Abstract

A traditional Shack–Hartmann wavefront sensor (SHWS) uses a physical microlens array to sample the incoming wavefront into a number of segments and to measure the phase profile over the cross section of a given light beam. We customized a digital SHWS by encoding a spatial light modulator (SLM) with a diffractive optical lens (DOL) pattern to function as a diffractive optical microlens array. This SHWS can offer great flexibility for various applications. Through fast-Fourier-transform (FFT) analysis and experimental investigation, we studied three sampling methods to generate the digitized DOL pattern, and we compared the results. By analyzing the diffraction efficiency of the DOL and the microstructure of the SLM, we proposed three important strategies for the proper implementation of DOLs and DOL arrays with a SLM. Experiments demonstrated that these design rules were necessary and sufficient for generating an efficient DOL and DOL array with a SLM.

© 2006 Optical Society of America

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References

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  1. B. C. Platt and R. Shack, "History and principles of Shack-Hartmann wavefront sensing," J. Refract. Surg. 17, 573-577 (2001).
  2. See http://holoeye.com/ (accessed on 31 May 2005).
  3. H. P. Herzig, Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997), pp. 19-23.
  4. J. R. Leger and M. P. Griswold, "Binary-optics miniature Talbot cavities for laser beam addition," Appl. Phys. Lett. 56, 4-6 (1990).
    [CrossRef]
  5. J. Jahns and S. J. Walker, "Two-dimensional array of diffractive microlens fabrication by thin film deposition," Appl. Opt. 29, 931-936 (1990).
    [CrossRef] [PubMed]
  6. W. C. Sweat, "Describing holographic and optical elements as lenses," J. Opt. Soc. Am. 67, 803-808 (1977).
    [CrossRef]
  7. E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1990), pp. 424-426.

2001

B. C. Platt and R. Shack, "History and principles of Shack-Hartmann wavefront sensing," J. Refract. Surg. 17, 573-577 (2001).

1990

J. R. Leger and M. P. Griswold, "Binary-optics miniature Talbot cavities for laser beam addition," Appl. Phys. Lett. 56, 4-6 (1990).
[CrossRef]

J. Jahns and S. J. Walker, "Two-dimensional array of diffractive microlens fabrication by thin film deposition," Appl. Opt. 29, 931-936 (1990).
[CrossRef] [PubMed]

1977

Griswold, M. P.

J. R. Leger and M. P. Griswold, "Binary-optics miniature Talbot cavities for laser beam addition," Appl. Phys. Lett. 56, 4-6 (1990).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1990), pp. 424-426.

Herzig, H. P.

H. P. Herzig, Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997), pp. 19-23.

Jahns, J.

Leger, J. R.

J. R. Leger and M. P. Griswold, "Binary-optics miniature Talbot cavities for laser beam addition," Appl. Phys. Lett. 56, 4-6 (1990).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, "History and principles of Shack-Hartmann wavefront sensing," J. Refract. Surg. 17, 573-577 (2001).

Shack, R.

B. C. Platt and R. Shack, "History and principles of Shack-Hartmann wavefront sensing," J. Refract. Surg. 17, 573-577 (2001).

Sweat, W. C.

Walker, S. J.

Appl. Opt.

Appl. Phys. Lett.

J. R. Leger and M. P. Griswold, "Binary-optics miniature Talbot cavities for laser beam addition," Appl. Phys. Lett. 56, 4-6 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Refract. Surg.

B. C. Platt and R. Shack, "History and principles of Shack-Hartmann wavefront sensing," J. Refract. Surg. 17, 573-577 (2001).

Other

See http://holoeye.com/ (accessed on 31 May 2005).

H. P. Herzig, Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997), pp. 19-23.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1990), pp. 424-426.

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Figures (10)

Fig. 1
Fig. 1

Schematic of the SHWS.

Fig. 2
Fig. 2

Diffractive lens with (a) continuous microreliefs and (b) multilevel microreliefs.

Fig. 3
Fig. 3

(a) Continuous phase profile and (b) staircaselike phase profile of a DOL.

Fig. 4
Fig. 4

Typical lenslet with d × d pixels.

Fig. 5
Fig. 5

DOLs ( d = 50   pixels , f = 75 mm ) generated by three different sampling methods.

Fig. 6
Fig. 6

FFT spectra for the three DOLs shown in Fig. 5.

Fig. 7
Fig. 7

Focusing spots for the three DOLs shown in Fig. 5.

Fig. 8
Fig. 8

DOL continuous phase profile (a) side view and (b) top view.

Fig. 9
Fig. 9

(a) SLM microstructure and (b) focal image of DOL ( d = 50   pixels , f = 60 mm ).

Fig. 10
Fig. 10

Image captured on the focal plane of a DOL ( 40   pixels , 125 mm , 3 × 3 ) array. Cross talk almost occurs owing to the improper pitch of the lenslet array.

Equations (48)

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800 × 600   pixels
ϕ ( r ) = 2 π ( a 2 r 2 + a 4 r 4 + ) ,
1 / f = 2 a 2 λ 0 m ,
λ 0
f 0
2 π
2 π
N 1 = 1 / a 2 b = 2 f λ b ,
N 1
f 64 b 2 / 2 λ .
32 μm
51.7 mm
2 N 1
d min = 2 2 f λ .
N = n n 1 b 2 f λ = 1 ,
n = f λ 2 b 2 + 1 2 + b 2 8 f λ .
d max = 2 f λ b + b .
2 2 f λ d 2 f λ b + b .
600 × 800   pixel
32 μm
p sin θ = m λ .
m = 1
λ = 632.8 μm
sin θ = m λ / p , = 632.8 × 10 - 9 32 × 10 - 6 = 0.019775
θ = 1.1331 ° .
S = s / n ( n = 1 , 2 , 3 , )
s = 70 % [ f ]
tan θ = 0.7 [ f ] × 32 × 10 - 6 f × 10 - 3 = 0.0224
θ = 1.2832 ° .
S = λ f / n p ,
n = 1 , 2 , 3 , .
125 mm
d = 77   pixels
77   pixels
39   pixels
3 × 3
40   pixel
1
2
3
d × d
d = 50   pixels
f = 75 mm
d = 50   pixels
f = 60 mm
40   pixels
125 mm
3 × 3

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