This script lives in /sdf/group/lcls/ds/ana/tutorials/psana1_examples/radInteg.py and demonstrates how to do an angular integration of a 2D area-detector image. If you don't have a 2D image, but instead have pixel values and positions, consider using the more general BinnedStatistic1D/BinnedStatistic2D/BinnedStatisticDD classes in skbeam.core.accumulators.binned_statistic (not documented here, but documentation is available within IPython).
This method for doing radial integrations is part of the world-reusable scikit-beam project hosted by BNL. This goal of this python library is to provide low-level building-blocks that can be easily installed around the world enabling scientists to reuse familiar tools at different laboratories.
This example shows three different integrations, one one-dimensional (projecting onto the radial axis) and two two-dimensional (projecting onto the radial and phi axes) with and without masks. This code is based on the scipy "binned_statistic" code which allows for very flexible binning and many different operations on the pixels within a bin (sum/mean/count/user-defined)
from skbeam.core.accumulators.binned_statistic import RadialBinnedStatistic, RPhiBinnedStatistic import numpy as np img = np.reshape(np.arange(9),(3,3)) print('Image:\n',img) mask = np.ones_like(img) mask[1][1]=0 print(f'\nMask:\n{mask}') radbinstat = RadialBinnedStatistic(img.shape, bins=3, statistic='sum', origin=(0,0), range = (0,2), mask=mask) rphibinstat = RPhiBinnedStatistic(img.shape, bins=(3,1), statistic='sum', origin=(0,0), range = ((0,2),(0,np.pi/3))) rphibinstat_mask = RPhiBinnedStatistic(img.shape, bins=(3,1), statistic='sum', origin=(0,0), range = ((0,2),(0,np.pi/3)), mask=mask) print('\nAngular integration with mask:') print(radbinstat(img)) print('\nBin edges and centers:') print(radbinstat.bin_edges) print(radbinstat.bin_centers) print('\n2D R/Phi Angular integration (1 phi bin) with phi range and mask:') print(rphibinstat_mask(img)) print('\n2D R/Phi Angular integration (1 phi bin) with phi range and no mask:') print(rphibinstat(img)) print('\nR/Phi bin edges:') print(rphibinstat.bin_edges[0]) print(rphibinstat.bin_edges[1])
The output of running this script is below. It attempts to demonstrate:
- the origin location (row=0, col=0)
- the range and mask argument: first integration results are 0, 4(=3+1), 8(=6+2) where the 4 value has been ignored because mask[1][1] is 0. Image values 5,7,8 are ignore because of the range limits.
- the units of R (pixels) and phi (radians) where phi is defined at arctan2(row/col) (i.e. x is array-column (second index) and y is array-row (first index))
Read the IPython help documentation using the "?" operator in IPython for more details, as well as the documentation for scipiy binned_statistic.
Image: [[0 1 2] [3 4 5] [6 7 8]] Mask: [[1 1 1] [1 0 1] [1 1 1]] Angular integration with mask: [ 0. 4. 8.] Bin edges and centers: [ 0. 0.66666667 1.33333333 2. ] [ 0.33333333 1. 1.66666667] 2D R/Phi Angular integration (1 phi bin) with phi range and mask: [[ 0.] [ 1.] [ 2.]] 2D R/Phi Angular integration (1 phi bin) with phi range and no mask: [[ 0.] [ 1.] [ 6.]] R/Phi bin edges: [ 0. 0.66666667 1.33333333 2. ] [ 0. 1.04719755]