Abstract

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.

© 1932 Optical Society of America

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References

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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.
    [Crossref]
  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.
    [Crossref]
  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.
    [Crossref]
  9. E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.
  10. 5×5 cm; f=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.
    [Crossref]
  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. Mannkopff, ZS. f. Phys.,  45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting ϕA=ϕB). 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.
    [Crossref]
  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.

1932 (1)

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.
[Crossref]

1929 (1)

J. H. Osgood, Phys. Rev.,  30, p. 567; 1929. M. Siegbahn and T. Magnusson, ZS. f. Phys.,  62, p. 435, 1930.
[Crossref]

1927 (3)

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. Mannkopff, ZS. f. Phys.,  45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting ϕA=ϕB). 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.

C. Runge and R. Mannkopff: ZS. f. Phys.,  45, p. 13; 1927.
[Crossref]

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.

1925 (1)

E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.

1922 (1)

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.
[Crossref]

1903 (1)

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.
[Crossref]

1897 (1)

Runge and F. Paschen, Wied. Ann.,  61, p. 644; 1897.

Burns, K.

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.
[Crossref]

Edlen, B.

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.
[Crossref]

Gehrcke, E.

E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.

Humphreys, W. J.

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.
[Crossref]

Kayser, H.

C. Runge in H. Kayser: Handbuch der Spektroskopie, I, p. 464; E. C. C. Baly: Spectroscopy, 3d Edition, I, p. 165.

Lau, E.

E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.

Mack, J. E.

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.
[Crossref]

Mannkopff, R.

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. Mannkopff, ZS. f. Phys.,  45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting ϕA=ϕB). 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.

C. Runge and R. Mannkopff: ZS. f. Phys.,  45, p. 13; 1927.
[Crossref]

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.

Meggers, W. F.

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.
[Crossref]

Osgood, J. H.

J. H. Osgood, Phys. Rev.,  30, p. 567; 1929. M. Siegbahn and T. Magnusson, ZS. f. Phys.,  62, p. 435, 1930.
[Crossref]

Paschen, F.

Runge and F. Paschen, Wied. Ann.,  61, p. 644; 1897.

Runge,

Runge and F. Paschen, Wied. Ann.,  61, p. 644; 1897.

Runge, C.

C. Runge and R. Mannkopff: ZS. f. Phys.,  45, p. 13; 1927.
[Crossref]

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.

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. Mannkopff, ZS. f. Phys.,  45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting ϕA=ϕB). 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.

C. Runge in H. Kayser: Handbuch der Spektroskopie, I, p. 464; E. C. C. Baly: Spectroscopy, 3d Edition, I, p. 165.

Stehn, J. R.

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.
[Crossref]

von Angerer, E.

E. von Angerer, Handbuch der Experimentalphysik, 21, p. 301.

von Rohr, M.

M. von Rohr: Optical Instruments, London, 1920, p. 550.

Ann. d. Phys. (1)

E. Gehrcke and E. Lau, Ann. d. Phys. 76, p. 679; 1925.

Astroph, J. (1)

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.
[Crossref]

J.O.S.A. (1)

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.
[Crossref]

Phys. Rev. (1)

J. H. Osgood, Phys. Rev.,  30, p. 567; 1929. M. Siegbahn and T. Magnusson, ZS. f. Phys.,  62, p. 435, 1930.
[Crossref]

Scient. Pap. Bur. of Stand. (1)

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.
[Crossref]

Wied. Ann. (1)

Runge and F. Paschen, Wied. Ann.,  61, p. 644; 1897.

ZS. f. Phys. (3)

C. Runge and R. Mannkopff: ZS. f. Phys.,  45, p. 13; 1927.
[Crossref]

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.

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. Mannkopff, ZS. f. Phys.,  45, p. 14; 1927, equations (1) and (2). The same system of equations holds for a concave mirror by putting ϕA=ϕB). 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.

Other (5)

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.

C. Runge in H. Kayser: Handbuch der Spektroskopie, I, p. 464; E. C. C. Baly: Spectroscopy, 3d Edition, I, p. 165.

M. von Rohr: Optical Instruments, London, 1920, p. 550.

E. von Angerer, Handbuch der Experimentalphysik, 21, p. 301.

5×5 cm; f=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.

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Figures (6)

Fig. 1
Fig. 1

Spectral line is a stigmatic image of source of light. (Runge and Mannkopff). L, source of light; C, spherical-cylindrical lens; S, slit; G, grating; P, plate; a, b: distance CL and CS; s, p: distances GS and GP.

Fig. 2
Fig. 2

Effective length of the slit (vertical plane). S, slit; G, grating; P, plate and inner focus; F, outer focus.

Fig. 3
Fig. 3

Cylindrical lens between grating and plate (vertical plane). S, slit; G, grating; C, cylindrical lens; p, plate; F, outer focus. x, y: distances CP and CF; p, f: distances GP and GF.

Fig. 4
Fig. 4

Comparison of resolving power of concave grating with and without cylindrical lens removing the astigmatism (absorption spectrum of iodine vapor; 7 times magnified; positive (a) Astigmatism removed; 10 sec. exposure; (c) Astigmatism not completely removed; 20 sec. exposure; (b), (d) Spectra taken without the cylindrical lens; 240 sec. exposure.

Fig. 5
Fig. 5

Astigmatism of the concave grating with grazing incidence. S, slit, G, grating; P, plate and inner focus; F, outer focus.

Fig. 6
Fig. 6

The prism spectrograph with cylindrical lenses. S, slit; C1, C2, C3, cylindrical lenses; Pr, prism; Pl, plate.