Abstract

Four-level transmission-type surface relief grating profiles with nearly flat efficiency over a spectral octave are designed by rigorous electromagnetic diffraction theory. Parametric optimization of the relief depths and transition points of the profile steps of these leads to efficiencies in the range 50–60% over the entire octave if the ratio of the grating period and the mean spectral wavelength is greater than ~ 3.

© 2006 Optical Society of America

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References

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  1. B. Braam, J. Okkonen, M. Aikio, K. Makisara, J. Bolton, "Design and first test results of the Finnish airborne imaging spectrometer for different applications, AISA", in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE 1937, 142-151 (1993).
    [CrossRef]
  2. S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
    [CrossRef]
  3. F. Salem and M. Kafatos, "Hyperspectral image analysis for oil spilling mitigation,", in Proceedings of 22nd Asian Conference on Remote Sensing, (CRISP, Singapore, 2001) pp. 748-753.
  4. E. Herrala and J. Okkonen, "Imaging spectrograph and camera solutions for industrial applications," Int. J. Pattern Recogn. Artif. Intellig. 10, 43-54 (1996).
    [CrossRef]
  5. R. O. Green, "Spectral calibration requirement for Earth-looking imaging spectrometers in the solar-reflected spectrum," Appl. Opt. 37,683-690 (1998).
    [CrossRef]
  6. P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, "Convex grating types for concentric imaging spectrometers," Appl. Opt. 37,7200-7208 (1998).
    [CrossRef]
  7. P. Mouroulis, "Spectral and spatial uniformity in pushbroom imaging spectrometers," in Imaging Spectrometry V, J. B. Rafert, W. J. Slough, C. A. Rohde, A. Pilant, L. J. Otten, A. D. Meigs, A. Jones, and E. W. Butler, eds. Proc. SPIE 3753, 133-141 (1999).
    [CrossRef]
  8. T. Hyvarinen, E. Herrala, and A. Dall’Ava, "Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications," in Digital Solid State Cameras: Design and Applications, G. M. Williams, ed., Proc. SPIE 3302, 165-175 (1998).
    [CrossRef]
  9. E. Herrala, J. Okkonen, T. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," in Optical Measurements and Sensors for the Process Industries, C. Gorecki and R.W. Preater, eds., Proc. SPIE 2248, 33-40 (1994).
    [CrossRef]
  10. D. E. Battey and J. B. Slater, "Compact holographic imaging spectrograph for process control applications," in Optical Methods for Chemical Process Control, S. Farquharson, ed., Proc. SPIE 2069, 60-64 (1997).
    [CrossRef]
  11. E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
    [CrossRef]
  12. P. Laakkonen, M. Kuittinen, J. Simonen, and J. Turunen, "Electron-beam-fabricated asymmetric transmission gratings for microspectrometry," Appl. Opt. 39, 3187-3191 (2000).
    [CrossRef]
  13. H. P. Herzig, ed., Micro-optics: Elements, Systems and Applications (Taylor & Francis, London, 1997).
  14. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997).
  15. M. C. Hutley, Diffraction Gratings (Academic Press, Orlando, 1982).
  16. R. Petit, ed., Electromagnetic Theory of Gratings (Springer, Berlin, 1980).
    [CrossRef]
  17. J. Turunen,M. Kuittinen, and F. Wyrowski, "Diffractive optics: electromagnetic approach," in Progress in Optics, E. Wolf, ed., vol. XL, chap. V (Elsevier, Amsterdam, 2000).
  18. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870- 1876 (1996).
    [CrossRef]
  19. E. Noponen and J. Turunen, "Binary high-frequency-carrier diffractive optical elements: electromagnetic theory" J. Opt. Soc. Am. A 11,1097-1109 (1994).
    [CrossRef]
  20. E. Noponen, A. Vasara, and J. Turunen, "Parametric optimization of multilevel diffractive optical elements by electromagnetic theory," Appl. Opt. 31, 5910-5912 (1992).
    [CrossRef] [PubMed]
  21. E. Noponen, J. Turunen, and A. Vasara, "Electromagnetic theory and design of diffractive-lens arrays," J. Opt. Soc. Am. A 10,434-443 (1993).
    [CrossRef]
  22. K. Blomstedt, E. Noponen, and J. Turunen, "Surface-profile optimization of diffractive imaging lenses," J. Opt. Soc. Am. A 18,521-525 (2001).
    [CrossRef]
  23. C. David "Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements," Microelectron. Eng. 53, 677-680 (2000).
    [CrossRef]
  24. K. Jefimovs, Ph.D. Thesis (University of Joensuu, 2003).

2001 (2)

S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
[CrossRef]

K. Blomstedt, E. Noponen, and J. Turunen, "Surface-profile optimization of diffractive imaging lenses," J. Opt. Soc. Am. A 18,521-525 (2001).
[CrossRef]

2000 (3)

P. Laakkonen, M. Kuittinen, J. Simonen, and J. Turunen, "Electron-beam-fabricated asymmetric transmission gratings for microspectrometry," Appl. Opt. 39, 3187-3191 (2000).
[CrossRef]

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

C. David "Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements," Microelectron. Eng. 53, 677-680 (2000).
[CrossRef]

1998 (2)

1996 (2)

E. Herrala and J. Okkonen, "Imaging spectrograph and camera solutions for industrial applications," Int. J. Pattern Recogn. Artif. Intellig. 10, 43-54 (1996).
[CrossRef]

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870- 1876 (1996).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

Blomstedt, K.

Cianci, E.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

David, C.

C. David "Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements," Microelectron. Eng. 53, 677-680 (2000).
[CrossRef]

Foglietti, V.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Giovine, E.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Green, R. O.

Herrala, E.

E. Herrala and J. Okkonen, "Imaging spectrograph and camera solutions for industrial applications," Int. J. Pattern Recogn. Artif. Intellig. 10, 43-54 (1996).
[CrossRef]

Kong, S. H.

S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
[CrossRef]

Kuittinen, M.

Laakkonen, P.

Li, L.

Lorenzetti, D.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Maker, P. D.

Mouroulis, P.

Muller, R. E.

Noponen, E.

Notargiacomo, A.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Okkonen, J.

E. Herrala and J. Okkonen, "Imaging spectrograph and camera solutions for industrial applications," Int. J. Pattern Recogn. Artif. Intellig. 10, 43-54 (1996).
[CrossRef]

Simonen, J.

Turunen, J.

Vasara, A.

Vitali, F.

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Wijngaards, D. D. L.

S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
[CrossRef]

Wilson, D. W.

Wolffenbuttel, R. F.

S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
[CrossRef]

Appl. Opt. (4)

Int. J. Pattern Recogn. Artif. Intellig. (1)

E. Herrala and J. Okkonen, "Imaging spectrograph and camera solutions for industrial applications," Int. J. Pattern Recogn. Artif. Intellig. 10, 43-54 (1996).
[CrossRef]

J. Opt. Soc. Am. A (4)

Microelectron. Eng. (2)

C. David "Fabrication of stair-case profiles with high aspect ratios for blazed diffractive optical elements," Microelectron. Eng. 53, 677-680 (2000).
[CrossRef]

E. Cianci, V. Foglietti, F. Vitali, D. Lorenzetti, A. Notargiacomo, and E. Giovine "Micromachined silicon grisms: high resolution spectroscopy in the near infrared," Microelectron. Eng. 53, 543-546 (2000).
[CrossRef]

Sensors and Actuators A (1)

S. H. Kong, D. D. L. Wijngaards, and R. F. Wolffenbuttel, "Infrared micro-spectrometer based on diffraction gratings," Sensors and Actuators A 92,88-95 (2001).
[CrossRef]

Other (12)

F. Salem and M. Kafatos, "Hyperspectral image analysis for oil spilling mitigation,", in Proceedings of 22nd Asian Conference on Remote Sensing, (CRISP, Singapore, 2001) pp. 748-753.

K. Jefimovs, Ph.D. Thesis (University of Joensuu, 2003).

H. P. Herzig, ed., Micro-optics: Elements, Systems and Applications (Taylor & Francis, London, 1997).

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997).

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

R. Petit, ed., Electromagnetic Theory of Gratings (Springer, Berlin, 1980).
[CrossRef]

J. Turunen,M. Kuittinen, and F. Wyrowski, "Diffractive optics: electromagnetic approach," in Progress in Optics, E. Wolf, ed., vol. XL, chap. V (Elsevier, Amsterdam, 2000).

P. Mouroulis, "Spectral and spatial uniformity in pushbroom imaging spectrometers," in Imaging Spectrometry V, J. B. Rafert, W. J. Slough, C. A. Rohde, A. Pilant, L. J. Otten, A. D. Meigs, A. Jones, and E. W. Butler, eds. Proc. SPIE 3753, 133-141 (1999).
[CrossRef]

T. Hyvarinen, E. Herrala, and A. Dall’Ava, "Direct sight imaging spectrograph: a unique add-on component brings spectral imaging to industrial applications," in Digital Solid State Cameras: Design and Applications, G. M. Williams, ed., Proc. SPIE 3302, 165-175 (1998).
[CrossRef]

E. Herrala, J. Okkonen, T. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," in Optical Measurements and Sensors for the Process Industries, C. Gorecki and R.W. Preater, eds., Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

D. E. Battey and J. B. Slater, "Compact holographic imaging spectrograph for process control applications," in Optical Methods for Chemical Process Control, S. Farquharson, ed., Proc. SPIE 2069, 60-64 (1997).
[CrossRef]

B. Braam, J. Okkonen, M. Aikio, K. Makisara, J. Bolton, "Design and first test results of the Finnish airborne imaging spectrometer for different applications, AISA", in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE 1937, 142-151 (1993).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

The type of transmission-grating profile considered in this paper, with illustration of the free optimization parameters xj , zj (j = 1,2,3), and θ.

Fig. 2.
Fig. 2.

Spectral efficiency curves of order -1 for unpolarized light with (a) d = 11μm and (b) d = 5 μm. Blue: regular staircase profile. Red: optimized overall efficiency. Green: flattened efficiency.

Fig. 3.
Fig. 3.

Grating profiles with (a) d = 11μm and (b) d = 5 μm. Blue: regular staircase profile. Red: profiles with optimized overall efficiency. Green: profiles with flattened efficiency.

Fig. 4.
Fig. 4.

Polarization sensitivity of flattened diffraction efficiency curves with (a) d = 11μm and (b) d = 5 μm. Blue: TE polarization. Red: TM polarization. Green: unpolarized light.

Tables (1)

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Table 1. Quantitative characterization of the grating profiles illustrated in Fig. 3.

Equations (2)

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MF = n = 1 N [ 1 2 η TE ( λ n ) + 1 2 η TM ( λ n ) η ̅ ] 2
η ̅ = 1 2 N n = 1 N [ η TE ( λ n ) + η TM ( λ n ) ]

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