Abstract

Two important features of three-dimensional structured illumination microscopy (3D-SIM) are its optical sectioning (OS) and super-resolution (SR) capabilities. Previous works on 3D-SIM systems show that these features are coupled. We demonstrate that a 3D-SIM system using a Fresnel biprism illuminated by multiple linear incoherent sources provides a structured illumination pattern whose lateral and axial modulation frequencies can be tuned separately. Therefore, the compact support of the synthetic optical transfer function (OTF) can be engineered to achieve the highest OS and SR capabilities for a particular imaging application. Theoretical performance of our engineered system based on the OTF support is compared to that achieved by other well-known SIM systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

2018 (1)

2012 (2)

2009 (1)

M. F. Langgorst, J. Schaffer, and B. Goetze, Biotechnol. J. 4, 858 (2009).
[Crossref]

2008 (2)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

D. Débarre, E. J. Botcherby, M. J. Booth, and T. Wilson, Opt. Express 16, 9290 (2008).
[Crossref]

1997 (1)

1993 (1)

Agard, D. A.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Booth, M. J.

Botcherby, E. J.

Cande, W. Z.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Carlton, P. M.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Débarre, D.

Deschout, H.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Doblas, A.

Escobar, I.

I. Escobar, E. Sanchez-Ortiga, G. Saavedra, and M. Martinez-Corral, in Optical Fluorescence Microscopy: From the Spectral to the Nano Dimension (Springer, 2011), pp. 85–99.

Fernandez-Rodrigue, J.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Förster, R.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Gao, L.

Goetze, B.

M. F. Langgorst, J. Schaffer, and B. Goetze, Biotechnol. J. 4, 858 (2009).
[Crossref]

Golubovskaya, I. N.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1966).

Gustafsson, M. G. L.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Hagen, N.

Hammoud, A. M.

Heintzmann, R.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

O. Mandula, M. Kielhorn, K. Wicker, G. Krampert, I. Kleppe, and R. Heintzmann, Opt. Express 20, 24167 (2012).
[Crossref]

Juskaitis, R.

Karras, C.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Kielhorn, M.

Kleppe, I.

Krampert, G.

Langgorst, M. F.

M. F. Langgorst, J. Schaffer, and B. Goetze, Biotechnol. J. 4, 858 (2009).
[Crossref]

Mandula, O.

Martinez-Corral, M.

I. Escobar, E. Sanchez-Ortiga, G. Saavedra, and M. Martinez-Corral, in Optical Fluorescence Microscopy: From the Spectral to the Nano Dimension (Springer, 2011), pp. 85–99.

Martínez-Corral, M.

M. Martínez-Corral and G. Saavedra, in The Resolution Challenge in 3D Optical Microscopy (Elsevier, 2009), Vol. 53, pp. 1–67.

Neil, M. A. A.

Preza, C.

Saavedra, G.

A. Doblas, H. Shabani, G. Saavedra, and C. Preza, Opt. Express 26, 30476 (2018).
[Crossref]

M. Martínez-Corral and G. Saavedra, in The Resolution Challenge in 3D Optical Microscopy (Elsevier, 2009), Vol. 53, pp. 1–67.

I. Escobar, E. Sanchez-Ortiga, G. Saavedra, and M. Martinez-Corral, in Optical Fluorescence Microscopy: From the Spectral to the Nano Dimension (Springer, 2011), pp. 85–99.

Sanchez-Ortiga, E.

I. Escobar, E. Sanchez-Ortiga, G. Saavedra, and M. Martinez-Corral, in Optical Fluorescence Microscopy: From the Spectral to the Nano Dimension (Springer, 2011), pp. 85–99.

Schaefer, L. H.

L. H. Schaefer and D. Schuster, “Method and device for reconstructing images,” U.S. patent8,041,142 (October18, 2011).

Schaffer, J.

M. F. Langgorst, J. Schaffer, and B. Goetze, Biotechnol. J. 4, 858 (2009).
[Crossref]

Schuster, D.

L. H. Schaefer and D. Schuster, “Method and device for reconstructing images,” U.S. patent8,041,142 (October18, 2011).

Sedat, J. W.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Shabani, H.

Shao, L.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Smedh, M.

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Snyder, D. L.

Tkaczyk, T. S.

Wang, C. J. R.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

White, R. L.

Wicker, K.

Wilson, T.

Biophys. J. (1)

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, Biophys. J. 94, 4957 (2008).
[Crossref]

Biotechnol. J. (1)

M. F. Langgorst, J. Schaffer, and B. Goetze, Biotechnol. J. 4, 858 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

C. Karras, M. Smedh, R. Förster, H. Deschout, J. Fernandez-Rodrigue, and R. Heintzmann, Opt. Commun. 436, 69 (2019).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Other (4)

L. H. Schaefer and D. Schuster, “Method and device for reconstructing images,” U.S. patent8,041,142 (October18, 2011).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1966).

I. Escobar, E. Sanchez-Ortiga, G. Saavedra, and M. Martinez-Corral, in Optical Fluorescence Microscopy: From the Spectral to the Nano Dimension (Springer, 2011), pp. 85–99.

M. Martínez-Corral and G. Saavedra, in The Resolution Challenge in 3D Optical Microscopy (Elsevier, 2009), Vol. 53, pp. 1–67.

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Figures (4)

Fig. 1.
Fig. 1. Relation of the SI design and synthetic OTF of the tunable-SIM system. (a)  x z section of 3D SI pattern and the | V ( z ) | (blue curve) of Eq. (3). (b) Schematic of the slit-element image at the back focal plane of the objective lens. (c)  u w section of the 3D pattern’s FT. (d)  u w section of the synthetic MTF for u m = u c - eff = 0.8 u c . OTF compact support for WFM and tunable-SIM shown by black and white dashed lines, respectively.
Fig. 2.
Fig. 2. Impact of slits’ parameters ( N and x 0 ) on the synthetic OTF’s compact support and OS capability of the tunable-SIM system. (a)–(c)  u w section of the synthetic MTF for different designs. (d) Integrated intensity profiles of (a)–(c), experimental (exp) and numerical (num) results. Legends, “dem” and “dec” stand for demodulated and deconvolved, respectively. For this study we used u m = u c - eff = 0.8 u c .
Fig. 3.
Fig. 3. Comparison of different systems’ performance. (a–e) u w section of the synthetic MTF for tunable-SIM and 3W-SIM systems at different designs. (f) Integrated intensity profiles obtained from the MTF of the systems (a)–(e), OS-SIM ( u m = 0.5 u c ), confocal microscope, and WFM. (g) HWHM and σ 2 values computed from integrated intensity curve.
Fig. 4.
Fig. 4. Performance of two 3D-SIM systems under noisy conditions. u w section of the synthetic MTF for tunable-SIM and 3W-SIM systems for (a–b) SNR = 20 dB and (c–d) SNR = 15 dB. Effective (e) lateral and (f) axial cutoff frequencies for different SNR levels.

Equations (6)

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H SIM ( u , w ) = H ( u , w ) 3 I ( u , w ) ,
i ( x , z ) 1 + V ( z ) cos ( 2 π u m x + ϕ ) ,
V ( z ) = sin ( 2 π N w m z ) N sin ( 2 π w m z ) ,
V ( w ) = 1 N n = 0 N 1 δ [ w ( 2 n N + 1 ) w m ] .
H SIM ( u , w ) = H ( u , w ) + n = 0 N 1 H [ u ± u m , v , w ( 2 n N + 1 ) w m ] 2 N ,
N max = 1 + ( 1 u m u c ) f L 1 d p 2 L 2 f L 2 x 0 ,

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