Abstract

We present the development of an imaging spectrometer for the near infrared (NIR) using a micro- opto-electromechanical system. A diffraction grating has been etched into the surface of a micro mechanical scanning mirror made of silicon and is used to scan the object space and to disperse the NIR radiation simultaneously. Beginning with the specific requirements of NIR hyperspectral imaging, a detailed analysis of the system approach resulting in an all-reflective optical design for the hyperspectral imager is presented. The investigation includes a thorough consideration of spectral and spatial distortion occurring by scanning the scene with a grating. Minimization of these aberrations leads to an improved spectrometer design.

© 2009 Optical Society of America

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References

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  1. H. W. Siesler, Near-Infrared Spectroscopy (Wiley-VCH2002).
  2. G. Tranter, J. Holmes, and J. Lindon, Encyclopedia of Spectroscopy and Spectrometry (Elsevier2000), Vols. 1-3.
  3. W. Kessler, Multivariate Data Analysis (Wiley-VCH2007).
  4. G. Reich, “Near-infrared spectroscopy and imaging: basic principles and pharmaceutical applications,” Advanced Drug Delivery Reviews, Vol. 57 of Science Direct (Elsevier2005), pp. 1109-1143.
  5. R. G. Sellar, G. D. Boreman, and L. E. Kirkland, “Comparison of signal collection abilities of different classes of imaging spectrometers,” Proc. SPIE 4816, 389-396 (2002).
    [CrossRef]
  6. D. E. Rockey, “High resolution imaging spectrometer (HIRIS)--a major advance in imaging spectrometry,” Proc. SPIE 1298, 93-104 (1990).
    [CrossRef]
  7. A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
    [CrossRef]
  8. L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE 4480, 1-14 (2002).
    [CrossRef]
  9. E. Ansbro, “A new wide field spectrograph,” Proc. SPIE 5492, 1290-1294 (2004).
    [CrossRef]
  10. C. Feng and A. Ahmad, “Design and modeling of a low-f-number wide-field of view imaging spectrometer,” Proc. SPIE 2819, 118-126 (1996).
    [CrossRef]
  11. P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39, 2210-2220 (2000).
    [CrossRef]
  12. P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
    [CrossRef]
  13. A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electron. Rev. 12, 221-245 (2004).
  14. R. N. Jorgensen, The VTTVIS Line Imaging Spectrometer--Principles, Error Sources, and Calibration (Riso National Laboratory, 2002).
  15. G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
    [CrossRef]
  16. P. Mouroulis, “Low-distortion imaging spectrometer designs utilizing convex gratings,” Proc. SPIE 3482, 594-601 (1998).
    [CrossRef]
  17. F. Dell'Endice, J. Nieke, D. Schläpfer, and K. I. Itten, “Scene-based method for spatial misregistration detection in hyperspectral imagery,” Appl. Opt. 46, 2803-2815 (2007).
    [CrossRef]
  18. C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).
  19. F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165-179 (1995).
    [CrossRef]
  20. J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 39, 8158-8160 (1998).
  21. J. E. Harvey, D. Bogunovic, and A. Krywonos, “Aberrations of diffracted wave fields,” Appl. Opt. 42, 1167-1174 (2003).
    [CrossRef]
  22. R. O. Green, “Calibration requirements for Earth-looking imaging spectrometers in the solar-reflected spectrum,” Appl. Opt. 37, 683-690 (1998).
    [CrossRef]
  23. H. Gross, Handbook of Optical Systems, Vol. 1 of Fundamentals of Technical Optics (Wiley-VCH, 2005).
  24. D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
    [CrossRef]
  25. H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
    [CrossRef]
  26. H. Schenk, Ein neuartiger Mikroaktor zur ein- und zweidimensionalen Ablenkung von Licht, Ph.D. dissertation (Gerhard-Mercator-Universität-Gesamthochschule Duisburg, 2000).
  27. F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
    [CrossRef]
  28. W. L. Wolfe, Optical Engineer's Desk Reference (Optical Society of America, 2003).
  29. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon1980).
  30. N. C. Das, “Aberration properties of a Czerny-Turner spectrograph using plane-holographic diffraction grating,” Appl. Opt. 30, 3589-3597 (1991).
    [CrossRef]
  31. A. Kutter, Der Schiefspiegler (Verlag F. Weichardt, 1953).
  32. H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Volume 4, Survey of Optical Instruments (Wiley-VCH2008).
  33. D. R. Hearn, “Characterization of instrument spectral resolution by the spectral modulation transfer function,” Proc. SPIE 3439, 400-407 (1998).
    [CrossRef]
  34. R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

2007 (3)

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
[CrossRef]

F. Dell'Endice, J. Nieke, D. Schläpfer, and K. I. Itten, “Scene-based method for spatial misregistration detection in hyperspectral imagery,” Appl. Opt. 46, 2803-2815 (2007).
[CrossRef]

2006 (1)

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

2004 (3)

E. Ansbro, “A new wide field spectrograph,” Proc. SPIE 5492, 1290-1294 (2004).
[CrossRef]

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electron. Rev. 12, 221-245 (2004).

2003 (2)

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

J. E. Harvey, D. Bogunovic, and A. Krywonos, “Aberrations of diffracted wave fields,” Appl. Opt. 42, 1167-1174 (2003).
[CrossRef]

2002 (2)

R. G. Sellar, G. D. Boreman, and L. E. Kirkland, “Comparison of signal collection abilities of different classes of imaging spectrometers,” Proc. SPIE 4816, 389-396 (2002).
[CrossRef]

L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE 4480, 1-14 (2002).
[CrossRef]

2000 (3)

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39, 2210-2220 (2000).
[CrossRef]

1998 (4)

J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 39, 8158-8160 (1998).

R. O. Green, “Calibration requirements for Earth-looking imaging spectrometers in the solar-reflected spectrum,” Appl. Opt. 37, 683-690 (1998).
[CrossRef]

D. R. Hearn, “Characterization of instrument spectral resolution by the spectral modulation transfer function,” Proc. SPIE 3439, 400-407 (1998).
[CrossRef]

P. Mouroulis, “Low-distortion imaging spectrometer designs utilizing convex gratings,” Proc. SPIE 3482, 594-601 (1998).
[CrossRef]

1996 (1)

C. Feng and A. Ahmad, “Design and modeling of a low-f-number wide-field of view imaging spectrometer,” Proc. SPIE 2819, 118-126 (1996).
[CrossRef]

1995 (1)

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165-179 (1995).
[CrossRef]

1991 (1)

1990 (1)

D. E. Rockey, “High resolution imaging spectrometer (HIRIS)--a major advance in imaging spectrometry,” Proc. SPIE 1298, 93-104 (1990).
[CrossRef]

Achtner, B.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Volume 4, Survey of Optical Instruments (Wiley-VCH2008).

Ahmad, A.

C. Feng and A. Ahmad, “Design and modeling of a low-f-number wide-field of view imaging spectrometer,” Proc. SPIE 2819, 118-126 (1996).
[CrossRef]

Ansbro, E.

E. Ansbro, “A new wide field spectrograph,” Proc. SPIE 5492, 1290-1294 (2004).
[CrossRef]

Beale, J.

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

Blechinger, F.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165-179 (1995).
[CrossRef]

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Volume 4, Survey of Optical Instruments (Wiley-VCH2008).

Bogunovic, D.

Boreman, G. D.

R. G. Sellar, G. D. Boreman, and L. E. Kirkland, “Comparison of signal collection abilities of different classes of imaging spectrometers,” Proc. SPIE 4816, 389-396 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon1980).

Carleton, C.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Chrien, T. G.

Das, N. C.

Dell'Endice, F.

Duncan, M.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Dürr, P.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Feng, C.

C. Feng and A. Ahmad, “Design and modeling of a low-f-number wide-field of view imaging spectrometer,” Proc. SPIE 2819, 118-126 (1996).
[CrossRef]

Fischer, R. E.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

Friend, M.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Green, R. O.

Greenaway, A. H.

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

Gross, H.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Volume 4, Survey of Optical Instruments (Wiley-VCH2008).

H. Gross, Handbook of Optical Systems, Vol. 1 of Fundamentals of Technical Optics (Wiley-VCH, 2005).

Grüger, H.

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

Haase, T.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Hanlon, T. J.

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

Harnisch, B.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165-179 (1995).
[CrossRef]

Harvey, A. R.

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

Harvey, J. E.

J. E. Harvey, D. Bogunovic, and A. Krywonos, “Aberrations of diffracted wave fields,” Appl. Opt. 42, 1167-1174 (2003).
[CrossRef]

J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 39, 8158-8160 (1998).

Hearn, D. R.

D. R. Hearn, “Characterization of instrument spectral resolution by the spectral modulation transfer function,” Proc. SPIE 3439, 400-407 (1998).
[CrossRef]

Heberer, A.

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

Hinrichs, J.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Holmes, J.

G. Tranter, J. Holmes, and J. Lindon, Encyclopedia of Spectroscopy and Spectrometry (Elsevier2000), Vols. 1-3.

Itten, K. I.

F. Dell'Endice, J. Nieke, D. Schläpfer, and K. I. Itten, “Scene-based method for spatial misregistration detection in hyperspectral imagery,” Appl. Opt. 46, 2803-2815 (2007).
[CrossRef]

D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
[CrossRef]

Jorgensen, R. N.

R. N. Jorgensen, The VTTVIS Line Imaging Spectrometer--Principles, Error Sources, and Calibration (Riso National Laboratory, 2002).

Keizer, L. C. P.

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

Kessler, W.

W. Kessler, Multivariate Data Analysis (Wiley-VCH2007).

Kirkland, L. E.

R. G. Sellar, G. D. Boreman, and L. E. Kirkland, “Comparison of signal collection abilities of different classes of imaging spectrometers,” Proc. SPIE 4816, 389-396 (2002).
[CrossRef]

Krywonos, A.

Kück, H.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Kunkel, B.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165-179 (1995).
[CrossRef]

Kunze, D.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Kutter, A.

A. Kutter, Der Schiefspiegler (Verlag F. Weichardt, 1953).

Lakner, H.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Lindon, J.

G. Tranter, J. Holmes, and J. Lindon, Encyclopedia of Spectroscopy and Spectrometry (Elsevier2000), Vols. 1-3.

Lomheim, T. S.

L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE 4480, 1-14 (2002).
[CrossRef]

Mouroulis, P.

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. 39, 2210-2220 (2000).
[CrossRef]

P. Mouroulis, “Low-distortion imaging spectrometer designs utilizing convex gratings,” Proc. SPIE 3482, 594-601 (1998).
[CrossRef]

Neumann, J.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Nieke, J.

F. Dell'Endice, J. Nieke, D. Schläpfer, and K. I. Itten, “Scene-based method for spatial misregistration detection in hyperspectral imagery,” Appl. Opt. 46, 2803-2815 (2007).
[CrossRef]

D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
[CrossRef]

Polder, G.

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

Reich, G.

G. Reich, “Near-infrared spectroscopy and imaging: basic principles and pharmaceutical applications,” Advanced Drug Delivery Reviews, Vol. 57 of Science Direct (Elsevier2005), pp. 1109-1143.

Rockey, D. E.

D. E. Rockey, “High resolution imaging spectrometer (HIRIS)--a major advance in imaging spectrometry,” Proc. SPIE 1298, 93-104 (1990).
[CrossRef]

Rogalski, A.

A. Rogalski, “Optical detectors for focal plane arrays,” Opto-Electron. Rev. 12, 221-245 (2004).

Schenk, H.

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

H. Schenk, Ein neuartiger Mikroaktor zur ein- und zweidimensionalen Ablenkung von Licht, Ph.D. dissertation (Gerhard-Mercator-Universität-Gesamthochschule Duisburg, 2000).

Schläpfer, D.

D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
[CrossRef]

F. Dell'Endice, J. Nieke, D. Schläpfer, and K. I. Itten, “Scene-based method for spatial misregistration detection in hyperspectral imagery,” Appl. Opt. 46, 2803-2815 (2007).
[CrossRef]

Schumann, L. W.

L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE 4480, 1-14 (2002).
[CrossRef]

Sellar, R. G.

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

R. G. Sellar, G. D. Boreman, and L. E. Kirkland, “Comparison of signal collection abilities of different classes of imaging spectrometers,” Proc. SPIE 4816, 389-396 (2002).
[CrossRef]

Shea, J. J.

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

Siesler, H. W.

H. W. Siesler, Near-Infrared Spectroscopy (Wiley-VCH2002).

Sobe, U.

H. Schenk, P. Dürr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kück, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715-722 (2000).
[CrossRef]

Tadic-Galeb, B.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

Tranter, G.

G. Tranter, J. Holmes, and J. Lindon, Encyclopedia of Spectroscopy and Spectrometry (Elsevier2000), Vols. 1-3.

van der Heijden, G. W. A. M.

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

Velasco, A.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Vernold, C. L.

J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 39, 8158-8160 (1998).

Warren, C. P.

C. P. Warren, M. Friend, A. Velasco, J. Hinrichs, C. Carleton, M. Duncan, and J. Neumann, “Miniaturization of a VNIR hyperspectral imager,” Proc. SPIE 6302, 594-601 (2006).

Williams, J.

A. R. Harvey, J. Beale, A. H. Greenaway, T. J. Hanlon, and J. Williams, “Technology options for imaging spectrometry,” Proc. SPIE 4132, 13-24 (2000).
[CrossRef]

Wilson, D. W.

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon1980).

Wolfe, W. L.

W. L. Wolfe, Optical Engineer's Desk Reference (Optical Society of America, 2003).

Wolter, A.

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

Young, I. T.

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

Zimmer, F.

F. Zimmer, H. Grüger, A. Heberer, A. Wolter, and H. Schenk, “Development of a NIR micro spectrometer based on a MOEMS scanning grating,” Proc. SPIE 5455, 9-18 (2004).
[CrossRef]

Appl. Opt. (6)

IEEE Trans. Geosci. Remote Sens. (1)

D. Schläpfer, J. Nieke, and K. I. Itten, “Spatial PSF nonuniformity effects in airborne pushbroom imaging spectrometry data,” IEEE Trans. Geosci. Remote Sens. 45, 458-468(2007).
[CrossRef]

J. Near Infrared Spectrosc. (1)

G. Polder, G. W. A. M. van der Heijden, L. C. P. Keizer, and I. T. Young, “Calibration and characterisation of imaging spectrographs,” J. Near Infrared Spectrosc. 11, 193-210 (2003).
[CrossRef]

Opt. Eng. (1)

P. Mouroulis, R. G. Sellar, D. W. Wilson, J. J. Shea, and R. O. Green, “Optical design of a compact imaging spectrometer for planetary mineralogy,” Opt. Eng. 46, 063001 (2007).
[CrossRef]

Opto-Electron. Rev. (1)

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Figures (17)

Fig. 1
Fig. 1

Schematic configuration of the MOEMS HSI.

Fig. 2
Fig. 2

Coordinate systems and parameters to describe the behavior of a grating used to scan a linear extended object field: a ray e i emerges from a linear object field in the far field of the reference coordinate system ( x , y , z ) ; the field position is defined by the field angle θ i ; the object field is extended in the y direction only and is inclined about the angle ψ i relative to the reference coordinate system; the diffraction grating with the normal vectors ( α , β , γ ) is arranged in the reference coordinate system, where the grating is tilted about the x axis at the mechanical scan angle φ; the direction of the diffracted ray e m is described by the angle along the x z plane ψ d and the angle perpendicular thereto θ d .

Fig. 3
Fig. 3

Illustration of the distortion of the principal ray in the image plane without inclination of the grating ( φ = 0 ° ) for a central object point (left) and with inclination φ = φ λ 0 for a marginal object point (right).

Fig. 4
Fig. 4

Relative spatial distortion | δ θ / Δ ψ d | against the relative wavelength λ / λ 0 and the angular alignment of the entrance slit ψ i .

Fig. 5
Fig. 5

Average spatial distortion RMS δ θ / Δ ψ d for a wavelength range of 0.6 λ 0 to 1.4 λ 0 against the relative grating constant d / λ 0 and the angle ψ i ; the minimal spatial distortion (dashed curve).

Fig. 6
Fig. 6

Relative spectral distortion | δ ψ / Δ ψ d | against the relative wavelength λ / λ 0 and the angular alignment of the entrance slit ψ i .

Fig. 7
Fig. 7

Average spectral distortion RMS δ ψ / Δ ψ d for a wavelength range of 0.6 λ 0 to 1.4 λ 0 against the relative grating constant d / λ 0 and the angle ψ i ; the minimal spatial distortion is indicated by the dashed line.

Fig. 8
Fig. 8

Average total distortion RMS δ υ / Δ ψ d for a wavelength range of 0.6 λ 0 to 1.4 λ 0 against the relative grating constant d / λ 0 and the angle ψ i ; the minimum total distortion is shown by the dashed curve.

Fig. 9
Fig. 9

Average spatial, spectral, and total distortion for a system with a relative grating constant d / λ 0 of 1.667 and a field angle of θ i = 6 ° .

Fig. 10
Fig. 10

MOEMS scanning mirror (left) [29] with diffraction grating, made by anisotropic silicon etching (right).

Fig. 11
Fig. 11

Optical layout of the objective mirror adapted to the MOEMS-imaging spectrograph.

Fig. 12
Fig. 12

Modulus of the optical transfer function (OTF) for spatial frequencies of 5, 10, and 20   cycles / mm versus the relative image field; the spatial frequencies represent 1, 2, and 4 times the projected detector frequency.

Fig. 13
Fig. 13

Optical layout of the MOEMS-imaging spectrograph.

Fig. 14
Fig. 14

Spot diagrams for five object field positions and for five wavelengths; the inner ellipse shows the airy disk and the box with a size of 50 μm represents one dimension of the detector array element size of 50 μm × 130 μm .

Fig. 15
Fig. 15

Spectral coregistered energy from the adjacent pixels versus object field for wavelengths of 1000, 1500, and 2000 nm .

Fig. 16
Fig. 16

Normalized spectral response function relative to the pixel center wavelengths for 1010, 1500, and 1990 nm . The spectral response function illustrates how one pixel accepts a single wavelength.

Fig. 17
Fig. 17

Distortion grid of the MOEMS-imaging spectrograph: the diagram shows the coordinate of the scanned entrance slit and the wavelength.

Tables (3)

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Table 1 Parameters of the Imaging Spectrograph

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Table 2 General System Parameters

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Table 3 Parameters of the Objective Lens

Equations (14)

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e i , r = ( cos θ i · sin ψ i sin θ i cos θ i · cos ψ i ) = ( x i y i z i ) .
e i , g = ( 1 0 0 0 cos φ sin φ 0 sin φ cos φ ) · e i = ( α i β i γ i ) .
e m , g = ( m · λ / d α i β i γ i 2 ( m · λ / d ) 2 + 2 · α i · m · λ / d ) .
e m , r = ( cos θ d · sin ψ d sin θ d cos θ d · cos ψ d ) .
sin θ d = cos 2 φ cos θ i ( tan θ i cos ψ i tan φ ) sin φ [ 1 ( m λ / d + cos θ i sin ψ i ) 2 cos 2 φ cos 2 θ i ( cos ψ i tan ϕ tan θ i ) ] 1 / 2 ,
tan ψ d = ( m λ / d + cos θ i sin ψ i ) / ( cos φ { sin φ cos θ i [ tan θ i cos ψ i tan φ ] + [ 1 ( m λ / d + cos θ i sin ψ i ) 2 cos 2 φ cos 2 θ i ( cos ψ i tan φ tan θ i ) 2 ] 1 / 2 } ) .
tan φ λ 0 = sin θ i / ( { [ m λ 0 / d ] 2 + 2 m λ 0 / d cos θ i sin θ i sin 2 θ i } { cos ψ i cos θ i [ 1 ( m λ 0 / d + cos θ i sin ψ i ) 2 ] 1 / 2 } ) .
δ θ d = | θ d ( φ = φ λ 0 , θ i , ψ i , λ , d ) | .
δ ψ d = | ψ d ( θ i , ψ i , λ , d ) ψ d ( θ i = 0 ° , ψ i , λ , d ) | .
RMS δ υ = 1 Δ λ ( δ θ d ) 2 + ( δ ψ d ) 2 d λ .
N pixel , slit = Δ x max δ x max ν det π · ν scan .
f re = w det 2 tan ( Δ ψ d / 2 ) .
f coll = N pixel , det w slit σ π ν scan 2 tan ( Δ ψ m / 2 ) ν det .
f / # w , coll = N pixel , det w slit σ 2 tan ( Δ ψ m / 2 ) w grating N pixel , slit .

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