# Example: Hansen–Law xenon¶

```# -*- coding: utf-8 -*-

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals

import numpy as np
import matplotlib.pyplot as plt

import abel
import scipy.misc

# This example demonstrates Hansen and Law inverse Abel transform
# of an image obtained using a velocity map imaging (VMI) photoelecton
# spectrometer to record the photoelectron angular distribution resulting
# from photodetachement of O2- at 454 nm.
# This spectrum was recorded in 2010
# ANU / The Australian National University
# J. Chem. Phys. 133, 174311 (2010) DOI: 10.1063/1.3493349

filename = 'data/Xenon_ATI_VMI_800_nm_649x519.tif'

# Name the output files
name = filename.split('.')[0].split('/')[1]
output_image = name + '_inverse_Abel_transform_HansenLaw.png'
output_text  = name + '_speeds_HansenLaw.dat'
output_plot  = 'plot_' + name + '_comparison_HansenLaw.png'

(rows, cols) = np.shape(im)
print('image size {:d}x{:d}'.format(rows, cols))

# Step 2: perform the Hansen & Law transform!
print('Performing Hansen and Law inverse Abel transform:')

recon = abel.Transform(im, method="hansenlaw", direction="inverse",
symmetry_axis=None, verbose=True,
origin=(240, 340)).transform

r, speeds = abel.tools.vmi.angular_integration_3D(recon)

# Set up some axes
fig = plt.figure(figsize=(15, 4))
ax1 = plt.subplot(131)
ax2 = plt.subplot(132)
ax3 = plt.subplot(133)

# raw data
im1 = ax1.imshow(im, origin='lower')
ax1.set_xlabel('x (pixels)')
ax1.set_ylabel('y (pixels)')
ax1.set_title('velocity map image')

# 2D transform
im2 = ax2.imshow(recon, origin='lower')
ax2.set_xlabel('x (pixels)')
ax2.set_ylabel('y (pixels)')
ax2.set_title('Hansen Law inverse Abel')

# 1D speed distribution
ax3.plot(speeds)
ax3.set_xlabel('Speed (pixel)')
ax3.set_ylabel('Yield (log)')
ax3.set_title('Speed distribution')
#ax3.set_yscale('log')

# Prettify the plot a little bit:
plt.tight_layout()

# Save a image of the plot
# plt.savefig(output_plot, dpi=100)

# Show the plots
plt.show()
```