nearBragg

diffraction image simulator for near- and far-field scattering from arbitrary electron locations in space

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 2 $\pi$ 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)

The 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 (see 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.

compile

gcc -O -O -o nearBragg nearBragg.c -lm -static

example usage

A 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 using ImageMagick.

convert -depth 16 -type Grayscale -colorspace GRAY -endian LSB -size 1024x1024+512 \
  -negate -normalize \
  GRAY:intimage.img intimage.png

A 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. Demonstration 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