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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 22, Iss. 8 — Aug. 1, 1932
  • pp: 441–452


O. OLDENBERG  »View Author Affiliations

JOSA, Vol. 22, Issue 8, pp. 441-452 (1932)

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The intensity of illumination of the spectrum from a concave grating is computed. The customary arrangements are compared of which some correct the astigmatism of the spectral lines (sections 1–6). A cylindrical lens in front of the plate, as suggested by Humphreys and Gehrcke, seems to be the only device that increases the intensity without reducing dispersion and resolving power. Thus for a small spectral range a reduction of the time of exposure to 1/24 has been realized without any loss of resolving power (section 6). The bearings of the results on the spectra from the grating at grazing incidence (vacuum spectrograph), the plane grating and the prism are discussed (sections 7–9). The main results are checked by experiments.


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  1. C. Runge in H. Kayser: Handbuch der Spektroskopie, I, p. 464; E. C. C. Baly: Spectroscopy, 3d Edition, I, p. 165.
  2. C. Runge and R. Mannkopff: ZS. f. Phys., 45, p. 13; 1927.
  3. M. von Rohr: Optical Instruments, London, 1920, p. 550.
  4. E. von Angerer, Handbuch der Experimentalphysik, 21, p. 301.
  5. The adjustment depends upon the wave length. This dependence, however, can be partly compensated by the chromatic error of the lenses. Cf. C. Runge and R. Mannkopff, ZS. f. Phys. 45, p. 24; 1927.
  6. Runge and F. Paschen, Wied. Ann., 61, p. 644; 1897.
  7. W. F. Meggers and K. Burns, Scient. Pap. Bur. of Stand. 18, p. 185; 1922. For other references cf. E. v. Angerer, Handbuch der Experimental physik, 21, 311.
  8. W. J. Humphreys, Astroph, J., 18, p. 324; 1903; ZS. f. Instr. Kde, 31, p. 217; 1911. E. Gehrcke, ZS. f. Instr. Kde, 31, pp. 87 and 217; 1911. E. Gehrcke and E. Lau, Ann. d. Phys., 76, p. 679; 1925. Cf. H. A. Rowland, Physical Papers, 489. Humphreys describes an arrangement in which the intensity of illumination is increased by means of mirrors fastened to the slit. These mirrors produce an apparent prolongation of the slit. This device is useful only if the effective length of the slit is not filled with light. In general, except for stellar spectra, it will be easier to fill the slit with light by means of some focusing device rather than of these mirrors. When used near the photographic plate, these mirrors have an effect. The increase of intensity can, however, never exceed the factor 3, since each mirror adds only once the original intensity.
  9. E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.
  10. 5×5 cm; ƒ=21.5 cm. The lens was made by C. P. Goerz, American Optical Company, New York City. I understand that the cylindrical lenses manufactured by this company for technical purposes are tested with interference methods.
  11. J. H. Osgood, Phys. Rev., 30, p. 567; 1929. M. Siegbahn and T. Magnusson, ZS. f. Phys., 62, p. 435, 1930.
  12. The curvature and position of this mirror may be computed easily. It may be located arbitrarily between the grating and the plate, its function being similar to that of the cylindrical lens in the preceding section. The astigmatism of the light leaving the grating may be calculated from Runge's formulas. (C. Runge and R. Manakopff, ZS. f. Phys., 45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting øAB). For an arbitrary angle of incidence, which should be chosen near grazing incidence, the same pair of equations yields the curvature of the mirror and the position of the image.
  13. Note added in proof: In a recent paper, J. E. Mack, J. R. Stehn and B. Edlen (J.O.S.A. 22, p. 257; 1932) recommend short rulings for the grating, to be used at grazing incidence.
  14. It is interesting to discuss the same problem on the basis of a general theorem in geometric optics. A diaphragm in front of a luminous screen transmits light as if it were radiating light itself with the same intrinsic intensity as the screen, independent of the distance between them. The same is true when the diaphragm is covered by a lens. The present problem is concerned with one component of an astigmatic bundle. This theorem is applied, therefore, in considering only the vertical spreading of light when the diaphragm (the grating) receiving light from a long slit is focused by a cylindrical lens on a photographic plate. The intensity of illumination on the plate turns out to be C/y, as before, provided that the slit has a certain minimum length.

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