Abstract

The liquid-crystal wave-front scanner (LCWS) is a highly sensitive wave-front sensor suited to the measurement of aberrations in optical systems and, more generally, of static wave fronts, and it is based on the Hartmann test. In the LCWS an incoming wave front is scanned sequentially by a programmable moving aperture that is implemented by use of a liquid-crystal display. The position of the diffraction spot is recorded behind an observation lens with a CCD detector and provides an estimation of the local slopes in two orthogonal directions at the aperture position. The wave front is then reconstructed from slope data by use of a least-squares method. Experiments are reported for nearly planar wave fronts as well as for strongly aberrated wave fronts, demonstrating both the large dynamic range and the great sensitivity of the LCWS. The LCWS is compared with the Shack–Hartmann wave-front sensor in terms of dynamic range and sensitivity.

© 2000 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, 1991).
  2. R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971); paper MG23, 1971 OSA Spring Optical Meeting.
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    [CrossRef] [PubMed]
  4. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
    [CrossRef] [PubMed]
  5. V. Laude, S. Olivier, C. Dirson, J.-P. Hiugnard, “Hartmann wave-front scanner,” Opt. Lett. 24, 1796–1798 (1999).
    [CrossRef]
  6. V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
    [CrossRef]
  7. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  8. G. Häusler, G. Schneider, “Testing optics by experimental ray tracing with a lateral effect photodiode,” Appl. Opt. 24, 4160–5164 (1988).
  9. C. Castellini, F. Francini, B. Tiribilli, “Hartmann test modification for measuring ophthalmic progressive lenses,” Appl. Opt. 33, 4120–4124 (1994).
    [CrossRef] [PubMed]
  10. R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing method for optical testing,” Opt. Lett. 24, 951–953 (1999).
    [CrossRef]

1999

1998

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

1994

1993

1988

G. Häusler, G. Schneider, “Testing optics by experimental ray tracing with a lateral effect photodiode,” Appl. Opt. 24, 4160–5164 (1988).

F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
[CrossRef] [PubMed]

1980

1971

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971); paper MG23, 1971 OSA Spring Optical Meeting.

Castellini, C.

Dirson, C.

Francini, F.

Häusler, G.

G. Häusler, G. Schneider, “Testing optics by experimental ray tracing with a lateral effect photodiode,” Appl. Opt. 24, 4160–5164 (1988).

Hiugnard, J.-P.

Laude, V.

V. Laude, S. Olivier, C. Dirson, J.-P. Hiugnard, “Hartmann wave-front scanner,” Opt. Lett. 24, 1796–1798 (1999).
[CrossRef]

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

Moreno-Barriuso, E.

Navarro, R.

Olivier, S.

Platt, B. C.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971); paper MG23, 1971 OSA Spring Optical Meeting.

Primot, J.

Roddier, F.

Schneider, G.

G. Häusler, G. Schneider, “Testing optics by experimental ray tracing with a lateral effect photodiode,” Appl. Opt. 24, 4160–5164 (1988).

Shack, R. V.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971); paper MG23, 1971 OSA Spring Optical Meeting.

Southwell, W. H.

Tiribilli, B.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, 1991).

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Figures (6)

Fig. 1
Fig. 1

Principle of the operation of the Hartmann wave-front scanner: (a) observation of the diffraction spots near the focal plane of the lens and (b) calibration and measurement of the optical system in two different planes.

Fig. 2
Fig. 2

Optical setup of the LCWS.

Fig. 3
Fig. 3

Measurement of the wave front from behind a divergent lens: (a) reconstructed wave front and (b) experimental wave-front slopes along the y direction.

Fig. 4
Fig. 4

Legendre and Zernike coefficients in the expansion of the wave front shown in Fig. 3(a).

Fig. 5
Fig. 5

Measurement of the wave front from behind a thin glass plate: (a) experimental wave-front slopes along the y direction, (b) reconstructed wave-front slopes along the y direction, (c) the reconstructed wave front.

Fig. 6
Fig. 6

Measurement of the wave front from behind a progressive ophthalmic lens: (a) experimental wave-front slopes along the x direction, (b) experimental wave-front slopes along the y direction, (c) the reconstructed wave front.

Tables (3)

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Table 1 Duration of Each Elementary Operation for One Sampling Point

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Table 2 First Seven Legendre Polynomials

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Table 3 Experimental Evaluation of the Measurement Noise as a Function of the Observation Distance

Equations (10)

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Wx, yx=sx, y=xd-1d-1fx,
sx, y=xmdm-xcdc-1dm-1dcx.
δθ=1qpD,
Wx, y=n=148 anPnx, y,
Wr, θ=p=228 bpZpr, θ.
bp=n=148 Pnr, θZpr, θrdrdθan,
Ea1, a2, , aL=1Nk=1Nsexxk, yk-smxxk, yk2+seyxk, yk-smyxk, yk2,
Eaˆ1, aˆ2, , aˆL=2σ2-LN σ2+reconstruction error.
ck= xIkxdx Ikxdx,
ckq xqIkxqq Ikxq,

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