PEG ("Parallel Efficiency of Gratings") is a tool for calculating the efficiency of diffraction gratings, particularly those used in the Soft X-ray regime. Developed by the Materials Research Group in the Department of Physics at the University of Saskatchewan (http://beamteam.usask.ca), it was used to characterize the optical components for the REIXS XES beamline at the Canadian Light Source. It implements the differential theory developed by Neviere, Vincent, and Petit [1], and is updated for stability using the S-matrix formulation of Li [2].
- Standard grating shape profiles: rectangular, blazed (triangular), trapezoidal, sinusoidal
- Custom grating shape profiles: any point-wise defined profile.
- Coatings: an optional coating layer on top of the grating (user-defined thickness; thick or inter-penetrating)
- Note: Coatings are not (yet) supported on custom profiles.
- Automatic lookup of complex refractive indexes for common materials from Henke data [3].
- Several built-in scanning modes: over wavelength, over incidence angle, over wavelength maintaining constant deviation ("monochromator mode")
- Support for scalable parallel calculation:
- fine parallelization of a single calculation, using OpenMP
- coarse parallelization of many efficiency points, using MPI on grid computers.
- Only the Transverse Electric (TE) polarization is computed. For Soft X-ray gratings used at grazing incidence, the TE and TM polarization efficiency is nearly identical.
- TODO: Calculate Transverse Magnetic (TM) polarization efficiency.
PEG requires the GNU Scientific Library (GSL), available at http://www.gnu.org/software/gsl/.
The 'qmake' build tool from the Qt Framework can be used to generate Makefiles based on PEG_mac.pro or PEG_ubuntu.pro. (The Qt library is not required to build PEG.) Edit one of these files to define the library paths for your system.
This will build the single-machine command-line program 'pegSerial':
qmake PEG_ubuntu.pro
make
The pegSerial application can take advantage of fine-grained parallelization to use more than one thread (for example, as many threads as CPU cores on your machine). This speeds up the calculation of a single efficiency data point.
There is also an application to exploit coarse-grained parallelization over an arbitrary number of nodes in a cluster or grid computer, using MPI. This speeds up the calculation of many efficiency data points. To build the pegMPI program, create a makefile based on src/Makefile.example.
Single-computer version 'pegSerial':
> ./pegSerial --mode constantIncidence --min 100 --max 900 --increment 5 --eV --incidenceAngle 87 --N 15 --gratingType blazed --gratingMaterial Pt --gratingPeriod 1.2 --gratingGeometry 1.2,30 --outputFile blazedResults.txt --progressFile progress.txt
Cluster-version:
> mpiexec -n <number of nodes> ./pegMPI --mode constantIncidence --min 100 --max 900 --increment 5 --eV --incidenceAngle 87 --N 15 --gratingType blazed --gratingMaterial Pt --gratingPeriod 1.2 --gratingGeometry 1.2,30 --outputFile blazedResults.txt --progressFile progress.txt
Command-line options:
Grating specification:
--gratingType <rectangular|blazed|sinusoidal|trapezoidal|custom>
--gratingPeriod <grating period in um>
--gratingGeometry <command-delimited list of geometry parameters, in um and/or degrees>
Rectangular profile: depth (um),valley width (um)
Blazed profile: blaze angle (deg),anti-blaze angle (deg)
Sinusoidal profile: depth (um)
Trapezoial profile: depth (um),valley width (um),blaze angle (deg),anti-blaze angle (deg)
Custom profile: depth (um), followed by list of (x,y) points that describe the surface profile y = g(x). [x followed by y for each]. The points must go from (0,0) to (1,0) inclusive, and will be scaled so that (0,0)->(1,1) maps to (0,0)->(period,depth). For example, an isosceles triangular profile with a depth of 0.1um would need three points; the geometry argument would be: {0.1,0,0,0.5,1,1,0}.
--gratingMaterial <grating substrate material>
This should be a name corresponding to a refractive index database filename, ex: Au, Ni, C, SiO2, etc.
--N <truncation index>
Specifies the number of positive and negative orders to include in the Fourier expansion. Will also determine the number of orders that are calculated, although if you only want to calculate 3 orders, you will still need a much larger truncation index for accurate results. In the soft x-ray range, convergence is usually attained with N ~ 15..45.
Operating mode:
--mode <constantIncidence|constantIncludedAngle|constantWavelength>
--min <min>
--max <max>
--increment <increment>
[Required, depending on the \c mode]
--incidenceAngle <incidence angle in degrees>
--includedAngle <deviation angle in degrees> --toOrder <diffraction order for the included angle>
--wavelength <wavelength in um>
In constant incidence mode, a calculation is performed for wavelengths from --min to --max in steps of --increment, at a fixed incidence angle given by --incidenceAngle.
In constant included angle mode, the incidence angle is calculated at each wavelength to ensure a constant included angle of --includedAngle between the incident light and the order specified in --toOrder. This is the operating mode for many monochromators. (Inside orders are negative, outside orders are positive.)
In constant wavelength mode, a calculation is performed for incidence angles from --min to --max in steps of --increment, for a fixed wavelength given by --wavelength.
Output:
--outputFile <file name>
The calculation output will be written to this file.
Optional:
--progressFile <file name>
If provided, the current status of the calculation will be written in this file; it can be monitored to determine the progress of long calculations. This provides an interface for other processes to monitor the status of this calculation (for example, a web-based or GUI front-end, etc.).
--eV
If this flag is included, all wavelength inputs (--min, --max, --increment, and --wavelength) will instead be interpreted as photon energies in electron volts (eV).
--coatingThickness <thickness in um>
If provided, creates a layer of --coatingMaterial on top of the basic grating profile, by translating the profile vertically by coatingThickness um. Used to model overcoated, oxidized, or dielectric gratings.
--coatingMaterial <coating material>
Required if a non-zero --coatingThickness is provided. This should be a name corresponding to a refractive index database filename, ex: Au, Ni, C, MgF2, etc.
--printDebugOutput
If this flag is included, each calculation will print intermediate results to standard output.
--measureTiming
If this flag is included, the solver will report the time required for each category of operations to standard output.
--integrationTolerance <tolerance>
If provided, specifies the error tolerance (eps) required at each step of the numerical integration process. Default if not provided is 1e-5.
# Input
mode=constantIncidence
incidenceAngle=88
units=eV
min=100
max=300
increment=5
gratingType=blazed
gratingPeriod=1.6
gratingGeometry=3.2,30.0
gratingMaterial=Au
N=5
integrationTolerance=1e-5
# Progress
status=succeeded (inProgress, someFailed, allFailed, succeeded)
completedSteps=41
totalSteps=41
# Output
100[tab]<e-5>,<e-4>,<e-3>,<e-2>,<e-1>,<e0>,<e1>,<e2>,<e3>,<e4>,<e5>
105[tab]<e-5>,<e-4>,<e-3>,<e-2>,<e-1>,<e0>,<e1>,<e2>,<e3>,<e4>,<e5>
110[tab]<e-5>,<e-4>,<e-3>,<e-2>,<e-1>,<e0>,<e1>,<e2>,<e3>,<e4>,<e5>
...
The Output table lists reflected efficiencies at each (wavelength/eV/incidence angle) sequentially from the -N order to the +N order. (Efficiencies are 0 if the orders are evanescent instead of propagating.) Note that we use the sign convention where inside diffraction orders are negative (n < 0), corresponding to the grating equation:
sin(beta) = sin(alpha) + n \lambda / d
PEG is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License, version 3. http://www.gnu.org/licenses/gpl.html
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M Nevière et al, Nouvelle Revue d'Optique 5 65 (1974) http://dx.doi.org/10.1088/0335-7368/5/2/301
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L. Li, JOSA A, Vol. 13, Issue 5, pp. 1024-1035 (1996) http://dx.doi.org/10.1364/JOSAA.13.001024
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B.L. Henke, E.M. Gullikson, and J.C. Davis. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92, Atomic Data and Nuclear Data Tables Vol. 54 (no.2), 181-342 (July 1993).