Abstract

Outstanding high-resolution gratings have now been obtained by ruling under interferometric control on the M.I.T. ruling engine, as a result of considerable improvements which have followed the application of two separate studies carried out for this purpose: (1) a general theory of the effects of grating errors on the distribution of light in the spectral images; and (2) a theory of the uncalled-for corrections introduced into an interferometric servomechanism by incorrect translation of the grating-blank motion into representative interferometric fringe signals. The errors found to be most detrimental to high-resolution grating, in that they affect the close neighborhood of the line centers, are rather extended small-amplitude deviations in the wave fronts. These can be caused in particular by errors of run in the ruling, as a result of inadequate temperature and servocontrol, by defects in flatness of the grating blanks and of the aluminum coatings, as well as by incorrect adjustments of the control interferometers. Reduction of these errors to less than λ/10 at 5461 A and corresponding improvements in the diamond-carriage adjustments have resulted in improvements on the order of 4 to 9 in the spectral quality of the high-angle gratings when compared to the 10-in. gratings previously described by G. R. Harrison and G. W. Stroke [ J. Opt. Soc. Am. 50, 1153 ( 1960)]. Precision replicas of these gratings permit high-resolution studies in spectrometers as short as 1 m and in spectrographs with as few as 1012 atoms in the source. Considerable further gains in luminosity, compactness and resolution should result from the use of gratings and echelles blazed at 76° in autocollimation rather than at 64°, as has been customary so far.

© 1961 Optical Society of America

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  1. G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
    [Crossref]
  2. G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, J. Opt. Soc. Am. 47, 15 (1957).
    [Crossref]
  3. aSome results of our work pertinent to the present paper were incorporated as a part of the review paper by G. R. Harrison, N. Sturgis, S. P. Davis, and Y. Yamada, J. Opt. Soc. Am. 49, 205 (1959). bThese results had also been reviewed by G. W. Stroke on May 7, 1958, at the International Commission of Optics Colloquium on Optics in Metrology, Brussels [Proceedings, “Optics in Metrology,” edited by Pol Mollet (Pergamon Press, New York, 1960), pp. 98–118].
  4. G. W. Stroke, J. Opt. Soc. Am. 45, 30 (1955).
    [Crossref]
  5. aG. W. Stroke, Interferometry Symposium, National Physical Laboratory, Teddington, June 10, 1959. (Symposium No. 11, Interferometry, N. P. L., Her Majesty’s Stationery Office, London, 1960); bG. W. Stroke, Paper No. 5, Fifth Conference of the International Commission of Optics, Stockholm, August, 1959; cG. W. Stroke, J. phys. radium 21, 57S (April, 1960).
  6. aG. R. Harrison, Proc. Am. Phil. Soc. 102, 438 (1958); bG. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960).
  7. aG. W. Stroke, Rev. opt.,  39, 291 (1960); bG. W. Stroke, thesis, The Sorbonne, Paris, 1960.
  8. aR. J. Hull and H. H. Stroke, Bull. Am. Phys. Soc. 5, 412 (1960); bR. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).
  9. R. Dupeyrat (private communication, 1960).
  10. aJ. W. Evans (private communication); bA. Keith Pierce, J. Opt. Soc. Am. 47, 6 (1957); cH. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951).
  11. Ch. Fehrenbach (private communication).
  12. G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957); J. Opt. Soc. Am. 48, 276 (1958); J. phys. radium 19, 415 (1958).
    [Crossref]
  13. The improvements are, of course, also applicable to other engines to which interferometric control is now being applied.
  14. These patterns will be simply described as hfs patterns in the remainder of this paper.
  15. aJ. Strong, J. Opt. Soc. Am. 50, 1148 (1960); bR. W. Ditchburn, Proc. Roy. Irish Acad. A39, 58 (1930); J. Strong, J. Opt. Soc. Am. 41, 3 (1951); H. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951); E. Hulthén and U. Uhler, Ark. Fysik 3, 393 (1952); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955); A. Keith Pierce, ibid. 47, 6 (1957); G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, ibid., 47, 15 (1957); D. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, ibid., 47, 631 (1957); G. R. Harrison, N. Sturgis, S. P. Davis, and Y. Yamada, ibid. 49, 205 (1959).
    [Crossref]
  16. The possibility of testing a grating interferometrically by simply placing it into one of the arms of a Michelson Twyman-Green interferometer has been previously described by G. W. Stroke [(J. Opt. Soc. Am. 45, 30 (1955); Rev. opt. 39, 291 (1960)]. The fringe pattern displays the diffracted wave-front topography and is formed as a result of interference between the diffracted wave front and a plane wave front reflected from a reference mirror. The wave-front interferograms have been found in practice to provide the most revealing and most useful information about the quality of a grating of all known grating-testing methods. Not only do they permit the immediate assessment of the ruling quality of a grating by simple inspection of the fringe deviations from straightness, but they also permit accurate predictions of the spectral quality of the grating or replica, with the help of known relations between the wave fronts and the diffraction patterns that they form.5,7
    [Crossref]
  17. Comparison of spectrometers and spectrographs can be made in terms of several parameters. Those which characterize the capability to separately detect and “resolve” (in space or time) photons emitted by the source and having slightly different energies are particularly significant. The two parameters generally used to describe the resolving and detection capability of a spectrometer are (1) the “resolving power” or “resolution” and (2) the “spectral efficiency” or “luminosity.” It should be clear that these two parameters are not independent. This has been emphasized in particular by Jacquinot24 in a paper dealing with the luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons. There does not yet appear to be a general agreement as to the exact terms by which these parameters can be best described: the quantity “radiant power reaching the detector in a unit of resolved spectral bandwidth” has been used with some advantage by R. Greenler,25 and the quantity “étendue” has appeared in French publications.19 But if “resolving power” and “luminosity” are properly defined, a consistent and simple comparison of spectroscopic instruments has been found to be possible.21,24 We find that the term “resolving power” is best suited for the description of a theoretical capability of spectral resolution, that is the capability of separately detecting photons of slightly different energies; one can speak with advantage of the “theoretical” resolving power of either a perfect instrument, or of an instrument of which the limitations are calculable, in order to emphasize that the resolving “power” applies to the instrument alone separately from the limitations set by the source (Doppler-broadened lines, for example) or by the detector (granularity and other receptor noise). The “limitations” in resolving power can be of a physical optics character, or more generally of an electromagnetic character, (such as the limitations resulting from the use of finite apertures in grating spectrometers, or the use of a finite number of beams in a Fabry-Perot etalon), or they can result from imperfections in the optical elements (grating defects, or (FP) etalon flatness and coating imperfections) of which the effects can be predicted by calculation,7,19,20 In that sense the use of source slits or source holes (focal diaphragms) of finite aperture, in both grating and FP spectrometers, can be considered as a “limitation” of which the importance can be simply established in any given case.18,21 In both grating and FP spectrometers, or spectrographs, the use of a finite source aperture results in the incidence of wave fronts, not only from a single direction (which is generally desired), but within a finite angular domain determined by the size of the source hole or slit as seen from the collimator. The term “resolving power” is generally understood to describe the quantity RP=λ/Δλ=σ/δδ, where Δλ or δσ refers to the difference in wavelength (or wave number) of the photons of neighboring energy (hν), or wavelength λ=c/ν, or wave number σ=1/λ (with λ in centimeters), which can be detected as “resolved in the limit” (c=velocity of light and h=Planck’s constant). It should be clear that the “limiting” resolution and “theoretical resolving power” are arbitrary quantities, even though they provide a good order of magnitude in usual spectroscopic applications: effective resolving powers considerably in excess of those predicted by classical theory can be obtained.26,7,5bFor the purpose of this paper we shall use the term “resolving power” as described by the equation RP=λ/Δλ=σ/δσ in agreement with general use. For the description of the other important detection quantity, we shall use the term “luminosity” as defined by Jacquinot21: “The luminosity of a spectrometer is defined as the ratio, L=ϕ/B, of the flux falling on the detector to the luminance of the source.” Here L=SΩτ, where S is the surface area of the plates (for an FP etalon) or the area of the projection of the grating surface on the diffracted wave front, Ω the solid angle limited by the focal diaphragm, and τ an appropriately defined transmission factor. As shown by Chabbal,19 the transmission factor of an FP spectrometer is itself a product of three factors, the reflectance and transmittance of the coatings, the effect of surface imperfections, and the effect of a finite source aperture. For a grating, the transmittance is simply given according to usual photometric definitions: in general, it can be considered to be equal to the ratio of the number of photons of a given energy attaining the detector in a given order of the grating, per unit time, to the total number of photons of that energy incident on the grating, per unit time, after collimation by a perfectly reflecting collimator (the reflectance of the collimator can be separately taken into account). Throughout this paper, we shall use the term “luminosity” according to the above definition, except where another description of the corresponding parameter appears to be more appropriate. (This meaning of “luminosity” is, of course, quite different from that of the same term in photometry.) The quantity “étendue” U is defined by U=SΩ, and is related to the quantity “luminosity” L by L=τU). We shall also use the expression “more or less luminous” to describe the fact that an optical element or spectrometer has the quantity “luminosity” to a greater or a smaller extent.
  18. P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) 6, 1 (1948).
  19. R. Chabbal, Rev. opt. 37, 49, 336, 501 (1958).
  20. R. Chabbal, thesis, The Sorbonne, Paris, 1957.
  21. P. Jacquinot, Repts. Progr. in Phys. Vol.  XXIII267 (1960).
    [Crossref]
  22. Colloquium on “Les progrès récents en spectroscopie interférentielle,” J. phys. radium 19, 185 (1958).
  23. G. R. Harrison, R. C. Lord, and J. R. Loofbourow, Practical Spectroscopy, (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948); R. A. Sawyer, Experimental Spectroscopy, (Prentice-Hall Inc.Englewood Cliffs, New Jersey, 1944).
  24. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [Crossref]
  25. R. Greenler, J. Opt. Soc. Am. 45, 788 (1955).
    [Crossref]
  26. aG. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955); J. Opt. Soc. Am. 46, 72 (1956); bJ. Arsac, Optica Acta (London) 6, 103 (1959); cA. I. Kartashev, Optika i Spektroskopiya 9, 204, 394 (1960).
  27. The author is grateful to Professor P. Jacquinot for numerous lengthy and invaluable discussions and clarifications dealing in particular with the field of interference spectroscopy: he also wishes to express his appreciation for Professor Jacquinot’s stimulating and constructive encouragements and suggestions, over the course of years, which have in no small measure contributed to the success in the ruling of the high-resolution gratings described in the present work. The author also wishes to stress that the conclusions presented here may be traced to the new availability of these 10×5-in. gratings and that they should not be taken as implying any conclusions by Professor Jacquinot and his associates except those that they have published themselves. The author is also grateful to Professor R. Chabbal for very enlightening discussions dealing with the field of interference spectroscopy and FP spectrometers, as well as for private communications clarifying in particular his own important contributions to this field.
  28. The author is grateful to Professor E. F. Barker and to Professor H. M. Randallfor a private communication describing the method of production and the quality of the gratings ruled for the infrared at the University of Michigan[see also H. M. Randall, J. Appl. Phys. 10, 768 (1939)]. The use of gratings in high-resolution infrared spectrometers has also been described by R. C. Lord and T. K. McCubbin, J. Opt. Soc. Am. 45, 441 (1955).
    [Crossref]
  29. R. Chabbal, J. phys. radium 19, 295 (1958).
    [Crossref]
  30. It is clear, of course, that for studies in the resolving power domains of 3 to 4×106 in the visible and ultraviolet which are not yet accessible to single gratings, and where a loss of light resulting from the association of an FP etalon with a low-resolution monochromator is acceptable, the etalon is the high-resolution device to be used. More generally, one can use an FP etalon in conjunction with an existing grating, or prism, low-resolution monochromator in order to increase its resolution (even though this may result in a more complicated scanning arrangement than that which could be used to obtain the same high resolution with a large grating monochromator). For ultimate resolutions, Conne’s spherical FP etalon31 does in fact yield considerably more flux per bandwidth than a plane FP etalon with otherwise comparable limitations in free spectral range.
  31. P. Connes, Rev. opt. 35, 37 (1956); J. phys. radium 19, 262 (1958).
  32. It is the very large free-spectral-range characteristic of the small groove depth in gratings and echelles which is one of the great assets of diffraction gratings in high-resolution spectroscopic studies.6b It is indeed the independence of free spectral range from both resolving power and dispersion which is at the heart of the advantages of diffraction gratings over FP etalons in high-resolution studies that fall within their domain. Unlike that in gratings, the free spectral range of an FP etalon varies inversely with its resolution and falls to extremely small values even at resolving powers which are very moderate in terms of its capabilities.21 Even a 1-cm FP etalon, of RP=106 at 5000 A (with a finesse of 25), has a free spectral range of only 12 cm-1, which is insufficient to study the hfs of either the blue or green mercury lines without a premonochromator. On the other hand, the same resolving power of 106 can be obtained faith a 300-groove/mm, 10-in. grating or a 10-groove/mm 10-in. echelle in autocollimation at 76°, with the very large free spectral ranges of 3×103 and 100 cm−1, respectively. One recalls that the free spectral range is the wave number range that can be obtained without overlapping. It is given by Δσ=1/(2t), where t is both the thickness of the FP etalon and the apparent groove depth of the grating, of which the spacing constant is a. (Thus t=a sini for a grating in autocollimation at an angle i.) For the FP, the resolving power RP=σ/δσ, where δσ=Δσ/N; the wave number σ=1/λ, with λ in centimeters; and N is the number of effective beams (N=25 for plates flat to λ/50, and in general N=m/2 for plates flat to λ/m). For a grating of ruled width W, the resolving power is RP=2W sini/λ, and the dispersion di′/dλ=2 tani′/λ; both are seen to be independent of the spacing constant a.
  33. G. W. Stroke and H. H. Stroke, Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (October, 1958), p. 54.
  34. The author is grateful to Dr. R. K. Brehm and the Jarrell-Ash Company for making this recording.
  35. H. M. Crosswhite and W. G. Fastie, J. Opt. Soc. Am. 46, 110, (1956); W. G. Fastie, ibid. 42, 641, 647, (1952).
    [Crossref]
  36. It might be observed that we have never experienced any difficulties in the stability of the 40-ft spectrographs mounted in the “35-ft room” at the spectroscopy laboratory at M.I.T., which is controlled to a few tenths of a degree F. For unusually long exposures of the order of hours, it may sometimes be necessary to correct for the change in wavelength which results from atmospheric-pressure variations and which affects all wavelengths by practically the same amount. All spectral lines can be maintained in position simultaneously (as long as the cosines of their angles are approximately the same) by appropriately rotating a thin quartz plate mounted next to the entrance slit on the collimator side.
  37. In this paper we do not distinguish between gratings or echelles except when necessary.
  38. aPrism double-pass arrangements had been previously used by A. Couderc, J. phys. radium p. 37S (1937) (the author is indebted to Professor P. Jacquinot for mentioning in a private communication this early prism double-pass arrangement on which he had worked); bA. Walsh, J. Opt. Soc. Am. 42, 94, (1952).
  39. aGrating double-pass arrangements:F. A. Jenkins and L. W. Alvarez, 42, 699 (1952); bW. G. Fastie and W. M. Sinton, ibid. 483A (1952); cD. H. Rank and T. A. Wiggins, ibid. 983 (1952); dJ. N. Shearer, T. A. Wiggins, A. H. Guenther, and D. H. Rank, J. Chem. Phys. 25, 724 (1956); eD. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, J. Opt. Soc. Am. 47, 631 (1957).
  40. Grating-immersion arrangements to increase the dispersion and resolving power have also been described by E. Hulthén and H. Neuhaus, Ark. Fysik 8, 343 (1954); O. Björklund, ibid. 13, 185 (1958).
  41. Between the first diffraction minima on both sides of the center.
  42. P. Connes, Optica Acta (Paris) 4, 136 (1957); J. phys. radium 19, 262 (1958); thesis, The Sorbonne, Paris, 1958.
    [Crossref]
  43. P. Girard, Optica Acta (Paris) 7, 81 (1960).
    [Crossref]
  44. M. J. E. Golay, J. Opt. Soc. Am. 41, 468 (1951).
    [Crossref] [PubMed]
  45. This corresponds to only 1.5×10−5 in the first order of a 15 000 lines/in. grating in the usual description of Rowland-ghost intensities.
  46. One diffraction unit (u) corresponds to the distance from the center of the first diffraction minimum for a rectangular aperture A=W cosi′. The first diffraction minimum is at u=(λ/A)f, where f is the focal length of the camera mirror in the spectrograph. For a 10-in. grating used at 64° the first minimum is at about 1 sec of arc from the center in the visible. For Hg 198 spectrograms of the satellite distributions in three wavelengths produced by the first-generation 10-in. grating 97, see references 7 and 6b.
  47. The reason why good high-resolution gratings might in a sense be considered as more perfect optical elements in the visible than the best of the available FP etalons may be that with a finesse of 25 (which multiplies the etalon flatness deviations by factors up to 25) an etalon good to 1/50 wavelength over its surface results in path-difference variations, between extreme beams, of up to λ/2.
  48. In French: lumière diffusée ou parasite. For an interesting theoretical study of scattered light see A. Maréchal, Optica Acta (Paris) 5, 70 (1958).
    [Crossref]
  49. The complete theory of the effects of grating errors and blank defects on the spectral image perfection, presented here in a form appropriate to the present paper, was developed by G. W. Stroke, Rev. opt. 39, 291–398 (1960), and is given there together with a historical background, review of past work pertinent to that study and a complete list of references. A detailed description of the theory and of the method of calculation of the distribution of light in spectral diffraction patterns by Fourier transformation of the phase distribution in the diffracted wave fronts, as it appears in a readily usable graphical form in the wave-front interferograms, is also fully given in that work. Some of the early qualitative aspects of that work were also incorporated into a paper by G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960) with particular reference to the attainment of high resolution with diffraction gratings and echelles.
    [Crossref]
  50. A. Maréchal, Imagerie géométrique, aberrations (Revue d’Optique, Paris, 1952), p. 215.
  51. H. H. Hopkins, Wave Theory of Aberrations, (Oxford University Press, New York, 1950), pp. 14–16.
  52. When diffracted wave fronts are curved, the curvature is generally not the same along the grating width and along the grating height: some astigmatism may then affect the height of the spectral lines, even though their width may be perfect in an ideal case.
  53. E. Mascart, Traité d’optique (Gauthier-Villars, Paris, 1889), Vol. I., p. 373; H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903); R. W. Wood, ibid. 48, 497 (1924); H. G. Gale, Astro. phys. J. 86, 437 (1937); G. R. Harrison, J. Opt. Soc. Am. 39, 413 (1949) gives many references and an excellent history of the grating ruling development; J. Strong, ibid. 41, 3 (1951); E. Ingelstam and E. Djurle, Ark. Fysik. 4, 423 (1952); Ark. Fysik. 6, 463 (1953); J. Opt. Soc. Am. 43, 572 (1953); G. W. Stroke, ibid. 42, 879A (1952); E. Djurle, Ark. Fysik. 8, 383 (1954); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955).
    [Crossref]
  54. It is known, of course, that the first secondary maximum corresponding to the rectangular aperture presented by a grating has an intensity of the order of 4% and that the peak appears at a distance of about two diffraction units from the line center. These are precisely the orders of magnitude of the spurious satellites of a few percent intensity with which we are dealing here.
  55. Computed diffraction patterns such as the one in Fig. 7 (which corresponds to an infinitely narrow perfectly monochromatic slit) have permitted correction of “errors of coincidence” resulting from systematic, center-of-gravity displacements of spectral lines. They should prove invaluable in spectral-line-shape studies, since the intensity distribution recorded in the spectrometer is simply equal to the convolution of the “true” intensity distribution in the spectrum (which is sought) with these (computed) diffraction-pattern intensity distributions (when the slit width has been taken into account, which presents no problem).7
  56. More classical ruling engine ways, such as the “doublevee” ways already used by Rowland, may also cause rotation problems, in particular as a result of lubrication irregularities.
  57. G. W. Stroke, J. Opt. Soc. Am. 51, 1340 (1961), following article.
    [Crossref]
  58. Ever since the engine was first put under continuous control we have been successfully using the equation Δm=3.31ΔPΔL for the amount of pressure correction. Here Δm=shift in 1/100 fringe, ΔP=pressure change in inches of mercury and ΔL=interferometer mirror separation in millimeters. The hybrid units used in this equation have resulted in a misprint in one of the early papers originating from the M.I.T. ruling project.59 We are grateful to H. W. Babcock for noting that the misprint had been carried along into subsequent publications, as well as for other private communications concerning his work on the control of grating ruling. A detailed discussion of the pressure correction for interferometric servomechanisms is given by G. W. Stroke, in Optics in Metrology, edited by Pol. Mollet (Pergamon Press, New York, 1960), p. 101.
  59. G. R. Harrison and J. E. Archer, J. Opt. Soc. Am. 41, 495 (1951).
    [Crossref]
  60. The correction of errors of this type (of which the possibility was first indicated by G. W. Stroke in 1957)12 resulted in the successful ruling of the first-generation 10-inch gratings. They were pictorially summarized for enclosure (as Fig. 7) in the paper by Harrison et al.,3 reviewing the work up to that stage.
  61. E. R. Peck, J. Opt. Soc. Am. 38, 1015 (1948); J. Opt. Soc. Am. 45, 931 (1955).
    [Crossref] [PubMed]
  62. aM. V. R. K. Murty, J. Opt. Soc. Am. 50, 7 (1960); bJ. Opt. Soc. Am. 50, 83 (1960).
  63. P. Connes (verbal communication, 1960).
  64. aA. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, Illinois, 1927), p. 39; bP. Fellgett, thesis, Cambridge University, Cambridge, England, 1951); J. phys. radium 19, 187, 237, (1958); cP. Jacquinot, XVIIe Congrès du G.A.M.S., Paris, (1954); J. phys. radium 19, 223 (1958); Optica Acta (London) 7, 291 (1960); dJ. Connes, thesis, The Sorbonne, Paris (1960); Rev. opt. 40, 45, 1961.
  65. It uses a tube of piezoelectric ceramic (lead zirconate titanate) to serve as an expander for the plastic shoe with respect to the diamond carriage [D. D. Scofield, M. S. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1961 (unpublished)].
  66. aA. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958); bA. Javan in Quantum Electronics, edited by C. H. Townes (Columbia University Press, New York, 1960), p. 564; cA. Javan, W. R. Bennett, and D. R. Herriott, Phys. Rev. Letters 6, 106 (1961).
  67. A period of 12 to 18 hr is usually required to raise the engine and oil to the operating temperature.
  68. The stirrers need to be carefully isolated from the floor and the engine to avoid vibrations in the control interferometers and the ruling diamond; 12-in.-thick neoprene pads on which the stirrers are loosely placed have been found to be sufficiently good vibration-isolators in practice. The operation of a 10 000-amp, 170-v generator for a Bitter 100 000-Gauss Zeeman-effect magnet,69 placed within some 50 ft from the engine, has occasionally caused vibrations in the interferometers and harmful resonance in the ruling diamond which both affect the groove quality and may tend to result in undesirable scattered light in spectral regions far removed from the line centers.
  69. F. Bitter and G. R. Harrison, Phys. Rev. 57, 15 (1940).
    [Crossref]
  70. The design and numerous very significant spectroscopic advantages of echelle-gratings were first described by G. R. Harrison in J. Opt. Soc. Am. 39, 522 (1949), and subsequently expanded in many papers.
    [Crossref]
  71. G. R. Harrison (private communication, 1959).
  72. R. P. Madden and J. Strong, Appendix P in Classical Optics, by J. Strong (Freeman & Company, San Francisco, California, 1958), p. 597.
  73. aJ. H. Rohrbaugh and R. D. Hatcher, J. Opt. Soc. Am. 48, 704 (1958); bJ. H. Rohrbaugh, C. Pine, W. G. Zoellner, and R. D. Hatcher, J. Opt. Soc. Am. 48, 710 (1958).
  74. A. Maréchal and G. W. Stroke, Compt. rend. 249, 2042 (1959).
  75. a Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907); bU. Fano, Ann. Physik 32, 393 (1938); cT. B. A. Senior, Can. J. Phys. 37, 787 (1959).
  76. This work was also presented as a part of the invited paper on “The two aspects of the diffraction of light by diffraction gratings,” given by G. W. Stroke at the October, 1960, meeting of the Optical Society of America. It is extensively described in Rev. opt.39, 291–398 (1960), and will be incorporated in a further paper in this series.
  77. W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
    [Crossref]
  78. R. F. Millar, Can. J. Phys. 39, 81, 104 (1961).
    [Crossref]
  79. V. Twersky, Proc. I. R. E. Trans. PGAP,  AP-4, p. 330 (1956).
  80. aR. W. Wood, Phil. Mag. 4, 396 (1902); Phil. Mag. 23, 310 (1912); Phys. Rev. 48, 928 (1935); b Rayleigh, Phil. Mag. 14, 60 (1907); cL. R. Ingersoll, Astrophys. J. 51, 129 (1920); dC. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).
  81. Both companies have, of course, been producing replicas of their own gratings.
  82. In one instance, over 100 good replicas of a concave grating have already been obtained by George Sintiris at the Jarrell-Ash Co.
  83. David Richardson (private communication); George Sintiris (private communication); the details of the successful replication processes are particular to the methods developed in different laboratories, but it is well known that a replica grating consists of a thin layer of an aluminized plastic resin, such as Epoxy or Laminac, molecularly adherent to a perfectly flat (or perfectly spherical) optical glass blank (for plane or concave gratings respectively). The evaporated aluminum layer with which the plastic is usually covered is similar to the layer used in original rulings. The clean separation of the replicas from the master ruling without deformation appears to be at the root of a successful replication.

1961 (2)

1960 (7)

P. Girard, Optica Acta (Paris) 7, 81 (1960).
[Crossref]

aM. V. R. K. Murty, J. Opt. Soc. Am. 50, 7 (1960); bJ. Opt. Soc. Am. 50, 83 (1960).

The complete theory of the effects of grating errors and blank defects on the spectral image perfection, presented here in a form appropriate to the present paper, was developed by G. W. Stroke, Rev. opt. 39, 291–398 (1960), and is given there together with a historical background, review of past work pertinent to that study and a complete list of references. A detailed description of the theory and of the method of calculation of the distribution of light in spectral diffraction patterns by Fourier transformation of the phase distribution in the diffracted wave fronts, as it appears in a readily usable graphical form in the wave-front interferograms, is also fully given in that work. Some of the early qualitative aspects of that work were also incorporated into a paper by G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960) with particular reference to the attainment of high resolution with diffraction gratings and echelles.
[Crossref]

aG. W. Stroke, Rev. opt.,  39, 291 (1960); bG. W. Stroke, thesis, The Sorbonne, Paris, 1960.

aR. J. Hull and H. H. Stroke, Bull. Am. Phys. Soc. 5, 412 (1960); bR. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).

aJ. Strong, J. Opt. Soc. Am. 50, 1148 (1960); bR. W. Ditchburn, Proc. Roy. Irish Acad. A39, 58 (1930); J. Strong, J. Opt. Soc. Am. 41, 3 (1951); H. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951); E. Hulthén and U. Uhler, Ark. Fysik 3, 393 (1952); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955); A. Keith Pierce, ibid. 47, 6 (1957); G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, ibid., 47, 15 (1957); D. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, ibid., 47, 631 (1957); G. R. Harrison, N. Sturgis, S. P. Davis, and Y. Yamada, ibid. 49, 205 (1959).
[Crossref]

P. Jacquinot, Repts. Progr. in Phys. Vol.  XXIII267 (1960).
[Crossref]

1959 (2)

1958 (8)

aJ. H. Rohrbaugh and R. D. Hatcher, J. Opt. Soc. Am. 48, 704 (1958); bJ. H. Rohrbaugh, C. Pine, W. G. Zoellner, and R. D. Hatcher, J. Opt. Soc. Am. 48, 710 (1958).

aA. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958); bA. Javan in Quantum Electronics, edited by C. H. Townes (Columbia University Press, New York, 1960), p. 564; cA. Javan, W. R. Bennett, and D. R. Herriott, Phys. Rev. Letters 6, 106 (1961).

G. W. Stroke and H. H. Stroke, Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (October, 1958), p. 54.

In French: lumière diffusée ou parasite. For an interesting theoretical study of scattered light see A. Maréchal, Optica Acta (Paris) 5, 70 (1958).
[Crossref]

Colloquium on “Les progrès récents en spectroscopie interférentielle,” J. phys. radium 19, 185 (1958).

aG. R. Harrison, Proc. Am. Phil. Soc. 102, 438 (1958); bG. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960).

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

R. Chabbal, J. phys. radium 19, 295 (1958).
[Crossref]

1957 (3)

1956 (4)

H. M. Crosswhite and W. G. Fastie, J. Opt. Soc. Am. 46, 110, (1956); W. G. Fastie, ibid. 42, 641, 647, (1952).
[Crossref]

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[Crossref]

P. Connes, Rev. opt. 35, 37 (1956); J. phys. radium 19, 262 (1958).

V. Twersky, Proc. I. R. E. Trans. PGAP,  AP-4, p. 330 (1956).

1955 (5)

1954 (2)

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

Grating-immersion arrangements to increase the dispersion and resolving power have also been described by E. Hulthén and H. Neuhaus, Ark. Fysik 8, 343 (1954); O. Björklund, ibid. 13, 185 (1958).

1951 (2)

1949 (1)

1948 (2)

E. R. Peck, J. Opt. Soc. Am. 38, 1015 (1948); J. Opt. Soc. Am. 45, 931 (1955).
[Crossref] [PubMed]

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) 6, 1 (1948).

1940 (1)

F. Bitter and G. R. Harrison, Phys. Rev. 57, 15 (1940).
[Crossref]

1907 (1)

a Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907); bU. Fano, Ann. Physik 32, 393 (1938); cT. B. A. Senior, Can. J. Phys. 37, 787 (1959).

1902 (1)

aR. W. Wood, Phil. Mag. 4, 396 (1902); Phil. Mag. 23, 310 (1912); Phys. Rev. 48, 928 (1935); b Rayleigh, Phil. Mag. 14, 60 (1907); cL. R. Ingersoll, Astrophys. J. 51, 129 (1920); dC. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).

Alvarez, L. W.

aGrating double-pass arrangements:F. A. Jenkins and L. W. Alvarez, 42, 699 (1952); bW. G. Fastie and W. M. Sinton, ibid. 483A (1952); cD. H. Rank and T. A. Wiggins, ibid. 983 (1952); dJ. N. Shearer, T. A. Wiggins, A. H. Guenther, and D. H. Rank, J. Chem. Phys. 25, 724 (1956); eD. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, J. Opt. Soc. Am. 47, 631 (1957).

Archer, J. E.

Babcock, H. W.

Ever since the engine was first put under continuous control we have been successfully using the equation Δm=3.31ΔPΔL for the amount of pressure correction. Here Δm=shift in 1/100 fringe, ΔP=pressure change in inches of mercury and ΔL=interferometer mirror separation in millimeters. The hybrid units used in this equation have resulted in a misprint in one of the early papers originating from the M.I.T. ruling project.59 We are grateful to H. W. Babcock for noting that the misprint had been carried along into subsequent publications, as well as for other private communications concerning his work on the control of grating ruling. A detailed discussion of the pressure correction for interferometric servomechanisms is given by G. W. Stroke, in Optics in Metrology, edited by Pol. Mollet (Pergamon Press, New York, 1960), p. 101.

Baker, S. C.

Barker, E. F.

The author is grateful to Professor E. F. Barker and to Professor H. M. Randallfor a private communication describing the method of production and the quality of the gratings ruled for the infrared at the University of Michigan[see also H. M. Randall, J. Appl. Phys. 10, 768 (1939)]. The use of gratings in high-resolution infrared spectrometers has also been described by R. C. Lord and T. K. McCubbin, J. Opt. Soc. Am. 45, 441 (1955).
[Crossref]

Bitter, F.

F. Bitter and G. R. Harrison, Phys. Rev. 57, 15 (1940).
[Crossref]

Chabbal, R.

R. Chabbal, J. phys. radium 19, 295 (1958).
[Crossref]

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

R. Chabbal, thesis, The Sorbonne, Paris, 1957.

The author is grateful to Professor P. Jacquinot for numerous lengthy and invaluable discussions and clarifications dealing in particular with the field of interference spectroscopy: he also wishes to express his appreciation for Professor Jacquinot’s stimulating and constructive encouragements and suggestions, over the course of years, which have in no small measure contributed to the success in the ruling of the high-resolution gratings described in the present work. The author also wishes to stress that the conclusions presented here may be traced to the new availability of these 10×5-in. gratings and that they should not be taken as implying any conclusions by Professor Jacquinot and his associates except those that they have published themselves. The author is also grateful to Professor R. Chabbal for very enlightening discussions dealing with the field of interference spectroscopy and FP spectrometers, as well as for private communications clarifying in particular his own important contributions to this field.

Connes, P.

P. Connes, Optica Acta (Paris) 4, 136 (1957); J. phys. radium 19, 262 (1958); thesis, The Sorbonne, Paris, 1958.
[Crossref]

P. Connes, Rev. opt. 35, 37 (1956); J. phys. radium 19, 262 (1958).

P. Connes (verbal communication, 1960).

Couderc, A.

aPrism double-pass arrangements had been previously used by A. Couderc, J. phys. radium p. 37S (1937) (the author is indebted to Professor P. Jacquinot for mentioning in a private communication this early prism double-pass arrangement on which he had worked); bA. Walsh, J. Opt. Soc. Am. 42, 94, (1952).

Crosswhite, H. M.

Davis, S. P.

Dufour, Ch.

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) 6, 1 (1948).

Dupeyrat, R.

R. Dupeyrat (private communication, 1960).

Evans, J. W.

aJ. W. Evans (private communication); bA. Keith Pierce, J. Opt. Soc. Am. 47, 6 (1957); cH. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951).

Fastie, W. G.

Fehrenbach, Ch.

Ch. Fehrenbach (private communication).

Girard, P.

P. Girard, Optica Acta (Paris) 7, 81 (1960).
[Crossref]

Golay, M. J. E.

Greenler, R.

Harrison, G. R.

Hatcher, R. D.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations, (Oxford University Press, New York, 1950), pp. 14–16.

Hull, R. J.

aR. J. Hull and H. H. Stroke, Bull. Am. Phys. Soc. 5, 412 (1960); bR. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).

Hulthén, E.

Grating-immersion arrangements to increase the dispersion and resolving power have also been described by E. Hulthén and H. Neuhaus, Ark. Fysik 8, 343 (1954); O. Björklund, ibid. 13, 185 (1958).

Jacquinot, P.

P. Jacquinot, Repts. Progr. in Phys. Vol.  XXIII267 (1960).
[Crossref]

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

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) 6, 1 (1948).

The author is grateful to Professor P. Jacquinot for numerous lengthy and invaluable discussions and clarifications dealing in particular with the field of interference spectroscopy: he also wishes to express his appreciation for Professor Jacquinot’s stimulating and constructive encouragements and suggestions, over the course of years, which have in no small measure contributed to the success in the ruling of the high-resolution gratings described in the present work. The author also wishes to stress that the conclusions presented here may be traced to the new availability of these 10×5-in. gratings and that they should not be taken as implying any conclusions by Professor Jacquinot and his associates except those that they have published themselves. The author is also grateful to Professor R. Chabbal for very enlightening discussions dealing with the field of interference spectroscopy and FP spectrometers, as well as for private communications clarifying in particular his own important contributions to this field.

aPrism double-pass arrangements had been previously used by A. Couderc, J. phys. radium p. 37S (1937) (the author is indebted to Professor P. Jacquinot for mentioning in a private communication this early prism double-pass arrangement on which he had worked); bA. Walsh, J. Opt. Soc. Am. 42, 94, (1952).

Jenkins, F. A.

aGrating double-pass arrangements:F. A. Jenkins and L. W. Alvarez, 42, 699 (1952); bW. G. Fastie and W. M. Sinton, ibid. 483A (1952); cD. H. Rank and T. A. Wiggins, ibid. 983 (1952); dJ. N. Shearer, T. A. Wiggins, A. H. Guenther, and D. H. Rank, J. Chem. Phys. 25, 724 (1956); eD. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, J. Opt. Soc. Am. 47, 631 (1957).

Loofbourow, J. R.

G. R. Harrison, R. C. Lord, and J. R. Loofbourow, Practical Spectroscopy, (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948); R. A. Sawyer, Experimental Spectroscopy, (Prentice-Hall Inc.Englewood Cliffs, New Jersey, 1944).

Lord, R. C.

G. R. Harrison, R. C. Lord, and J. R. Loofbourow, Practical Spectroscopy, (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948); R. A. Sawyer, Experimental Spectroscopy, (Prentice-Hall Inc.Englewood Cliffs, New Jersey, 1944).

Madden, R. P.

R. P. Madden and J. Strong, Appendix P in Classical Optics, by J. Strong (Freeman & Company, San Francisco, California, 1958), p. 597.

Maréchal, A.

A. Maréchal and G. W. Stroke, Compt. rend. 249, 2042 (1959).

In French: lumière diffusée ou parasite. For an interesting theoretical study of scattered light see A. Maréchal, Optica Acta (Paris) 5, 70 (1958).
[Crossref]

A. Maréchal, Imagerie géométrique, aberrations (Revue d’Optique, Paris, 1952), p. 215.

Mascart, E.

E. Mascart, Traité d’optique (Gauthier-Villars, Paris, 1889), Vol. I., p. 373; H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903); R. W. Wood, ibid. 48, 497 (1924); H. G. Gale, Astro. phys. J. 86, 437 (1937); G. R. Harrison, J. Opt. Soc. Am. 39, 413 (1949) gives many references and an excellent history of the grating ruling development; J. Strong, ibid. 41, 3 (1951); E. Ingelstam and E. Djurle, Ark. Fysik. 4, 423 (1952); Ark. Fysik. 6, 463 (1953); J. Opt. Soc. Am. 43, 572 (1953); G. W. Stroke, ibid. 42, 879A (1952); E. Djurle, Ark. Fysik. 8, 383 (1954); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955).
[Crossref]

Meecham, W. C.

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[Crossref]

Michelson, A. A.

aA. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, Illinois, 1927), p. 39; bP. Fellgett, thesis, Cambridge University, Cambridge, England, 1951); J. phys. radium 19, 187, 237, (1958); cP. Jacquinot, XVIIe Congrès du G.A.M.S., Paris, (1954); J. phys. radium 19, 223 (1958); Optica Acta (London) 7, 291 (1960); dJ. Connes, thesis, The Sorbonne, Paris (1960); Rev. opt. 40, 45, 1961.

Millar, R. F.

R. F. Millar, Can. J. Phys. 39, 81, 104 (1961).
[Crossref]

Murty, M. V. R. K.

Neuhaus, H.

Grating-immersion arrangements to increase the dispersion and resolving power have also been described by E. Hulthén and H. Neuhaus, Ark. Fysik 8, 343 (1954); O. Björklund, ibid. 13, 185 (1958).

Peck, E. R.

Randall, H. M.

The author is grateful to Professor E. F. Barker and to Professor H. M. Randallfor a private communication describing the method of production and the quality of the gratings ruled for the infrared at the University of Michigan[see also H. M. Randall, J. Appl. Phys. 10, 768 (1939)]. The use of gratings in high-resolution infrared spectrometers has also been described by R. C. Lord and T. K. McCubbin, J. Opt. Soc. Am. 45, 441 (1955).
[Crossref]

Rayleigh,

a Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907); bU. Fano, Ann. Physik 32, 393 (1938); cT. B. A. Senior, Can. J. Phys. 37, 787 (1959).

Richardson, David

David Richardson (private communication); George Sintiris (private communication); the details of the successful replication processes are particular to the methods developed in different laboratories, but it is well known that a replica grating consists of a thin layer of an aluminized plastic resin, such as Epoxy or Laminac, molecularly adherent to a perfectly flat (or perfectly spherical) optical glass blank (for plane or concave gratings respectively). The evaporated aluminum layer with which the plastic is usually covered is similar to the layer used in original rulings. The clean separation of the replicas from the master ruling without deformation appears to be at the root of a successful replication.

Rohrbaugh, J. H.

Schawlow, A. L.

aA. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958); bA. Javan in Quantum Electronics, edited by C. H. Townes (Columbia University Press, New York, 1960), p. 564; cA. Javan, W. R. Bennett, and D. R. Herriott, Phys. Rev. Letters 6, 106 (1961).

Scofield, D. D.

It uses a tube of piezoelectric ceramic (lead zirconate titanate) to serve as an expander for the plastic shoe with respect to the diamond carriage [D. D. Scofield, M. S. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1961 (unpublished)].

Stroke, G. W.

G. W. Stroke, J. Opt. Soc. Am. 51, 1340 (1961), following article.
[Crossref]

The complete theory of the effects of grating errors and blank defects on the spectral image perfection, presented here in a form appropriate to the present paper, was developed by G. W. Stroke, Rev. opt. 39, 291–398 (1960), and is given there together with a historical background, review of past work pertinent to that study and a complete list of references. A detailed description of the theory and of the method of calculation of the distribution of light in spectral diffraction patterns by Fourier transformation of the phase distribution in the diffracted wave fronts, as it appears in a readily usable graphical form in the wave-front interferograms, is also fully given in that work. Some of the early qualitative aspects of that work were also incorporated into a paper by G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960) with particular reference to the attainment of high resolution with diffraction gratings and echelles.
[Crossref]

aG. W. Stroke, Rev. opt.,  39, 291 (1960); bG. W. Stroke, thesis, The Sorbonne, Paris, 1960.

A. Maréchal and G. W. Stroke, Compt. rend. 249, 2042 (1959).

G. W. Stroke and H. H. Stroke, Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (October, 1958), p. 54.

G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, J. Opt. Soc. Am. 47, 15 (1957).
[Crossref]

G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957); J. Opt. Soc. Am. 48, 276 (1958); J. phys. radium 19, 415 (1958).
[Crossref]

The possibility of testing a grating interferometrically by simply placing it into one of the arms of a Michelson Twyman-Green interferometer has been previously described by G. W. Stroke [(J. Opt. Soc. Am. 45, 30 (1955); Rev. opt. 39, 291 (1960)]. The fringe pattern displays the diffracted wave-front topography and is formed as a result of interference between the diffracted wave front and a plane wave front reflected from a reference mirror. The wave-front interferograms have been found in practice to provide the most revealing and most useful information about the quality of a grating of all known grating-testing methods. Not only do they permit the immediate assessment of the ruling quality of a grating by simple inspection of the fringe deviations from straightness, but they also permit accurate predictions of the spectral quality of the grating or replica, with the help of known relations between the wave fronts and the diffraction patterns that they form.5,7
[Crossref]

G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
[Crossref]

G. W. Stroke, J. Opt. Soc. Am. 45, 30 (1955).
[Crossref]

aG. W. Stroke, Interferometry Symposium, National Physical Laboratory, Teddington, June 10, 1959. (Symposium No. 11, Interferometry, N. P. L., Her Majesty’s Stationery Office, London, 1960); bG. W. Stroke, Paper No. 5, Fifth Conference of the International Commission of Optics, Stockholm, August, 1959; cG. W. Stroke, J. phys. radium 21, 57S (April, 1960).

This work was also presented as a part of the invited paper on “The two aspects of the diffraction of light by diffraction gratings,” given by G. W. Stroke at the October, 1960, meeting of the Optical Society of America. It is extensively described in Rev. opt.39, 291–398 (1960), and will be incorporated in a further paper in this series.

Stroke, H. H.

aR. J. Hull and H. H. Stroke, Bull. Am. Phys. Soc. 5, 412 (1960); bR. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).

G. W. Stroke and H. H. Stroke, Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (October, 1958), p. 54.

Strong, J.

Sturgis, N.

Toraldo di Francia, G.

Townes, C. H.

aA. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958); bA. Javan in Quantum Electronics, edited by C. H. Townes (Columbia University Press, New York, 1960), p. 564; cA. Javan, W. R. Bennett, and D. R. Herriott, Phys. Rev. Letters 6, 106 (1961).

Twersky, V.

V. Twersky, Proc. I. R. E. Trans. PGAP,  AP-4, p. 330 (1956).

Wood, R. W.

aR. W. Wood, Phil. Mag. 4, 396 (1902); Phil. Mag. 23, 310 (1912); Phys. Rev. 48, 928 (1935); b Rayleigh, Phil. Mag. 14, 60 (1907); cL. R. Ingersoll, Astrophys. J. 51, 129 (1920); dC. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).

Yamada, Y.

Ark. Fysik (1)

Grating-immersion arrangements to increase the dispersion and resolving power have also been described by E. Hulthén and H. Neuhaus, Ark. Fysik 8, 343 (1954); O. Björklund, ibid. 13, 185 (1958).

Bull. Am. Phys. Soc. (1)

aR. J. Hull and H. H. Stroke, Bull. Am. Phys. Soc. 5, 412 (1960); bR. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).

Can. J. Phys. (1)

R. F. Millar, Can. J. Phys. 39, 81, 104 (1961).
[Crossref]

Compt. rend. (1)

A. Maréchal and G. W. Stroke, Compt. rend. 249, 2042 (1959).

J. Appl. Phys. (1)

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[Crossref]

J. Opt. Soc. Am. (18)

aJ. H. Rohrbaugh and R. D. Hatcher, J. Opt. Soc. Am. 48, 704 (1958); bJ. H. Rohrbaugh, C. Pine, W. G. Zoellner, and R. D. Hatcher, J. Opt. Soc. Am. 48, 710 (1958).

The design and numerous very significant spectroscopic advantages of echelle-gratings were first described by G. R. Harrison in J. Opt. Soc. Am. 39, 522 (1949), and subsequently expanded in many papers.
[Crossref]

G. W. Stroke, J. Opt. Soc. Am. 51, 1340 (1961), following article.
[Crossref]

G. R. Harrison and J. E. Archer, J. Opt. Soc. Am. 41, 495 (1951).
[Crossref]

E. R. Peck, J. Opt. Soc. Am. 38, 1015 (1948); J. Opt. Soc. Am. 45, 931 (1955).
[Crossref] [PubMed]

aM. V. R. K. Murty, J. Opt. Soc. Am. 50, 7 (1960); bJ. Opt. Soc. Am. 50, 83 (1960).

M. J. E. Golay, J. Opt. Soc. Am. 41, 468 (1951).
[Crossref] [PubMed]

G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
[Crossref]

G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, J. Opt. Soc. Am. 47, 15 (1957).
[Crossref]

aSome results of our work pertinent to the present paper were incorporated as a part of the review paper by G. R. Harrison, N. Sturgis, S. P. Davis, and Y. Yamada, J. Opt. Soc. Am. 49, 205 (1959). bThese results had also been reviewed by G. W. Stroke on May 7, 1958, at the International Commission of Optics Colloquium on Optics in Metrology, Brussels [Proceedings, “Optics in Metrology,” edited by Pol Mollet (Pergamon Press, New York, 1960), pp. 98–118].

G. W. Stroke, J. Opt. Soc. Am. 45, 30 (1955).
[Crossref]

G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957); J. Opt. Soc. Am. 48, 276 (1958); J. phys. radium 19, 415 (1958).
[Crossref]

aJ. Strong, J. Opt. Soc. Am. 50, 1148 (1960); bR. W. Ditchburn, Proc. Roy. Irish Acad. A39, 58 (1930); J. Strong, J. Opt. Soc. Am. 41, 3 (1951); H. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951); E. Hulthén and U. Uhler, Ark. Fysik 3, 393 (1952); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955); A. Keith Pierce, ibid. 47, 6 (1957); G. R. Harrison, N. Sturgis, S. C. Baker, and G. W. Stroke, ibid., 47, 15 (1957); D. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, ibid., 47, 631 (1957); G. R. Harrison, N. Sturgis, S. P. Davis, and Y. Yamada, ibid. 49, 205 (1959).
[Crossref]

The possibility of testing a grating interferometrically by simply placing it into one of the arms of a Michelson Twyman-Green interferometer has been previously described by G. W. Stroke [(J. Opt. Soc. Am. 45, 30 (1955); Rev. opt. 39, 291 (1960)]. The fringe pattern displays the diffracted wave-front topography and is formed as a result of interference between the diffracted wave front and a plane wave front reflected from a reference mirror. The wave-front interferograms have been found in practice to provide the most revealing and most useful information about the quality of a grating of all known grating-testing methods. Not only do they permit the immediate assessment of the ruling quality of a grating by simple inspection of the fringe deviations from straightness, but they also permit accurate predictions of the spectral quality of the grating or replica, with the help of known relations between the wave fronts and the diffraction patterns that they form.5,7
[Crossref]

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

R. Greenler, J. Opt. Soc. Am. 45, 788 (1955).
[Crossref]

aG. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955); J. Opt. Soc. Am. 46, 72 (1956); bJ. Arsac, Optica Acta (London) 6, 103 (1959); cA. I. Kartashev, Optika i Spektroskopiya 9, 204, 394 (1960).

H. M. Crosswhite and W. G. Fastie, J. Opt. Soc. Am. 46, 110, (1956); W. G. Fastie, ibid. 42, 641, 647, (1952).
[Crossref]

J. phys. radium (2)

Colloquium on “Les progrès récents en spectroscopie interférentielle,” J. phys. radium 19, 185 (1958).

R. Chabbal, J. phys. radium 19, 295 (1958).
[Crossref]

J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) (1)

P. Jacquinot and Ch. Dufour, J. recherches centre natl. recherches sci., Labs. Bellevue (Paris) 6, 1 (1948).

Optica Acta (Paris) (3)

P. Connes, Optica Acta (Paris) 4, 136 (1957); J. phys. radium 19, 262 (1958); thesis, The Sorbonne, Paris, 1958.
[Crossref]

P. Girard, Optica Acta (Paris) 7, 81 (1960).
[Crossref]

In French: lumière diffusée ou parasite. For an interesting theoretical study of scattered light see A. Maréchal, Optica Acta (Paris) 5, 70 (1958).
[Crossref]

Phil. Mag. (1)

aR. W. Wood, Phil. Mag. 4, 396 (1902); Phil. Mag. 23, 310 (1912); Phys. Rev. 48, 928 (1935); b Rayleigh, Phil. Mag. 14, 60 (1907); cL. R. Ingersoll, Astrophys. J. 51, 129 (1920); dC. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).

Phys. Rev. (2)

aA. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958); bA. Javan in Quantum Electronics, edited by C. H. Townes (Columbia University Press, New York, 1960), p. 564; cA. Javan, W. R. Bennett, and D. R. Herriott, Phys. Rev. Letters 6, 106 (1961).

F. Bitter and G. R. Harrison, Phys. Rev. 57, 15 (1940).
[Crossref]

Proc. Am. Phil. Soc. (1)

aG. R. Harrison, Proc. Am. Phil. Soc. 102, 438 (1958); bG. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960).

Proc. I. R. E. Trans. PGAP (1)

V. Twersky, Proc. I. R. E. Trans. PGAP,  AP-4, p. 330 (1956).

Proc. Roy. Soc. (London) (1)

a Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907); bU. Fano, Ann. Physik 32, 393 (1938); cT. B. A. Senior, Can. J. Phys. 37, 787 (1959).

Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (1)

G. W. Stroke and H. H. Stroke, Quart. Rept. Mass. Inst. Technol. Research Lab. of Electronics (October, 1958), p. 54.

Repts. Progr. in Phys. (1)

P. Jacquinot, Repts. Progr. in Phys. Vol.  XXIII267 (1960).
[Crossref]

Rev. opt. (4)

The complete theory of the effects of grating errors and blank defects on the spectral image perfection, presented here in a form appropriate to the present paper, was developed by G. W. Stroke, Rev. opt. 39, 291–398 (1960), and is given there together with a historical background, review of past work pertinent to that study and a complete list of references. A detailed description of the theory and of the method of calculation of the distribution of light in spectral diffraction patterns by Fourier transformation of the phase distribution in the diffracted wave fronts, as it appears in a readily usable graphical form in the wave-front interferograms, is also fully given in that work. Some of the early qualitative aspects of that work were also incorporated into a paper by G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 50, 1153 (1960) with particular reference to the attainment of high resolution with diffraction gratings and echelles.
[Crossref]

P. Connes, Rev. opt. 35, 37 (1956); J. phys. radium 19, 262 (1958).

aG. W. Stroke, Rev. opt.,  39, 291 (1960); bG. W. Stroke, thesis, The Sorbonne, Paris, 1960.

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

Other (42)

R. Chabbal, thesis, The Sorbonne, Paris, 1957.

Comparison of spectrometers and spectrographs can be made in terms of several parameters. Those which characterize the capability to separately detect and “resolve” (in space or time) photons emitted by the source and having slightly different energies are particularly significant. The two parameters generally used to describe the resolving and detection capability of a spectrometer are (1) the “resolving power” or “resolution” and (2) the “spectral efficiency” or “luminosity.” It should be clear that these two parameters are not independent. This has been emphasized in particular by Jacquinot24 in a paper dealing with the luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons. There does not yet appear to be a general agreement as to the exact terms by which these parameters can be best described: the quantity “radiant power reaching the detector in a unit of resolved spectral bandwidth” has been used with some advantage by R. Greenler,25 and the quantity “étendue” has appeared in French publications.19 But if “resolving power” and “luminosity” are properly defined, a consistent and simple comparison of spectroscopic instruments has been found to be possible.21,24 We find that the term “resolving power” is best suited for the description of a theoretical capability of spectral resolution, that is the capability of separately detecting photons of slightly different energies; one can speak with advantage of the “theoretical” resolving power of either a perfect instrument, or of an instrument of which the limitations are calculable, in order to emphasize that the resolving “power” applies to the instrument alone separately from the limitations set by the source (Doppler-broadened lines, for example) or by the detector (granularity and other receptor noise). The “limitations” in resolving power can be of a physical optics character, or more generally of an electromagnetic character, (such as the limitations resulting from the use of finite apertures in grating spectrometers, or the use of a finite number of beams in a Fabry-Perot etalon), or they can result from imperfections in the optical elements (grating defects, or (FP) etalon flatness and coating imperfections) of which the effects can be predicted by calculation,7,19,20 In that sense the use of source slits or source holes (focal diaphragms) of finite aperture, in both grating and FP spectrometers, can be considered as a “limitation” of which the importance can be simply established in any given case.18,21 In both grating and FP spectrometers, or spectrographs, the use of a finite source aperture results in the incidence of wave fronts, not only from a single direction (which is generally desired), but within a finite angular domain determined by the size of the source hole or slit as seen from the collimator. The term “resolving power” is generally understood to describe the quantity RP=λ/Δλ=σ/δδ, where Δλ or δσ refers to the difference in wavelength (or wave number) of the photons of neighboring energy (hν), or wavelength λ=c/ν, or wave number σ=1/λ (with λ in centimeters), which can be detected as “resolved in the limit” (c=velocity of light and h=Planck’s constant). It should be clear that the “limiting” resolution and “theoretical resolving power” are arbitrary quantities, even though they provide a good order of magnitude in usual spectroscopic applications: effective resolving powers considerably in excess of those predicted by classical theory can be obtained.26,7,5bFor the purpose of this paper we shall use the term “resolving power” as described by the equation RP=λ/Δλ=σ/δσ in agreement with general use. For the description of the other important detection quantity, we shall use the term “luminosity” as defined by Jacquinot21: “The luminosity of a spectrometer is defined as the ratio, L=ϕ/B, of the flux falling on the detector to the luminance of the source.” Here L=SΩτ, where S is the surface area of the plates (for an FP etalon) or the area of the projection of the grating surface on the diffracted wave front, Ω the solid angle limited by the focal diaphragm, and τ an appropriately defined transmission factor. As shown by Chabbal,19 the transmission factor of an FP spectrometer is itself a product of three factors, the reflectance and transmittance of the coatings, the effect of surface imperfections, and the effect of a finite source aperture. For a grating, the transmittance is simply given according to usual photometric definitions: in general, it can be considered to be equal to the ratio of the number of photons of a given energy attaining the detector in a given order of the grating, per unit time, to the total number of photons of that energy incident on the grating, per unit time, after collimation by a perfectly reflecting collimator (the reflectance of the collimator can be separately taken into account). Throughout this paper, we shall use the term “luminosity” according to the above definition, except where another description of the corresponding parameter appears to be more appropriate. (This meaning of “luminosity” is, of course, quite different from that of the same term in photometry.) The quantity “étendue” U is defined by U=SΩ, and is related to the quantity “luminosity” L by L=τU). We shall also use the expression “more or less luminous” to describe the fact that an optical element or spectrometer has the quantity “luminosity” to a greater or a smaller extent.

The improvements are, of course, also applicable to other engines to which interferometric control is now being applied.

These patterns will be simply described as hfs patterns in the remainder of this paper.

aG. W. Stroke, Interferometry Symposium, National Physical Laboratory, Teddington, June 10, 1959. (Symposium No. 11, Interferometry, N. P. L., Her Majesty’s Stationery Office, London, 1960); bG. W. Stroke, Paper No. 5, Fifth Conference of the International Commission of Optics, Stockholm, August, 1959; cG. W. Stroke, J. phys. radium 21, 57S (April, 1960).

R. Dupeyrat (private communication, 1960).

aJ. W. Evans (private communication); bA. Keith Pierce, J. Opt. Soc. Am. 47, 6 (1957); cH. D. Babcock and H. W. Babcock, ibid. 41, 776 (1951).

Ch. Fehrenbach (private communication).

It is the very large free-spectral-range characteristic of the small groove depth in gratings and echelles which is one of the great assets of diffraction gratings in high-resolution spectroscopic studies.6b It is indeed the independence of free spectral range from both resolving power and dispersion which is at the heart of the advantages of diffraction gratings over FP etalons in high-resolution studies that fall within their domain. Unlike that in gratings, the free spectral range of an FP etalon varies inversely with its resolution and falls to extremely small values even at resolving powers which are very moderate in terms of its capabilities.21 Even a 1-cm FP etalon, of RP=106 at 5000 A (with a finesse of 25), has a free spectral range of only 12 cm-1, which is insufficient to study the hfs of either the blue or green mercury lines without a premonochromator. On the other hand, the same resolving power of 106 can be obtained faith a 300-groove/mm, 10-in. grating or a 10-groove/mm 10-in. echelle in autocollimation at 76°, with the very large free spectral ranges of 3×103 and 100 cm−1, respectively. One recalls that the free spectral range is the wave number range that can be obtained without overlapping. It is given by Δσ=1/(2t), where t is both the thickness of the FP etalon and the apparent groove depth of the grating, of which the spacing constant is a. (Thus t=a sini for a grating in autocollimation at an angle i.) For the FP, the resolving power RP=σ/δσ, where δσ=Δσ/N; the wave number σ=1/λ, with λ in centimeters; and N is the number of effective beams (N=25 for plates flat to λ/50, and in general N=m/2 for plates flat to λ/m). For a grating of ruled width W, the resolving power is RP=2W sini/λ, and the dispersion di′/dλ=2 tani′/λ; both are seen to be independent of the spacing constant a.

The author is grateful to Dr. R. K. Brehm and the Jarrell-Ash Company for making this recording.

It might be observed that we have never experienced any difficulties in the stability of the 40-ft spectrographs mounted in the “35-ft room” at the spectroscopy laboratory at M.I.T., which is controlled to a few tenths of a degree F. For unusually long exposures of the order of hours, it may sometimes be necessary to correct for the change in wavelength which results from atmospheric-pressure variations and which affects all wavelengths by practically the same amount. All spectral lines can be maintained in position simultaneously (as long as the cosines of their angles are approximately the same) by appropriately rotating a thin quartz plate mounted next to the entrance slit on the collimator side.

In this paper we do not distinguish between gratings or echelles except when necessary.

aPrism double-pass arrangements had been previously used by A. Couderc, J. phys. radium p. 37S (1937) (the author is indebted to Professor P. Jacquinot for mentioning in a private communication this early prism double-pass arrangement on which he had worked); bA. Walsh, J. Opt. Soc. Am. 42, 94, (1952).

aGrating double-pass arrangements:F. A. Jenkins and L. W. Alvarez, 42, 699 (1952); bW. G. Fastie and W. M. Sinton, ibid. 483A (1952); cD. H. Rank and T. A. Wiggins, ibid. 983 (1952); dJ. N. Shearer, T. A. Wiggins, A. H. Guenther, and D. H. Rank, J. Chem. Phys. 25, 724 (1956); eD. H. Rank, A. H. Guenther, C. R. Burnett, and T. A. Wiggins, J. Opt. Soc. Am. 47, 631 (1957).

It is clear, of course, that for studies in the resolving power domains of 3 to 4×106 in the visible and ultraviolet which are not yet accessible to single gratings, and where a loss of light resulting from the association of an FP etalon with a low-resolution monochromator is acceptable, the etalon is the high-resolution device to be used. More generally, one can use an FP etalon in conjunction with an existing grating, or prism, low-resolution monochromator in order to increase its resolution (even though this may result in a more complicated scanning arrangement than that which could be used to obtain the same high resolution with a large grating monochromator). For ultimate resolutions, Conne’s spherical FP etalon31 does in fact yield considerably more flux per bandwidth than a plane FP etalon with otherwise comparable limitations in free spectral range.

G. R. Harrison, R. C. Lord, and J. R. Loofbourow, Practical Spectroscopy, (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948); R. A. Sawyer, Experimental Spectroscopy, (Prentice-Hall Inc.Englewood Cliffs, New Jersey, 1944).

The author is grateful to Professor P. Jacquinot for numerous lengthy and invaluable discussions and clarifications dealing in particular with the field of interference spectroscopy: he also wishes to express his appreciation for Professor Jacquinot’s stimulating and constructive encouragements and suggestions, over the course of years, which have in no small measure contributed to the success in the ruling of the high-resolution gratings described in the present work. The author also wishes to stress that the conclusions presented here may be traced to the new availability of these 10×5-in. gratings and that they should not be taken as implying any conclusions by Professor Jacquinot and his associates except those that they have published themselves. The author is also grateful to Professor R. Chabbal for very enlightening discussions dealing with the field of interference spectroscopy and FP spectrometers, as well as for private communications clarifying in particular his own important contributions to this field.

The author is grateful to Professor E. F. Barker and to Professor H. M. Randallfor a private communication describing the method of production and the quality of the gratings ruled for the infrared at the University of Michigan[see also H. M. Randall, J. Appl. Phys. 10, 768 (1939)]. The use of gratings in high-resolution infrared spectrometers has also been described by R. C. Lord and T. K. McCubbin, J. Opt. Soc. Am. 45, 441 (1955).
[Crossref]

A. Maréchal, Imagerie géométrique, aberrations (Revue d’Optique, Paris, 1952), p. 215.

H. H. Hopkins, Wave Theory of Aberrations, (Oxford University Press, New York, 1950), pp. 14–16.

When diffracted wave fronts are curved, the curvature is generally not the same along the grating width and along the grating height: some astigmatism may then affect the height of the spectral lines, even though their width may be perfect in an ideal case.

E. Mascart, Traité d’optique (Gauthier-Villars, Paris, 1889), Vol. I., p. 373; H. S. Allen, Phil. Mag. 3, 92 (1902); Phil. Mag. 6, 559 (1903); R. W. Wood, ibid. 48, 497 (1924); H. G. Gale, Astro. phys. J. 86, 437 (1937); G. R. Harrison, J. Opt. Soc. Am. 39, 413 (1949) gives many references and an excellent history of the grating ruling development; J. Strong, ibid. 41, 3 (1951); E. Ingelstam and E. Djurle, Ark. Fysik. 4, 423 (1952); Ark. Fysik. 6, 463 (1953); J. Opt. Soc. Am. 43, 572 (1953); G. W. Stroke, ibid. 42, 879A (1952); E. Djurle, Ark. Fysik. 8, 383 (1954); D. H. Rank, J. N. Shearer, and J. M. Bennett, J. Opt. Soc. Am. 45, 762 (1955).
[Crossref]

It is known, of course, that the first secondary maximum corresponding to the rectangular aperture presented by a grating has an intensity of the order of 4% and that the peak appears at a distance of about two diffraction units from the line center. These are precisely the orders of magnitude of the spurious satellites of a few percent intensity with which we are dealing here.

Computed diffraction patterns such as the one in Fig. 7 (which corresponds to an infinitely narrow perfectly monochromatic slit) have permitted correction of “errors of coincidence” resulting from systematic, center-of-gravity displacements of spectral lines. They should prove invaluable in spectral-line-shape studies, since the intensity distribution recorded in the spectrometer is simply equal to the convolution of the “true” intensity distribution in the spectrum (which is sought) with these (computed) diffraction-pattern intensity distributions (when the slit width has been taken into account, which presents no problem).7

More classical ruling engine ways, such as the “doublevee” ways already used by Rowland, may also cause rotation problems, in particular as a result of lubrication irregularities.

Between the first diffraction minima on both sides of the center.

This corresponds to only 1.5×10−5 in the first order of a 15 000 lines/in. grating in the usual description of Rowland-ghost intensities.

One diffraction unit (u) corresponds to the distance from the center of the first diffraction minimum for a rectangular aperture A=W cosi′. The first diffraction minimum is at u=(λ/A)f, where f is the focal length of the camera mirror in the spectrograph. For a 10-in. grating used at 64° the first minimum is at about 1 sec of arc from the center in the visible. For Hg 198 spectrograms of the satellite distributions in three wavelengths produced by the first-generation 10-in. grating 97, see references 7 and 6b.

The reason why good high-resolution gratings might in a sense be considered as more perfect optical elements in the visible than the best of the available FP etalons may be that with a finesse of 25 (which multiplies the etalon flatness deviations by factors up to 25) an etalon good to 1/50 wavelength over its surface results in path-difference variations, between extreme beams, of up to λ/2.

A period of 12 to 18 hr is usually required to raise the engine and oil to the operating temperature.

The stirrers need to be carefully isolated from the floor and the engine to avoid vibrations in the control interferometers and the ruling diamond; 12-in.-thick neoprene pads on which the stirrers are loosely placed have been found to be sufficiently good vibration-isolators in practice. The operation of a 10 000-amp, 170-v generator for a Bitter 100 000-Gauss Zeeman-effect magnet,69 placed within some 50 ft from the engine, has occasionally caused vibrations in the interferometers and harmful resonance in the ruling diamond which both affect the groove quality and may tend to result in undesirable scattered light in spectral regions far removed from the line centers.

This work was also presented as a part of the invited paper on “The two aspects of the diffraction of light by diffraction gratings,” given by G. W. Stroke at the October, 1960, meeting of the Optical Society of America. It is extensively described in Rev. opt.39, 291–398 (1960), and will be incorporated in a further paper in this series.

G. R. Harrison (private communication, 1959).

R. P. Madden and J. Strong, Appendix P in Classical Optics, by J. Strong (Freeman & Company, San Francisco, California, 1958), p. 597.

P. Connes (verbal communication, 1960).

aA. A. Michelson, Studies in Optics, (University of Chicago Press, Chicago, Illinois, 1927), p. 39; bP. Fellgett, thesis, Cambridge University, Cambridge, England, 1951); J. phys. radium 19, 187, 237, (1958); cP. Jacquinot, XVIIe Congrès du G.A.M.S., Paris, (1954); J. phys. radium 19, 223 (1958); Optica Acta (London) 7, 291 (1960); dJ. Connes, thesis, The Sorbonne, Paris (1960); Rev. opt. 40, 45, 1961.

It uses a tube of piezoelectric ceramic (lead zirconate titanate) to serve as an expander for the plastic shoe with respect to the diamond carriage [D. D. Scofield, M. S. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1961 (unpublished)].

The correction of errors of this type (of which the possibility was first indicated by G. W. Stroke in 1957)12 resulted in the successful ruling of the first-generation 10-inch gratings. They were pictorially summarized for enclosure (as Fig. 7) in the paper by Harrison et al.,3 reviewing the work up to that stage.

Ever since the engine was first put under continuous control we have been successfully using the equation Δm=3.31ΔPΔL for the amount of pressure correction. Here Δm=shift in 1/100 fringe, ΔP=pressure change in inches of mercury and ΔL=interferometer mirror separation in millimeters. The hybrid units used in this equation have resulted in a misprint in one of the early papers originating from the M.I.T. ruling project.59 We are grateful to H. W. Babcock for noting that the misprint had been carried along into subsequent publications, as well as for other private communications concerning his work on the control of grating ruling. A detailed discussion of the pressure correction for interferometric servomechanisms is given by G. W. Stroke, in Optics in Metrology, edited by Pol. Mollet (Pergamon Press, New York, 1960), p. 101.

Both companies have, of course, been producing replicas of their own gratings.

In one instance, over 100 good replicas of a concave grating have already been obtained by George Sintiris at the Jarrell-Ash Co.

David Richardson (private communication); George Sintiris (private communication); the details of the successful replication processes are particular to the methods developed in different laboratories, but it is well known that a replica grating consists of a thin layer of an aluminized plastic resin, such as Epoxy or Laminac, molecularly adherent to a perfectly flat (or perfectly spherical) optical glass blank (for plane or concave gratings respectively). The evaporated aluminum layer with which the plastic is usually covered is similar to the layer used in original rulings. The clean separation of the replicas from the master ruling without deformation appears to be at the root of a successful replication.

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Figures (12)

Fig. 1
Fig. 1

Wave-front interferograms (left) and corresponding mercury green line hfs patterns (right) produced in autocollimation at 64° by two 10-in. gratings ruled one before (b), Gr. 97, and the other after (a), Gr. 143, the new engine improvements had been carried out. (P=projection distance of spectrographs.) Components a, b, A, d, O, g, f, h and C are all real spectral lines. (For resolution of central group O, see Fig. 4.) A perfect grating produces a perfectly straight, horizontal fringe pattern in the interferogram. (The grooves project vertically on these interferograms, and lateral groove displacements on the grating, as well as blank or coating defects, produce vertical fringe deviations from straightness in the interferograms.) The residual wave-front deviations appearing in the new grating 143 are still due to residual coating imperfections which are now being even further reduced: in this case they are seen to produce no harmful effects on the spectrum, while a set of spurious satellites described by “s” appears in grating 97 with an intensity very similar to that of component “a” and results in loss of resolution on the fast spectrographic plates 103aF, used in normal work, when the exposures are long enough to bring out the weaker spectral components, as is the case here. Visual aspect of hfs patterns in spectrographs, as well as fine-grain spectrograms, generally appear much better than the hfs rendition on fast, but coarse-grain plates. (For hfs pattern obtained with grating 97 on slow, fine-grain film, see Fig. 3.)

Fig. 2
Fig. 2

Comparison of early low-resolution (a) and early high-resolution (b) grating wave-front interferograms2: (a) section of grating No. 256 on speculum metal, finished by J. A. Anderson on April 14, 1914, (b) section of same width of early grating ruled under interferometric control at M.I.T. Both interferograms were obtained in autocollimation at 45° in λ5461 A. The sensitivity of the wave-front deviations to ruling errors increases with the sine of the grating angle, and the sensitivity of spectral-image quality to ruling errors generally increases with the square of the sine of the grating angle in autocollimation. Grating a was usable as a good grating only at small angles (up to 10° or so). Both low-resolution and high-resolution gratings ruled nowadays are considerably better than the ones shown here for historical purposes.

Fig. 3
Fig. 3

Hfs pattern of green mercury line 5461 A obtained with same grating 97 and same spectrograph as used in Fig. 1(b), but now on fine-grain low-contrast Panatomix X film, at 3 times the exposure of Fig. 1. The divisions shown are 0.1 mm in the focal plane of the 40-ft (12.2 m) spectrograph. The photographic conditions shown here are not generally practical in normal work. But as they tend to conceal rather than enhance residual spectral line imperfections, they permit extraction of a maximum amount of the spectroscopic information available in the diffracted wave fronts and aerial images. It appears from a comparison of Figs. 3 and 1 that gratings are best compared with spectrograms obtained under similar conditions, and even better with the help of diffracted wave-front interferograms4,7 (see text).

Fig. 4
Fig. 4

Resolution of central components of mercury green line hfs pattern, showing resolving power in excess of 1.2 million. The entire pattern of five components in the center shown here corresponds to component 0 of Fig. 1(a). (The wave-number scale is reversed with respect to Fig. 1 as shown by position of component “A”). The dispersion is twice that of Figs. 1 and 3 and is obtained by using two 7.5-in. gratings in series as described elsewhere.33,5a,5b The exposure was about 10 min on a 103aF plate with an electrodeless discharge tube excited by an RF oscillator at about 100 mc/sec and cooled to 0°C.

Fig. 5
Fig. 5

Photoelectric recording of mercury 4358-A hfs pattern obtained by direct scanning of a 7 1 4 -in. grating around 64° in a 1-m high-resolution f/10 spectrometer, showing resolution in excess of 500.000 at the scanning speed 2 A/min (a). One notes the smoothness of the scanning, obtained by rotation of grating, even at the slower scanning speed (b), used to exploit more closely the theoretical resolution of 760.000. (The spectrogram shown was obtained with the 10-in. grating No. 143 on a 103aF plate in a 15-sec exposure, with a different source, at a resolution in excess of 1 million.)

Fig. 6
Fig. 6

Effect of a typical “linear” wavefront deviation caused by a grating-blank coating defect. A very prominent spurious satellite line (such as that shown at 0.25 mm in the “unmasked grating” spectrogram on right) is produced by a linear deviation from either a straight or a parabolically curved reference wavefront (in practice a wavefront with a circular section as it appears here). As borne out by the Hg198 spectrogram (which should be a single line under any exposure except for spurious satellites caused by grating imperfections) the position (Δl′) of the satellite corresponding to the 40-mm “linear” deviation from the (circular) reference wave front can be simply predicted7 by noting that the deviation may be interpreted as resulting from a linear spacing variation (Δa/a) in the corresponding grating section. In fact, cumulative ruling errors, as well as grating mounted under stress (or even poorly shaped mirrors) may result in the creation of similar satellites, which disappear when the responsible grating section is masked off (as shown in “masked grating” spectrogram). (A rotating sector giving intensity steps in ratios of 2 is used in all Hg198 spectrograms shown in the various figures.)

Fig. 7
Fig. 7

“Controlled-error” grating ruled to permit a study of the effects of a “pure” linear wave-front aberration deliberately introduced under interferometric control over a 25-mm section of an otherwise perfect 135-mm grating. A notable characteristic of extended “linear” aberrations is that the principal satellite lines which they produce are at a distance from the line-centers which is wavelength independent at a given grating angle, as borne out by the Hg198 spectrograms in two wavelengths in the green and the ultraviolet, on right (satellite “C”). The geometrical calculation of the satellite position is similar to that of Fig. 6. Furthermore, and equally unlike the general case, the relative intensity of the principal satellite “C” is also wavelength independent for this special type of aberration: in fact, the relative satellite intensity is comparable to the ratio of the 25-mm error region to the 135-mm width of the grating. In a sense, the error region may be considered as a “satellite-grating” inclined at some small angle with respect to the main grating. (When attempting to predict the effect of wave-front aberrations, it should be remembered that it is the complex amplitudes and not the intensities of the light-distribution in the images which need to be summed.) (A normally wavelength-dependent, fine structure appears around the satellites “C” in the two wavelengths, respectively.) As borne out by the Fourier-transform calculation,7 even the apparently simple “linear” aberration results in very complex, spectral-line imperfections.

Fig. 8
Fig. 8

Wave-front interferogram and Hg 198 spectrogram showing corresponding satellite distribution for an early 10-in. grating having numerous, rather extended departures from regularity. The computed intensity distribution in the diffraction pattern (for the spectrogram angle) is also shown, for the same wavelength 5461 A, and is obtained by Fourier transformation of the phase distribution in the wave front as it appears in graphical form in the wave-front interferogram7 (1 fringe=2π). The computation was carried out for 53.8° by noting that the fringe and phase aberrations increase with the sine of the angle for ruling errors, 1 fringe ruling error causing 1 fringe wave-front deviation at 90° in autocollimation. The excellent agreement between the computed diffraction pattern and the spectrogram, including all its various spurious satellites, illustrates the fact that the various satellites are simply diffraction-pattern imperfections as caused by the entire wave front. It is clear that no simple relation can be given here between any particular satellite in the spectrogram and a given error-region in the wavefront. Only in the case of the “linear” aberrations of Figs. 6 and 7, and for periodic errors, can simple relations be accurately predicted by a mere inspection of the interferograms. However, the grating shown illustrates the important fact that extended small-amplitude error regions in the wavefronts tend to produce harmful satellites in the near-vicinity of the line centers (note the 0.1 mm scale in the focal plane of the 12-m spectrograph: if the 2-mm periodic error of the M.I.T. screw were not so well suppressed by interferometric control, Rowland ghosts would appear at about ±6 mm on either side of the line-center here at 53.8°, and at about ±8 mm at 64° in 5461 A). The qualitative effect of the small-amplitude extended aberrations can thus be immediately predicted by inspection of the interferograms: they affect the immediate neighborhood of the line centers and are thus most detrimental in high-resolution use of the gratings. (Local errors originating from a few grooves, or from a few millimeters on a 10-inch grating tend to produce their most harmful effects in regions considerably more removed from the line centers, and are thus much less harmful in high-resolution gratings.)

Fig. 9
Fig. 9

Wave-front interferograms of 10-in. gratings in 5461 A at 64° illustrating the effect of the recent engine improvements described in the text: (a) grating 130 ruled before and (b) grating 143 ruled after the improvements had been carried out. Residual coating defects at right and left of grating b are at the origin of the slightly curved fringe deviations from straightness, which could under considerable photographic overexposure lead to weak out-of-focus background near the lines, but cause no harmful defects in the use of this grating [see Fig. 1(a)]. The ruling control and engine conditions are seen to have been almost perfect in this case. In fact, even when completely unmasked, this grating 143 has been found to be superior in resolution, clean line shape and lack of satellites, to any previous 10-in. high-resolution grating.

Fig. 10
Fig. 10

Interferogram from a 1 1 2 -in. test section of grating ruled on the M.I.T. ruling engine without control to illustrate the amount of mechanical error that can be effectively removed by the interferometric servocontrol described in the text and in references.16 The interferogram here has been taken at 16° with only 1 3 the sensitivity of the wave fronts to ruling errors obtained at 64° (as in Fig. 9). The effect of ruling errors on the spectral-image quality is 10 times greater at 64° than at 16°, and 100 times greater at 64° than at 5° in autocollimation.

Fig. 11
Fig. 11

Ruling error (21) resulting from incorrect centering (h2h1) of interferometer mirror (axis) on ruling plane (at tip of diamond D) in the presence of a pitchlike rotation (Δα) occurring in the course of the grating advance.

Fig. 12
Fig. 12

Recent interferogram of a now 5-year-old replica grating (Replica) produced in 1956 from the 8-in. M.I.T. grating No. 672 shown at top (Original). The remarkable fidelity and stability typical of modern grating-replication methods appear from the comparison of the two interferograms, both obtained at 23.5°.