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Abd M. Kassim and David L. Shealy, "Design and analysis of a two-channel three-mirror x-ray telescope: errata," Appl. Opt. 23, 3482-3486 (1984)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-23-19-3482

References

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  1. H. Wolter, “Glancing Incidence Mirror Systems as Imaging Optics for X-rays,” Ann. Physik. 10, 94 (1952).
    [CrossRef]
  2. R. Giacconi, B. Rossi, “A Telescope for Soft X-ray Astronomy,” J. Geophys. Res. 65, 773 (1960).
    [CrossRef]
  3. J. H. Underwood, “X-Ray Optics,” Am. Sci. 66, 476 (1978).
  4. L. P. VanSpeybroeck, R. C. Chase, “Design Parameters of Paraboloid-Hyperboloid Telescopes for X-Ray Astronomy,” Appl. Opt. 11, 440 (1972).
    [CrossRef] [PubMed]
  5. R. B. Hoover, “Three Mirror Glancing Incidence System for X-Ray Telescope,” U.S. Patent Office, No. 3821556 (1974).
  6. J. W. Foreman, J. M. Cardone, “Design and Mathematical Analysis of a Three Mirror X-Ray Telescope Based on ATM-S056 X-Ray Telescope Hardware,” final report under contract NA 58-2730, Marshall Space Flight Center, Huntsville, Ala. (1973).
  7. D. G. Burkhard, D. L. Shealy, G. L. Strobel, “Imaging Characteristics of a Conical Primary, Aspheric Secondary X-ray Telescope,” Appl. Opt. 21, 3713 (1982).
    [CrossRef] [PubMed]
  8. H. Wolter, “A Generalized Schwarschild Mirror Systems For Use at Glancing Incidence for X-ray Imaging,” Ann. Physik. 10, 286 (1952).
    [CrossRef]
  9. R. C. Chase, L. P. VanSpeybroeck, “Wolter-Schwarzschild Telescopes for X-Ray Astronomy,” Appl. Opt. 12, 1042 (1973).
    [CrossRef] [PubMed]
  10. O. N. Stavroudies, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), p. 84.
  11. R. J. Gagnon, “Spot-Diagram of Maximum Sharpness,” J. Opt. Soc. Am. 58, 1160 (1968).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 198.
  13. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 158.
  14. Abd M. Kassim, “The Design and Analysis of Several Configurations for a Two Channel, Three Mirror X-Ray Telescope,” M.S. Thesis, University of Alabama, Birmingham, 1981.
  15. A. Greenbaum, A. J. Glass, J. B. Trenholme, “Lens and Mirror Design Via the Principal Surface,” Appl. Opt. 15, 2579 (1976).
    [CrossRef] [PubMed]
  16. Scientific subroutine package, IBM Application Program, IBM, White Plains, N.Y., 1970.
  17. International Mathematical and Statistical Libraries, Edition 6, Houston, Tex., 1979.
  18. J. D. Mangus, J. H. Underwood, “Optical Design of a Glancing Incidence X-Ray Telescope,” Appl. Opt. 8, 95 (1969).
    [CrossRef] [PubMed]

1982 (1)

1978 (1)

J. H. Underwood, “X-Ray Optics,” Am. Sci. 66, 476 (1978).

1976 (1)

1973 (1)

1972 (1)

1969 (1)

1968 (1)

1960 (1)

R. Giacconi, B. Rossi, “A Telescope for Soft X-ray Astronomy,” J. Geophys. Res. 65, 773 (1960).
[CrossRef]

1952 (2)

H. Wolter, “Glancing Incidence Mirror Systems as Imaging Optics for X-rays,” Ann. Physik. 10, 94 (1952).
[CrossRef]

H. Wolter, “A Generalized Schwarschild Mirror Systems For Use at Glancing Incidence for X-ray Imaging,” Ann. Physik. 10, 286 (1952).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 198.

Burkhard, D. G.

Cardone, J. M.

J. W. Foreman, J. M. Cardone, “Design and Mathematical Analysis of a Three Mirror X-Ray Telescope Based on ATM-S056 X-Ray Telescope Hardware,” final report under contract NA 58-2730, Marshall Space Flight Center, Huntsville, Ala. (1973).

Chase, R. C.

Foreman, J. W.

J. W. Foreman, J. M. Cardone, “Design and Mathematical Analysis of a Three Mirror X-Ray Telescope Based on ATM-S056 X-Ray Telescope Hardware,” final report under contract NA 58-2730, Marshall Space Flight Center, Huntsville, Ala. (1973).

Gagnon, R. J.

Giacconi, R.

R. Giacconi, B. Rossi, “A Telescope for Soft X-ray Astronomy,” J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Glass, A. J.

Greenbaum, A.

Hoover, R. B.

R. B. Hoover, “Three Mirror Glancing Incidence System for X-Ray Telescope,” U.S. Patent Office, No. 3821556 (1974).

Kassim, Abd M.

Abd M. Kassim, “The Design and Analysis of Several Configurations for a Two Channel, Three Mirror X-Ray Telescope,” M.S. Thesis, University of Alabama, Birmingham, 1981.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 158.

Mangus, J. D.

Rossi, B.

R. Giacconi, B. Rossi, “A Telescope for Soft X-ray Astronomy,” J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Shealy, D. L.

Stavroudies, O. N.

O. N. Stavroudies, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), p. 84.

Strobel, G. L.

Trenholme, J. B.

Underwood, J. H.

VanSpeybroeck, L. P.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 198.

Wolter, H.

H. Wolter, “Glancing Incidence Mirror Systems as Imaging Optics for X-rays,” Ann. Physik. 10, 94 (1952).
[CrossRef]

H. Wolter, “A Generalized Schwarschild Mirror Systems For Use at Glancing Incidence for X-ray Imaging,” Ann. Physik. 10, 286 (1952).
[CrossRef]

Am. Sci. (1)

J. H. Underwood, “X-Ray Optics,” Am. Sci. 66, 476 (1978).

Ann. Physik. (2)

H. Wolter, “Glancing Incidence Mirror Systems as Imaging Optics for X-rays,” Ann. Physik. 10, 94 (1952).
[CrossRef]

H. Wolter, “A Generalized Schwarschild Mirror Systems For Use at Glancing Incidence for X-ray Imaging,” Ann. Physik. 10, 286 (1952).
[CrossRef]

Appl. Opt. (5)

J. Geophys. Res. (1)

R. Giacconi, B. Rossi, “A Telescope for Soft X-ray Astronomy,” J. Geophys. Res. 65, 773 (1960).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (8)

R. B. Hoover, “Three Mirror Glancing Incidence System for X-Ray Telescope,” U.S. Patent Office, No. 3821556 (1974).

J. W. Foreman, J. M. Cardone, “Design and Mathematical Analysis of a Three Mirror X-Ray Telescope Based on ATM-S056 X-Ray Telescope Hardware,” final report under contract NA 58-2730, Marshall Space Flight Center, Huntsville, Ala. (1973).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 198.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 158.

Abd M. Kassim, “The Design and Analysis of Several Configurations for a Two Channel, Three Mirror X-Ray Telescope,” M.S. Thesis, University of Alabama, Birmingham, 1981.

O. N. Stavroudies, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), p. 84.

Scientific subroutine package, IBM Application Program, IBM, White Plains, N.Y., 1970.

International Mathematical and Statistical Libraries, Edition 6, Houston, Tex., 1979.

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Figures (5)

Fig. 1
Fig. 1

Cross-sectional diagram of a three-mirror x-ray telescope.

Fig. 2
Fig. 2

Comparison between the resolution of H-A channel of Foreman’s results (Δ) and the ray-trace results (solid line) coma-free design. The base system was a Wolter type I (S056) telescope.

Fig. 3
Fig. 3

Comparison between the resolution of H-A channel, Foreman’s results (Δ), and the resolution of WS-A inner-channel no-spherical-aberration design (solid) and the coma-free design (dashed).

Fig. 4
Fig. 4

Comparison between the resolution of WS-A inner channel for both locations of the third aspheric mirror given in Table II, first location (a) and second location (b), for coma-free design.

Fig. 5
Fig. 5

Resolution of WS-A inner channel (coma-free design) as a function of field angles for different primary mirror zones: zone 1-rear (solid), zone 2-middle (dashed), and zone 3-front (dotted).

Tables (3)

Tables Icon

Table I Numerical Values of Wolter Type I S056 X-Ray Telescope Parameters with the Origin of the Coordinate System at the Focal Point of the Paraboloid

Tables Icon

Table II Numerical Values of WS-A, Three-Mirror X-Ray Telescope, Parameters for Two Locations of the Third Aspheric Mirror (Coma-Free Design), Where the Origin of the Coordinate System is at the Telescope Focal Point

Tables Icon

Table III rms Blur Circle Radius (Min of Arc) as a Function of the Off-Axis Field Angles for the Three-Mirror X-Ray Telescope

Equations (10)

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R 2 sin θ = F 2 , const ,
sin θ * = X 3 max ( X 3 max 2 + Z 3 max 2 ) 1 / 2 .
F 2 = R 2 max / sin θ * .
A 2 x A 2 z = - 2 Z 2 ( 1 - Z 2 2 ) ,
A 3 x A 3 z = [ A 2 x ( Z 3 2 - 1 ) - 2 A 2 z Z 3 ] A 2 z ( 1 - Z 3 2 ) - 2 A 2 x Z 3 ,
tan θ = A 3 x / A 3 z .
Z 3 = A 2 z cos θ - A 2 x sin θ - 1 A 2 x cos θ + A 2 z sin θ .
( X 3 - X 2 ) ( 1 - Z 2 2 ) + 2 Z 2 ( Z 3 - Z 2 ) = 0 ,
S ( Z i ) = { [ C ( I , 3 ) D + C ( I , 2 ] D + C ( I , 1 ) } D + Y ( I ) ,
R p 2 = p ( 2 Z p + p ) , ( Z H - c ) 2 a 2 - R H 2 b 2 = 1 ,

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