Abstract

The total reflection of x-rays is applied to focusing the rays issuing from a fine slit. A method of computing the geometrical optics of surfaces of bent beams is given; it is shown that under certain conditions lateral aberrations for practical apertures are of the order of one micron or less. These results are confirmed by experiment.

© 1949 Optical Society of America

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References

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  1. (a)W. Ehrenberg, Nature 160, 330 (1947);(b)P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
    [Crossref] [PubMed]
  2. Sir R. Glazebrook, A Dictionary of Applied Physics (MacMillan Company, Ltd., London, England, 1922), Vol. 1, p. 810.

1947 (1)

(a)W. Ehrenberg, Nature 160, 330 (1947);(b)P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
[Crossref] [PubMed]

Ehrenberg, W.

(a)W. Ehrenberg, Nature 160, 330 (1947);(b)P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
[Crossref] [PubMed]

Glazebrook, Sir R.

Sir R. Glazebrook, A Dictionary of Applied Physics (MacMillan Company, Ltd., London, England, 1922), Vol. 1, p. 810.

Nature (1)

(a)W. Ehrenberg, Nature 160, 330 (1947);(b)P. Kirkpatrick and A. V. Baez, J. Opt. Soc. Am. 38, 766 (1948).
[Crossref] [PubMed]

Other (1)

Sir R. Glazebrook, A Dictionary of Applied Physics (MacMillan Company, Ltd., London, England, 1922), Vol. 1, p. 810.

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Figures (11)

F. 1
F. 1

Reflection of x-rays by a bent optical flat.

F. 2
F. 2

Bending an optical flat by a symmetric pair of couples.

F. 3
F. 3

Simplest method of bending an optical flat.

F. 4–7
F. 4–7

Lateral (S) and longitudinal (Δ) aberrations and the corresponding angles ϕ between the x axis and the outgoing rays, arising on focusing x-rays by differently bent optical flats.

F 8 and 9
F 8 and 9

Displacement of object from correct position.

F. 10
F. 10

Varying the thrusts indicated by arrows while the diameters of the supporting pins Yl and Yr are fixed.

F. 11
F. 11

Diagram of camera. The surface bb is flat and serves as a reference. Rays issuing from the object slit are defined by the selector slit and after reflection reunited in the plane of the photographic plate.

F. 12
F. 12

Slit consisting of two parallel cylinders.

F. 13
F. 13

Mechanism for bending optical flat.

F. 14
F. 14

Microphotograph of image of slit obtained by reflection of x-rays on a bent optical flat.

F. 15
F. 15

Definition of rays by a pair of slits.

Tables (2)

Equations (20)

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ψ = y
ϕ = y / ( a + x )
χ = ϕ ψ
ω = ϕ 2 ψ
F = y / ω + x = a + Δ
S = ω Δ
Φ = ϕ ( x ) ϕ ( x + ) .
y = 0 , y = b = a 2 y , y = b / a 2 = 1 / r .
y = b ( 1 2 r ) x 2 ( 1 8 r 3 ) x 4 + .
y = b ( 1 2 r ) x 2 = b ( b / 2 a 2 ) x 2 .
y = b ( b / l γ a 2 ) [ | x | 3 + 3 l x 2 / 2 + 3 l 2 | x | ( 1 2 γ ) 2 + l 3 ( 1 2 γ ) 3 ] ,
y = b ( b / 2 a 2 ) x 2 + ( b / 3 l a 2 ) | x | 3 .
y = b ( b / 2 a 2 ) x 2 ( b / 8 a 4 ) x 4 + .
z = 2 a δ / ( b + δ ) d = 2 δ ( b + δ ) / ( b δ ) .
F = ( y + d + δ ) / ω + x = a + z + Δ .
z = 4 + 10 2 / a d = 4 b / a + 14 b 2 / a 2 .
F = ( γ + d ) / ω + x = a + z + Δ .
d Y 2 ( 1.75 Y r / a 3 ) d a .
I = Φ / 2 l .
I = 1 l 1 3 2 δ l = 2 δ / 3 l 2 = 2 W / 9 l 2 .