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ratory. 0003-6935/82/020167-02$01.00/0. © 1982 Optical Society of America. In recent years echelle gratings have increasingly been

used by astronomers to obtain high spectral resolution with Cassegrain spectrographs. The high blaze angle (63.4 or 76°) yields high angular dispersion, which combined with camera focal lengths 0.5-1 m can achieve reciprocal dispersions 1-3 Å mm - 1 at 5000 Å.1 Previously such plate factors had been available only on long-camera coude spectrographs. The challenges in echelle spectrograph design are efficient light management, order separation, and accommodation of odd geometrical effects, such as nonlinear dispersion with slit-image rotation.2 Both the desirable and difficult properties of echelles are strong functions of a single grating parameter, the blaze angle, ΘB.Knowing ΘB is crucial for efficient echelle spectrograph design, but its determination is not trivial. We describe here an innovative procedure for measuring ΘB that is free of systematic effects associated with an alternate ap­proach. Our measurement of ΘB for the Bausch & Lomb R4 echelle grating (Catalog #35-13-*-402) indicates the actual blaze angle is ΘB = 72.5°, which is 3.5° smaller than the manufacturer's specification of 76.0°.

Bottema3 has discussed the effect of facet diffraction on the blaze function when an echelle grating is used off-Littrow. In particular, the direction of maximum efficiency does not coincide with the maximum of the single-slit diffraction pat­tern of a single facet, and this deviation increases with longer wavelength. The apparent wavelength dependence of the blaze direction is an artifact of the off-Littrow geometry and does not refer to a physical property of the grating. A blaze angle measurement in the Littrow condition should be wavelength independent and locate the actual direction of the grating facet normal.

Bausch & Lomb4 inform us that the ruling diamond for the R4 grating was formed accurately to 76°, and it was tilted 1.5° toward a steeper blaze angle in the engine. ΘB was determined by Bausch & Lomb from a series of measurements in which the grating was used in an in-plane and off-Littrow configu­ration (deviation angle = 7.6°).

We have measured the angular distribution of intensity from a replication (#B05-4-l-l) of the Bausch & Lomb R4

Fig. 1. Geometry of the quasi-Littrow grating mount. N is the grating normal, Z is the vertical direction, and the incident and dif­fracted light beams î and d are in the horizontal plane. The angle θ can be changed mechanically to keep î and d in the horizontal plane for any wavelength. θ = θB at the blaze function peak, and then the

facet normal lies in the horizontal plane with î and d.

Fig. 2. Our measurements of the blaze function for light at two wavelengths. The line shows a nonlinear least squares fit to the He-Ne data using the single-slit diffraction pattern of a single-grating facet [Eqs. (1) and (2)]. The Hg data points were plotted at modified abscissa values [Eq. (3)] to permit direct comparison with the He-Ne points. We find ΘB = 72.5°, whereas Bausch & Lomb specifies the

blaze angle of this grating to be 76.0°.

15 January 1982 / Vol. 21, No. 2 / APPLIED OPTICS 167

Actual blaze angle of the Bausch & Lomb R4 echelle grating Robert A. Brown, R. L. Hilliard, and Amy L. Phillips

Robert Brown is with University of Arizona, Lunar & Planetary Laboratory, Tucson, Arizona 85721; R. L. Hil­liard is with Optomechanics Research, Inc., P.O. Box 36522, Tucson, Arizona 85740; and Amy Phillips is with University of Southern California, Space Science Insti­tute, Tucson Laboratories, Tucson, Arizona 85713. Received 2 November 1981. Sponsored by W. R. Hunter, U.S. Naval Research Labo-

echelle grating. The test jig was a spectrograph designed to use this grating for planetary astronomy at the University of Arizona. The grating mount maintains the off-plane Littrow configuration at all times. Figure 1 shows the instrumental geometry. Collimated light is incident along î, and the dif­fracted beam d is adjusted to lie in the plane ⊥ z by varying γ; that is, by mechanically solving the diffraction equation mλ = 2σ · cosΓ · sinθ, where the groove spacing is σ = 1/79.01 mm. The range of γ was 8-18°. The light in the diffracted beam I(θ) was measured using a photomultiplier. The angle θ was varied by tilting the grating about its facets, and the mea­surement of I(θ) was repeated.

The blaze function I(θ)/I(ΘB) is expected to be the single-slit diffraction pattern of a single-grating facet. The effective facet width is

Then

where the θ,θB are in radians on the RHS. Our measurements (Fig. 2) were made using: (1) an un-

polarized He-Ne laser (λ 6328 Å); and (2) a mercury lamp with the green line isolated (λ 5461 Å). We performed a nonlinear least squares fit to the He-Ne data based on Eq. (2) with θB and α as free parameters. We find θB = 72.°5 ± 0.3 and α ≃ 2°.

The mercury data are plotted in Fig. 2 at modified abscissa values to compensate for the wavelength dependence in Eq. (2) so comparison with the He-Ne is direct:

The mercury points are consistent with the He-Ne points, indicating wavelength independence of the experiment over this range.

The Arizona spectrograph operates in the off-plane Littrow mode at all wavelengths. The most important spectrograph performance parameters, the angular dispersion and the resolution-throughput product, vary as 1/COSθB and tanθB, respectively. Since

the delivered grating will degrade by 20% the actual spectro­graph performance from the design based on the Bausch & Lomb blaze angle specification.

The spectrograph construction project is supported by NSF grant AST-7916476. Robert A. Brown is supported by NASA grant NSF-7634 to the University of Arizona. Amy L. Phillips is supported by NASA grant NSG-7644 to the University of Southern California.

References 1. F. H. Chaffee, Jr., and D. J. Schroeder, Ann. Rev. Astron. Astro-

phys. 14, 23 (1976). 2. D. J. Schroeder, Publ. Astron. Soc. Pac. 82, 1253 (1970). 3. M. Bottema, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 171

(1981). 4. E. G. Loewen, Bausch & Lomb; private communication.

168 APPLIED OPTICS / Vol. 21, No. 2 / 15 January 1982