Abstract

In the last two decades, three-dimensional sensors based on misfocusing have been suggested. This research addresses the question of measuring several focal depths simultaneously. Two options for generating the necessary array of spots are analyzed: the use of a lenslet array and the use of a Dammann grating. Finally, a combination of the two approaches is proposed. Such a combination enables tailoring the system performance to the exact needs of the user.

© 1998 Optical Society of America

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References

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  1. Y. Fainman, E. Lenz, J. Shamir, “Optical profilometer: a new method for high sensitivity and wide dynamic range,” Appl. Opt. 21, 3200–3208 (1982).
    [CrossRef] [PubMed]
  2. M. C. Hutley, R. F. Stevens, “The use of zone-plate monochromator as a displacement transducer,” J. Phys. E 21, 1037–1044 (1988).
    [CrossRef]
  3. D. Mendlovic, “Three-dimensional image sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
    [CrossRef]
  4. H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  5. J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
    [CrossRef]
  6. G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
    [CrossRef]
  7. G. Hausler, D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. 32, 7164–7169 (1993).
    [CrossRef] [PubMed]

1993 (2)

D. Mendlovic, “Three-dimensional image sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

G. Hausler, D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. 32, 7164–7169 (1993).
[CrossRef] [PubMed]

1989 (1)

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

1988 (1)

M. C. Hutley, R. F. Stevens, “The use of zone-plate monochromator as a displacement transducer,” J. Phys. E 21, 1037–1044 (1988).
[CrossRef]

1984 (1)

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

1982 (1)

1971 (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dammann, H.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Downs, M. M.

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Fainman, Y.

Gortler, K.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Hausler, G.

Hutley, M. C.

M. C. Hutley, R. F. Stevens, “The use of zone-plate monochromator as a displacement transducer,” J. Phys. E 21, 1037–1044 (1988).
[CrossRef]

Jahns, J.

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Lenz, E.

Mendlovic, D.

D. Mendlovic, “Three-dimensional image sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

Molesini, G.

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

Pedrini, G.

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

Poggy, P.

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

Prise, M. E.

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Quercioli, F.

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

Ritter, D.

Shamir, J.

Stevens, R. F.

M. C. Hutley, R. F. Stevens, “The use of zone-plate monochromator as a displacement transducer,” J. Phys. E 21, 1037–1044 (1988).
[CrossRef]

Streibl, N.

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Walker, S. J.

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Appl. Opt. (2)

J. Phys. E (1)

M. C. Hutley, R. F. Stevens, “The use of zone-plate monochromator as a displacement transducer,” J. Phys. E 21, 1037–1044 (1988).
[CrossRef]

Opt. Commun. (3)

D. Mendlovic, “Three-dimensional image sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

G. Molesini, G. Pedrini, P. Poggy, F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[CrossRef]

Opt. Eng. (1)

J. Jahns, M. E. Prise, M. M. Downs, S. J. Walker, N. Streibl, “Dammann grating for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Setup based on a lenslet array used for depth sensing.

Fig. 2
Fig. 2

(a) Defect in the zone plate. (b) View of the defect in the Fourier (focus) plane. (c), (d) View of the defect in the forward and backward out-of-focus plane, respectively.

Fig. 3
Fig. 3

(a) Optical beam broadening according to the geometric optics approximation. (b) Optical beam broadening according to diffractive optics.

Fig. 4
Fig. 4

Dammann-grating-based setup for depth sensing: BS, beam splitter.

Fig. 5
Fig. 5

Combined lenslet-array–Dammann-grating setup.

Tables (1)

Tables Icon

Table 1 Energy Distribution in Different Diffraction Orders, Generated by Several Dammann Gratingsa

Equations (8)

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sinc d ν λ f exp - i π d ν λ f ,
W Beam = Z   P Nf
W Beam Z = θ Beam = λ π W 0 .
Δ = P / N .
W Beam = Z   P F .
Δ   Im Im = 8 2 η 1 / 2 N 3 / 2 1 Q .
D ν =   A m δ ν λ f - m d
Z λ f 2 N Pd .

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