Abstract

The Shack–Hartmann wavefront sensor (SHWS) recently has been extensively researched for optical surface metrology due to its extendable dynamic range compared with interferometry technique. In this paper, we proposed to use a digital SHWS to measure toroidal surfaces, which are widely used in many optical systems due to their different symmetries and curvatures in the X and Y directions. For what is believed to be the first time, an asymmetrical optical lenslet array implemented by a spatial light modulator was presented to tackle the measurement challenge. This unconventional design approach has a great advantage to provide different optical powers in the X and Y directions so that focusing spots can be formed and captured on the detector plane for accurate centroid finding and precise wavefront evaluation for 3D shape reconstruction of the toroidal surface. A digital SHWS system with this extraordinary microlens array was built to verify the design concept, and the experimental results were presented and analyzed.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]

2006

2004

C. Pruss and H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233, 15-19 (2004).
[CrossRef]

2003

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

2002

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

2001

1998

1986

Asundi, A. Krishna

Bai, N.

Bode, A.

J. Pfund, A. Bode, N. Lindlein, and J. Schwider, http://www.optik.uni-erlangen.de/jabe/pdf/page_42.pdf.

Fang, Z.

Li, X.

Lindlein, N.

Malacara, D.

Menchaca, C.

Neal, D. A.

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

Neal, D. R.

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

Ong, L. S.

Pfund, J.

Pruss, C.

C. Pruss and H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233, 15-19 (2004).
[CrossRef]

Pulaski, P. D.

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

Ratte, K.

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

Raymond, T. D.

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

Roller, J. P.

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

Schwider, J.

Tiziani, H. J.

C. Pruss and H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233, 15-19 (2004).
[CrossRef]

Zhao, L.

Appl. Opt.

Opt. Commun.

C. Pruss and H. J. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233, 15-19 (2004).
[CrossRef]

Opt. Lett.

Proc SPIE

D. R. Neal, P. D. Pulaski, T. D. Raymond, and D. A. Neal, “Testing highly aberrated large optics with a Shack-Hartmann wavefront sensor,” Proc SPIE 5162, 129-138(2003).

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, “Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor,” Proc SPIE 4767, 44-52 (2002).

Other

J. Pfund, A. Bode, N. Lindlein, and J. Schwider, http://www.optik.uni-erlangen.de/jabe/pdf/page_42.pdf.

D. Malacara, Optical Shop Testing (Wiley, 1992).

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Figures (9)

Fig. 1
Fig. 1

Scheme to illustrate the optical system design in the x dimension for toroidal surface measurement—top view.

Fig. 2
Fig. 2

Scheme to illustrate the optical system design in the y dimension for toroidal surface measurement—side view.

Fig. 3
Fig. 3

Spot image captured by CMOS ( 1280 × 1024 pixels ) with a normal microlens array.

Fig. 4
Fig. 4

Scheme to illustrate the diverging power in the y dimension of the wavefront incident into the microlens array after being reflected back from the toroidal surface under test and exiting from the spherical lens L1.

Fig. 5
Fig. 5

Conventional DOL array pattern and the cross section phase profile of each lenslet.

Fig. 6
Fig. 6

Asymmetrical DOL array pattern and the cross section phase profile of each lenslet.

Fig. 7
Fig. 7

Spot images captured with traditional microlens array located at different planes.

Fig. 8
Fig. 8

Spot images captured with asymmetrical microlens array located at different planes.

Fig. 9
Fig. 9

Geometry to calculate the number of spots to be captured by CCD.

Tables (1)

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Table 1 Specifications of the Sample Toroidal Surface

Equations (12)

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1 f y = 1 d o + 1 d i ,
1 f L = 1 s o + 1 s i ,
1 f y = 1 f y + 1 f x ,
f R x 2 h 1 x 2 = h 2 x h 1 x ,
h 2 y H = s i D ,
s 0 d i 2 h 1 y 2 = h 2 y h 1 y .
ϕ ( r ) = 2 π ( a 2 r 2 ) ,
f = 1 2 a 2 λ 0 m ,
ϕ ( r ) = 2 π ( a 2 x x 2 + a 2 y y 2 ) ,
1280 pixels × 12 μm 40 pixels × 32 μm = 12  spots .
H CCD D + f x = H SLM D .
H SLM H = N CCDSpots N SLMLenslets ,

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