, power=1, fig=None, ax=None)

all arguments have these default values.  The axes of plot2d will span (-max_freq, max_freq) on both x and y.

The complete API documentation is below.

----

.. autoclass:: prysm.otf.MTF
    :members:
    :undoc-members:
    :show-inheritance: