X-ray mirror optics with multiple hyperboloidal/hyperbolic surface profiles
An x-ray mirror optic includes a plurality of surface segments with quadric cross-sections having differing quadric parameters. The quadric cross-sections of the surface segments share a common axis and are configured to reflect x-rays in a plurality of reflections along a single optical axis or in a scattering plane defined as containing an incident x-ray and a corresponding reflected x-ray.
1. An x-ray mirror optic comprising:
a plurality of surface segments with quadric cross-sections having differing quadric parameters, the quadric cross-sections of the plurality of surface segments sharing a common axis, and configured to reflect x-rays in a plurality of reflections along a single optical axis or in a scattering plane defined as containing an incident x-ray and a corresponding reflected x-ray, the plurality of surface segments comprising:
a first surface segment having a first hyperbolic or hyperboloidal cross-sectional shape and a first asymptotic slope, the first surface segment having a first focus and a second focus, the first focus configured to be substantially coincident with an x-ray source; and
a second surface segment having a second hyperbolic or hyperboloidal cross-sectional shape and a second asymptotic slope smaller than the first asymptotic slope, the second surface segment having a third focus and a fourth focus, the third focus substantially coincident with the second focus of the first surface segment.
2. The x-ray mirror optic of claim 1 , wherein the differing quadric parameters comprise hyperbolic or hyperboloidal parameters.
3. The x-ray mirror optic of claim 1 , wherein the plurality of surface segments are curved in one dimension.
4. The x-ray mirror optic of claim 1 , wherein the plurality of surface segments are curved in two dimensions.
5. The x-ray mirror optic of claim 1 , wherein the first hyperbolic or hyperboloidal cross-sectional shape is axially symmetric to a first axis, and the second hyperbolic or hyperboloidal cross-sectional shape is axially symmetric to the first axis.
6. The x-ray mirror optic of claim 5 , wherein the first surface segment is configured to reflect x-rays emitted from the x-ray source, and the second surface segment is configured to reflect x-rays reflected by the first surface segment.
7. The x-ray mirror optic of claim 5 , wherein the plurality of surface segments further comprises a third surface segment having a third hyperbolic or hyperboloidal cross-sectional shape that is axially symmetric to the first axis and has a third asymptotic slope smaller than the second asymptotic slope, the third surface segment having a fifth focus and a sixth focus, the fifth focus substantially coincident with the fourth focus of the second surface segment.
8. The x-ray mirror optic of claim 7 , wherein the third surface segment is configured to reflect x-rays reflected by the second surface segment.
9. The x-ray mirror optic of claim 5 , wherein the plurality of surface segments further comprises a paraboloidal surface segment having a paraboloidal shape, a focus of the paraboloidal shape substantially coincident with the fourth focus of the second surface segment.
10. The x-ray mirror optic of claim 9 , wherein the paraboloidal surface segment is configured to collimate the x-rays emitted by the x-ray source, reflected by the first surface segment, and then reflected by the second surface segment.
11. An x-ray mirror optic comprising:
a first plurality of non-axially symmetric mirror sections; and
a second plurality of non-axially symmetric mirror sections,
wherein the first plurality of non-axially symmetric mirror sections and/or the second plurality of non-axially symmetric mirror sections comprises:
a first mirror segment having a first hyperbolic or hyperboloidal shape having a first asymptotic slope, the first mirror segment having a first focus and a second focus, the first focus configured to be substantially coincident with an x-ray source; and
a second mirror segment having a second hyperbolic or hyperboloidal shape having a second asymptotic slope smaller than the first asymptotic slope, the second mirror segment having a third focus and a fourth focus, the third focus substantially coincident with the second focus of the first mirror segment.
12. The x-ray mirror optic of claim 11 , wherein the first plurality of non-axially symmetric mirror sections and/or the second plurality of non-axially symmetric mirror sections comprises pairs of mirror sections, each pair of the pairs of mirror sections comprising two mirror sections that have substantially a same quadric surface shape and quadric surface parameters as one another, and are on opposite sides of an optical axis of the x-ray mirror optic.
13. The x-ray mirror optic of claim 11 , wherein the first plurality of non-axially symmetric mirror sections is configured to provide focusing along a first direction, and the second plurality of non-axially symmetric mirror sections is configured to provide focusing along a second direction substantially perpendicular to the first direction.
14. The x-ray mirror optic of claim 11 , wherein the first plurality of non-axially symmetric mirror sections are nested with one another and/or the second plurality of non-axially symmetric mirror sections are nested with one another.
15. The x-ray mirror optic of claim 11 , wherein the first plurality of non-axially symmetric mirror sections are substantially parallel with one another and/or the second plurality of mirror sections are substantially parallel with one another.
16. The x-ray mirror optic of claim 15 , wherein the second plurality of non-axially symmetric mirror sections are oriented substantially perpendicularly to the first plurality of non-axially symmetric mirror sections.
17. The x-ray mirror optic of claim 11 , wherein the first plurality of non-axially symmetric mirror sections and the second plurality of non-axially symmetric mirror sections are interweaved with one another.
18. A method of fabricating an x-ray mirror optic, the method comprising:
etching a first plurality of non-axially symmetric mirror sections and/or a second plurality of non-axially symmetric mirror sections into a substrate, wherein the first plurality of non-axially symmetric mirror sections and/or the second plurality of non-axially symmetric mirror sections comprises:
a first mirror segment having a first hyperbolic or hyperboloidal shape having a first asymptotic slope, the first mirror segment having a first focus and a second focus, the first focus configured to be substantially coincident with an x-ray source; and
a second mirror segment having a second hyperbolic or hyperboloidal shape having a second asymptotic slope smaller than the first asymptotic slope, the second mirror segment having a third focus and a fourth focus, the third focus substantially coincident with the second focus of the first mirror segment.