Abstract

We demonstrate a method to calibrate a Shack–Hartmann sensor as an orthographic camera. This calibration method permits us to obtain the distance, the rotation matrix between the microlens array and CCD imaging planes, and the projection matrix, which models the projection of the incoming rays to the CCD imaging plane. The proposed calibration method introduces a very compact matrix notation and allows wavefront reconstruction without an explicit centroid search between the reference and distorted spot diagrams. We show a set of simulations in code V that prove the effectiveness of the proposed method.

© 2010 Optical Society of America

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References

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  1. D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
    [CrossRef]
  2. J. Pfund, N. Lindlein, and J. Schwider, Appl. Opt. 37, 22 (1998).
    [CrossRef]
  3. D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).
  4. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2004).
    [CrossRef]

2002 (1)

D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
[CrossRef]

1998 (1)

Copland, J.

D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
[CrossRef]

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2004).
[CrossRef]

Kathman, A. D.

D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Lindlein, N.

Neal, D.

D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
[CrossRef]

Neal, D. N.

D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
[CrossRef]

O’Shea, D.

D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Pfund, J.

Prather, D. W.

D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Schwider, J.

Suleski, T. J.

D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2004).
[CrossRef]

Appl. Opt. (1)

Proc. SPIE (1)

D. N. Neal, J. Copland, and D. Neal, Proc. SPIE 4779, 148 (2002).
[CrossRef]

Other (2)

D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge U. Press, 2004).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Scheme of the SH imaging process of two chief rays passing through a microlens with different implying angles.

Fig. 2
Fig. 2

3D scheme of the SH imaging process.

Tables (3)

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Table 1 Computed Projection Matrices and Root Mean Square Errors

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Table 2 Recovered α, β, and γ Tilt Errors in Euler Notation

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Table 3 Computed Distances d

Equations (6)

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

[ Δ W ] i j = [ ( Δ W x Δ W y ) ] i j = [ 1 d ( Δ x Δ y ) ] i j ,
m = H M = [ κ x 0 μ x 0 κ y μ y 0 0 1 ] [ r 1 T 0 r 2 T 0 0 T 1 ] M ,
[ x i j k y i j k 1 ] = [ κ x r 11 κ x r 12 μ x k κ y r 21 κ y r 22 μ y k 0 0 1 ] [ X i j Y i j 1 ] .
d = μ 2 μ 1 tan ( ξ ) .
[ x ^ i j y ^ i j 1 ] = [ κ x r 11 κ x r 12 μ ^ x , i j κ y r 21 κ y r 22 μ ^ y , i j 0 0 1 ] [ X i j Y i j 1 ] ,
[ Δ W ] i j = [ ( Δ W x Δ W y ) ] i j = [ 1 d ( μ ^ x μ ^ y ) ] i j .

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