Abstract

It has been observed that some stray light (x-rays) is thrown into the neighborhood of the focus obtained if x-rays are focused by a bent optical flat. Most of this extra light is due to imperfections of the optical flats, while halation, Fresnel diffraction at the slits and air scattering make only minor contributions. An analysis of the distribution of this extra light, a study of the effect of controlled irregularities and pin hole images of surfaces taken with x-rays lead to definite conclusions about the structure of such surfaces.

© 1949 Optical Society of America

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References

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  1. H. Kiessig, Ann. d. Physik 10, 715 (1931).
    [Crossref]
  2. C. F. Ellis, Am. J. Phys. 16, 8 (1948).
    [Crossref]
  3. F. Jentzsch, Physik. Zeits. 30, 268 (1929).
  4. F. Coeterier and M. C. Teves, Physika 3, 968 (1937).
  5. Tolansky and Wilcock, Proc. Roy. Soc. A191, 182 (1947).
    [Crossref]
  6. H. Kiessig, Ann. d. Physik 10, 715 (1931).
    [Crossref]
  7. E. Nähring, Physik. Zeits. 32, 730 (1931).
  8. A. I. Alichanow and L. A. Arzimovic, Zeits. f. Physik. 82, 489 (1933).
    [Crossref]

1948 (1)

C. F. Ellis, Am. J. Phys. 16, 8 (1948).
[Crossref]

1947 (1)

Tolansky and Wilcock, Proc. Roy. Soc. A191, 182 (1947).
[Crossref]

1937 (1)

F. Coeterier and M. C. Teves, Physika 3, 968 (1937).

1933 (1)

A. I. Alichanow and L. A. Arzimovic, Zeits. f. Physik. 82, 489 (1933).
[Crossref]

1931 (3)

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

E. Nähring, Physik. Zeits. 32, 730 (1931).

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

1929 (1)

F. Jentzsch, Physik. Zeits. 30, 268 (1929).

Alichanow, A. I.

A. I. Alichanow and L. A. Arzimovic, Zeits. f. Physik. 82, 489 (1933).
[Crossref]

Arzimovic, L. A.

A. I. Alichanow and L. A. Arzimovic, Zeits. f. Physik. 82, 489 (1933).
[Crossref]

Coeterier, F.

F. Coeterier and M. C. Teves, Physika 3, 968 (1937).

Ellis, C. F.

C. F. Ellis, Am. J. Phys. 16, 8 (1948).
[Crossref]

Jentzsch, F.

F. Jentzsch, Physik. Zeits. 30, 268 (1929).

Kiessig, H.

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

Nähring, E.

E. Nähring, Physik. Zeits. 32, 730 (1931).

Teves, M. C.

F. Coeterier and M. C. Teves, Physika 3, 968 (1937).

Tolansky,

Tolansky and Wilcock, Proc. Roy. Soc. A191, 182 (1947).
[Crossref]

Wilcock,

Tolansky and Wilcock, Proc. Roy. Soc. A191, 182 (1947).
[Crossref]

Am. J. Phys. (1)

C. F. Ellis, Am. J. Phys. 16, 8 (1948).
[Crossref]

Ann. d. Physik (2)

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

H. Kiessig, Ann. d. Physik 10, 715 (1931).
[Crossref]

Physik. Zeits. (2)

E. Nähring, Physik. Zeits. 32, 730 (1931).

F. Jentzsch, Physik. Zeits. 30, 268 (1929).

Physika (1)

F. Coeterier and M. C. Teves, Physika 3, 968 (1937).

Proc. Roy. Soc. (1)

Tolansky and Wilcock, Proc. Roy. Soc. A191, 182 (1947).
[Crossref]

Zeits. f. Physik. (1)

A. I. Alichanow and L. A. Arzimovic, Zeits. f. Physik. 82, 489 (1933).
[Crossref]

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Figures (7)

F. 1 (a–e)
F. 1 (a–e)

Change of appearance of the x-ray optical image of a slit with time of exposure.

F. 1f
F. 1f

Shadow of wire in heavily darkened region of image.

F. 2
F. 2

The blobs caused by halation are clearly distinguished from the streaks due to Fresnel diffraction (b, c). The streaks can be suppressed by shaping the diffracting slit (e).

F. 3
F. 3

Reflection of x-rays by a “flat” with super-imposed sinusoidal variation in height.

F. 4
F. 4

Diffraction of x-rays of 1.5-A wave-length by a sinusoidal grating of evaporated gold, of 0.7-mm period.

F. 5
F. 5

Rays issuing uniformly from a fine slit (a) are modulated on reflection by optical surfaces, disclosing their uneveness (b–d).

F. 6
F. 6

Diffraction of x-rays of 1.5-A wave-length by a “thick” grating of 0.7-mm period.

Tables (1)

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Table I

Equations (12)

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h = h 0 sin ω x = h 0 sin 2 π x / d .
cos ( x μ + h μ ) ,
μ = ( 2 π / λ ) ( cos θ cos θ ) μ = ( 2 π / λ ) ( sin θ + sin θ ) .
A = 0 l d x cos ( μ x + h 0 μ sin ω x ) ,
A = 0 l d x ( cos μ x h 0 μ sin ω x sin μ x ) = 0 l d x ( cos μ x ( h 0 μ / 2 ) cos ( ω μ ) x + ( h 0 μ / 2 ) cos ( ω + μ ) x ) = sin l μ μ 1 2 h 0 μ sin ( ω μ ) l ω μ + 1 2 h 0 μ sin ( ω + μ ) l ω + μ .
μ = 0 ω μ = 0 ω + μ = 0 ,
μ 2 π ϕ sin θ / λ
ϕ = ± λ / d sin θ ± λ / d θ .
I = A 2 d ϕ ,
I 0 + d ϕ sin 2 [ ( 2 π / λ ) l ϕ sin θ ] [ ( 2 π / λ ) ϕ sin θ ] 2 = l λ 2 sin θ
I ± ( h 0 μ / 2 ) 2 l λ / 2 sin θ ,
I ± / I 0 = ( h 0 μ / 2 ) 2 .