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).
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.
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)].
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.
Between the first diffraction minima on both sides of the center.
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).
R. Chabbal, thesis, The Sorbonne, Paris, 1957.
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).
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.
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).
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 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.
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).
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.
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 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.
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.
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.
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.
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.