Michael C. Hettrick,
Michael E. Cuneo,
John L. Porter,
Larry E. Ruggles,
Walter W. Simpson,
Mark F. Vargas,
and David F. Wenger
M. C. Hettrick (hettrickscientific@yahoo.com) is with Hettrick Scientific, 1-39-59 Tama-cho, Fuchu-shi, Tokyo, Japan 183-0002.
M. E. Cuneo, J. L. Porter, L. E. Ruggles, W. W. Simpson, M. F. Vargas, and D. F. Wenger are with Sandia National Laboratories, Albuquerque, New Mexico 87185-1193 USA
Michael C. Hettrick, Michael E. Cuneo, John L. Porter, Larry E. Ruggles, Walter W. Simpson, Mark F. Vargas, and David F. Wenger, "Profiled bar transmission gratings: soft-x-ray calibration of new Kirchoff solutions," Appl. Opt. 43, 3772-3796 (2004)
A new analytical model, derived rigorously from scalar diffraction theory, accurately fits soft-x-ray measurements of symmetrical profile gold transmission gratings in all diffracted orders. The calibration system selects numerous photon energies by use of a high-resolution grazing-incidence monochromator and a dc e-beam source. Fine-period free-standing gratings exhibit limited performance and require such testing to determine parameters of and select acceptable gratings for use in time-resolved (0.25 ns) spectrographs of known radiometric response. Unfolded spectra yield a Z-pinch plasma peak kT ∼250 eV, total radiated energy ∼900 kJ, and a pinch-driven gold-wall hohlraum Planckian kT ∼86 eV.
Michael C. Hettrick, Michael E. Cuneo, John L. Porter, Larry E. Ruggles, Walter W. Simpson, Mark F. Vargas, and David F. Wenger, "Profiled bar transmission gratings: soft-x-ray calibration of new Kirchoff solutions—erratum," Appl. Opt. 43, 4785-4785 (2004) https://opg.optica.org/ao/abstract.cfm?uri=ao-43-25-4785
Michael C. Hettrick, Michael E. Cuneo, John L. Porter, Larry E. Ruggles, Walter W. Simpson, Mark F. Vargas, and David F. Wenger Appl. Opt. 43(25) 4785-4785 (2004)
Ralf K. Heilmann, Minseung Ahn, Alex Bruccoleri, Chih-Hao Chang, Eric M. Gullikson, Pran Mukherjee, and Mark L. Schattenburg Appl. Opt. 50(10) 1364-1373 (2011)
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Calibrated zo values from this study are compared with values specified by the manufacturer (in parenthesis).
L-fit is the accuracy of efficiency ratios (1/0 and 2/1) with a linear (trapezoidal-like) fit (Subsection 3.A), and S-fit is accuracy of weighted absolute efficiencies (typically 1, 2, 3, 4) with a multistep (free-form) fit to the side-wall profile (Subsection 3.B).
Support structure is gold for HD6 and FS194_Z and is nickel for all others. OAR is the open-area-ratio of support structure.
HD6 manufactured by Heidenhain GmbH; all others manufactured by MIT Space Nanostructures Laboratory.
HD6 and FS194_Z calibrated with SNR monochromator; subsequent series gratings calibrated with SXR monochromator.
HD6, FS194_Z, X21, and X27 calibrated with early model Photometrics CCD; subsequent gratings calibrating with current model Princeton Instruments CCD.
FS194 inferred to have an organic film (identified by the manufacturer as black wax) residue extending well in between the gold bars, acting as a base collector of source contaminants. The current calibration of FS194_Z was after its use in the Z accelerator, which may have resulted in additional deposit of organics and debris upon the wax base; combined with the subtraction of only the detector background (no off-line spectra) for this grating the accuracy of the fits is seen to be lower.
HS14_Z is HS14 recalibrated after 1 yr on the Z source.
Low efficiencies of X-series gratings are due to a low OAR of the nickel support structure.
Scatter is measured as a fraction of the peak intensity at spectral order m = 1 and is considered marginally acceptable at a value of 0.01.
Gratings HD6 and X27 were specified as thin-bar low-energy gratings and therefore the high efficiency of X27 at 2042 eV is unsatisfactory (because of the gold bars being nearly twice the specified thickness); all other gratings (d = 200 nm period) were specified to have thick bars for optimization at high energies.
High contamination from second-order efficiency (η2/η1 ratio) for HD, FS, and X series results from gap-to-period (a/
d) ratios that are significantly below the ideal value of 0.5.
Absent soft-x-ray selection, no grating series generally conforms to the design parameters or performs acceptably in all of the three basic categories, with the e identifying unsatisfactory or marginal values for the intended application; selection of acceptable gratings (e.g., HS14 and a handful of others) therefore relies on soft-x-ray calibration of numerous gratings whose parameters are otherwise not well characterized.
Low efficiency at 183 eV (below the carbon photoabsorption edge, see Fig.
27) for FS-series grating indicates the presence of black wax film residue from the grating fabrication process and subsequent accumulation of contaminants onto this wax film.
Low efficiency at 2042 eV for XS series is due to thin gold bars (<200 nm).
Calibrated zo values from this study are compared with values specified by the manufacturer (in parenthesis).
L-fit is the accuracy of efficiency ratios (1/0 and 2/1) with a linear (trapezoidal-like) fit (Subsection 3.A), and S-fit is accuracy of weighted absolute efficiencies (typically 1, 2, 3, 4) with a multistep (free-form) fit to the side-wall profile (Subsection 3.B).
Support structure is gold for HD6 and FS194_Z and is nickel for all others. OAR is the open-area-ratio of support structure.
HD6 manufactured by Heidenhain GmbH; all others manufactured by MIT Space Nanostructures Laboratory.
HD6 and FS194_Z calibrated with SNR monochromator; subsequent series gratings calibrated with SXR monochromator.
HD6, FS194_Z, X21, and X27 calibrated with early model Photometrics CCD; subsequent gratings calibrating with current model Princeton Instruments CCD.
FS194 inferred to have an organic film (identified by the manufacturer as black wax) residue extending well in between the gold bars, acting as a base collector of source contaminants. The current calibration of FS194_Z was after its use in the Z accelerator, which may have resulted in additional deposit of organics and debris upon the wax base; combined with the subtraction of only the detector background (no off-line spectra) for this grating the accuracy of the fits is seen to be lower.
HS14_Z is HS14 recalibrated after 1 yr on the Z source.
Low efficiencies of X-series gratings are due to a low OAR of the nickel support structure.
Scatter is measured as a fraction of the peak intensity at spectral order m = 1 and is considered marginally acceptable at a value of 0.01.
Gratings HD6 and X27 were specified as thin-bar low-energy gratings and therefore the high efficiency of X27 at 2042 eV is unsatisfactory (because of the gold bars being nearly twice the specified thickness); all other gratings (d = 200 nm period) were specified to have thick bars for optimization at high energies.
High contamination from second-order efficiency (η2/η1 ratio) for HD, FS, and X series results from gap-to-period (a/
d) ratios that are significantly below the ideal value of 0.5.
Absent soft-x-ray selection, no grating series generally conforms to the design parameters or performs acceptably in all of the three basic categories, with the e identifying unsatisfactory or marginal values for the intended application; selection of acceptable gratings (e.g., HS14 and a handful of others) therefore relies on soft-x-ray calibration of numerous gratings whose parameters are otherwise not well characterized.
Low efficiency at 183 eV (below the carbon photoabsorption edge, see Fig.
27) for FS-series grating indicates the presence of black wax film residue from the grating fabrication process and subsequent accumulation of contaminants onto this wax film.
Low efficiency at 2042 eV for XS series is due to thin gold bars (<200 nm).