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   "source": [
    "# MTFs\n",
    "\n",
    "`prysm` models often include analysis of Modulation Transfer Function (MTF) data. The MTF is formally defined as:\n",
    "\n",
    "> the normalized magnitude of the Fourier transform of the Point Spread Function\n",
    "\n",
    "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.\n",
    "\n",
    "Initializing an MTF model should feel similar to a [PSF](./PSFs.ipynb),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from prysm import MTF\n",
    "x = y = 1/np.linspace(-1,1,128)\n",
    "z = np.random.random((128,128))\n",
    "mt = MTF(data=z, x=x, y=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MTFs are usually created from a PSF instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from prysm import Pupil, PSF\n",
    "pu = Pupil(dia=10, wavelength=0.5)\n",
    "ps = PSF.from_pupil(pu, efl=20)\n",
    "mt = MTF.from_psf(ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If modeling the MTF directly from a pupil plane, the intermediate PSF plane may be skipped;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mt = MTF.from_pupil(pu, Q=2, efl=20)  # Q, efl same as PSF.from_pupil"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much like a PSF or other Convolvable, MTFs have quick-access slices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mt.tan, mt.sag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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.\n",
    "\n",
    "The MTF at exact frequencies may be queried through any of the following methods: `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. `exact_xy` follows the same semantics, but with Cartesian coordinates instead of polar. `exact_tan` and `exact_sag` both take a single argument of freq, which may be an int, float, or ndarray.\n",
    "\n",
    "Finally, MTFs may be plotted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mt.plot_tan_sag(max_freq=1000, fig=None, ax=None, labels=('Tangential', 'Sagittal'))\n",
    "mt.plot2d(max_freq=1000, power=2, fig=None, ax=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "all arguments have these default values. The axes of plot2d will span (-max_freq, max_freq) on both x and y.\n",
    "\n",
    "This example should be familiar as the diffraction limited MTF of a circular aperture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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