Abstract

Phase-shifting fringe projection is an effective method to perform 3D shape measurements. Conventionally, fringe projection systems utilize a digital projector that images fringes into the measurement plane. The performance of such systems is limited to the visible spectral range, as most projectors experience technical limitations in UV or IR spectral ranges. However, for certain applications these spectral ranges are of special interest. We present a wideband fringe projector that has been developed on the basis of a picture generating beamshaping mirror. This mirror generates a sinusoidal fringe pattern in the measurement plane without any additional optical elements. Phase shifting is realized without any mechanical movement by a multichip LED. As the system is based on a single mirror, it is wavelength-independent in a wide spectral range and therefore applicable in UV and IR spectral ranges. We present the design and a realized setup of this fringe projection system and the characterization of the generated intensity distribution. Experimental results of 3D shape measurements are presented.

© 2013 Optical Society of America

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  1. F. Chen and G. M. Brown, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  2. R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
    [CrossRef]
  3. P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
    [CrossRef]
  4. M. Brennesholtz and E. Stupp, Projection Displays, 2nd ed. (Wiley, 2008).
  5. R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
    [CrossRef]
  6. S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
    [CrossRef]
  7. T. M. Kreis, J. Geldmacher, and W. P. O. Jüptner, “Phasenschiebe-Verfahren in der interferometrischen Messtechnik: Ein Vergleich,” in Laser in der Technik, W. Waidelich, ed. (Springer, 1993), pp. 119–126.
  8. C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.
  9. K. Kinnstaetter, A. W. Lohmann, J. Schwider, and N. Streibl, “Accuracy of phase shifting interferometry,” Appl. Opt. 27, 5082–5089 (1988).
    [CrossRef]
  10. W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
    [CrossRef]
  11. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge, 2004).
  12. R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier, 2005).
  13. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590–595 (2002).
    [CrossRef]
  14. D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
    [CrossRef]
  15. M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).
  16. D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
    [CrossRef]
  17. S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
    [CrossRef]
  18. S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
    [CrossRef]
  19. S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
    [CrossRef]
  20. H. Lindner, H. Brauer, and C. Lehmann, Taschenbuch der Elektrotechnik und Elektronik, 9th ed. (Hanser, 2008).
  21. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7444 (2002).
    [CrossRef]
  22. H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135(1981).
    [CrossRef]

2012 (3)

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
[CrossRef]

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

2011 (2)

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[CrossRef]

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
[CrossRef]

2009 (1)

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

2008 (1)

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

2007 (1)

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

2002 (2)

2000 (3)

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[CrossRef]

F. Chen and G. M. Brown, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

1988 (1)

1981 (2)

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135(1981).
[CrossRef]

Benitez, P.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier, 2005).

Brauer, H.

H. Lindner, H. Brauer, and C. Lehmann, Taschenbuch der Elektrotechnik und Elektronik, 9th ed. (Hanser, 2008).

Bräuer, A.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[CrossRef]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Bräuer-Burchardt, C.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

Brennesholtz, M.

M. Brennesholtz and E. Stupp, Projection Displays, 2nd ed. (Wiley, 2008).

Brodbelt, R.

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

Brown, G. M.

F. Chen and G. M. Brown, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Burton, D. R.

Chen, F.

F. Chen and G. M. Brown, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Fan, P.

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

Feßler, R.

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Franzl, Y.

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

Frazer-Dib, J.

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

Gdeisat, M. A.

Gebhardt, A.

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Geldmacher, J.

T. M. Kreis, J. Geldmacher, and W. P. O. Jüptner, “Phasenschiebe-Verfahren in der interferometrischen Messtechnik: Ein Vergleich,” in Laser in der Technik, W. Waidelich, ed. (Springer, 1993), pp. 119–126.

Gerber, J.

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge, 2004).

Heinze, M.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

Heist, S.

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

Herráez, M. A.

Jegorov, J.

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
[CrossRef]

Jegorovs, J.

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Jüptner, W. P. O.

T. M. Kreis, J. Geldmacher, and W. P. O. Jüptner, “Phasenschiebe-Verfahren in der interferometrischen Messtechnik: Ein Vergleich,” in Laser in der Technik, W. Waidelich, ed. (Springer, 1993), pp. 119–126.

Kinnstaetter, K.

Kowarschik, R.

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

Kreis, T. M.

T. M. Kreis, J. Geldmacher, and W. P. O. Jüptner, “Phasenschiebe-Verfahren in der interferometrischen Messtechnik: Ein Vergleich,” in Laser in der Technik, W. Waidelich, ed. (Springer, 1993), pp. 119–126.

Kudaev, S.

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Kühmstedt, P.

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
[CrossRef]

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

Kurz, M.

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Lalor, M. J.

Lehmann, C.

H. Lindner, H. Brauer, and C. Lehmann, Taschenbuch der Elektrotechnik und Elektronik, 9th ed. (Hanser, 2008).

Lindner, H.

H. Lindner, H. Brauer, and C. Lehmann, Taschenbuch der Elektrotechnik und Elektronik, 9th ed. (Hanser, 2008).

Lohmann, A. W.

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135(1981).
[CrossRef]

Michaelis, D.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[CrossRef]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Minano, J. C.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier, 2005).

Möller, M.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

Munckelt, C.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Munkelt, C.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

Muschaweck, J.

Notni, G.

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
[CrossRef]

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

O’Brien, W.

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

Oberschmidt, D.

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Ries, H.

Schreiber, P.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[CrossRef]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Schreiber, W.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[CrossRef]

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

Schwider, J.

Siedow, N.

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Steinkopf, R.

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

Streibl, N.

Stupp, E.

M. Brennesholtz and E. Stupp, Projection Displays, 2nd ed. (Wiley, 2008).

Winston, R.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier, 2005).

Yu, R.

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge, 2004).

Zwick, S.

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express 20, 3642–3653 (2012).
[CrossRef]

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
[CrossRef]

Appl. Opt. (2)

J. Dent. Res. (1)

R. Brodbelt, W. O’Brien, P. Fan, J. Frazer-Dib, and R. Yu, “Translucency of human dental enamel,” J. Dent. Res. 60, 1749–1753 (1981).
[CrossRef]

J. Opt. Soc. Am. A (1)

Mikroproduktion (1)

M. Kurz, D. Oberschmidt, N. Siedow, R. Feßler, and J. Jegorovs, “Mit schnellem Algorithmus zur perfekten Freiformoptik,” Mikroproduktion 3, 10–12 (2009).

Nature (1)

H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135(1981).
[CrossRef]

Opt. Eng. (3)

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[CrossRef]

F. Chen and G. M. Brown, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, and G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (5)

D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE 7059, 705905 (2008).
[CrossRef]

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

S. Zwick, P. Kühmstedt, and G. Notni, “Phase-shifting fringe projection system using freeform optics,” Proc. SPIE 8169, 81690W (2011).
[CrossRef]

S. Zwick, S. Heist, Y. Franzl, R. Steinkopf, P. Kühmstedt, and G. Notni, “3D measurement system on the basis of a tailored free-form mirror,” Proc. SPIE 8494, 84940F (2012).
[CrossRef]

S. Zwick, R. Feßler, J. Jegorov, and G. Notni, “Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces,” Proc. SPIE 8429, 842913 (2012).
[CrossRef]

Other (6)

H. Lindner, H. Brauer, and C. Lehmann, Taschenbuch der Elektrotechnik und Elektronik, 9th ed. (Hanser, 2008).

T. M. Kreis, J. Geldmacher, and W. P. O. Jüptner, “Phasenschiebe-Verfahren in der interferometrischen Messtechnik: Ein Vergleich,” in Laser in der Technik, W. Waidelich, ed. (Springer, 1993), pp. 119–126.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Determining exact point correspondences in 3D measurement systems using fringe projection—concepts, algorithms, and accuracy determination,” in Applied Measurement Systems, Z. Haq, ed. (InTech, 2012), pp. 211–228.

M. Brennesholtz and E. Stupp, Projection Displays, 2nd ed. (Wiley, 2008).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge, 2004).

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier, 2005).

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Figures (20)

Fig. 1.
Fig. 1.

Projection systems. (a) Conventional fringe projection system with one camera (from Zwick et al. [6]). (b) Fringe projection system utilizing a free-form mirror (from Zwick et al. [6]).

Fig. 2.
Fig. 2.

Triangulation principle in two dimensions.

Fig. 3.
Fig. 3.

Influence of the extended light source on the Michelson contrast. (a) Illumination with an extended light source: Each point on the free-form surface is related to a blurry spot in the picture (from Zwick et al. [6]). (b) Michelson contrast C of a sinusodial pattern with a period p generated by a free-form surface when illuminating with an extended light source (see Zwick et al. [6]).

Fig. 4.
Fig. 4.

Setup of fringe projector and detector image in the design plane simulated with Zemax.

Fig. 5.
Fig. 5.

Surface of the free-form mirror. (a) Design surface of the free-form mirror. Tilt, defocus, astigmatism, coma and trefoil are subtracted in order to make the small structures visible. (b) Manufactured free-form mirror.

Fig. 6.
Fig. 6.

Experimental setup consisting of a light source (UV or Vis), a free-form mirror, a measurement object, and a camera (UV or Vis). (a) Experimental setup. (b) Arrangement of the ACULED.

Fig. 7.
Fig. 7.

Measured intensity distribution in the design plane Δz=0.

Fig. 8.
Fig. 8.

Influence of the extended light source on the intensity distribution. (a) Schematic. (b) Simulation using extended and point light source.

Fig. 9.
Fig. 9.

Irregularities in the measured intensity distribution. (a) In the design plane Δz=0. (b) Screen is tilted around x axis in order to increase the visibility of the irregularities.

Fig. 10.
Fig. 10.

Measurement of the fabricated free-form surface. The measured surface was imported in Zemax in order to perform simulations. Simulated and measured intensity distribution [Fig. 9(a)] match. (a) Residual fabrication error. (b) Simulation of intensity pattern generated with measured surface file in Zemax (point light source). (c) Simulation of intensity pattern generated with measured surface file in Zemax (light source 1mm×1mm).

Fig. 11.
Fig. 11.

Measured intensity distribution in different z planes. (a) Δz=70mm. (b) Δz=0mm. (c) Δz=100mm. (d) cross section, Δz=70mm. (e) cross section, Δz=0mm. (f) cross section, Δz=100mm.

Fig. 12.
Fig. 12.

Michelson contrast and modulation of the measured intensity distributions in different z planes. (a) Michelson contrast. (b) Modulation.

Fig. 13.
Fig. 13.

DF of the measured intensity distributions. (a) Distortion factor of the measured intensity distributions in different z planes. (b) Distortion factor as a function of Δz for x1 and x2.

Fig. 14.
Fig. 14.

Phase shift between simulated intensity patterns when using a linear displacement of the light source. (a) 1→2. (b) 2→3. (c) 3→4.

Fig. 15.
Fig. 15.

Phase shift between simulated intensity patterns when using a square multi-chip LED. (a) 1→2. (b) 2→3. (c) 3→4.

Fig. 16.
Fig. 16.

Phase shift between measured intensity patterns when using a square multi-chip LED. (a) 1→2. (b) 2→3. (c) 3→4.

Fig. 17.
Fig. 17.

Wrapped phase images of the measurement of a flat object. (a) Camera 1. (b) Camera 2.

Fig. 18.
Fig. 18.

Unwrapped phase images and 3D point cloud of the measurement of a flat object. The black lines in the 2 phase images indicate the same phase value. (a) Phase image (camera 1). (b) Phase image (camera 2). (c) 3D point cloud.

Fig. 19.
Fig. 19.

Photograph, unwrapped phase image, and 3D point cloud of a free-form object. (a) Photograph. (b) Unwrapped phase image. (c) 3D point cloud.

Fig. 20.
Fig. 20.

Photograph and 3D point cloud of a cylinder and a screw. (a) Photograph. (b) 3D point cloud. (c) Photograph. (d) 3D point cloud.

Equations (3)

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ϕ(η,ξ)=arctan[I4(η,ξ)I2(η,ξ)I1(η,ξ)I3(η,ξ)]=ϕ(η,ξ)mod(2π)
Dblur=bg·Dsource
DF=n=2Pn2n=1Pn2·100%.

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