Abstract

Several trade-offs relevant to the design of a two-dimensional high-speed Shack–Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack–Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Liang, B. Grimm, S. Goelz, and J. Bille, "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor," J. Opt. Soc. Am. A 11, 1949-1957 (1994).
    [CrossRef]
  2. T. Salmon, L. Thibos, and A. Bradley, "Comparison of the eye's wave-front aberration measured psychophysically and with the Shack-Hartmann wave-front sensor," J. Opt. Soc. Am. A 15, 2457-2465 (1998).
    [CrossRef]
  3. J. Ares, T. Mancebo, and S. Bará, "Position and displacement sensing with Shack-Hartmann wave-front sensors," Appl. Opt. 39, 1511-1520 (2000).
    [CrossRef]
  4. B. Schäfer and K. Mann, "Determination of beam parameters and coherence properties of laser radiation by use of an extended Hartmann-Shack wave-front sensor," Appl. Opt. 41, 2809-2817 (2002).
    [CrossRef] [PubMed]
  5. B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

2002 (1)

2000 (1)

1998 (1)

1996 (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

1994 (1)

Ares, J.

Bará, S.

Bille, J.

Bradley, A.

Duncan, B.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

Goelz, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grimm, B.

Harris, S. R.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

Lempert, W.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

Liang, J.

Mancebo, T.

Mann, K.

Salmon, T.

Samimy, M.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

Schäfer, B.

Thibos, L.

Thurow, B.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

Widiker, J.

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," paper AIAA-2003-0684 presented at the Forty-First Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 6-9 January 2003.

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

Schematic diagram of an elementary SH WFS with minimal optics. The wavefront tilt θ is measured as a function of spot displacement δ from a reference position.

Fig. 2
Fig. 2

Shown is a 2 × 2 array of lenslet apertures and their corresponding focal spots. The lower-left spot is exhibiting the maximum displacement allowed. The spot at the upper left has exceeded this criterion and may cause spot-tracking errors.

Fig. 3
Fig. 3

Schematic diagram of a modified SH WFS incorporating (1) a 4-F relay system, (2) a singlet lens used to alter the lenslet array's effective focal length, and (3) a spot pattern relay lens. Note that the inversions caused by the 4-F system and the spot pattern relay lens cancel.

Fig. 4
Fig. 4

Preliminary experimental setup consisting of a collimated laser source, an adjustable aperture, and a long focal-length lens.

Fig. 5
Fig. 5

Typical results of a camera-tracking routine pair characterization experiment, assuming use of a low fill factor, high-speed camera, and a 2-D least-squares-fit spot-tracking routine. Other camera-tracking routine pairs may yield different results.

Fig. 6
Fig. 6

Flow chart showing the portion of our design procedure related to satisfying the SSR * design specification. The dashed connectors indicate the path taken by the design example in Section 6.

Fig. 7
Fig. 7

Flow chart showing the portion of our design procedure related to satisfying the θ max * design specification. The dashed connectors indicate the path taken by the design example in Section 6. DNR, dynamic range.

Fig. 8
Fig. 8

Flow chart showing the portion of our design procedure related to establishing an initial value of the spot pattern relay lens magnification M 2 ( 1 ) that satisfies the σ θ * design specification. Since this initial value of M 2 may result in a large loss of sampled area, an iterative approach can be used beyond this. The dashed connectors indicate the path taken by the design example in Section 6.

Fig. 9
Fig. 9

Flow chart showing the iterative loop of our design procedure used to optimize σ θ and the sampled area A. The dashed connectors indicate the path taken by the design example in Section 6.

Tables (3)

Tables Icon

Table 1 Effects of Increasing Elementary SH WFS Design Parameters

Tables Icon

Table 2 Effects of Various SH WFS Design Parameter Choices Introduced by Use of Additional Optics

Tables Icon

Table 3 Parameters of the Example System During Each Step of the Design

Equations (28)

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

θ tan θ = δ f μ ,
σ θ = σ δ f μ ,
I = ( Δ 2 λ f μ ) 2 sinc 2 ( Δ λ f μ x ) sinc 2 ( Δ λ f μ y ) ,
W spot = 2 λ f μ Δ .
θ max = 1 2 ( f / # ) λ Δ ,
[ y final θ final ] = [ y initial M 1 θ initial / M 1 ] ,
SSR = 1 Δ eff = | M 1 | Δ ,
θ max = | M 1 | f μ ( Δ 2 λ f μ Δ ) ,
σ θ = | M 1 |   σ δ f μ ,
1 f eq = 1 f μ + 1 f s .
θ max = | M 1 | f eq ( Δ 2 λ f eq Δ ) ,
σ θ = | M 1 |   σ δ ( f eq , ) f eq ,
W spot = 2 | M 2 | λ f eq Δ .
σ θ = σ δ ( f eq , M 2 , ) | M 1 | | M 2 | f eq .
A = A 0 ( M 1 ) 2 ,
θ tan θ = δ | M 1 | | M 2 | f eq .
| M 1 | = f 2 f 1 SSR * Δ ,
θ max = | M 1 | Δ 2 f eq | M 1 | λ Δ .
f s = | M 1 | ( f μ ) 2 2 f ∕#   f μ θ max * | M 1 | f μ + 2 | M 1 | λ ( f ∕# ) 2 ,
| M 1 | = θ max * ( Δ 2 f eq - λ Δ ) ,
σ δ ( W spot ) σ θ * f eq | M 2 | | M 1 | .
σ δ ( 0 ) = σ θ * f eq | M 1 | ,
W spot ( 0 ) = 2 λ f eq Δ ,
| M 2 ( 1 ) | W spot ( 1 ) W spot ( 0 ) ,
σ δ ( n ) = | M 2 ( n ) | σ δ ( 0 ) ,
| M 2 ( n + 1 ) | W spot ( n + 1 ) W spot ( 0 ) .
σ δ ( n ) σ δ ( n 1 ) 0.
| W spot ( n ) - W spot ( n - 1 ) | < 1 pixel ,

Metrics