Source code for tomopy.sim.propagate

#!/usr/bin/env python
# -*- coding: utf-8 -*-

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"""
Module for simulation of x-rays.
"""

from __future__ import (absolute_import, division, print_function,
                        unicode_literals)

import numpy as np
import logging

logger = logging.getLogger(__name__)


__author__ = "Doga Gursoy"
__copyright__ = "Copyright (c) 2015, UChicago Argonne, LLC."
__docformat__ = 'restructuredtext en'
__all__ = ['calc_intensity',
           'propagate_tie',
           'probe_gauss']


[docs]def propagate_tie(mu, delta, pixel_size, dist): """ Propagate emitting x-ray wave based on Transport of Intensity. Parameters ---------- mu : ndarray, optional 3D tomographic data for attenuation. delta : ndarray 3D tomographic data for refractive index. pixel_size : float Detector pixel size in cm. dist : float Propagation distance of the wavefront in cm. Returns ------- ndarray 3D propagated tomographic intensity. """ i1 = np.exp(-mu) i2 = np.zeros(delta.shape) for m in range(delta.shape[0]): dx, dy = np.gradient(delta[m], pixel_size) d2x, _ = np.gradient(i1[m] * dx, pixel_size) _, d2y = np.gradient(i1[m] * dy, pixel_size) i2[m] = i1[m] + dist * (d2x + d2y) return i2
[docs]def probe_gauss(nx, ny, fwhm=None, center=None, max_int=1): """ Simulate incident x-ray beam (probe) as a square Gaussian kernel. Parameters ---------- nx, ny : int Grid size along x and y axes. fwhm : float, optional Effective radius of the source. center : array_like, optional x and y coordinates of the center of the gaussian function. max_int : int Maximum x-ray intensity. Returns ------- ndarray 2D source intensity distribution. """ if fwhm is None: fwhm = max(nx, ny) // 2 if center is None: x0, y0 = nx // 2, ny // 2 else: x0, y0 = np.array(center) x, y = np.mgrid[0:nx, 0:ny] return max_int * np.exp(-4 * np.log(2) * ( (x - x0 + 0.5) ** 2 + (y - y0 + 0.5) ** 2) / fwhm ** 2)
def _rect_scan_coords(probe_grid, proj_grid, shift_x, shift_y): """ Calculate upper-left scan coordinates of a rectangular kernel given a projection image. Parameters ---------- proj_grid : (int, int) Grid size of the projection image along x and y axes. shift_x, shift_y : int Relative shift distace of the source along x and y axes. Returns ------- array x coordinates of upper-left scan coordinates array y coordinates of upper-left scan coordinates """ x = np.arange(0, proj_grid[0], shift_x) y = np.arange(0, proj_grid[1], shift_y) while x.size * shift_x > proj_grid[0] - probe_grid[0] + shift_x: x = x[:-1] while y.size * shift_y > proj_grid[1] - probe_grid[1] + shift_y: y = y[:-1] return x, y def _rect_scan_probe(probe, proj, shift_x=None, shift_y=None): """ Calculate individual raster scanned images for a given rectangular x-ray probe and an object plane intensity. Parameters ---------- probe : ndarray Rectangular x-ray source kernel. proj : ndarray Object plane intensity image. shift_x, shift_y : int, optional Shift amount of probe along x and y axes. Returns ------- ndarray Individual raster scanned images as 3D array. """ sx, sy = probe.shape px, py = proj.shape # Assume half overlap. if shift_x is None: shift_x = sx // 2 if shift_y is None: shift_y = sy // 2 # Calculate upper-left scan coordinates along x and y axes. x, y = _rect_scan_coords(probe.shape, proj.shape, shift_x, shift_y) # Convert to image stack. arr = [probe * proj[i:i + sx, j:j + sy] for i in x for j in y] return np.array(arr)
[docs]def calc_intensity(probe, proj, shift_x=None, shift_y=None, mode='near'): """ Calculate far field intensity. Parameters ---------- probe : ndarray Rectangular x-ray source kernel. proj : ndarray Object plane intensity image. shift_x, shift_y : int, optional Shift amount of probe along x and y axes. mode : str, optional Specify the regime. 'near' or 'far' Returns ------- ndarray Individual raster scanned far field images as 3D array. """ psi = _rect_scan_probe(probe, proj, shift_x, shift_y) if mode == 'near': intensity = abs(psi) ** 2 elif mode == 'far': intensity = abs(np.fft.fftshift(np.fft.fft2(psi))) ** 2 return intensity