Abstract

In this paper, we describe a zonal wavefront sensor in which the photodetector array can have a smaller number of rows. The test wavefront is incident on a two-dimensional array of diffraction gratings followed by a single focusing lens. The periodicity and the orientation of the grating rulings of each grating can be chosen such that the +1 order beam from the gratings forms an array of focal spots in the detector plane. We show that by using a square array of zones, it is possible to generate an array of +1 order focal spots having a smaller number of rows, thus reducing the height of the required detector array. The phase profile of the test wavefront can be estimated by measuring the displacements of the +1 order focal spots for the test wavefront relative to the +1 order focal spots for a plane reference wavefront. The narrower width of the photodetector array can offer several advantages, such as a faster frame rate of the wavefront sensor, a reduced amount of cross talk between the nearby detector zones, and a decrease in the maximum thermal noise. We also present experimental results of a proof-of-concept experimental arrangement using the proposed wavefront sensing scheme.

© 2011 Optical Society of America

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References

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  1. R. Shack and B. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).
  2. G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
    [Crossref]
  3. W. Su, Y. Zhou, and Q. Zhao, “Sequential wavefront sensor,” U.S. patent 7,445,335 (4 November 2008).
  4. D. Neal, R. Copland, and D. Neal, “System and method of measuring and mapping three dimensional structures,” U.S. patent 7,455,407 (25 November 2008).
  5. T. Nirmaier, G. Pudasaini, and J. Bille, “Very fast wave-front measurements at the human eye with a custom CMOS-based Hartmann–Shack sensor,” Opt. Express 11, 2704–2716 (2003).
    [Crossref] [PubMed]
  6. D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
    [Crossref]
  7. P. Martinez and A. Klotz, A Practical Guide to CCD Astronomy (Cambridge University Press, 1998).
  8. http://learn.hamamatsu.com/explore/.
  9. A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.
  10. T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
    [Crossref]
  11. B. R. Boruah, “Zonal wavefront sensing using an array of gratings,” Opt. Lett. 35, 202–204 (2010).
    [Crossref] [PubMed]
  12. J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
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    [Crossref]
  14. V. Mahajan, “Zernike circle polynomials and optical aberrations of systems with circular pupils,” Appl. Opt. 33, 8121–8124 (1994).
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    [Crossref]
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    [Crossref]

2010 (1)

2009 (1)

B. R. Boruah, “Dynamic manipulation of a laser beam using a liquid crystal spatial light modulator,” Am. J. Phys. 77, 331–336 (2009).
[Crossref]

2008 (1)

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

2006 (1)

G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
[Crossref]

2005 (1)

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

2004 (1)

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
[Crossref]

2003 (1)

1998 (2)

1994 (1)

1980 (1)

1971 (1)

R. Shack and B. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Allinson, N.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Bille, J.

Bohndiek, S. E.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Booth, M. J.

Boruah, B. R.

B. R. Boruah, “Zonal wavefront sensing using an array of gratings,” Opt. Lett. 35, 202–204 (2010).
[Crossref] [PubMed]

B. R. Boruah, “Dynamic manipulation of a laser beam using a liquid crystal spatial light modulator,” Am. J. Phys. 77, 331–336 (2009).
[Crossref]

Clark, A. T.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Copland, R.

D. Neal, R. Copland, and D. Neal, “System and method of measuring and mapping three dimensional structures,” U.S. patent 7,455,407 (25 November 2008).

Crooks, J.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

de Lima Monteiro, D.

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
[Crossref]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Guerrini, N.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Hafner, J.

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

Haist, T.

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

Klotz, A.

P. Martinez and A. Klotz, A Practical Guide to CCD Astronomy (Cambridge University Press, 1998).

Mahajan, V.

Martinez, P.

P. Martinez and A. Klotz, A Practical Guide to CCD Astronomy (Cambridge University Press, 1998).

Nagy, L.

G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
[Crossref]

Neal, D.

D. Neal, R. Copland, and D. Neal, “System and method of measuring and mapping three dimensional structures,” U.S. patent 7,455,407 (25 November 2008).

D. Neal, R. Copland, and D. Neal, “System and method of measuring and mapping three dimensional structures,” U.S. patent 7,455,407 (25 November 2008).

Neil, M. A. A.

Nirmaier, T.

Osten, W.

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

Pantanelli, S.

G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
[Crossref]

Pickering, T.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Platt, B.

R. Shack and B. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Pudasaini, G.

Renato, T.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

Sarro, P.

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
[Crossref]

Shack, R.

R. Shack and B. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Southwell, W.

Su, W.

W. Su, Y. Zhou, and Q. Zhao, “Sequential wavefront sensor,” U.S. patent 7,445,335 (4 November 2008).

Vdovin, G.

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
[Crossref]

Warber, M.

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

Wilson, T.

Yoon, G.

G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
[Crossref]

Zhao, Q.

W. Su, Y. Zhou, and Q. Zhao, “Sequential wavefront sensor,” U.S. patent 7,445,335 (4 November 2008).

Zhou, Y.

W. Su, Y. Zhou, and Q. Zhao, “Sequential wavefront sensor,” U.S. patent 7,445,335 (4 November 2008).

Am. J. Phys. (1)

B. R. Boruah, “Dynamic manipulation of a laser beam using a liquid crystal spatial light modulator,” Am. J. Phys. 77, 331–336 (2009).
[Crossref]

Appl. Opt. (1)

J. Biomed. Opt. (1)

G. Yoon, S. Pantanelli, and L. Nagy, “Large-dynamic-range Shack–Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030502 (2006).
[Crossref]

J. Opt. Soc. Am. (2)

R. Shack and B. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

W. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (1)

T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE 7064, 70640M (2008).
[Crossref]

Sens. Actuators A: Phys. (1)

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuators A: Phys. 109, 220–230 (2004).
[Crossref]

Other (6)

P. Martinez and A. Klotz, A Practical Guide to CCD Astronomy (Cambridge University Press, 1998).

http://learn.hamamatsu.com/explore/.

A. T. Clark, N. Guerrini, N. Allinson, S. E. Bohndiek, J. Crooks, T. Pickering, and T. Renato, “A 54 mm×54 mm—1.8 megapixel CMOS image sensor for medical imaging,” presented at the IEEE Nuclear Science Symposium, Dresden, Germany, 19–25 October 2008.

W. Su, Y. Zhou, and Q. Zhao, “Sequential wavefront sensor,” U.S. patent 7,445,335 (4 November 2008).

D. Neal, R. Copland, and D. Neal, “System and method of measuring and mapping three dimensional structures,” U.S. patent 7,455,407 (25 November 2008).

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

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Figures (4)

Fig. 1
Fig. 1

(a) Patterns representing the transmittance functions of the grating arrays of the dimensions 4 × 4 to produce a + 1 order focal spot array comprising four rows, (b) two rows, and (c) one row, while (d)–(f) are the corresponding + 1 order spots obtained numerically.

Fig. 2
Fig. 2

Schematic of the grating-array-based wavefront sensor.

Fig. 3
Fig. 3

(a)  + 1 order focal spot arrays of dimensions 4 × 4 , (b)  2 × 8 and (c)  1 × 16 , (i) corresponding to the reference beam, (ii) after adding aberrations to the reference beam, and (iii) after aberration correction. The inset adjacent to each figure is the corresponding single hologram + 1 order focal spot.

Fig. 4
Fig. 4

(a) Three-dimensional plots of the wavefront added and (b) measured wavefronts using + 1 order focal spot arrays of dimensions 4 × 4 , (c)  2 × 8 , and (d)  1 × 16 . The color bar represents the phase values in radians.

Tables (1)

Tables Icon

Table 1 Coefficients of the Zernike Modes Applied a j a and Measured a j m Using Focal Spot Arrays Comprising Four Rows (4R), Two Rows (2R), and One Row (1R)

Equations (18)

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t g ( ξ , η ) = { 1 2 + 1 2 sin ( 2 π ν ξ ) } circ ( ρ w ) ,
circ ( ρ w ) = { 1 if     ρ w 1 0 otherwise .
U ( u , v ) = e i k f i λ f t g ( ξ , η ) e i 2 π ξ u + η v λ f d ξ d η .
{ g h } ( x , y ) = h ( x ξ , y η ) g ( ξ , η ) d ξ d η .
U ( u , v ) = e i k f i λ f F [ 1 2 + 1 2 sin ( 2 π ν ξ ) ] F [ circ ( ρ w ) ] .
F [ 1 2 + 1 2 sin ( 2 π ν ξ ) ] = 1 2 [ δ ( f x , f y ) + 1 2 i { δ ( f x ν , f y ) δ ( f x + ν , f y ) } ] .
F [ circ ( ρ w ) ] = S A r ( f x , f y ) ,
A r ( f x , f y ) = J 1 ( 2 π w f x 2 + f y 2 ) π w f x 2 + f y 2 ,
U ( f x , f y ) = S e i k f i 2 λ f [ A r ( f x , f y ) + 1 2 i { A r ( f x ν , f y ) A r ( f x + ν , f y ) } ] .
I ( f x , f y ) = S 2 4 λ 2 f 2 [ A r 2 ( f x , f y ) + 1 4 { A r 2 ( f x ν , f y ) + A r 2 ( f x + ν , f y ) } ] .
I = S 2 4 λ 2 f 2 [ A r 2 ( f x , f y ) + 1 4 { A r 2 ( f x ν x , f y ν y ) + A r 2 ( f x + ν x , f y + ν y ) } ] .
I = S 2 4 λ 2 f 2 [ A r 2 ( f x m x , f y m y ) + 1 4 { A r 2 ( f x ν x m x , f y ν y m y ) + A r 2 ( f x + ν x m x , f y + ν y m y ) } ] .
t g ( ξ , η ) = 1 2 + n 2 n π sin ( n 2 π ν ξ ) ,
I ( f x , f y ) = S 2 4 λ 2 f 2 [ A r 2 ( f x , f y ) + n 4 π 2 n 2 { A r 2 ( f x ± n ν , f y ) } ] .
I = S 2 4 λ 2 f 2 [ A r 2 ( f x m x , f y m y ) + n 4 π 2 n 2 { A r 2 ( f x ± n ν x m x , f y ± n ν y m y ) } ] .
ν x = ν 0 x + ( Rem { ( j + ( i 1 ) N 1 ) , S i j } S i j ) Δ ν x ν y = ν 0 y + ( i m 1 ) Δ ν y ,
ϕ ( ξ , η ) = k = 1 M a k Z k ( ξ , η ) ,
a = ( A A ) 1 A T .

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