Abstract

The properties of convex gratings fabricated by electron-beam lithography are investigated. Three grating types are shown. The first is a single-panel, true blazed grating in which the blaze angle stays constant relative to the local surface normal. This grating provides high peak efficiencies of approximately 88% in the first order and 85% in the second order. The second grating has two concentric panels, with each panel blazed at a different angle. This type permits flexibility in matching the grating response to a desired form. The third type has a groove shape that departs from the sawtooth blazed profile to increase the second-order bandwidth. All these types are difficult or impossible to produce with conventional techniques. The gratings compare favorably with conventional (holographic and ruled) types in terms of efficiency and scatter. Simple scalar models are shown to predict the wavelength response accurately. These gratings allow the optical designer to realize fully the considerable advantages of concentric spectrometer forms.

© 1998 Optical Society of America

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1997 (2)

1994 (1)

1992 (1)

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. 10, 2516–2519 (1992).
[CrossRef]

1990 (1)

1989 (2)

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

1987 (1)

C. G. Wynne, “Monocentric telescopes for microlithography,” Opt. Eng. 26, 300–303 (1987).
[CrossRef]

1980 (1)

1979 (1)

H. H. Zwick, “Evaluation results from a pushbroom imager for remote sensing,” Can. J. Remote Sens. 5, 101–117 (1979).

1977 (1)

1975 (1)

A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14, 130–132 (1975).
[CrossRef]

1970 (1)

H. Dammann, “Blazed synthetic phase only holograms,” Optik 31, 95–104 (1970).

1959 (1)

Ackerman, T. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Andrada, T.

T. J. Brown, F. J. Corbett, T. J. Spera, T. Andrada, “Thermal infrared pushbroom imagery acquisition and processing,” in Modern Utilization of Infrared Technology VII, I. J. Spiro, ed., Proc. SPIE304, 37–56 (1981).
[CrossRef]

Behrmann, G. P.

Brown, T. J.

T. J. Brown, F. J. Corbett, T. J. Spera, T. Andrada, “Thermal infrared pushbroom imagery acquisition and processing,” in Modern Utilization of Infrared Technology VII, I. J. Spiro, ed., Proc. SPIE304, 37–56 (1981).
[CrossRef]

Bruegge, C. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Buralli, D. A.

Charlton, D.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Clark, J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Corbett, F. J.

T. J. Brown, F. J. Corbett, T. J. Spera, T. Andrada, “Thermal infrared pushbroom imagery acquisition and processing,” in Modern Utilization of Infrared Technology VII, I. J. Spiro, ed., Proc. SPIE304, 37–56 (1981).
[CrossRef]

Dammann, H.

H. Dammann, “Blazed synthetic phase only holograms,” Optik 31, 95–104 (1970).

Daniels, J. A.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Danielson, E. D.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Davancens, R.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Davies, R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Diner, D. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Donnadieu, O.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Duignan, M. T.

Duval, V. G.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Dyson, J.

Fabbricotti, M.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Gerstl, S. A. W.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Gordon, H. R.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Harnisch, B.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Hoose, J.

Hunter, W. R.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, Orlando, Fla., 1982).

Klaasen, K. P.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Kunkel, B.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Leger, J. R.

Lilienthal, G. W.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Lobb, D. R.

D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33, 2648–2658 (1994).
[CrossRef] [PubMed]

D. R. Lobb, “Imaging spectrometers using concentric optics,” in Imaging Spectrometry III, M. R. Descour, S. S. Shen, eds., Proc. SPIE3118, 339–347 (1997).
[CrossRef]

Loewen, E. G.

Maker, P. D.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. 10, 2516–2519 (1992).
[CrossRef]

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made be E-beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Vol. 62 of SPIE Critical Reviews Series (SPIE, Bellingham, Wash., 1996), pp. 415–430.

P. D. Maker, R. E. Muller, “Continuous phase and amplitude holographic elements,” U.S. patent5,393,634 (28February1995).

Martonchik, J. V.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Menardi, A.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Mertz, L.

Meynart, R.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Morris, G. M.

Muller, R. E.

P. D. Maker, R. E. Muller, “Phase holograms in polymethyl methacrylate,” J. Vac. Sci. Technol. 10, 2516–2519 (1992).
[CrossRef]

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made be E-beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Vol. 62 of SPIE Critical Reviews Series (SPIE, Bellingham, Wash., 1996), pp. 415–430.

P. D. Maker, R. E. Muller, “Continuous phase and amplitude holographic elements,” U.S. patent5,393,634 (28February1995).

Nakamoto, D. I.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Neviere, M.

Offner, A.

A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14, 130–132 (1975).
[CrossRef]

Pagano, R. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Popov, E. K.

Preston, D.

P. Silverglate, K. L. Shu, D. Preston, J. Stein, F. Sileo, “Concepts for spaceborne hyperspectral imagery using prism spectrometers,” in Advanced Microdevices and Space Science Sensors, J. A. Cutts, ed., Proc. SPIE2267, 112–120 (1995).
[CrossRef]

Rediker, R. H.

Reilly, T. H.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Reininger, F.

F. Reininger and 46 coauthors, “VIRTIS: visible infrared thermal imaging spectrometer for the Rosetta mission,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 66–77 (1996).
[CrossRef]

Rogers, J. R.

Saint-Pe, O.

O. Saint-Pe, O. Donnadieu, R. Davancens, D. Charlton, A. Menardi, M. Fabbricotti, B. Harnisch, R. Meynart, B. Kunkel, “Development of a 2-D array for 1 to 2.35 μm hyperspectral imager,” in Infrared Detectors for Remote Sensing: Physics, Materials, and Devices, R. E. Longshore, J. W. Baars, eds., Proc. SPIE2816, 138–149 (1997).
[CrossRef]

Sellers, P. J.

D. J. Diner, C. J. Bruegge, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, P. J. Sellers, J. Clark, J. A. Daniels, E. D. Danielson, V. G. Duval, K. P. Klaasen, G. W. Lilienthal, D. I. Nakamoto, R. J. Pagano, T. H. Reilly, “MISR: a multiangle imaging spectroradiometer for geophysical and climatological research,” IEEE Trans. Geosci. Remote Sens. 27, 200–214 (1989).
[CrossRef]

Shu, K. L.

P. Silverglate, K. L. Shu, D. Preston, J. Stein, F. Sileo, “Concepts for spaceborne hyperspectral imagery using prism spectrometers,” in Advanced Microdevices and Space Science Sensors, J. A. Cutts, ed., Proc. SPIE2267, 112–120 (1995).
[CrossRef]

Sileo, F.

P. Silverglate, K. L. Shu, D. Preston, J. Stein, F. Sileo, “Concepts for spaceborne hyperspectral imagery using prism spectrometers,” in Advanced Microdevices and Space Science Sensors, J. A. Cutts, ed., Proc. SPIE2267, 112–120 (1995).
[CrossRef]

Silverglate, P.

P. Silverglate, K. L. Shu, D. Preston, J. Stein, F. Sileo, “Concepts for spaceborne hyperspectral imagery using prism spectrometers,” in Advanced Microdevices and Space Science Sensors, J. A. Cutts, ed., Proc. SPIE2267, 112–120 (1995).
[CrossRef]

Spera, T. J.

T. J. Brown, F. J. Corbett, T. J. Spera, T. Andrada, “Thermal infrared pushbroom imagery acquisition and processing,” in Modern Utilization of Infrared Technology VII, I. J. Spiro, ed., Proc. SPIE304, 37–56 (1981).
[CrossRef]

Stein, J.

P. Silverglate, K. L. Shu, D. Preston, J. Stein, F. Sileo, “Concepts for spaceborne hyperspectral imagery using prism spectrometers,” in Advanced Microdevices and Space Science Sensors, J. A. Cutts, ed., Proc. SPIE2267, 112–120 (1995).
[CrossRef]

Tsonev, L. V.

Wang, X.

Wilson, D. W.

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Figures (16)

Fig. 1
Fig. 1

Typical Offner spectrometer. The grating lies upon the convex secondary mirror. The slit is at the top left, perpendicular to the plane of the paper. The grating grooves are also perpendicular to the paper. The object and image planes are not identical, although they are very similar in this case. The spectrometer volume (including conjugates) is 14 cm × 11 cm × 7 cm.

Fig. 2
Fig. 2

Atomic-force microscope scan of typical grating grooves. The blaze angle is only ∼2°. It is highly exaggerated for clarity. Left, area around the boundary between two grating sections with different blaze angles. Right top, profile of the section marked by a dark line in the grating section shown at the bottom.

Fig. 3
Fig. 3

Schematic of the experimental setup for the evaluation of convex gratings.

Fig. 4
Fig. 4

Relative diffraction efficiency of a true blazed grating upon a convex substrate (first order). The solid curve is derived from Eq. (2).

Fig. 5
Fig. 5

Relative diffraction efficiency of a true blazed grating upon a convex substrate (second order). The theoretical curve is derived from Eq. (2) and is chosen to match the experimental points in peak efficiency.

Fig. 6
Fig. 6

Relative diffraction efficiency of a dual-blaze grating in the first order. The theoretical curve is derived from Eq. (3).

Fig. 7
Fig. 7

Relative diffraction efficiency of a dual-blaze grating in the second order (same grating as for Fig. 6). The theoretical curve is derived from Eq. (3).

Fig. 8
Fig. 8

Profiles of dual-blaze gratings (a) with peaks aligned and (b) with equal average heights. In the first case there is a mean phase difference between the two blaze areas that depends on the height difference Δh.

Fig. 9
Fig. 9

Relative efficiency of the two blaze areas in the first order. The curves are normalized to unity peak efficiency.

Fig. 10
Fig. 10

Relative phase difference between the two blaze areas in the first order. The two bottom curves represent the actual gratings manufactured. The topmost curve (triangles) represents a grating with the peaks matched, as in Fig. 8(a).

Fig. 11
Fig. 11

Relative efficiency of the two blaze areas in the second order. The curves are normalized to unity peak efficiency.

Fig. 12
Fig. 12

Relative phase difference between the two blaze areas in the second order. The top two curves shown represent the two dual-blaze gratings that were manufactured with approximately matched average heights. The bottom curve (triangles) shows the phase difference for an ideal grating with perfectly matched average heights.

Fig. 13
Fig. 13

Groove profile of a dual-angle blazed grating. There are two different linear segments. The slopes and the groove depth are highly exaggerated for clarity. The actual values for the slopes of the two segments were approximately 1.5° and 2.8°.

Fig. 14
Fig. 14

Relative diffraction efficiency of a dual-angle blazed grating in the first and second orders. The experimental points are shown by the symbols: squares, first order; triangles, second order. The solid curves show the theoretical fit obtained by a Fourier transformation of the groove profile.

Fig. 15
Fig. 15

p-versus-s efficiency for the dual-angle blazed grating in the second order. The average efficiency, as calculated from these two curves, matches the second-order curve of Fig. 14 with a few-percent error.

Fig. 16
Fig. 16

Comparison of diffraction efficiencies of a ruled, three-panel grating and a dual-blaze EB grating. The second-order efficiency is shown up to 1000 nm, and the first-order efficiency beyond that point. A theoretical curve to the ruled grating efficiency is also shown.

Tables (1)

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Table 1 Grating Parameters

Equations (3)

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θ = α - β / 2 ,
D i = D 0 i sin π λ 0 λ - i π λ 0 λ - i 2 ,
D = D 0 i 0.33 D ai + 0.67 D bi .

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