Abstract

Even after good calibration, the measurement accuracy of a Shack-Hartmann sensor can be affected by the fabrication and alignment tolerances of the wavefront sensing optical system. The shifts of the Shack-Hartmann spots caused by misalignments correspond to ray intercept errors on the detector that typically have to be converted into a meaningful input wavefront measurement error. This conversion cannot be directly obtained from a conventional tolerance analysis using optical design software, because of the intrinsic wavefront sampling by the lenslet array. The tolerancing method proposed in this paper solves the problem of converting conventional merit function degradation into input wavefront measurement error without employing a separate wavefront reconstruction algorithm. Using the proposed method, this investigation shows the effect of fabrication and misalignment errors on the accuracy of a calibrated Shack-Hartmann sensor, as a function of input wavefront vergence.

© 2006 Optical Society of America

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References

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    [CrossRef]
  8. Mary G. Turner, Tolerancing and Alignment using ZEMAX, (Focus Software, Inc., 2000
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  10. G. Curatu, D. V. Wick, D. M Payne, T. Martinez, J. Harriman, J. E. Harvey, "Wide field-of-view imaging system using a liquid crystal spatial light modulator," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 80-86 (2005).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Proc. SPIE

G. Curatu, D. V. Wick, D. M Payne, T. Martinez, J. Harriman, J. E. Harvey, "Wide field-of-view imaging system using a liquid crystal spatial light modulator," in Current Developments in Lens Design and Optical Engineering VI, P. Z. Mouroulis, W. J. Smith, and R. B. Johnson, eds., Proc. SPIE 5874, 80-86 (2005).

Other

Joseph M. Geary, Introduction to Wavefront Sensors (SPIE PRESS, Bellingham, WA, 1995).

R.K.Tyson, Introduction to Adaptive Optics (SPIE PRESS Bellingham, WA, 2000).
[CrossRef]

Adaptive Optics Associates Inc. "Classic Hartmann Technique", <a href="http://www.aoainc.com/technologies/adaptiveandmicrooptics/tutorial.html">http://www.aoainc.com/technologies/adaptiveandmicrooptics/tutorial.html</a>

C. Curatu, G. Curatu, "Tolerance analysis of optical systems containing sampling devices" in Optical Design and Engineering II, L. Mazuray and R. Wartmann, eds., Proc. SPIE 5962, 359-366 (2005).

Mary G. Turner, Tolerancing and Alignment using ZEMAX, (Focus Software, Inc., 2000

R. C. Juergens, Code V Reference Manual, (Optical Research Associates, 2005).

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Figures (8)

Fig. 1.
Fig. 1.

Conceptual layout of a Shack-Hartmann sensor with an afocal expansion lens and demagnification relay optics

Fig. 2.
Fig. 2.

Nominal design layout

Fig. 3.
Fig. 3.

Coordinates of one S-H spot, for WF0, WFR and WFL - nominal design

Fig. 4.
Fig. 4.

Shack-Hartmann spot diagram with selected reference ray-intercepts on the CCD plane

Fig. 5.
Fig. 5.

Calculating spot reference coordinates for WFR and WFL – taking into account calibration

Fig. 6.
Fig. 6.

Discrepancy between calculated reference spot coordinates and actual spot coordinates for WFR and WFL

Fig. 7.
Fig. 7.

Misaligned system with variable Zernike surface ready for optimization

Fig. 8.
Fig. 8.

Measurement error as a function of the sensor dynamic range

Tables (2)

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Table 1. Nominal design specifications

Tables Icon

Table 2. Tolerance values used in the analysis

Equations (8)

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Δ L = x L y L x 0 y 0
Δ R = x R y R x 0 y 0
x CL y CL = x C 0 y C 0 + Δ L
x CR y CR = x C 0 y C 0 + Δ R
x TL y TL x CL y CL 0
x TR y TR x CR y CR 0
W ρ θ = c n m . z n m ρ θ
RMS WF Error = ( c n m ) 2

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