Abstract

We describe a simple and robust approach for characterizing the spatially varying pupil aberrations of microscopy systems. In our demonstration with a standard microscope, we derive the location-dependent pupil transfer functions by first capturing multiple intensity images at different defocus settings. Next, a generalized pattern search algorithm is applied to recover the complex pupil functions at ~350 different spatial locations over the entire field-of-view. Parameter fitting transforms these pupil functions into accurate 2D aberration maps. We further demonstrate how these aberration maps can be applied in a phase-retrieval based microscopy setup to compensate for spatially varying aberrations and to achieve diffraction-limited performance over the entire field-of-view. We believe that this easy-to-use spatially-varying pupil characterization method may facilitate new optical imaging strategies for a variety of wide field-of-view imaging platforms.

© 2013 OSA

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2013 (1)

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

2012 (1)

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (4)

2009 (1)

2008 (1)

2007 (2)

2006 (2)

2004 (2)

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett.29(15), 1787–1789 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase - retrieved pupil functions in wide - field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

2003 (4)

2002 (2)

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three - dimensional microscope point spread function using a Shack - Hartmann wavefront sensor,” J. Microsc.205(1), 61–75 (2002).
[CrossRef] [PubMed]

2001 (1)

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

2000 (1)

1999 (1)

1997 (1)

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun.133(1-6), 339–346 (1997).
[CrossRef]

1994 (1)

Q. Gong and S. S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng.33(4), 1176–1186 (1994).
[CrossRef]

1993 (2)

1992 (2)

R. G. Lane and M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt.31(32), 6902–6908 (1992).
[CrossRef] [PubMed]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” JOSA A9(7), 1072–1085 (1992).
[CrossRef]

1989 (1)

1987 (1)

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” JOSA A4(1), 118–123 (1987).
[CrossRef]

1986 (1)

J. Fienup and C. Wackerman, “Phase-retrieval stagnation problems and solutions,” JOSA A3(11), 1897–1907 (1986).
[CrossRef]

1984 (2)

1982 (2)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21(5), 215829 (1982).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982).
[CrossRef] [PubMed]

1975 (1)

1972 (1)

R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237 (1972).

Agard, D. A.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase - retrieved pupil functions in wide - field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett.28(10), 801–803 (2003).
[CrossRef] [PubMed]

Allen, L.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

Audet, C.

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

Barbastathis, G.

Bernard, A.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Beverage, J. L.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three - dimensional microscope point spread function using a Shack - Hartmann wavefront sensor,” J. Microsc.205(1), 61–75 (2002).
[CrossRef] [PubMed]

Bolcar, M. R.

Booth, M. J.

Bowers, C. W.

Brady, D. J.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Brady, G. R.

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4(6), 388–394 (2010).
[CrossRef]

Cossairt, O. S.

Das, B.

Dean, B. H.

Debarre, D.

Dennis, J. E.

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

Descour, M. R.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three - dimensional microscope point spread function using a Shack - Hartmann wavefront sensor,” J. Microsc.205(1), 61–75 (2002).
[CrossRef] [PubMed]

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4(6), 388–394 (2010).
[CrossRef]

Dong, H.-W.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Feller, S. D.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Fienup, J.

J. Fienup and C. Wackerman, “Phase-retrieval stagnation problems and solutions,” JOSA A3(11), 1897–1907 (1986).
[CrossRef]

Fienup, J. R.

Gehm, M. E.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Gerchberg, R.

R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237 (1972).

Golish, D. R.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Gong, Q.

Q. Gong and S. S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng.33(4), 1176–1186 (1994).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21(5), 215829 (1982).
[CrossRef]

Guizar-Sicairos, M.

Gureyev, T. E.

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun.133(1-6), 339–346 (1997).
[CrossRef]

Gustafsson, M. G.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase - retrieved pupil functions in wide - field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett.28(10), 801–803 (2003).
[CrossRef] [PubMed]

Hanser, B. M.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase - retrieved pupil functions in wide - field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett.28(10), 801–803 (2003).
[CrossRef] [PubMed]

Higgins, C.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Hsu, S. S.

Q. Gong and S. S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng.33(4), 1176–1186 (1994).
[CrossRef]

Johnson, E. G.

Karten, H. J.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Kawano, Y.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Kittle, D. S.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Kobayashi, S.

Kohno, T.

Kou, S. S.

Lane, R. G.

Liesener, J.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun.216(4-6), 313–319 (2003).
[CrossRef]

Lohmann, A. W.

Ma, M.

Marks, D. L.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Marron, J. C.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics4(6), 388–394 (2010).
[CrossRef]

Miau, D.

Nayar, S. K.

Nomura, H.

Nugent, K. A.

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun.133(1-6), 339–346 (1997).
[CrossRef]

Nyhus, J.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Ohnishi, K.

Osten, W.

Oxley, M.

L. Allen and M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun.199(1-4), 65–75 (2001).
[CrossRef]

Paxman, R. G.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” JOSA A9(7), 1072–1085 (1992).
[CrossRef]

Pedrini, G.

Pitchumani, M.

Sato, T.

Schilling, T.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Schulz, T. J.

J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Hubble Space Telescope characterized by using phase-retrieval algorithms,” Appl. Opt.32(10), 1747–1767 (1993).
[CrossRef] [PubMed]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” JOSA A9(7), 1072–1085 (1992).
[CrossRef]

Sedat, J. W.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase - retrieved pupil functions in wide - field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett.28(10), 801–803 (2003).
[CrossRef] [PubMed]

Seifert, L.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun.216(4-6), 313–319 (2003).
[CrossRef]

Seldin, J. H.

Shack, R. V.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three - dimensional microscope point spread function using a Shack - Hartmann wavefront sensor,” J. Microsc.205(1), 61–75 (2002).
[CrossRef] [PubMed]

Sheppard, C. J.

Stack, R. A.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun.49(1), 6–10 (1984).
[CrossRef]

Sung, J.

Takeda, M.

Tallon, M.

Tawarayama, K.

Tian, L.

Tiziani, H. J.

Vera, E. M.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature486(7403), 386–389 (2012).
[CrossRef] [PubMed]

Wackerman, C.

J. Fienup and C. Wackerman, “Phase-retrieval stagnation problems and solutions,” JOSA A3(11), 1897–1907 (1986).
[CrossRef]

Waller, L.

Wang, F.

Wang, X.

Wilson, T.

Yamamoto, Y.

Y. Kawano, C. Higgins, Y. Yamamoto, J. Nyhus, A. Bernard, H.-W. Dong, H. J. Karten, and T. Schilling, “Darkfield adapter for whole slide imaging: Adapting a darkfield internal reflection illumination system to extend wsi applications,” PLoS ONE8(3), e58344 (2013).
[CrossRef] [PubMed]

Yelleswarapu, C. S.

Yokozeki, S.

Zhang, Y.

Appl. Opt. (12)

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt.28(23), 4996–4998 (1989).
[CrossRef] [PubMed]

S. Yokozeki and K. Ohnishi, “Spherical aberration measurement with shearing interferometer using Fourier imaging and moiré method,” Appl. Opt.14(3), 623–627 (1975).
[CrossRef] [PubMed]

M. Ma, X. Wang, and F. Wang, “Aberration measurement of projection optics in lithographic tools based on two-beam interference theory,” Appl. Opt.45(32), 8200–8208 (2006).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

Multi-plane phase retrieval with defocus diversity. (a) Multiple intensity images I(s) (s = −2, −1, 0, 1, 2) are captured at different defocus settings. (b) Multi-plane iterative phase retrieval algorithm presented in [29].

Fig. 2
Fig. 2

Pupil function recovery at one off-axis position. Two cropped areas of one set of defocused intensity images are used for algorithm input. One cropped set Ic(s) is centered on a microsphere at the images’ central FOV (left), while the other cropped set Id(s) is centered on a microsphere at an off-axis position (right). Each cropped image set contains 17 intensity measurements (here only 5 are shown) at different defocus distances (−400 µm to + 400 µm, 50 µm per step). We approximate an unknown pupil function W with 8 Zernike coefficients (x-tilt, y-tilt, x-astigmatism, y-astigmatism, defocus, x-coma, y-coma and spherical aberration). We use this pupil function estimate to modify the 17 “ground truth” images Ic(s) of the central microsphere to generate a new set of aberrated intensity images, Ia(s) (middle). We then adjust the values of the 8 unknown Zernike coefficients to minimize the difference between Ia(s) and the actual intensity measurements of the off-axis microsphere, Id(s) (right). The corresponding pupil function described by 8 Zernike coefficients is recovered when the mean-squared error difference between these two image sets is minimized.

Fig. 3
Fig. 3

Off-axis aberration characterization with a calibration target. (a) ~350 microspheres are automatically identified on a microscope slide, each denoted by a red dot. (b) The recovered pupil function at position (x1, y1). (c1)-(c5) Intensity measurements Id(s) of the microsphere centered at (x1, y1) under different amounts of defocus. (d1)-(d5) The corresponding aberrated image estimates generated using the pupil function in Fig. 3(b).

Fig. 4
Fig. 4

Spatially varying aberrations of the 2X objective lens. Each data point, denoted by a blue dot, represents the extracted Zernike coefficient weight for one microsphere. ~350 microspheres are identified over the entire FOV and their corresponding parameters are fitted to a 2D surface for each type of aberration. (a)-(f) correspond to x-astigmatism, y-astigmatism defocus, x-coma, y-coma and spherical aberration.

Fig. 5
Fig. 5

Recovered defocus parameter function p5(x, y) with (color surface) and without (blue grid) +50 µm of sample defocus. The difference between these two surfaces corresponds to a defocus distance of +48.9 µm, which is in a good agreement with the actual displacement distance.

Fig. 6
Fig. 6

Resolution characterization using a USAF resolution target. (a) The USAF resolution target is placed at 3 different locations indicated by color arrows (b)-(d). Full FOV corresponds to circular region with 1.3 cm diameter. The original images captured using the aberrated objective lens at the center (b1), 60% away from the center (c1), and 95% away from the center (d1). (b2)-(d2) are the corresponding processed images using the deconvolution scheme. Group 7, element 1 (line width of 3.9 µm) of the USAF target can be resolved from the corrected images, in a good agreement with the Abbe diffraction limit of 3.94 µm.

Fig. 7
Fig. 7

Full FOV image deconvolution of the microsphere calibration target. (a) The aberration-corrected full FOV image. (b1)-(e1) Recovered pupil functions corresponding to highlighted regions in (a). (b2)-(e2) The corrected images of highlighted regions in (a). (b3)-(e3) The original images of the test target without aberration correction.

Fig. 8
Fig. 8

Full FOV image deconvolution of a new test target, containing a mixture of microspheres with different diameters (5-20 µm). (a) The aberration-corrected full FOV image. (b1)-(e1) Recovered pupil functions corresponding to highlighted regions in (a). (b2)-(e2) The corrected images of highlighted regions in (a). (b3)-(e3) The original images of the test target without aberration correction.

Equations (4)

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W( k x , k y , x 0 , y 0 )=exp[iπ( p 1 ( x 0 , y 0 ) Z 1 1 ( k x , k y )+ p 2 ( x 0 , y 0 ) Z 1 1 ( k x , k y )+... p 3 ( x 0 , y 0 ) Z 2 2 ( k x , k y )+ p 4 ( x 0 , y 0 ) Z 2 2 ( k x , k y )+ p 5 ( x 0 , y 0 ) Z 2 0 ( k x , k y )+ p 6 ( x 0 , y 0 ) Z 3 1 ( k x , k y )+... + p 7 ( x 0 , y 0 ) Z 3 1 ( k x , k y )+ p 8 ( x 0 , y 0 ) Z 4 0 ( k x , k y ))]
I a (s)=| F 1 (W( k x , k y , x 0 , y 0 )×F( I truth e i φ truth )× e i k z δs | 2 ,
( p 1 , p 2 ... p 8 ) | (x= x 0 ,y= y 0 ) = argmin ( p 1 , p 2 ... p 8 ) s=8 8 ( I a (s) I d (s) ) 2
I cor (n)= | 1 (( I seg e i φ seg )/W( k x , k y , x c (n),y (n) c )) | 2 ,

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