Abstract

In this article the problem of achieving fast scanning of a time-of-flight range sensor with a large optical receiver aperture at low system cost is targeted. The presented approach to solve this problem consists of a micromirror-based transmitter unit and a receiver unit consisting of a large aperture lens system with a small field of view and a detector array. A concept, which is called synchronous detector switching, is applied to the detector array. Thereby electronic steering of the small receiver field of view is possible. The overall approach is compared to alternative approaches, and the underlying concept of synchronous detector switching is demonstrated experimentally in an implementation of a three-dimensional time-of-flight range sensor. It is theoretically shown that the presented concept is potentially cheaper than the alternative approaches for applications with a field of view of less than 60×60°. After a discussion of the strengths and limitations of the approach, its effect on broader scientific issues is outlined.

© 2014 Optical Society of America

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  1. R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.
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  4. N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
    [CrossRef]
  5. S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
    [CrossRef]
  6. J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.
  7. H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).
  8. H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
    [CrossRef]
  9. H. Schenk, P. Durr, T. Haase, D. Kunze, U. Sobe, H. Lakner, and H. Kuck, “Large deflection micromechanical scanning mirrors for linear scans and pattern generation,” IEEE J. Sel. Top. Quantum Electron. 6, 715–722 (2000).
    [CrossRef]
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  11. T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
    [CrossRef]
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  17. S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
    [CrossRef]
  18. D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.
  19. M. J. Riedl, Optical Design Fundamentals for Infrared Systems, 2nd ed. (SPIE, 2001).
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    [CrossRef]
  21. K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
    [CrossRef]
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    [CrossRef]
  23. A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
    [CrossRef]
  24. D. Malacara, Optical Shop Testing, 3rd. ed. (Wiley-Interscience, 2007).
  25. S. Poujouly and B. Journet, “A twofold modulation frequency laser range finder,” J. Opt. A 4, S356–S363 (2002).
    [CrossRef]
  26. T. Bosch and M. Lescure, “Experimental determination of the useful reflection coefficient of non-cooperative targets for a time-of-flight laser rangefinder,” Opt. Rev. 2, 289–291 (1995).
    [CrossRef]
  27. B. Schwarz, “Lidar: mapping the world in 3d,” Nat. Photonics 4, 429–430 (2010).
    [CrossRef]
  28. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48, 6241–6251 (2009).
    [CrossRef]

2012 (5)

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

2011 (2)

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
[CrossRef]

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

2010 (3)

A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

B. Schwarz, “Lidar: mapping the world in 3d,” Nat. Photonics 4, 429–430 (2010).
[CrossRef]

2009 (1)

2005 (1)

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

2002 (2)

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

S. Poujouly and B. Journet, “A twofold modulation frequency laser range finder,” J. Opt. A 4, S356–S363 (2002).
[CrossRef]

2001 (1)

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37, 390–397 (2001).
[CrossRef]

2000 (1)

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

1995 (1)

T. Bosch and M. Lescure, “Experimental determination of the useful reflection coefficient of non-cooperative targets for a time-of-flight laser rangefinder,” Opt. Rev. 2, 289–291 (1995).
[CrossRef]

Ailisto, H.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Alenya, G.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
[CrossRef]

Baulig, C.

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

Baumgart, M.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

Berge, A.

J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.

Beuth, T.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

Bogatscher, S.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

S. Bogatscher, N. Heussner, and W. Stork, “Considering laser modulation for classification of scanning laser devices,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, S. Danilova, and W. Stork, “The impact of the revisions to the laser safety standard on the classification of scanned-beam projection systems,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, and W. Stork, “Optimizing flying-spot display designs based on the upcoming edition of the laser safety standard,” J. Soc. Inf. Disp. (to be published).

Bosch, T.

T. Bosch and M. Lescure, “Experimental determination of the useful reflection coefficient of non-cooperative targets for a time-of-flight laser rangefinder,” Opt. Rev. 2, 289–291 (1995).
[CrossRef]

Buller, G. S.

Buxbaum, B.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Chen, R.

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

Collins, R. J.

Conrad, H.

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

Danilova, S.

N. Heussner, S. Bogatscher, S. Danilova, and W. Stork, “The impact of the revisions to the laser safety standard on the classification of scanned-beam projection systems,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

Duong, H.

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

Durr, P.

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

Fernández, V.

Fischer, H.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Foix, S.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
[CrossRef]

Frank, A.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

Fuste, P.

J. Radmer, P. Fuste, H. Schmidt, and J. Kruger, “Incident light related distance error study and calibration of the pmd-range imaging camera,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (IEEE, 2008), pp. 1–6.

Gao, L.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

Gaumont, E.

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

Georgelin, G.

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

Gerwig, C.

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

Giesel, C.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

Grahmann, J.

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

Graßhoff, T.

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

Haase, T.

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

Hagen, N.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

Heikkinen, V.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Heinol, H.-G.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Heussner, N.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

S. Bogatscher, N. Heussner, and W. Stork, “Considering laser modulation for classification of scanning laser devices,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, S. Danilova, and W. Stork, “The impact of the revisions to the laser safety standard on the classification of scanned-beam projection systems,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, and W. Stork, “Optimizing flying-spot display designs based on the upcoming edition of the laser safety standard,” J. Soc. Inf. Disp. (to be published).

Journet, B.

S. Poujouly and B. Journet, “A twofold modulation frequency laser range finder,” J. Opt. A 4, S356–S363 (2002).
[CrossRef]

Jung, D.

D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.

Kallweit, D.

D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.

Kenda, A.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

Kester, R. T.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

Kirkhus, T.

J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.

Klein, R.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Koskinen, M.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Kostamovaara, J.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Krichel, N. J.

Kruger, J.

J. Radmer, P. Fuste, H. Schmidt, and J. Kruger, “Incident light related distance error study and calibration of the pmd-range imaging camera,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (IEEE, 2008), pp. 1–6.

Kuck, H.

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

Kunze, D.

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

Lakner, H.

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

Lange, R.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37, 390–397 (2001).
[CrossRef]

Lefsky, M.

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

Lescure, M.

T. Bosch and M. Lescure, “Experimental determination of the useful reflection coefficient of non-cooperative targets for a time-of-flight laser rangefinder,” Opt. Rev. 2, 289–291 (1995).
[CrossRef]

Liao, K.-M.

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd. ed. (Wiley-Interscience, 2007).

Mäntyniemi, A.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

McCarthy, A.

Mitikka, R.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Myllylä, R.

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Olk, J.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Poujouly, S.

S. Poujouly and B. Journet, “A twofold modulation frequency laser range finder,” J. Opt. A 4, S356–S363 (2002).
[CrossRef]

Radmer, J.

J. Radmer, P. Fuste, H. Schmidt, and J. Kruger, “Incident light related distance error study and calibration of the pmd-range imaging camera,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (IEEE, 2008), pp. 1–6.

Ramond, T.

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

Riedl, M. J.

M. J. Riedl, Optical Design Fundamentals for Infrared Systems, 2nd ed. (SPIE, 2001).

Sandner, T.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.

Satzer, B.

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

Schenk, H.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

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

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.

Schmidt, H.

J. Radmer, P. Fuste, H. Schmidt, and J. Kruger, “Incident light related distance error study and calibration of the pmd-range imaging camera,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (IEEE, 2008), pp. 1–6.

Schmoger, M.

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

Schulte, J.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Schwarte, R.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Schwarz, B.

B. Schwarz, “Lidar: mapping the world in 3d,” Nat. Photonics 4, 429–430 (2010).
[CrossRef]

Schwarzer, S.

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

Seitz, P.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37, 390–397 (2001).
[CrossRef]

Shinohara, L.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

Skotheim, O.

J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.

Sobe, U.

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

Stork, W.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
[CrossRef]

N. Heussner, S. Bogatscher, and W. Stork, “Optimizing flying-spot display designs based on the upcoming edition of the laser safety standard,” J. Soc. Inf. Disp. (to be published).

S. Bogatscher, N. Heussner, and W. Stork, “Considering laser modulation for classification of scanning laser devices,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, S. Danilova, and W. Stork, “The impact of the revisions to the laser safety standard on the classification of scanned-beam projection systems,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

Streck, A.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
[CrossRef]

Thielemann, J.

J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.

Tkaczyk, T. S.

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

Torras, C.

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
[CrossRef]

Tortschanoff, A.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

Umesh-Babu, H.

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

Wagner, A.

A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
[CrossRef]

Wallace, A. M.

Wang, Y.-C.

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

Weimer, C.

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

Wildenhain, M.

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

Wölfelschneider, H.

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

Wolter, A.

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

Xu, Z.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

Yeh, C.-H.

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37, 390–397 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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

IEEE Sens. J. (1)

S. Foix, G. Alenya, and C. Torras, “Lock-in time-of-flight (tof) cameras: a survey,” IEEE Sens. J. 11, 1917–1926 (2011).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

H. Duong, M. Lefsky, T. Ramond, and C. Weimer, “The electronically steerable flash lidar: a full waveform scanning system for topographic and ecosystem structure applications,” IEEE Trans. Geosci. Remote Sens. 50, 4809–4820 (2012).
[CrossRef]

J. Microlith. Microfab. Microsyst. (1)

K.-M. Liao, Y.-C. Wang, C.-H. Yeh, and R. Chen, “Closed-loop adaptive control for electrostatically driven torsional micromirrors,” J. Microlith. Microfab. Microsyst. 4, 041503 (2005).
[CrossRef]

J. Opt. A (2)

S. Poujouly and B. Journet, “A twofold modulation frequency laser range finder,” J. Opt. A 4, S356–S363 (2002).
[CrossRef]

H. Ailisto, V. Heikkinen, R. Mitikka, R. Myllylä, J. Kostamovaara, A. Mäntyniemi, and M. Koskinen, “Scannerless imaging pulsed-laser range finding,” J. Opt. A 4, S337–S346 (2002).

Nat. Photonics (1)

B. Schwarz, “Lidar: mapping the world in 3d,” Nat. Photonics 4, 429–430 (2010).
[CrossRef]

Opt. Eng. (1)

N. Hagen, R. T. Kester, L. Gao, and T. S. Tkaczyk, “Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems,” Opt. Eng. 51, 111702 (2012).
[CrossRef]

Opt. Rev. (1)

T. Bosch and M. Lescure, “Experimental determination of the useful reflection coefficient of non-cooperative targets for a time-of-flight laser rangefinder,” Opt. Rev. 2, 289–291 (1995).
[CrossRef]

Proc. SPIE (6)

A. Tortschanoff, M. Baumgart, A. Frank, M. Wildenhain, T. Sandner, H. Schenk, and A. Kenda, “Optical position feedback for electrostatically driven moems scanners,” Proc. SPIE 8252, 82520S (2012).
[CrossRef]

J. Grahmann, T. Graßhoff, H. Conrad, T. Sandner, and H. Schenk, “Integrated piezoresistive position detection for electrostatic driven micro scanning mirrors,” Proc. SPIE 7930, 79300V (2011).
[CrossRef]

A. Streck, W. Stork, and A. Wagner, “High power high bandwidth laser diode driver for next generation laser projectors,” Proc. SPIE 7618, 761805 (2010).
[CrossRef]

S. Bogatscher, C. Giesel, T. Beuth, H. Umesh-Babu, L. Shinohara, N. Heussner, A. Streck, and W. Stork, “Fast scan-fail device for class 1 operation of scanning micromirrors at a high laser power in the near-infrared region,” Proc. SPIE 8512, 85120E (2012).
[CrossRef]

T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010).
[CrossRef]

B. Satzer, C. Baulig, T. Sandner, and S. Schwarzer, “Micromirror-based sending and detection optical assembly for time-of-flight laser scanners,” Proc. SPIE 8439, 84390Z (2012).
[CrossRef]

Other (11)

“IEC 60825-1: Safety of laser products - part 1: Equipment classification and requirements (Ed. 2.0)” (International Electrotechnical Commission, 2007).

S. Bogatscher, N. Heussner, and W. Stork, “Considering laser modulation for classification of scanning laser devices,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, S. Danilova, and W. Stork, “The impact of the revisions to the laser safety standard on the classification of scanned-beam projection systems,” in 9th International Conference on Optics-photonics Design & Fabrication, Itabashi, Japan (2014).

N. Heussner, S. Bogatscher, and W. Stork, “Optimizing flying-spot display designs based on the upcoming edition of the laser safety standard,” J. Soc. Inf. Disp. (to be published).

D. Kallweit, D. Jung, T. Sandner, and H. Schenk, “Fabrication of a quasistatic-resonant microscanner by implementing a vertical combdrive through wafer assembly actuation,” in 2011 International Conference on Optical MEMS and Nanophotonics (2011), pp. 147–148.

M. J. Riedl, Optical Design Fundamentals for Infrared Systems, 2nd ed. (SPIE, 2001).

E. Gaumont, A. Wolter, H. Schenk, G. Georgelin, and M. Schmoger, “Mechanical and electrical failures and reliability of micro scanning mirrors,” in Proceedings of the 9th International Symposium on the Physical and Failure Analysis of Integrated Circuits (2002), pp. 212–217.

R. Schwarte, Z. Xu, H.-G. Heinol, J. Olk, R. Klein, B. Buxbaum, H. Fischer, and J. Schulte, “New electro-optical mixing and correlating sensor: facilities and applications of the photonic mixer device (pmd),” in Sensors, Sensor Systems, and Sensor Data Processing, Vol. 3100 (SPIE, 1997), pp. 245–253.

J. Radmer, P. Fuste, H. Schmidt, and J. Kruger, “Incident light related distance error study and calibration of the pmd-range imaging camera,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (IEEE, 2008), pp. 1–6.

J. Thielemann, A. Berge, O. Skotheim, and T. Kirkhus, “Fast high resolution 3d laser scanning by real-time object tracking and segmentation,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2012), pp. 3899–3906.

D. Malacara, Optical Shop Testing, 3rd. ed. (Wiley-Interscience, 2007).

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Figures (15)

Fig. 1.
Fig. 1.

Illustration showing the top view of a driverless vehicle before target approach. The exemplary route including correction cycles is shown in blue. The exemplary load that should be lifted is a EUR-pallet, shown in brown. The route in case (a) contains unnecessary correction cycles due to position uncertainty, where case (b) shows an exemplary optimized route.

Fig. 2.
Fig. 2.

Side view illustration of approach 1, consisting of collimated laser source (1), scanning micromirror (2), scattering object (3), and 2D array consisting of synchronously scanned micromirrors (4), followed by collection lens (5) and detector (6).

Fig. 3.
Fig. 3.

Side view illustration of approach 2, consisting of collimated laser source (1), scanning micromirror (2), scattering object (3), and collection lens (5), followed by synchronously switched 2D detector array (6).

Fig. 4.
Fig. 4.

Side view illustration of approach 3, consisting of collimated laser source (1), scanning micromirrors (2), scattering object (3), array of synchronously scanned micromirrors in one axis (4), collection lens (5), and one-dimensional array of synchronously switched detectors in the other scanning axis (6).

Fig. 5.
Fig. 5.

Comparison of utilization of wafer area (lower is better) as a function of maximum half incidence angle for different aspect ratios a=αmax,h/αmax,v. The plot indicates that approach 1 requires the least wafer area for large fields of view, whereas approach 2 needs less for smaller fields of view. As approach 3 is a hybrid between approaches 1 and 2 the blue curve is in between the black and the red curves. Increasing the aspect ratio a, the intersection point between approaches 1 and 2 moves to larger fields of view.

Fig. 6.
Fig. 6.

Side view illustration of the system concept used in this paper, consisting of collimated laser source (1), scanning micromirror (2), scattering object (3), galvanometer mirror scanning along the slow axis (4), collection lens (5), and synchronously switched 1D detector array (6) along the fast axis.

Fig. 7.
Fig. 7.

Photographs of the proof-of-concept setup, showing (a) optical and (b) electronic components.

Fig. 8.
Fig. 8.

Zemax rendering of optical beam path, showing laser diode (1) emitting a collimated laser beam, micromirror (2) in package (micromirror not visible), scattering object (3) at 10 m distance, galvanometer mirror (4), Fresnel lenses (5), and glass lid in front of detector array and detectorarray (6).

Fig. 9.
Fig. 9.

Simulated normalized intensity at detector array for three optical tilt angles of the micromirror αmm at an object distance of 10 m: (a) αmm=12°, (b) αmm=0°, and (c) αmm=12°. In case (b) the intensity is reduced because the spot is split between two detectors. The gap between detector elements is shown in black.

Fig. 10.
Fig. 10.

Block diagram of the complete signal processing chain of the proof-of-concept setup. Optical signal paths in red, electrical signal paths in black.

Fig. 11.
Fig. 11.

Measured standard deviation of distance measurements versus distance. Each point is derived from 1.6·106 subsequent measurements at a rate of rPix=353kHz.

Fig. 12.
Fig. 12.

Measured distance versus real distance, showing the distance dependent systematic measurement error.

Fig. 13.
Fig. 13.

Measured standard deviation versus vertical and horizontal field angle (pixel). The standard deviation is derived from nfr=246 subsequent frames at a constant measurement distance of 1 m. The standard deviation is increased in the switching regions between detectors, which is only used along the vertical axis.

Fig. 14.
Fig. 14.

Sketch of a scan mirror, showing the connection between the vertical component of the receiver aperture (length of line a) and incidence angle β. The mirror is shown in black.

Fig. 15.
Fig. 15.

Top view illustration of the receiver part of approach 3, showing an example of a horizontal incidence angle.

Tables (2)

Tables Icon

Table 1. Target Specifications of SARI Project

Tables Icon

Table 2. Specification Details of Proof-of-Concept Setup

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

Arec,1=Arec,2=Arec,3=Arec.
Arec,1(αmax,h,αmax,v)=ΓMEMS,1·AMEMS,1·cos(αmax,h2)·cos(αmax,vα0)2·[cos(αmax,vα02)+sin(αmax,vα02)].
AMEMS,1(αmax,h,αmax,v)=Arec·2·[cos(αmax,vα02)+sin(αmax,vα02)]ΓMEMS,1·cos(αmax,h2)·cos(αmax,vα0).
Aw,1(αmax,h,αmax,v)=AMEMS,1(αmax,h,αmax,v)+Adet,1.
Adet,2(αmax,h,αmax,v)=wdet,2(αmax,h)·hdet,2(αmax,v),
Aw,2(αmax,h,αmax,v)=AMEMS,2+Adet,2(αmax,h,αmax,v).
Arec,3(αmax,h,αmax,v)=ΓMEMS,3·AMEMS,3·cos(αmax,h)·cos(αmax,vα0)2·[cos(αmax,vα02)+sin(αmax,vα02)].
AMEMS,3(αmax,h,αmax,v)=Arec·2·[cos(αmax,vα02)+sin(αmax,vα02)]ΓMEMS,3·cos(αmax,h)·cos(αmax,vα0).
Adet,3(αmax,h)=wdet,3(αmax,h)·hdet,3,
Aw,3(αmax,h,αmax,v)=AMEMS,3(αmax,v)+Adet,3(αmax,h).
ηi=Aw,iArec,i.
Δλ=λ0·(11(sinαneff)2),
Pr=A·sin(2πfmt+φ),
Pr,I=A2·[cos(φ)cos(4πfmt+φ)]
Pr,Q=A2·[sin(φ)+sin(4πfmt+φ)]
Arec=a·d,
a=b·cosβ.
2·γ+β+90°=180°
γ=45°β2.
2·b=c·cosγ.
cos(xy)=cosx·cosy+sinx·siny
a=c·cosβ2·[cos(β2)+sin(β2)].
β=αvα0
d=e·sinαh2·[cos(αh2π4)+sin(αh2π4)]
d=e·sinαh2·sin(αh2),
d=e·cos(αh2).
e=g2·f,
f=k·tanαh,
d=e·cosαh.
d=g·cosαh2·k·sinαh.
Arec=AMEMS,3·[cos(αh)2kg·sinαh]·cos(αvα0)2·[cos(αvα02)+sin(αvα02)].

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