Abstract

Guidestar hologram based digital adaptive optics (DAO) is one recently emerging active imaging modality. It records each complex distorted line field reflected or scattered from the sample by an off-axis digital hologram, measures the optical aberration from a separate off-axis digital guidestar hologram, and removes the optical aberration from the distorted line fields by numerical processing. In previously demonstrated DAO systems, the optical aberration was directly retrieved from the guidestar hologram by taking its Fourier transform and extracting the phase term. For the direct retrieval method (DRM), when the sample is not coincident with the guidestar focal plane, the accuracy of the optical aberration retrieved by DRM undergoes a fast decay, leading to quality deterioration of corrected images. To tackle this problem, we explore here an image metrics-based iterative method (MIM) to retrieve the optical aberration from the guidestar hologram. Using an aberrated objective lens and scattering samples, we demonstrate that MIM can improve the accuracy of the retrieved aberrations from both focused and defocused guidestar holograms, compared to DRM, to improve the robustness of the DAO.

© 2017 Optical Society of America

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References

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2016 (2)

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

P. Pande, Y. Z. Liu, F. A. South, and S. A. Boppart, “Automated computational aberration correction method for broadband interferometric imaging techniques,” Opt. Lett. 41(14), 3324–3327 (2016).
[Crossref] [PubMed]

2015 (1)

C. Liu and M. K. Kim, “Digital adaptive optics line-scanning confocal imaging system,” J. Biomed. Opt. 20(11), 111203 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (2)

2012 (2)

2011 (1)

2009 (3)

2008 (2)

2003 (1)

2002 (1)

2000 (1)

1997 (1)

1994 (1)

1977 (1)

1965 (1)

J. W. Cooley and J. W. Tuley, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[Crossref]

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Boppart, S. A.

Campbell, M.

Choi, S. S.

Cooley, J. W.

J. W. Cooley and J. W. Tuley, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[Crossref]

Donnelly Iii, W.

Evans, J. W.

Ferguson, R. D.

Fienup, J. R.

Franke, G.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Fuller, A. R.

Goy, A. S.

Grow, T. D.

Hain, C.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Hamann, B.

Hammer, D. X.

Hampson, K. M.

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55(21), 3425–3467 (2008).
[Crossref]

Hardy, J. W.

Hebert, T.

Hillmann, D.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Höft, T. A.

Hüttmann, G.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Iftimia, N.

Jüptner, W.

Kendrick, R. L.

Kim, M. K.

Koliopoulos, C. L.

Lefebvre, J. E.

Liang, J.

Liu, C.

Liu, Y. Z.

Marchesini, S.

Marron, J. C.

Miller, D. T.

Miller, J. J.

Mujat, M.

Pande, P.

Pfäffle, C.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Psaltis, D.

Queener, H.

Romero-Borja, F.

Roorda, A.

Schnars, U.

Seldomridge, N.

South, F. A.

Spahr, H.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Sudkamp, H.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Thurman, S. T.

Tuley, J. W.

J. W. Cooley and J. W. Tuley, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[Crossref]

Unser, M.

Werner, J. S.

Williams, D. R.

Winter, C.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Yu, X.

Zawadzki, R. J.

Appl. Opt. (3)

Biomed. Opt. Express (1)

J. Biomed. Opt. (1)

C. Liu and M. K. Kim, “Digital adaptive optics line-scanning confocal imaging system,” J. Biomed. Opt. 20(11), 111203 (2015).
[Crossref] [PubMed]

J. Mod. Opt. (1)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55(21), 3425–3467 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Math. Comput. (1)

J. W. Cooley and J. W. Tuley, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Publ. Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[Crossref]

Sci. Rep. (1)

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Other (6)

M. K. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications (Springer, 2011), pp. 55–93.

J. Goodman, Introduction to Fourier optics (Roberts & Company Publishers, 2005), pp. 105–107.

E. Polak, Computational Methods in Optimization (Academic, 1971), pp. 28–58.

J. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2005), Chap. 3.

V. N. Mahajan, Aberration Theory Made Simple (SPIE, 1991), pp. 69–109.

R. Paschotta, Field Guide to Lasers (SPIE, 2008), pp. 16–21.

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Figures (5)

Fig. 1
Fig. 1 Experimental setup of DAO. LD: laser diode. CO: collimator. BS1-BS6: beamsplitters. L1-L7: regular lens. Their focal lengths are 150 mm, 60 mm, 300 mm, 120 mm, 60 mm, 20mm, and 100 mm respectively. CL: cylindrical lens of a focal length 75 mm. GSM: Galvanometer scanning mirror. A: aberrator. OL: objective lens. S: sample. (A) Schematic drawing of the optical apparatus. (B) Photo of the aberrated objective lens that consists of the aberrator A and objective lens OL.
Fig. 2
Fig. 2 Digital confocal imaging without and with aberrator in place. (a) One representative baseline off-axis digital line hologram, generated without aberrator in place. (b) Phase distribution at the pupil obtained by taking FT of (a) and extracting the image order [11]. It is displayed in a blue-white-red colormap corresponding to the phase value (-π, π]. (c) Reconstructed line field intensity obtained by taking inverse FT of the complex amplitude represented by (b). (d) Reconstructed baseline en face confocal image. (e) White light transmission image of the target with the teflon film removed. (f) One representative off-axis digital line hologram distorted by the aberrator. (g) Distorted phase map at the pupil plane from (f). (h) Distorted line intensity. (i) Distorted en face confocal image. Scale bars: 30 μm.
Fig. 3
Fig. 3 Image corrections by the focused guiestar hologram. (a) Intensity of the guidestar field. (b) Phase aberration from (a) through DRM. (c) Corrected image by (b). (d) Corrected guidestar field. (e) Phase distribution from (a) through MIM. (f) Corrected image by (f). (g) First mask. (h) Second mask. (i) Convergence curves. Scalebars: 30 μm.
Fig. 4
Fig. 4 Corrections by defocused guidestar when the sample is 50 μm away from the focal plane towards the objective lens side. (a) Intensity of the guidestar field. (b) Phase aberration from (a) through DRM. (c) Corrected image by (b). (d) Corrected guide star. (e) Phase distribution from (a) through MIM. (f) Corrected image by (e). Scale bars: 30 μm.
Fig. 5
Fig. 5 Corrections by the defocused guidestar hologram generated when the sample is put 50 μm from the focal plane opposite the side of the objective lens. (a) intensity of the guidestar field. (b) phase aberration from (a) through DRM. (c) Corrected image by (b). (d) corrected guide star. (e) phase distribution from (a) through MIM. (f) corrected image by (e). Scalebars: 30 μm.

Equations (20)

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O( x c , y c ,n)=IFT{O( x p , y p ,n)}( f x , f y ),
f x = x c λ d 1 f y = y c λ d 1 ,
O( x p , y p ,n)= O U ( x p , y p ,n)P( x p , y p )exp[jΦ( x p , y p )],
I Conf ( x c ,n)= y C slit | O( x c , y c ,n) | 2 ,
g( f x , f y )=IFT{A( x p , y p )exp[j Φ G ( x p , y p )]},
Φ G ( x p , y p )=Φ( x p , y p )+ Φ E ( x p , y p ).
O ( x c , y c ,n) C =IFT{O( x p , y p ,n)exp[j Φ R ( x p , y p )]}( f x , f y ).
I Conf C ( x c ,n)= y C slit | O C ( x c , y c ,n) | 2 .
T= f x , f y M( f x , f y )S[I( f x , f y )] .
M( f x , f y )={ 1 f x 2 + f y 2 R 0 f x 2 + f y 2 >R .
S[I( f x , f y )]=I ( f x , f y ) 1.5 ,
I( f x , f y )= g C ( f x , f y ) g C * ( f x , f y ),
g C ( f x , f y )= 1 N 2 x p , y p {A( x p , y p )exp[j Φ G ( x p , y p )]× exp[j Φ R ( x p , y p )]exp[j2π( x p f x N + y p f y N )]},
Φ R ( x p , y p )= k=1 J a k Z k ( x p , y p ),
T a k = 2 N 2 x P , y P Z k ( x p , y p )Im{A( x p , y p )exp[j Φ G ( x p , y p )]exp[j Φ R ( x p , y p )]× {DFT[1.5 I 0.5 ( f x , f y ) g C ( f x , f y )M( f x , f y )]} * },
DFT[1.5 I 0.5 ( f x , f y ) g C ( f x , f y )M( f x , f y )] = f x , f y [1.5 I 0.5 ( f x , f y ) g C ( f x , f y )M( f x , f y )]exp[j2π( x p f x N + y p f y N ) ,
g C ( f x , f y ) Φ R ( x p , y p ) = j N 2 A( x p , y p )exp[j Φ G ( x p , y p )]× exp[j Φ R ( x p , y p )]exp[j2π( x p f x N + y p f y N )].
I( f x , f y ) Φ R ( x p , y p ) = g C ( f x , f y ) Φ R ( x p , y p ) g C * ( f x , f y )+ g C * ( f x , f y ) Φ R ( x p , y p ) g C ( f x , f y ) = g C ( f x , f y ) Φ R ( x p , y p ) g C * ( f x , f y )+C.C. = j N 2 g C * ( f x , f y )A( x p , y p )exp[j Φ G ( x p , y p )]× exp[j Φ R ( x p , y p )]exp[j2π( x p f x N + y p f y N )]+C.C. = 2 N 2 Im{ g C * ( f x , f y )A( x p , y p )exp[j Φ G ( x p , y p )]× exp[j Φ R ( x p , y p )]exp[j2π( x p f x N + y p f y N )]},
T Φ R ( x p , y p ) = f x , f y M( f x , f y ) dS[I( f x , f y )] dI( f x , f y ) I( f x , f y ) Φ R ( x p , y p ) = 2 N 2 f x , f y Im{A( x p , y p )exp[j Φ G ( x p , y p )]exp[j Φ R ( x p , y p )] × M( f x , f y )[1.5 I 0.5 ( f x , f y )] g C * ( f x , f y )exp[j2π( x p f x N + y p f y N )]} = 2 N 2 Im{A( x p , y p )exp[j Φ G ( x p , y p )]exp[j Φ R ( x p , y p )]× {DFT[1.5 I 0.5 ( f x , f y ) g C ( f x , f y )M( f x , f y )]} * }.
T a k = x p , y p T Φ R ( x p , y p ) Φ R ( x p , y p ) a k = x p , y p T Φ R ( x p , y p ) Z k ( x p , y p ).

Metrics