Abstract

Computational imaging, or post-processing of images, allows the resolution limit of optical microscopy to be exceeded. Here we present an image-inversion approach to improve the resolution of a confocal laser scanning microscope (CLSM). The method combines a full-wave modeling of CLSM and an inverse reconstruction algorithm. The inverse reconstruction is cast into an optimization problem, where the distribution of refractive index of objects that yields the best match between computed images and experimental images is identified. The reconstructed image is a quantitative image based on the distribution of refractive index. Experimental results demonstrate a 35 nm edge-to-edge resolution using a two-disk pattern with 105 nm disk diameter. The proposed computational imaging approach greatly improves the resolution, without the need to change the existing microscopy system, at moderate computational cost.

© 2016 Optical Society of America

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References

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    [Crossref]
  42. M. Bertero, P. Boccacci, and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, II: the case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
    [Crossref]
  43. M. Bertero, C. De Mol, E. R. Pike, and J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis IV. The case of uncertain localization or non-uniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
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2015 (4)

K. Agarwal, R. Chen, L. S. Koh, C. J. R. Sheppard, and X. Chen, “Crossing the resolution limit in near-infrared imaging of silicon chips: targeting 10-nm node technology,” Phys. Rev. X 5, 021014 (2015).
[Crossref]

J. E. McGregor, C. A. Mitchell, and N. A. Hartell, “Post-processing strategies in image scanning microscopy,” Methods 88, 28–36 (2015).
[Crossref]

A. C. Sobieranski, F. Inci, H. C. Tekin, M. Yuksekkaya, E. Comunello, D. Cobra, A. von Wangenheim, and U. Demirci, “Portable lensless wide-field microscopy imaging platform based on digital inline holography and multi-frame pixel super-resolution,” Light Sci. Appl. 4, e346 (2015).
[Crossref]

M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photon. 7, 241–275 (2015).
[Crossref]

2014 (3)

L. Zhu, L. Li, L. Gao, and L. V. Wang, “Multiview optical resolution photoacoustic microscopy,” Optica 1, 217–222 (2014).
[Crossref]

Y. Yan, L. Li, C. Feng, W. Guo, S. Lee, and M. Hong, “Microsphere-coupled scanning laser confocal nanoscope for sub-diffraction-limited imaging at 25  nm lateral resolution in the visible spectrum,” ACS Nano 8, 1809–1816 (2014).

K. Nasrollahi and T. B. Moeslund, “Super-resolution: a comprehensive survey,” Mach. Vis. Appl. 25, 1423–1468 (2014).
[Crossref]

2013 (7)

O. Schulz, C. Pieper, M. Clever, J. Pfaff, A. Ruhlandt, R. H. Kehlenbach, F. S. Wouters, J. Großhans, G. Bunt, and J. Enderlein, “Resolution doubling in fluorescence microscopy with confocal spinning-disk image scanning microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110, 21000–21005 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, “Instant super-resolution imaging in live cells and embryos via analog image processing,” Nat. Methods 10, 1122–1126 (2013).
[Crossref]

R. Chen, K. Agarwal, C. J. R. Sheppard, J. C. H. Phang, and X. Chen, “A complete and computationally efficient numerical model of aplanatic solid immersion lens scanning microscope,” Opt. Express 21, 14316–14330 (2013).
[Crossref]

C. J. R. Sheppard, S. B. Mehta, and R. Heintzmann, “Superresolution by image scanning microscopy using pixel reassignment,” Opt. Lett. 38, 2889–2892 (2013).
[Crossref]

R. Chen, K. Agarwal, C. J. R. Sheppard, and X. Chen, “Imaging using cylindrical vector beams in a high-numerical-aperture microscopy system,” Opt. Lett. 38, 3111–3114 (2013).
[Crossref]

R. W. Lu, B. Q. Wang, Q. X. Zhang, and X. C. Yao, “Super-resolution scanning laser microscopy through virtually structured detection,” Biomed. Opt. Express 4, 1673–1682 (2013).
[Crossref]

2012 (2)

Y. W. Wen and R. H. Chan, “Parameter selection for total-variation-based image restoration using discrepancy principle,” IEEE Trans. Image Process. 21, 1770–1781 (2012).
[Crossref]

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[Crossref]

2011 (1)

Z. B. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. C. Chen, and M. H. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[Crossref]

2010 (2)

2009 (1)

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498–501 (2009).
[Crossref]

2008 (1)

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

2007 (3)

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[Crossref]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

2006 (2)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[Crossref]

P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23(3), 32–45 (2006).
[Crossref]

2003 (2)

R. Heintzmann, V. Sarafis, P. Munroe, J. Nailon, Q. S. Hanley, and T. M. Jovin, “Resolution enhancement by subtraction of confocal signals taken at different pinhole sizes,” Micron 34, 293–300 (2003).
[Crossref]

B. K. Gunturk, A. U. Batur, Y. Altunbasak, M. H. Hayes, and R. M. Mersereau, “Eigenface-domain super-resolution for face recognition,” IEEE Trans. Image Process. 12, 597–606 (2003).
[Crossref]

2000 (4)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

G. M. P. van Kempen and L. J. van Vliet, “Background estimation in nonlinear image restoration,” J. Opt. Soc. Am. A 17, 425–433 (2000).
[Crossref]

G. M. P. van Kempen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. Microsc. 198, 63–75 (2000).
[Crossref]

1999 (1)

R. C. Dunn, “Near-field scanning optical microscopy,” Chem. Rev. 99, 2891–2928 (1999).
[Crossref]

1996 (1)

J. Pawley and B. R. Masters, “Handbook of biological confocal microscopy,” Opt. Eng. 35, 2765–2766 (1996).
[Crossref]

1994 (2)

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
[Crossref]

R. R. Schultz and R. L. Stevenson, “A Bayesian approach to image expansion for improved definition,” IEEE Trans. Image Process. 3, 233–242 (1994).
[Crossref]

1992 (2)

A. Schatzberg and A. J. Devaney, “Super-resolution in diffraction tomography,” Inverse Prob. 8, 149–164 (1992).
[Crossref]

M. Defrise and C. Demol, “Superresolution in confocal scanning microscopy-generalized inversion formulas,” Inverse Prob. 8, 175–185 (1992).
[Crossref]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[Crossref]

1988 (1)

C. J. R. Sheppard, “Super-resolution in confocal imaging,” Optik 80, 53–54 (1988).

1987 (1)

M. Bertero, P. Brianzi, and E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Prob. 3, 195–212 (1987).
[Crossref]

1984 (1)

M. Bertero, C. De Mol, E. R. Pike, and J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis IV. The case of uncertain localization or non-uniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[Crossref]

1982 (2)

M. Bertero, P. Boccacci, and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, II: the case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[Crossref]

M. Bertero and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, I: the case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[Crossref]

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[Crossref]

Agarwal, K.

Altunbasak, Y.

B. K. Gunturk, A. U. Batur, Y. Altunbasak, M. H. Hayes, and R. M. Mersereau, “Eigenface-domain super-resolution for face recognition,” IEEE Trans. Image Process. 12, 597–606 (2003).
[Crossref]

Batur, A. U.

B. K. Gunturk, A. U. Batur, Y. Altunbasak, M. H. Hayes, and R. M. Mersereau, “Eigenface-domain super-resolution for face recognition,” IEEE Trans. Image Process. 12, 597–606 (2003).
[Crossref]

Bertero, M.

M. Bertero, P. Brianzi, and E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Prob. 3, 195–212 (1987).
[Crossref]

M. Bertero, C. De Mol, E. R. Pike, and J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis IV. The case of uncertain localization or non-uniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[Crossref]

M. Bertero, P. Boccacci, and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, II: the case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[Crossref]

M. Bertero and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, I: the case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[Crossref]

Betzig, E.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

Blanc-Feraud, L.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[Crossref]

Boccacci, P.

M. Bertero, P. Boccacci, and E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis, II: the case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[Crossref]

Bose, R.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498–501 (2009).
[Crossref]

Brianzi, P.

M. Bertero, P. Brianzi, and E. R. Pike, “Superresolution in confocal scanning microscopy,” Inverse Prob. 3, 195–212 (1987).
[Crossref]

Bunt, G.

O. Schulz, C. Pieper, M. Clever, J. Pfaff, A. Ruhlandt, R. H. Kehlenbach, F. S. Wouters, J. Großhans, G. Bunt, and J. Enderlein, “Resolution doubling in fluorescence microscopy with confocal spinning-disk image scanning microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110, 21000–21005 (2013).
[Crossref]

Chan, R. H.

Y. W. Wen and R. H. Chan, “Parameter selection for total-variation-based image restoration using discrepancy principle,” IEEE Trans. Image Process. 21, 1770–1781 (2012).
[Crossref]

Chandris, P.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, “Instant super-resolution imaging in live cells and embryos via analog image processing,” Nat. Methods 10, 1122–1126 (2013).
[Crossref]

Chen, R.

K. Agarwal, R. Chen, L. S. Koh, C. J. R. Sheppard, and X. Chen, “Crossing the resolution limit in near-infrared imaging of silicon chips: targeting 10-nm node technology,” Phys. Rev. X 5, 021014 (2015).
[Crossref]

R. Chen, K. Agarwal, C. J. R. Sheppard, J. C. H. Phang, and X. Chen, “A complete and computationally efficient numerical model of aplanatic solid immersion lens scanning microscope,” Opt. Express 21, 14316–14330 (2013).
[Crossref]

R. Chen, K. Agarwal, C. J. R. Sheppard, and X. Chen, “Imaging using cylindrical vector beams in a high-numerical-aperture microscopy system,” Opt. Lett. 38, 3111–3114 (2013).
[Crossref]

R. Chen, “Modeling and designing aplanatic solid immersion lens microscope for failure analysis of integrated circuits,” Ph.D. thesis (National University of Singapore, 2013).

Chen, X.

Chen, Z. C.

Z. B. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. C. Chen, and M. H. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[Crossref]

Chitnis, A.

A. G. York, P. Chandris, D. D. Nogare, J. Head, P. Wawrzusin, R. S. Fischer, A. Chitnis, and H. Shroff, “Instant super-resolution imaging in live cells and embryos via analog image processing,” Nat. Methods 10, 1122–1126 (2013).
[Crossref]

Clever, M.

O. Schulz, C. Pieper, M. Clever, J. Pfaff, A. Ruhlandt, R. H. Kehlenbach, F. S. Wouters, J. Großhans, G. Bunt, and J. Enderlein, “Resolution doubling in fluorescence microscopy with confocal spinning-disk image scanning microscopy,” Proc. Natl. Acad. Sci. U.S.A. 110, 21000–21005 (2013).
[Crossref]

Cobra, D.

A. C. Sobieranski, F. Inci, H. C. Tekin, M. Yuksekkaya, E. Comunello, D. Cobra, A. von Wangenheim, and U. Demirci, “Portable lensless wide-field microscopy imaging platform based on digital inline holography and multi-frame pixel super-resolution,” Light Sci. Appl. 4, e346 (2015).
[Crossref]

Comunello, E.

A. C. Sobieranski, F. Inci, H. C. Tekin, M. Yuksekkaya, E. Comunello, D. Cobra, A. von Wangenheim, and U. Demirci, “Portable lensless wide-field microscopy imaging platform based on digital inline holography and multi-frame pixel super-resolution,” Light Sci. Appl. 4, e346 (2015).
[Crossref]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

De Mol, C.

M. Bertero, C. De Mol, E. R. Pike, and J. G. Walker, “Resolution in diffraction-limited imaging, a singular value analysis IV. The case of uncertain localization or non-uniform illumination of the object,” Opt. Acta 31, 923–946 (1984).
[Crossref]

Defrise, M.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of a complete model of the microscopy system. This numerical model consists of focusing of incident light, interaction of focal field with the object structures, and imaging of the scattered light. OL, objective lens; TL, tube lens; BS, beam splitter; PH, pinhole; PMT, photomultiplier tube. The inset shows the focal spot and computational domain (the red line box) used in the subsystem II. The laser light of 405 nm wavelength is focused by 150×NA0.9 objective lens and the intensity is recorded by a PMT with a pinhole of 20 μm diameter.
Fig. 2.
Fig. 2. Experimental demonstration of the proposed optical model. (a) Experimental configuration of a CLSM. A circularly polarized laser beam of 405 nm is focused by 150×NA0.9 objective lens. The scattering light is recorded by a PMT with a pinhole of 20 μm diameter. (b) and (c) show images of 400 and 240 nm pitch gratings, including SEM image (top left), simulated image (top right) using the proposed model, experimental image (bottom left) using the CLSM setup, and normalized intensity distribution (bottom right) along the dashed lines.
Fig. 3.
Fig. 3. Schematic diagram of the proposed iterative reconstruction algorithm. The image reconstruction is formulated as an inverse problem, which employs PR-CGM to obtain images that match with the recorded CLSM images as well as prior knowledge. RI denotes refractive index.
Fig. 4.
Fig. 4. CLSM images of two-square and two-disk patterns with several sizes. (a) SEM image of the fabricated two-square and two-disk patterns. (b) CLSM images using the experimental setup with pinhole of diameter 20 μm. (c) Intensity distribution along two lines marked by two pairs of arrows as shown in (b). For each type pattern, the center-to-center distances are 400, 320, 280, 240, 200, 160, 140, and 120 nm and the edge-to-edge distances are 160, 120, 80, 60, 60, 40, 35, and 25 nm. Scale bars in (a) and (b) are 0.8 μm.
Fig. 5.
Fig. 5. Image reconstruction using two-square and two-disk patterns with (I) 200 nm pitch and 60 nm edge-to-edge distance, (II) 160 nm pitch and 40 nm edge-to-edge distance, and (III) 140 nm pitch and 35 nm edge-to-edge distance. (a) and (b) show SEM images of two-square and two-disk patterns. (c) and (d) show simulated images of two-square and two-disk patterns using the proposed optical model. (e) and (f) show calibrated images from experimental images of two-square and two-disk patterns using the CLSM setup. The calibrated factors a1 and a0 can be found in Supplement 1, Table S1. (g) and (h) show inverse reconstruction images based on images in (e) and (f) using the proposed imaging-inversion approach with (I) 40, (II) 36, and (III) 20 iterations and regularization parameter γ (I) 0.02, (II) 0.02, and (III) 0.05. (i) and (j) show reconstruction images based on images in (e) and (f) using deconvolution algorithm, i.e., Richardson–Lucy algorithm, with (I-III) 10 iterations. Scale bars in (I–III) are 100, 80, and 70 nm. The left and right column images share the same scale bars in (a) and (b), respectively.
Fig. 6.
Fig. 6. Inverse reconstruction using four-square (first column) and four-disk (second column) patterns with 120 nm pitch and 40 nm edge-to-edge distance. (a) and (b) show SEM images of four-square and four-disk patterns. (c) and (d) show simulated images of four-square and four-disk patterns using the proposed optical model. (e) and (f) show calibrated images from experimental images of four-square and four-disk patterns using the CLSM setup. The calibrated factors a1 and a0 can be found in Supplement 1, Table S1. (g) and (h) show inverse reconstruction images based on images in (e) and (f) using the proposed imaging-inversion approach with 56 times of iterations. The regularization parameter γ for (g) and (h) is 0.05 and 0.5, respectively. (i) and (j) show reconstruction images based on images in (e) and (f) using deconvolution algorithm, i.e., Richardson–Lucy algorithm, with 10 times of iterations. Scale bars in (a) and (b) are 80 nm. The left and right column images share the same scale bars in (a) and (b), respectively.

Tables (1)

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Table 1. Computation Time of Optimization for 200, 160, and 140 nm Pitch Size Patterns

Equations (7)

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K¯¯α¯+B¯¯β¯t=0¯,
P¯¯α¯+Q¯¯β¯t=b¯,
E¯sca=L¯¯α¯t+M¯¯β¯t,
n¯r=argminf(n¯r),
I¯mea=a1I¯exp+a0,
f(n¯r)=I¯sim(n¯r)I¯mea(n¯r)I¯mea(n¯r)2+γΔ(n¯r),
Δ(n¯r)=V|n¯r|2+ζ2dv

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