Abstract

We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front–sensing system.

© 1999 Optical Society of America

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References

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  1. J. Turunen, F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, GmbH, Berlin, 1997).
  2. B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
    [CrossRef] [PubMed]
  3. M. Li, A. Larsson, N. Eriksson, M. Hagberg, J. Bengtsson, “Continuous-level phase-only computer-generated hologram realized by dislocated binary gratings,” Opt. Lett. 21, 1516–1518 (1996).
    [CrossRef] [PubMed]
  4. P. M. Blanchard, A. H. Greenaway, R. N. Anderton, R. Appleby, “Phase calibration of arrays at optical and millimeter wavelengths,” J. Opt. Soc. Am. A 13, 1593–1600 (1996).
    [CrossRef]
  5. T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
    [CrossRef]
  6. J. Braat, “Influence of substrate thickness on optical disk readout,” Appl. Opt. 36, 8056–8062 (1997).
    [CrossRef]
  7. H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).
  8. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
    [CrossRef]
  9. F. Roddier, “Wave-front sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990).
    [CrossRef] [PubMed]
  10. R. L. Kendrick, D. S. Acton, A. L. Duncan, “Phase-diversity wave-front sensor for imaging systems,” Appl. Opt. 33, 6533–6546 (1994).
    [CrossRef] [PubMed]
  11. G. Vdovin, S. Middelhoek, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
    [CrossRef]

1999

T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
[CrossRef]

1997

J. Braat, “Influence of substrate thickness on optical disk readout,” Appl. Opt. 36, 8056–8062 (1997).
[CrossRef]

G. Vdovin, S. Middelhoek, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

1996

1994

1990

1982

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

1966

Acton, D. S.

Anderton, R. N.

Appleby, R.

Bengtsson, J.

Blanchard, P. M.

Braat, J.

Brown, B. R.

Duncan, A. L.

Eriksson, N.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

Greenaway, A. H.

Hagberg, M.

Kendrick, R. L.

Larsson, A.

Li, M.

Lohmann, A. W.

Lou, H.

T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
[CrossRef]

Middelhoek, S.

G. Vdovin, S. Middelhoek, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Milster, T. D.

T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
[CrossRef]

Roddier, F.

Rosen, H. J.

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

Rubin, K. A.

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

Sincerbox, G. T.

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

Strand, T. C.

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

Upton, R. S.

T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
[CrossRef]

Vdovin, G.

G. Vdovin, S. Middelhoek, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Zavislan, J. M.

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

T. D. Milster, R. S. Upton, H. Lou, “Objective lens design for multiple-layer optical data storage,” Opt. Eng. 38, 295–301 (1999).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

G. Vdovin, S. Middelhoek, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Opt. Lett.

Other

J. Turunen, F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, GmbH, Berlin, 1997).

H. J. Rosen, K. A. Rubin, G. T. Sincerbox, T. C. Strand, J. M. Zavislan, “Multiple data surface optical data storage system,” U.S. patent5202875 (13April1993).

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Figures (11)

Fig. 1
Fig. 1

Grating displacement by Δ x .

Fig. 2
Fig. 2

Gratings distorted according to Eq. (4) with R = 20d: (a) W 20 = 1λ and (b) W 20 = 3λ. The grating origin (0, 0) is at the center of the circular aperture.

Fig. 3
Fig. 3

Use of a defocus-grating–lens combination for imaging: (a) a single object imaged onto multiple image planes and (b) multiple objects imaged onto a single image plane.

Fig. 4
Fig. 4

Contour plot of the intensity in a meridional plane near the focus of a combination of a quadratically distorted grating (W 20 = 1λ and a grating period of 631λ) and a lens with a single point source. The intensity of each diffraction order is normalized to unity. Dimensionless units of u = 2π(r/ f)2 z/λ and v = 2π(r/ f)y/λ. Contours are located at 0.9, 0.5, 0.1, 0.05, and 0.01.

Fig. 5
Fig. 5

Experimental images of a single object plane with the camera positioned in image planes (a) 2, (b) 1, (c) 3, as shown in Fig. 3(a). Because an amplitude grating was used, the intensity of the nonzero orders was lower than that of the zero order. The images are normalized by adjustment of the gray-level scaling in each diffraction order to equalize their peak intensities. The raw intensity in the three orders could be equalized by use of a binary phase grating with a phase step of 0.639π.

Fig. 6
Fig. 6

Experimental arrangement for imaging three object planes.

Fig. 7
Fig. 7

Experimental images of three objects at different ranges. The diffraction orders are normalized.

Fig. 8
Fig. 8

(a) Crossed amplitude gratings with W 20 = λ/2, 3λ/2. (b) Computed point-spread function showing nine images with different levels of defocus. The intensity of each image is normalized.

Fig. 9
Fig. 9

Movement of the diffraction orders with the grating position (x 0, y 0).

Fig. 10
Fig. 10

Distorted binary amplitude grating with W 20 = 1λ and W 40 = 4λ.

Fig. 11
Fig. 11

Experimental images taken simultaneously on a single camera by use of a defocus-grating–lens combination. The central (zero-order) image shows the uniformly illuminated deformable mirror surface. The left-hand (+1-order) image and the right-hand (-1-order) image represent images of planes that are a distance of approximately 1 m on either side of the mirror surface. Four electrodes are switched on, causing four regions of localized curvature.

Equations (18)

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

ϕmx, y=2πmΔxx, yd,
ϕr=2πλf-f2-r21/2,
ϕr=2πλr22f+r48f3+r616f5+.
Δxx, y=W20dλR2x2+y2,
ϕmx, y=m 2πW20λR2x2+y2.
xd0+W20x2+y2λR2=n,
xn=-λR22W20d0,
Cn=nλR2W20+λR22d0W2021/2.
d=d0λR2λR2-2d0W20x0.
dmin=d0λRλR+2d0W20.
fm=R22mW20,
fm=fR2R2+2fmW20.
δzm=-2mz2W20R2+2mzW20,
δzm-2mzR2W20,
ϕmx, y=2mπW20λR2x-x02+y-y02,
ϕmx, y=2mπW20λR2x2+y2-2x0x-2y0y+x02+y02,
xd0+j=1W2j,0x2+y2jλR2j=n.
x0=λR22d0W20,

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