Yale-BASEX is a Python implementation of the BASEX algorithm created by Dribinski, Ossadtchi, Mandelshtam, and Reisler [Rev. Sci. Instrum. 73 2634, (2002)]. This project is forked from PyAbel's python implementation of the BASEX algorithm, found here. The primary difference between Yale-BASEX and PyAbel is that Yale-BASEX is stripped down version of PyAbel focused exclusively on analyzing images of coflow flames, which do not have the I(r,-z) = I(r,z) symmetry. It does not have all the bells and whistles of the full blown PyAbel program, nor does it implement any other Abel inversion algorithms besides BASEX.
The main function of this program is to perform the inverse Abel transform on a two-dimensional flame image (which is assumed to be cylindrically symmetric around a vertical axis at r = 0). The inverse Abel transform takes a 2D projection of a cylindrically symmetric 3D image and return the central slice (2D) of the 3D distribution. The BASEX implementation uses modified Gaussian basis functions to find the transform instead of analytically solving the inverse Abel transform or applying the Fourier-Hankel method, as both the analytical solution and the Fourier-Hankel methods provide lower quality transforms when applied to real-world datasets (see the RSI paper).
In this code, the axis of cylindrical symmetry is in assumed to be in the vertical direction. If this is not the case for your data, the numpy.rot90 function may be useful.
To install this module run,
python setup.py install --user
To tinker with the module yourself, run
python setup.py develop
from BASEX import BASEX
import matplotlib.pyplot as plt
import scipy as sc
# Import example flame image
filename = 'examples/data/flames/raw_flame.dat'
raw_data = sc.genfromtxt(filename)
# Specify the center column of the image
center = 191
print('Performing the inverse Abel transform:')
# Load (or pre-calculate if needed) the basis set for a 1601x383 image
inv_ab = BASEX(n_vert = 1601, n_horz = 383,
nbf_vert = 1601, nbf_horz = 191,
basis_dir = './', verbose = True)
# Calculate the inverse Abel transform for the centered data
recon = inv_ab(raw_data, center)
# Plot the inverted images
plt.imshow(recon)
plt.show()
Have fun!