Abstract

Geometrical optic techniques are used to analyze and compare the symmetrical spherical mirror to the unsymmetrical spherical-mirror Czerny-Turner spectrometer. The aberration problems due to diffraction from the grating are analyzed and methods of partial correction of the aberrations are derived. The flux and resolution advantage of gratings with high blaze angles used in the unsymmetrical spherical-mirror Czerny-Turner is shown. A design and ray tracing routine employing a digital computer is utilized to illustrate the geometric effects of the diffraction grating and the partial corrective measures. Slit curvature is analyzed numerically and some general results are abstracted from the numerical data. It may be inferred from the results of theory and numerical calculations that the unsymmetrical Czerny-Turner spectrometer using two spherical mirrors can be made superior to a similar symmetrical Czerny-Turner spectrometer. A comparison of luminosity is made between the Czerny-Turner spectrometer, utilizing a high blaze grating, and various interferometric and modulating spectrometers and it is shown that the luminosity of the Czerny-Turner spectrometer is comparable or superior.

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  1. M. Czerny and A. F. Turner, Z. Physik. 61, 792 (1930).
  2. W. G. Fastie, J. Opt. Soc. Am. 42, 641, 647 (1952).
  3. H. Ebert, Wiedemann Ann. 38, 489 (1889).
  4. K. Kudo, Sci. Light (Tokyo) 9, 1 (1960).
  5. W. Leo, Z. Angew. Phys. 8, 196 (1956).
  6. W. Leo, Z. Instrumentenk. 66, 240 (1958); 70, 9 (1962).
  7. W. R. Hamilton, Mathematical Papers, Geometrical Optics (Cambridge University Press, London, 1931); Vol. I, Chap. 17, p. 168; J. L. Synge, Geometrical Optics, Cambridge University Press (1937); J. L. Synge, Hamilton's Method in Geometrical Optics (The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, 1951); J. L. Synge, J. Opt. Soc. Am. 27, 75 (1937); M. Herzberger, ibid., p. 133.
  8. P. Jacquinot and C. Dufour, J. Rech. Centre, Natl. Rech. Sci. Lab, Bellevue (Paris) No. 6, 91 (1948).
  9. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
  10. G. W. Stroke, J. Opt. Soc. Am. 51, 1321 (1961). Stroke has stressed with the help of numerical values, the advantages in using high-blazed gratings in spectrometers and spectrographs. See also, G. W. Stroke, Progr. Opt. 2, 3 (1963).
  11. V. I. Malyshev and S. G. Rautian, Opt. i Spectroskopiya 6, 550 (1959) [English transl.: Opt. Spectry 6, 351 (1959)].
  12. R. Chabbal, Rev. Opt. 37, 49, 336, 501 (1958).
  13. P. Jacquinot, Rept. Progr. Phys. 23, 267 (1960).
  14. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
  15. G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962), has derived Eq. (15) without the dependence upon the radii of curvature, by utilizing a different geometrical optic technique. W. G. Fastie (private communication and U. S. Patent 3,011,391) has derived an equation similar to (17) but without the dependence upon the radii of curvature.
  16. W. G. Fastie experimentally noted that the effect of coma may be corrected by tilting the second mirror [Symp. Toter-ferometry, No. 11, 243 (1960), Natl. Phys. Lab., G. Brit.]. The large, high-resolution Ebert spectrometer, which has a focal length of 183cm [W. G. Fastie, H. M. Crosswhite, and P. Gloersen, J. Opt. Soc. Am. 48, 106 (1958)], achieved a resolving power in excess of 500,000. This was done at an f number >20, i.e., a projected grating width <˜9 cm. A re-examination of the lines revealed an asymmetry and a coma-like flare (private communication). After a discussion with one of the authors, R. Brower (private communication) of Brower Laboratories, Wellesley Hills, Massachusetts set up a point source, two spherical mirrors, and grating. By using the grating in the zeroth norder and aligning the instrument, the effect of coma is eliminated with a symmetrical arrangement; to eliminate the effect of coma for the first or higher orders of diffraction of an echellette grating, the second mirror had to be tilted. When R2 is made <R1, Brower found that the image quality is superior to that with R1=R2.
  17. K. Nienhuis, thesis, University of Groningen, 1948.
  18. N. G. Van Kampen, Physica 15, 575 (1949).
  19. K. Nienhuis and B. R. A. Nijborn, Physica 15, 590 (1949).
  20. M. Born and E. Wolf, Principles of Optics (Pergamon Press Inc., New York, 1959), p. 477.
  21. M. Cagnet, M. Francon, and J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1963).
  22. E. Wolf, Rept. Progr. Phys. 14, 95 (1951).
  23. To illustrate the sensitivity of the slit curvature upon the distance from the entrance slit to the collimating mirror: for one of the instruments analyzed, a shift of 0.3 mm distorted the slit curvature from a circle to a smooth curve which deviates from a circle by ≈6 µ at the slit center to ≈0.2 µ, 2.75 cm above or below the slit center.
  24. J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).
  25. R. G. Greenler, J. Opt. Soc. Am. 47, 642 (1957).
  26. We shall be interested only in resolution ≤ 1 cm-1. in the above stated wavelength region. This value of resolution, to the author's knowledge, has not been achieved by interferometers employing the Fourier transformation techniques. In the spectral region where photomultiplying tubes can be used as detectors (<˜ 1 µ) the signal/noise advantage of these types of interferometers is nullified. The argument shall proceed under the assumption that higher resolution will be obtained in the future.
  27. J. Connes, J. Phys. Radium 19, 197 (1958); Symposium on Interferometry, National Physics Laboratory, Great Britian No. 11, 409 (1960).
  28. A. Girard, Opt. Acta, 7, 81 (1960).
  29. A. Girard, Appl. Opt. 2, 79 (1963).
  30. G. Stroke (private communication) informed us that he gave Girard a grating blazed at 45°. Evidently Girard did not use it in the previous referenced papers since the scanning range was 37° <θ<22° in a Littrow system. If the grille spectrometer is used with a grating of 45° blaze angle, then the luminosity advantage of the grille spectrometer over the Czerny-Turner monochromator would be ≈30 to 1.3.

Beutler, H. G.

H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press Inc., New York, 1959), p. 477.

Cagnet, M.

M. Cagnet, M. Francon, and J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1963).

Chabbal, R.

J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).

R. Chabbal, Rev. Opt. 37, 49, 336, 501 (1958).

Connes, J.

J. Connes, J. Phys. Radium 19, 197 (1958); Symposium on Interferometry, National Physics Laboratory, Great Britian No. 11, 409 (1960).

Czerny, M.

M. Czerny and A. F. Turner, Z. Physik. 61, 792 (1930).

Dufour, C.

P. Jacquinot and C. Dufour, J. Rech. Centre, Natl. Rech. Sci. Lab, Bellevue (Paris) No. 6, 91 (1948).

Ebert, H.

H. Ebert, Wiedemann Ann. 38, 489 (1889).

Fastie, W. G.

W. G. Fastie experimentally noted that the effect of coma may be corrected by tilting the second mirror [Symp. Toter-ferometry, No. 11, 243 (1960), Natl. Phys. Lab., G. Brit.]. The large, high-resolution Ebert spectrometer, which has a focal length of 183cm [W. G. Fastie, H. M. Crosswhite, and P. Gloersen, J. Opt. Soc. Am. 48, 106 (1958)], achieved a resolving power in excess of 500,000. This was done at an f number >20, i.e., a projected grating width <˜9 cm. A re-examination of the lines revealed an asymmetry and a coma-like flare (private communication). After a discussion with one of the authors, R. Brower (private communication) of Brower Laboratories, Wellesley Hills, Massachusetts set up a point source, two spherical mirrors, and grating. By using the grating in the zeroth norder and aligning the instrument, the effect of coma is eliminated with a symmetrical arrangement; to eliminate the effect of coma for the first or higher orders of diffraction of an echellette grating, the second mirror had to be tilted. When R2 is made <R1, Brower found that the image quality is superior to that with R1=R2.

W. G. Fastie, J. Opt. Soc. Am. 42, 641, 647 (1952).

Francon, M.

M. Cagnet, M. Francon, and J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1963).

Girard, A.

A. Girard, Opt. Acta, 7, 81 (1960).

A. Girard, Appl. Opt. 2, 79 (1963).

Greenler, R. G.

R. G. Greenler, J. Opt. Soc. Am. 47, 642 (1957).

Hamilton, W. R.

W. R. Hamilton, Mathematical Papers, Geometrical Optics (Cambridge University Press, London, 1931); Vol. I, Chap. 17, p. 168; J. L. Synge, Geometrical Optics, Cambridge University Press (1937); J. L. Synge, Hamilton's Method in Geometrical Optics (The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, 1951); J. L. Synge, J. Opt. Soc. Am. 27, 75 (1937); M. Herzberger, ibid., p. 133.

Jacquinot, P.

P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).

P. Jacquinot, Rept. Progr. Phys. 23, 267 (1960).

P. Jacquinot and C. Dufour, J. Rech. Centre, Natl. Rech. Sci. Lab, Bellevue (Paris) No. 6, 91 (1948).

Kudo, K.

K. Kudo, Sci. Light (Tokyo) 9, 1 (1960).

Leo, W.

W. Leo, Z. Instrumentenk. 66, 240 (1958); 70, 9 (1962).

W. Leo, Z. Angew. Phys. 8, 196 (1956).

Mack, J. E.

J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).

Malyshev, V. I.

V. I. Malyshev and S. G. Rautian, Opt. i Spectroskopiya 6, 550 (1959) [English transl.: Opt. Spectry 6, 351 (1959)].

McNutt, D. P.

J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).

Nienhuis, K.

K. Nienhuis, thesis, University of Groningen, 1948.

K. Nienhuis and B. R. A. Nijborn, Physica 15, 590 (1949).

Nijborn, B. R. A.

K. Nienhuis and B. R. A. Nijborn, Physica 15, 590 (1949).

Rautian, S. G.

V. I. Malyshev and S. G. Rautian, Opt. i Spectroskopiya 6, 550 (1959) [English transl.: Opt. Spectry 6, 351 (1959)].

Roesler, F. L.

J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).

Rosendahl, G.

G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962), has derived Eq. (15) without the dependence upon the radii of curvature, by utilizing a different geometrical optic technique. W. G. Fastie (private communication and U. S. Patent 3,011,391) has derived an equation similar to (17) but without the dependence upon the radii of curvature.

Stroke, G.

G. Stroke (private communication) informed us that he gave Girard a grating blazed at 45°. Evidently Girard did not use it in the previous referenced papers since the scanning range was 37° <θ<22° in a Littrow system. If the grille spectrometer is used with a grating of 45° blaze angle, then the luminosity advantage of the grille spectrometer over the Czerny-Turner monochromator would be ≈30 to 1.3.

Stroke, G. W.

G. W. Stroke, J. Opt. Soc. Am. 51, 1321 (1961). Stroke has stressed with the help of numerical values, the advantages in using high-blazed gratings in spectrometers and spectrographs. See also, G. W. Stroke, Progr. Opt. 2, 3 (1963).

Thrierr, J. C.

M. Cagnet, M. Francon, and J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1963).

Turner, A. F.

M. Czerny and A. F. Turner, Z. Physik. 61, 792 (1930).

Van Kampen, N. G.

N. G. Van Kampen, Physica 15, 575 (1949).

Wolf, E.

E. Wolf, Rept. Progr. Phys. 14, 95 (1951).

M. Born and E. Wolf, Principles of Optics (Pergamon Press Inc., New York, 1959), p. 477.

Other (30)

M. Czerny and A. F. Turner, Z. Physik. 61, 792 (1930).

W. G. Fastie, J. Opt. Soc. Am. 42, 641, 647 (1952).

H. Ebert, Wiedemann Ann. 38, 489 (1889).

K. Kudo, Sci. Light (Tokyo) 9, 1 (1960).

W. Leo, Z. Angew. Phys. 8, 196 (1956).

W. Leo, Z. Instrumentenk. 66, 240 (1958); 70, 9 (1962).

W. R. Hamilton, Mathematical Papers, Geometrical Optics (Cambridge University Press, London, 1931); Vol. I, Chap. 17, p. 168; J. L. Synge, Geometrical Optics, Cambridge University Press (1937); J. L. Synge, Hamilton's Method in Geometrical Optics (The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, 1951); J. L. Synge, J. Opt. Soc. Am. 27, 75 (1937); M. Herzberger, ibid., p. 133.

P. Jacquinot and C. Dufour, J. Rech. Centre, Natl. Rech. Sci. Lab, Bellevue (Paris) No. 6, 91 (1948).

P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).

G. W. Stroke, J. Opt. Soc. Am. 51, 1321 (1961). Stroke has stressed with the help of numerical values, the advantages in using high-blazed gratings in spectrometers and spectrographs. See also, G. W. Stroke, Progr. Opt. 2, 3 (1963).

V. I. Malyshev and S. G. Rautian, Opt. i Spectroskopiya 6, 550 (1959) [English transl.: Opt. Spectry 6, 351 (1959)].

R. Chabbal, Rev. Opt. 37, 49, 336, 501 (1958).

P. Jacquinot, Rept. Progr. Phys. 23, 267 (1960).

H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).

G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962), has derived Eq. (15) without the dependence upon the radii of curvature, by utilizing a different geometrical optic technique. W. G. Fastie (private communication and U. S. Patent 3,011,391) has derived an equation similar to (17) but without the dependence upon the radii of curvature.

W. G. Fastie experimentally noted that the effect of coma may be corrected by tilting the second mirror [Symp. Toter-ferometry, No. 11, 243 (1960), Natl. Phys. Lab., G. Brit.]. The large, high-resolution Ebert spectrometer, which has a focal length of 183cm [W. G. Fastie, H. M. Crosswhite, and P. Gloersen, J. Opt. Soc. Am. 48, 106 (1958)], achieved a resolving power in excess of 500,000. This was done at an f number >20, i.e., a projected grating width <˜9 cm. A re-examination of the lines revealed an asymmetry and a coma-like flare (private communication). After a discussion with one of the authors, R. Brower (private communication) of Brower Laboratories, Wellesley Hills, Massachusetts set up a point source, two spherical mirrors, and grating. By using the grating in the zeroth norder and aligning the instrument, the effect of coma is eliminated with a symmetrical arrangement; to eliminate the effect of coma for the first or higher orders of diffraction of an echellette grating, the second mirror had to be tilted. When R2 is made <R1, Brower found that the image quality is superior to that with R1=R2.

K. Nienhuis, thesis, University of Groningen, 1948.

N. G. Van Kampen, Physica 15, 575 (1949).

K. Nienhuis and B. R. A. Nijborn, Physica 15, 590 (1949).

M. Born and E. Wolf, Principles of Optics (Pergamon Press Inc., New York, 1959), p. 477.

M. Cagnet, M. Francon, and J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1963).

E. Wolf, Rept. Progr. Phys. 14, 95 (1951).

To illustrate the sensitivity of the slit curvature upon the distance from the entrance slit to the collimating mirror: for one of the instruments analyzed, a shift of 0.3 mm distorted the slit curvature from a circle to a smooth curve which deviates from a circle by ≈6 µ at the slit center to ≈0.2 µ, 2.75 cm above or below the slit center.

J. E. Mack, D. P. McNutt, F. L. Roesler, and R. Chabbal, Appl. Opt. 2, 855 (1963).

R. G. Greenler, J. Opt. Soc. Am. 47, 642 (1957).

We shall be interested only in resolution ≤ 1 cm-1. in the above stated wavelength region. This value of resolution, to the author's knowledge, has not been achieved by interferometers employing the Fourier transformation techniques. In the spectral region where photomultiplying tubes can be used as detectors (<˜ 1 µ) the signal/noise advantage of these types of interferometers is nullified. The argument shall proceed under the assumption that higher resolution will be obtained in the future.

J. Connes, J. Phys. Radium 19, 197 (1958); Symposium on Interferometry, National Physics Laboratory, Great Britian No. 11, 409 (1960).

A. Girard, Opt. Acta, 7, 81 (1960).

A. Girard, Appl. Opt. 2, 79 (1963).

G. Stroke (private communication) informed us that he gave Girard a grating blazed at 45°. Evidently Girard did not use it in the previous referenced papers since the scanning range was 37° <θ<22° in a Littrow system. If the grille spectrometer is used with a grating of 45° blaze angle, then the luminosity advantage of the grille spectrometer over the Czerny-Turner monochromator would be ≈30 to 1.3.

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