Abstract

Several conceivable methods for the formation of optical images by x-rays are considered, and a method employing concave mirrors is adopted as the most promising. A concave spherical mirror receiving radiation at grazing incidence (a necessary arrangement with x-rays) images a point into a line in accordance with a focal length f=Ri/2 where R is the radius of curvature and i the grazing angle. The image is subject to an aberration such that a ray reflected at the periphery of the mirror misses the focal point of central rays by a distance given approximately by S=1.5Mr2/R, where M is the magnification of the image and r is the radius of the mirror face. The theoretically possible resolving power is such as to resolve point objects separated by about 70A, a limit which is independent of the wave-length used. Point images of points and therefore extended images of extended objects may be produced by causing the radiation to reflect from two concave mirrors in series. Sample results are presented.

© 1948 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. C. Roentgen, Sitzungsberichte der Würzburger Physikalischen-Medicinischen Gesellschaft (1895).
  2. Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.
  3. W. Ehrenberg, Nature 160, 330 (1947). This brief communication describes the formation of line images by reflection of x-rays from a point source at a gilded glass plate which had been bent so as to form an approximate circular cylinder.
    [Crossref]
  4. Paul Kirkpatrick and A. V. Baez, Bull. Am. Phys. Soc. 23, 10 (1948).

1948 (1)

Paul Kirkpatrick and A. V. Baez, Bull. Am. Phys. Soc. 23, 10 (1948).

1947 (1)

W. Ehrenberg, Nature 160, 330 (1947). This brief communication describes the formation of line images by reflection of x-rays from a point source at a gilded glass plate which had been bent so as to form an approximate circular cylinder.
[Crossref]

1895 (1)

W. C. Roentgen, Sitzungsberichte der Würzburger Physikalischen-Medicinischen Gesellschaft (1895).

Baez, A. V.

Paul Kirkpatrick and A. V. Baez, Bull. Am. Phys. Soc. 23, 10 (1948).

Ehrenberg, W.

W. Ehrenberg, Nature 160, 330 (1947). This brief communication describes the formation of line images by reflection of x-rays from a point source at a gilded glass plate which had been bent so as to form an approximate circular cylinder.
[Crossref]

Hillier,

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Kirkpatrick, Paul

Paul Kirkpatrick and A. V. Baez, Bull. Am. Phys. Soc. 23, 10 (1948).

Morton,

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Ramberg,

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Roentgen, W. C.

W. C. Roentgen, Sitzungsberichte der Würzburger Physikalischen-Medicinischen Gesellschaft (1895).

Vance,

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Zworykin,

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Bull. Am. Phys. Soc. (1)

Paul Kirkpatrick and A. V. Baez, Bull. Am. Phys. Soc. 23, 10 (1948).

Nature (1)

W. Ehrenberg, Nature 160, 330 (1947). This brief communication describes the formation of line images by reflection of x-rays from a point source at a gilded glass plate which had been bent so as to form an approximate circular cylinder.
[Crossref]

Sitzungsberichte der Würzburger Physikalischen-Medicinischen Gesellschaft (1)

W. C. Roentgen, Sitzungsberichte der Würzburger Physikalischen-Medicinischen Gesellschaft (1895).

Other (1)

Zworykin, Morton, Ramberg, Hillier, and Vance, Electron Optics and the Electron Microscope (John Wiley and Sons, New York, 1946), p. 111.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Pinhole image of target of a deep-therapy x-ray tube. The focal spot is a crude copy of the cathode filament structure.

Fig. 2
Fig. 2

X-ray image of copper gauze of 200 meshes per linear inch, formed by a shadow projection method. The x-rays diverged from a small hole and passed through the gauze on the way to the film, producing a 98-fold magnification.

Fig. 3
Fig. 3

Shaded areas represent conditions of wave-length (λ) and grazing angle (i) for which total reflection of x-rays occurs.

Fig. 4
Fig. 4

Line images of a short and narrow slit from which x-rays diverged to a spherical concave mirror of 11-m radius. Grazing angle of incidence about 0.01 radian. The film receiving the reflected radiation was placed at eight successive positions, which included a position of good focus.

Fig. 5
Fig. 5

Reflection of radiation from a spherical mirror at small grazing angles. Meaning of symbols used in the text is shown.

Fig. 6
Fig. 6

Outside circle represents profile of a mirror for which intermediate circle includes conjugate foci of unit magnification and inside circle is the locus of principal focal points.

Fig. 7
Fig. 7

Detail of ray intersections at the image of a point, formed by a spherical mirror illuminated at a small grazing angle.

Fig. 8
Fig. 8

Image formation with an elliptical mirror. The spherical aberration of Fig. 7 is avoided. The bundle shown includes all rays from a point object whose grazing angle of incidence does not exceed a critical value i. Magnification is unity.

Fig. 9
Fig. 9

Image formation by two parabolic mirrors with incidence at sub-critical grazing angles. The spherical aberration of Fig. 7 is removed and magnification is possible.

Fig. 10
Fig. 10

Limitation of resolving power of a spherical mirror by diffraction. Grazing angle of incidence is small. Diffraction pattern of a point object is represented.

Fig. 11
Fig. 11

Arrangement of concave mirrors to produce real images of extended objects with incidence at small grazing angles.

Fig. 12
Fig. 12

Pattern produced by mirrors arranged as in Fig. 11. Object was a monel screen having 350 meshes per linear inch. In addition to the full image of the screen two partial images, each formed by one mirror, and a large spot caused by direct radiation appear above.

Fig. 13
Fig. 13

Further enlargement of the full image shown in Fig. 12 showing definition limited only by photographic grain.

Fig. 14
Fig. 14

Image of monel screen (350 meshes per linear inch) formed at a magnification of 29 diameters by a system like that of Fig. 11.

Fig. 15
Fig. 15

Arrangement of concave mirrors to produce real images of extended objects with incidence at small grazing angles. This combination obviates a type of image distortion inherent in the arrangement shown in Fig. 11.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

p = R α ( i + - α / 2 )
q δ = R α ( i - δ + α / 2 ) ,
1 q + 2 a f + 1 p - 2 a f ( 2 - a 2 + a ) = 1 f ( 1 + a / 2 ) ,
q / q 0 = ( M + 1 ) - 1 [ 1 - 2 a + ( M + a / 2 - a 2 M ) ( 1 - 3 2 a M ) - 1 ] .
q - q 0 = q 0 a M + 1 [ 1 + 3 M 2 2 - 3 a M - 2 ] .
δ = α [ 2 - 3 a M M + 1 - 2 a M ] .
S = 3 M p a α M + 1 [ M 2 + 2 a M - 1 M + 1 - 2 a M ] ,
S = ( 3 / 2 ) R M α 2 [ M - 1 M + 2 a M M + 1 ] .
S / M = ( 3 / 2 ) R α 2 = 3 · k 2 / 2 R ,