Approaching ultimate resolution for soft x-ray spectrometers

Sorin G. Chiuzbăian; Coryn F. Hague; Jan Lüning

doi:10.1364/AO.51.004684

Applied Optics
Vol. 51,
Issue 20,
pp. 4684-4690
(2012)
•https://doi.org/10.1364/AO.51.004684

Approaching ultimate resolution for soft x-ray spectrometers

Sorin G. Chiuzbăian, Coryn F. Hague, and Jan Lüning

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Sorin G. Chiuzbăian, Coryn F. Hague, and Jan Lüning, "Approaching ultimate resolution for soft x-ray spectrometers," Appl. Opt. 51, 4684-4690 (2012)

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Abstract

We explore the potential performance of soft x-ray spectrometers based on the use of varied-line-spacing spherical diffraction gratings (VLS-SG). The quantitative assessment is based on an optimization procedure to obtain both negligible optical aberrations at full illumination of the grating and a quasi linear focal curve. It involves high-order optical aberration cancellation to calculate the focal curves. We also examine the validity of small divergence closed-form formulas describing the light path function. Optimizing the optical and geometric parameters gives an ultimate resolving power, at 930 eV, of between 10 800 for a 3 m long instrument and 34 000 for an 11 m spectrometer according to the Rayleigh criterion. Typical fabrication tolerances would scale these values down by about 10%. The findings are validated by ray-tracing simulations.

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Grating parameters	Performance at $E = 930 eV$
$R = 102.208 m$	$F_{N 0}$ parameters:
$a_{0} = 3200 {mm}^{- 1}$	$r = 1.6137 m$
$a_{1} = - 5.4134 \times 10^{- 1} {mm}^{- 2}$	$r^{'} = 6.3880 m$
$a_{2} = - 5.7086 \times 10^{- 5} {mm}^{- 3}$	$α = 88.399 °$
$a_{3} = - 1.6782 \times 10^{- 7} {mm}^{- 4}$	$γ = 20 °$
$a_{4} = - 1.0676 \times 10^{- 10} {mm}^{- 5}$
$M = 1.1473$ at 930 eV	$R = 38970$

Grating parameters	Performance at $E = 930 eV$
$R = 102.2 m$	$r = 1.614 m$
$a_{0} = 3200 {mm}^{- 1}$	$r^{'} = 6.388 m$
$a_{1} = - 5.41 \times 10^{- 1} {mm}^{- 2}$	$α = 88.399 °$
$a_{2} = - 5.71 \times 10^{- 5} {mm}^{- 3}$	$γ = 20 °$
$a_{3} = - 1.60 \times 10^{- 7} {mm}^{- 4}$
$a_{4} = 0$	$R = 36800$

Grating parameters	Performance at $E = 930 eV$
$R = 102.208 m$	$F_{N 0}$ parameters:
$a_{0} = 3200 {mm}^{- 1}$	$r = 1.6137 m$
$a_{1} = - 5.4134 \times 10^{- 1} {mm}^{- 2}$	$r^{'} = 6.3880 m$
$a_{2} = - 5.7086 \times 10^{- 5} {mm}^{- 3}$	$α = 88.399 °$
$a_{3} = - 1.6782 \times 10^{- 7} {mm}^{- 4}$	$γ = 20 °$
$a_{4} = - 1.0676 \times 10^{- 10} {mm}^{- 5}$
$M = 1.1473$ at 930 eV	$R = 38970$

Grating parameters	Performance at $E = 930 eV$
$R = 102.2 m$	$r = 1.614 m$
$a_{0} = 3200 {mm}^{- 1}$	$r^{'} = 6.388 m$
$a_{1} = - 5.41 \times 10^{- 1} {mm}^{- 2}$	$α = 88.399 °$
$a_{2} = - 5.71 \times 10^{- 5} {mm}^{- 3}$	$γ = 20 °$
$a_{3} = - 1.60 \times 10^{- 7} {mm}^{- 4}$
$a_{4} = 0$	$R = 36800$

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Equations (11)

Applied Optics