nearBragg

program for assumption-free calculation of total scattering

The nearBragg program is a very simplistic yet general calculation of the total scattering from a bunch of "atoms" which the user provides as a 3-column text file of x-y-z coordinates in Angstroms. Each atom is considered to be a point with a structure factor of 1.0 (a single "electron"). The detector is represented as an array of pixels some distance away from the "crystal" (in mm), and the "source" is one or more points arranged in space. These all have sensible defaults. Scattering is calculated by computing the linear distance from each point in the source to each of the user-provided "atoms", and then on to the center of each pixel in the detector. The sin and cos of 2pi times the number of wavelenghs involved in this total distance is then added up and the amplitude and phase of the resultant wave from the whole sample (and the whole source) are obtained for each pixel. The intensity at each pixel is the square of the amplitude.
No assumptions are made about Bragg's Law, unit cells, shape transforms, or any of that. It is simply a calculation of the scattering from the user-provided points.
source code: nearBragg.c (20K) (pre-compiled binaries: linux, OSX, Cygwin, Windows
auxillary programs float_add and float_func may be used to add up the raw "float" binary files output by nearBragg so that renderings may be divided up on separate CPUs and then combined together. The resulting raw files may be converted to images with nearBragg using the -accumulate option (below)
also, the phase_color.c program will convert the sinimage and cosimage files output by nearBragg into a pretty color-by-phase image. However, if you want to display the phase of the traditional "structure factor", then you need to divide the wave scattered by your structure by the sinimage and cosimage produced for a single point electron at the origin using the same camera parameters. This complex_divide.csh script may be helpful for this.

example usage:

compile it 

gcc -O -O -o nearBragg nearBragg.c -lm -static
one atom case 
echo "0 0 0" >! atoms.txt
run the simulation 
./nearBragg -file ./atoms.txt -lambda 1.0
view the result 
adxv intimage.img
convert and re-scale as regular graphics file 
convert -depth 16 -type Grayscale -colorspace GRAY -endian LSB -size 1024x1024+512 \
  -negate -normalize \
  GRAY:intimage.img intimage.png
two atom case 
cat << EOF >! atoms.txt
0 0 0
0 10 0
EOF
run the simulation 
./nearBragg -file ./atoms.txt -lambda 1.0
view the result 
adxv intimage.img
convert and re-scale as regular graphics file 
convert -depth 16 -type Grayscale -colorspace GRAY -endian LSB -size 1024x1024+512 \
  -negate -normalize \
  GRAY:intimage.img intimage.png
make a 11x11x11 cube grid with the cell spacing of silicon 
echo "5 5.43071" | ./makelattice.awk >! silicon_nanoparticle.txt
twirl it around 
./rotate.awk -v phix=10 -v phiy=20 -v phiz=30 silicon_nanoparticle.txt >! rotated_xtal.txt
jiggle the atoms by a B factor of 5 
awk '{print $0,5}' rotated_xtal.txt | ./Bscatter.awk >! atoms.txt
do a fast calculation with a "perfect" beam 
./nearBragg -file ./atoms.txt -lambda 1.0 -dispersion 0 \
   -hdivrange 0.0 -vdivrange 0.0 \
 -intfile intimage_ideal.img -floatfile floatimage_ideal.bin
view the result 
adxv intimage_ideal.img

add some divergence and dispersion 

./nearBragg -file ./atoms.txt -lambda 1.0 -dispersion 0.1 \
   -hdivrange 0.062 -vdivrange 0.062 -hdivstep 0.031 -vdivstep 0.031 \
 -intfile intimage_realistic.img -floatfile floatimage_realistic.bin
view the result 
adxv intimage_realistic.img
same number of atoms, but a round particle 
echo "10 5.43071" | ./makelattice.awk |\
awk '{R=sqrt($1*$1+$2*$2+$3*$3)} R<37.625{print}' |\
cat >! silicon_nanoparticle.txt
twirl it around 
./rotate.awk -v phix=10 -v phiy=20 -v phiz=30 silicon_nanoparticle.txt >! rotated_xtal.txt
jiggle the atoms by a B factor of 5 
awk '{print $0,5}' rotated_xtal.txt | ./Bscatter.awk >! atoms.txt
do a fast calculation with a "perfect" beam 
./nearBragg -file ./atoms.txt -lambda 1.0 -dispersion 0 \
   -hdivrange 0.0 -vdivrange 0.0 \
 -intfile intimage_round.img -floatfile floatimage_ideal.bin
view the result 
adxv intimage_round.img

Other examples:

1. Demonstration of Bragg's Law
2. Deminstration of coherence length
Command-line options:
-atom
number of atoms in the following file
-file filename.txt
text file containing point scatterer coordinates in Angstrom relative to the origin. The x axis is the x-ray beam and Y and Z are parallel to the detector Y and X coordinates, respectively
-hdivrange
horizontal angular spread of source points (mrad). Default: 0
-vdivrange
vertical angular spread of source points (mrad). Default: 0
-hdivstep
number of source points in the horizontal. Default: 1
-vdivstep
number of source points in the vertical. Default: 1
-distance
distance from origin to detector center (mm)
-source_distance
distance from origin to source (mm)
-source_depth
distance from front of source to back (mm)
-depthstep
number of source points along path to sample. Default: 1
-detsize
detector size in x and y (mm)
-detsize_x
detector size in x direction (mm)
-detsize_y
detector size in y direction (mm)
-pixel
detector pixel size (mm)
-detpixels
detector size in x and y (pixels)
-detpixels_x
detector size in x direction (pixels)
-detpixels_y
detector size in y direction (pixels)
-Xbeam
direct beam position in x direction (mm) Default: center
-Ybeam
direct beam position in y direction (mm) Default: center
-curved_det
all detector pixels same distance from sample (origin)
-oversample
number of sub-pixels per pixel. Default: 1
-roi xmin xmax ymin ymax
only render pixels within a set range. Default: all detector
-lambda
incident x-ray wavelength (Angstrom). Default: 1
-dispersion
spectral dispersion: delta-lambda/lambda (percent). Default: 0
-dispsteps
number of wavelengths in above range. Default: 1
-floatfile
name of binary pixel intensity output file (4-byte floats)
-sinfile
name of binary imaginary structure factor output file (4-byte floats)
-cosfile
name of binary real structure factor output file (4-byte floats)
-intfile
name of smv-formatted output file.
-scale
scale factor for intfile. Default: fill dynamic range
-coherent
coherently add everything, even different wavelengths. Not the default
-accumulate
import contents of floatfile or sinfile/cosfile and add to them. Not the default
-point_pixel
turn off solid-angle correction for square flat pixels
-printout
print pixel values out to the screen
-noprogress
turn off the progress meter