Abstract

We propose an innovative method for localized wavefront correction based on area-mapped phase-shift (AMPS) interferometry. In this Letter, we present the theory and then experimentally compare it with a previously demonstrated method based on spot-optimized phase-stepping (SOPS) interferometry. We found that AMPS outperforms SOPS interferometry in terms of speed by threefold, although in noisy environments the improvements may be larger. AMPS yielded similar point-spread functions (PSF) as SOPS for moderate system-induced aberrations, but yielded a slightly less ideal PSF for larger aberrations. The method described in this Letter may prove crucial for applications where the phase-stepping solution does not have sufficient speed.

© 2011 Optical Society of America

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References

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  1. W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
    [CrossRef]

2010 (3)

J. W. Cha, J. Ballesta, and P. T. C. So, J. Biomed. Opt. 15, 046022 (2010).
[CrossRef] [PubMed]

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
[CrossRef]

2009 (1)

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

2008 (2)

2006 (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl. Acad. Sci. USA 103, 17137 (2006).
[CrossRef] [PubMed]

2003 (1)

1998 (1)

M. Booth, M. A. A. Neil, and T. Wilson, J. Microsc. 192, 90 (1998).
[CrossRef]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Ballesta, J.

J. W. Cha, J. Ballesta, and P. T. C. So, J. Biomed. Opt. 15, 046022 (2010).
[CrossRef] [PubMed]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Booth, M.

M. Booth, M. A. A. Neil, and T. Wilson, J. Microsc. 192, 90 (1998).
[CrossRef]

Bowman, R. W.

R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
[CrossRef]

Burns, D.

Cha, J. W.

J. W. Cha, J. Ballesta, and P. T. C. So, J. Biomed. Opt. 15, 046022 (2010).
[CrossRef] [PubMed]

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

Denk, W.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl. Acad. Sci. USA 103, 17137 (2006).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

Girkin, J.

Girkin, J. M.

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl. Acad. Sci. USA 103, 17137 (2006).
[CrossRef] [PubMed]

Marsh, P. N.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Mosk, A. P.

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

Neil, M. A. A.

M. Booth, M. A. A. Neil, and T. Wilson, J. Microsc. 192, 90 (1998).
[CrossRef]

Padgett, M. J.

R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
[CrossRef]

Poland, S. P.

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl. Acad. Sci. USA 103, 17137 (2006).
[CrossRef] [PubMed]

So, P. T. C.

J. W. Cha, J. Ballesta, and P. T. C. So, J. Biomed. Opt. 15, 046022 (2010).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Wilson, T.

M. Booth, M. A. A. Neil, and T. Wilson, J. Microsc. 192, 90 (1998).
[CrossRef]

Wright, A. J.

R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
[CrossRef]

S. P. Poland, A. J. Wright, and J. M. Girkin, Appl. Opt. 47, 731 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Biomed. Opt. (1)

J. W. Cha, J. Ballesta, and P. T. C. So, J. Biomed. Opt. 15, 046022 (2010).
[CrossRef] [PubMed]

J. Microsc. (1)

M. Booth, M. A. A. Neil, and T. Wilson, J. Microsc. 192, 90 (1998).
[CrossRef]

J. Opt. (1)

R. W. Bowman, A. J. Wright, and M. J. Padgett, J. Opt. 12, 124004 (2010).
[CrossRef]

Nat. Methods (1)

N. Ji, D. E. Milkie, and E. Betzig, Nat. Methods 7, 141 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

Opt. Commun. (1)

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

Opt. Express (1)

Proc. Natl. Acad. Sci. USA (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl. Acad. Sci. USA 103, 17137 (2006).
[CrossRef] [PubMed]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Supplementary Material (3)

» Media 1: AVI (3558 KB)     
» Media 2: AVI (3976 KB)     
» Media 3: AVI (4092 KB)     

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup. (b) Definition of scan and reference regions. (c) Illustration of the SOPS and AMPS methods. I: Flat SLM and corresponding zero-order diffraction. II: Scan region activated by applying a phase gradient. Corresponding scan region’s PSF appears on the CCD (circled). III: Reference region activated and an interferogram appears (circled) (Media 1). IV: SOPS (Media 2), V: AMPS (Media 3).

Fig. 2
Fig. 2

System wavefront corrections. (a) Wavefronts obtained with AMPS (I) and SOPS (II). The number of regions used is indicated. (b) PSFs corresponding to the AMPS wavefront. Size of the scale bar is 50 μm. (c) Effect of wavefront detail on PSF intensity (both peak and FWHM averaged). (d) Radial PSF comparisons for AMPS, SOPS, uncorrected and ideal systems. (N/C: no correction).

Fig. 3
Fig. 3

Highly aberrated glass. (a) Illustration of the nature of the aberration through a photograph. (b) AMPS and SOPS retrieved wavefronts. (c) PSFs without (N/C) and including corrections. Scale bar size is 50 μm. (d) Comparison of PSF radial profiles with the ideal system profile.

Equations (9)

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O j k ( x , y ) = e i 2 π ( x T x + y T y ) [ e i ϕ j rect ( x x j H ) rect ( y y j H ) + e i ϕ k rect ( x x k H ) rect ( y y k H ) ] .
I ( x i , y i ) = | W ( x i , y i ) | 2 · [ 2 + 2 cos ( 2 π f λ ( D x x i + D y y i ) + Δ ϕ ) ] .
W ( x i , y i ) = H 2 sinc [ ( x i λ f T x ) H ] · sinc [ ( y i λ f T y ) H ] ,
R SOPS ( ϕ s ) = | W ( x i 0 , y i 0 ) | 2 · [ 2 + 2 cos ( 2 π f λ ( D x x i 0 + D y y i 0 ) + Δ ϕ + ϕ s ) ] .
( ϕ s ) fit = ϕ opt = 2 π f λ ( D x x i 0 + D y y i 0 ) Δ ϕ .
ϕ a = 2 π f λ ( D x x i + D y y i ) .
R AMPS ( ϕ a ) = | W ( x i , y i ) | 2 [ 2 + 2 cos ( Δ ϕ + ϕ a ) ] .
ϕ opt = 2 π f λ ( D x x i 0 + D y y i 0 ) + ( ϕ a ) fit .
T = M N 2 ( T CCD + T SLM + T delays ) = M N 2 T iteration .

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