Abstract

We describe a diagram, named the projection diagram (PD), that can be used for the interpretation of fringe projection operations in a similar way as the Holodiagram is used in holography and other branches in optics. It is obtained as a Moiré pattern between two spoke targets that mimic central projections, the same as those in a projection and observation system or two projection systems. N. Abramson [Academic, London (1981)] has already proposed its use in systems with two observation points (i.e., stereoscopic observation). By using this PD, several interesting features dealing with fringe projection are highlighted. Information on the sensitivity vector and the geometry of the contouring surfaces can be straightforwardly obtained in a graphical way. The effect of defocusing can also be included in the diagram.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, pp. 70–74.
  2. P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
    [CrossRef]
  3. X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).
  4. A review of incoherent techniques including fringes projection can be found in Opt. Eng., July–August21, (1982).
  5. N. Abramson, “The Holodiagram, a practical device for making and evaluating holograms,” Appl. Opt. 8, 1235–1240 (1969).
    [CrossRef] [PubMed]
  6. N. Abramson, Light in Flight, or the Holodiagram: Columbi Egg of Optics, (SPIE Optical Engineering Press, Bellingham, Wash., 1996).
  7. G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
    [CrossRef]
  8. H. Rabal, “The Holodiagram with Virtual Sources,” Optik (Stuttgart) 112, 487–492 (2001).
    [CrossRef]
  9. Alan J. MacGovern, “Projected fringes and holography,” Appl. Opt. 11, 2972–2974 (1972).
    [CrossRef] [PubMed]
  10. P. Theokaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969), pp. 123–127.
  11. G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Tonawanda, N.Y., 1969), p. 28.
  12. Ref. 11, pp. 23 and 38.
  13. For a description of the horopter see, for example, B. Julesz, Foundations of Cyclopean Perception (University of Chicago, Chicago, 1971), pp. 144–146.
  14. L. Pirodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).
    [CrossRef]
  15. P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

2001

G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
[CrossRef]

H. Rabal, “The Holodiagram with Virtual Sources,” Optik (Stuttgart) 112, 487–492 (2001).
[CrossRef]

1999

P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
[CrossRef]

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

1998

P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

1982

A review of incoherent techniques including fringes projection can be found in Opt. Eng., July–August21, (1982).

L. Pirodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).
[CrossRef]

1972

1969

Abramson, N.

N. Abramson, “The Holodiagram, a practical device for making and evaluating holograms,” Appl. Opt. 8, 1235–1240 (1969).
[CrossRef] [PubMed]

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, pp. 70–74.

N. Abramson, Light in Flight, or the Holodiagram: Columbi Egg of Optics, (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

Baldwin, G.

G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
[CrossRef]

Cap, N.

P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

De Zela, F.

G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
[CrossRef]

Hu, Q.

P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
[CrossRef]

Jin, F.

P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
[CrossRef]

Julesz, B.

For a description of the horopter see, for example, B. Julesz, Foundations of Cyclopean Perception (University of Chicago, Chicago, 1971), pp. 144–146.

MacGovern, Alan J.

Oster, G.

G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Tonawanda, N.Y., 1969), p. 28.

Peng, X.

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

Pirodda, L.

L. Pirodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).
[CrossRef]

Rabal, H.

G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
[CrossRef]

H. Rabal, “The Holodiagram with Virtual Sources,” Optik (Stuttgart) 112, 487–492 (2001).
[CrossRef]

P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

Su, C. J.

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

Theokaris, P.

P. Theokaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969), pp. 123–127.

Torroba, P.

P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

Tseng, M. M.

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

Wang, P. S.

P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
[CrossRef]

Zhu, S. M.

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

Appl. Opt.

Opt. Eng.

L. Pirodda, “Shadow and projection moiré techniques for absolute or relative mapping of surface shapes,” Opt. Eng. 21, 640–649 (1982).
[CrossRef]

P. S. Wang, Q. Hu, F. Jin, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1171 (1999).
[CrossRef]

A review of incoherent techniques including fringes projection can be found in Opt. Eng., July–August21, (1982).

Optik (Stuttgart)

X. Peng, S. M. Zhu, C. J. Su, M. M. Tseng, “Model-based digital moiré topography,” Optik (Stuttgart) 110, 184–190 (1999).

G. Baldwin, F. De Zela, H. Rabal, “Refraction holodiagrams,” Optik (Stuttgart) 112, 555–560 (2001).
[CrossRef]

H. Rabal, “The Holodiagram with Virtual Sources,” Optik (Stuttgart) 112, 487–492 (2001).
[CrossRef]

P. Torroba, N. Cap, H. Rabal, “Correction of defocusing using structured illumination,” Optik (Stuttgart) 108, 68–77 (1998).

Other

N. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), Chap. 3, pp. 70–74.

P. Theokaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969), pp. 123–127.

G. Oster, The Science of Moiré Patterns (Edmund Scientific Co., Tonawanda, N.Y., 1969), p. 28.

Ref. 11, pp. 23 and 38.

For a description of the horopter see, for example, B. Julesz, Foundations of Cyclopean Perception (University of Chicago, Chicago, 1971), pp. 144–146.

N. Abramson, Light in Flight, or the Holodiagram: Columbi Egg of Optics, (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Experimental set up for double fringes projection.

Fig. 2
Fig. 2

Spoke target.

Fig. 3
Fig. 3

Moiré of two spoke targets. Indicial representation.

Fig. 4
Fig. 4

(a) How the moiré patterns are formed, (b) PD of the subtractive moiré (circumferences), (c) PD of the additive moiré (hyperbolas).

Fig. 5
Fig. 5

(a) PD due to the projection of two equally spaced gratings in the space domain (Ronchi rulings), (b) PD due to two Ronchi rulings with different spacing.

Fig. 6
Fig. 6

(a) Chirp spoke target, (b) PD due to two chip gratings (subtractive moiré), (c) PD due to two chirp gratings (additive moiré).

Fig. 7
Fig. 7

Geometry of the definition of the two sensitivity vectors.

Fig. 8
Fig. 8

(a) Loci of points with equal sensitivity for the PD shown in Figure 4(b), (b) the same for the PD shown in Figure 4(c).

Fig. 9
Fig. 9

(a) Effect of defocusing in a single projection, (b) the same with double projection.

Equations (9)

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

n+m=k
n-m=k
n+m=k+1
n-m=k+1.
eR=RtanΔφ.
Δn=S · D,
|Si|=1eiR
S=S1+S2,
Δn=S · D.

Metrics