Abstract

We present a new two-snapshot structured light illumination (SLI) reconstruction algorithm for fast image acquisition. The new algorithm, which only requires two mutually π phase-shifted raw structured images, is implemented on a custom-built temporal focusing fluorescence microscope (TFFM) to enhance its axial resolution via a digital micromirror device (DMD). First, the orientation of the modulated sinusoidal fringe patterns is automatically identified via spatial frequency vector detection. Subsequently, the modulated in-focal-plane images are obtained via rotation and subtraction. Lastly, a parallel amplitude demodulation method, derived based on Hilbert transform, is applied to complete the decoding processes. To demonstrate the new SLI algorithm, a TFFM is custom-constructed, where a DMD replaces the generic blazed grating in the system and simultaneously functions as a diffraction grating and a programmable binary mask, generating arbitrary fringe patterns. The experimental results show promising depth-discrimination capability with an axial resolution enhancement factor of 1.25, which matches well with the theoretical estimation, i.e, 1.27. Imaging experiments on pollen grain and mouse kidney samples have been performed. The results indicate that the two-snapshot algorithm presents comparable contrast reconstruction and optical cross-sectioning capability than those adopting the conventional root-mean-square (RMS) reconstruction method. The two-snapshot method can be readily applied to any sinusoidally modulated illumination systems to realize high-speed 3D imaging as less frames are required for each in-focal-plane image restoration, i.e., the image acquisition speed is improved by 2.5 times for any two-photon systems.

© 2017 Optical Society of America

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2016 (1)

2015 (2)

J. Jiang, D. Zhang, S. Walker, C. Gu, Y. Ke, W. H. Yung, and S. C. Chen, “Fast 3-D temporal focusing microscopy using an electrically tunable lens,” Opt. Express 23(19), 24362–24368 (2015).
[Crossref] [PubMed]

M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (4)

2012 (1)

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

2011 (2)

E. Y. S. Yew, H. Choi, D. Kim, and P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and HiLo background rejection,” Proc. SPIE 7903, 79031O (2011).
[Crossref]

H. Dana and S. Shoham, “Numerical evaluation of temporal focusing characteristics in transparent and scattering media,” Opt. Express 19(6), 4937–4948 (2011).
[Crossref] [PubMed]

2010 (3)

A. Straub, M. E. Durst, and C. Xu, “High speed multiphoton axial scanning through an optical fiber in a remotely scanned temporal focusing setup,” Biomed. Opt. Express 2(1), 80–88 (2010).
[Crossref] [PubMed]

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
[Crossref] [PubMed]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

2008 (3)

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008).
[Crossref] [PubMed]

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron 39(7), 808–818 (2008).
[Crossref] [PubMed]

D. Lim, K. K. Chu, and J. Mertz, “Wide-field fluorescence sectioning with hybrid speckle and uniform-illumination microscopy,” Opt. Lett. 33(16), 1819–1821 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref] [PubMed]

2005 (3)

2002 (1)

J. D. Lechleiter, D.-T. Lin, and I. Sieneart, “Multi-photon laser scanning microscopy using an acoustic optical deflector,” Biophys. J. 83(4), 2292–2299 (2002).
[Crossref] [PubMed]

2001 (1)

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

2000 (2)

M. A. Neil, A. Squire, R. Juskaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197(1), 1–4 (2000).
[Crossref] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (2)

J. Bewersdorf, R. Pick, and S. W. Hell, “Multifocal multiphoton microscopy,” Opt. Lett. 23(9), 655–657 (1998).
[Crossref] [PubMed]

A. H. Buist, M. Muller, J. Squier, and G. J. Brakenhoff, “Real time two-photon absorption microscopy using multi point excitation,” J. Microsc. 192(2), 217–226 (1998).
[Crossref]

1997 (1)

1996 (1)

G. J. Brakenhoff, J. Squier, T. Norris, A. C. Bliton, M. H. Wade, and B. Athey, “Real-time two-photon confocal microscopy using a femtosecond, amplified Ti:sapphire system,” J. Microsc. 181(3), 253–259 (1996).
[Crossref] [PubMed]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

1969 (1)

Ammar, D. A.

Andresen, P.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Anselmi, F.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Athey, B.

G. J. Brakenhoff, J. Squier, T. Norris, A. C. Bliton, M. H. Wade, and B. Athey, “Real-time two-photon confocal microscopy using a femtosecond, amplified Ti:sapphire system,” J. Microsc. 181(3), 253–259 (1996).
[Crossref] [PubMed]

Bahlmann, K.

Bao, Z.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
[Crossref] [PubMed]

Bastiaens, P. I.

M. A. Neil, A. Squire, R. Juskaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197(1), 1–4 (2000).
[Crossref] [PubMed]

Bègue, A.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Bewersdorf, J.

Bliton, A. C.

G. J. Brakenhoff, J. Squier, T. Norris, A. C. Bliton, M. H. Wade, and B. Athey, “Real-time two-photon confocal microscopy using a femtosecond, amplified Ti:sapphire system,” J. Microsc. 181(3), 253–259 (1996).
[Crossref] [PubMed]

Block, E.

Brakenhoff, G. J.

A. H. Buist, M. Muller, J. Squier, and G. J. Brakenhoff, “Real time two-photon absorption microscopy using multi point excitation,” J. Microsc. 192(2), 217–226 (1998).
[Crossref]

G. J. Brakenhoff, J. Squier, T. Norris, A. C. Bliton, M. H. Wade, and B. Athey, “Real-time two-photon confocal microscopy using a femtosecond, amplified Ti:sapphire system,” J. Microsc. 181(3), 253–259 (1996).
[Crossref] [PubMed]

Brown, J. Q.

Buehler, C.

Buist, A. H.

A. H. Buist, M. Muller, J. Squier, and G. J. Brakenhoff, “Real time two-photon absorption microscopy using multi point excitation,” J. Microsc. 192(2), 217–226 (1998).
[Crossref]

Chang, C.-Y.

Chang, H.-Y.

Chen, S. C.

Chen, S.-J.

Cheng, L.-C.

Chien, F.-C.

Chitnis, A. B.

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Choi, H.

Chu, K. K.

Combs, C. A.

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Da Sie, Y.

Dalle Nogare, D.

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Dana, H.

de Sars, V.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Denk, W.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005).
[Crossref] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Dong, C. Y.

Durfee, C.

Durst, M.

Durst, M. E.

Elfer, K. N.

Emiliani, V.

M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
[Crossref] [PubMed]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Fantini, S.

Fischer, R. S.

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

Fricke, M.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Glückstad, J.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Greco, M.

Gu, C.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Hallacoglu, B.

Heffer, E. L.

Hell, S. W.

Hellweg, D.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2(12), 932–940 (2005).
[Crossref] [PubMed]

Hoogland, T. M.

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref] [PubMed]

Hu, Y. Y.

Isacoff, E. Y.

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Isobe, K.

Iyer, V.

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref] [PubMed]

Jiang, J.

Juskaitis, R.

M. A. Neil, A. Squire, R. Juskaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197(1), 1–4 (2000).
[Crossref] [PubMed]

Juškaitis, R.

Kahook, M. Y.

Kannari, F.

Karadaglic, D.

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron 39(7), 808–818 (2008).
[Crossref] [PubMed]

Kawano, H.

Ke, Y.

Keller, P. J.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
[Crossref] [PubMed]

Khairy, K.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
[Crossref] [PubMed]

Kim, D.

E. Y. S. Yew, H. Choi, D. Kim, and P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and HiLo background rejection,” Proc. SPIE 7903, 79031O (2011).
[Crossref]

Kim, K. H.

Kumagai, A.

Lauterbach, M. A.

M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
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E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Parekh, S. H.

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
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Patorski, K.

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Ragan, T.

Ronzitti, E.

M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
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V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
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Schmidt, A. D.

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
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A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
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J. D. Lechleiter, D.-T. Lin, and I. Sieneart, “Multi-photon laser scanning microscopy using an acoustic optical deflector,” Biophys. J. 83(4), 2292–2299 (2002).
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M. A. Neil, A. Squire, R. Juskaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197(1), 1–4 (2000).
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P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
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M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
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P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
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M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
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A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
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Zhang, D.

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Biomed. Opt. Express (7)

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H. Choi, E. Y. S. Yew, B. Hallacoglu, S. Fantini, C. J. R. Sheppard, and P. T. C. So, “Improvement of axial resolution and contrast in temporally focused widefield two-photon microscopy with structured light illumination,” Biomed. Opt. Express 4(7), 995–1005 (2013).
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Biophys. J. (1)

J. D. Lechleiter, D.-T. Lin, and I. Sieneart, “Multi-photon laser scanning microscopy using an acoustic optical deflector,” Biophys. J. 83(4), 2292–2299 (2002).
[Crossref] [PubMed]

J. Microsc. (5)

G. J. Brakenhoff, J. Squier, T. Norris, A. C. Bliton, M. H. Wade, and B. Athey, “Real-time two-photon confocal microscopy using a femtosecond, amplified Ti:sapphire system,” J. Microsc. 181(3), 253–259 (1996).
[Crossref] [PubMed]

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[Crossref]

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
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J. Neurophysiol. (1)

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
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J. Opt. Soc. Am. (1)

Micron (1)

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron 39(7), 808–818 (2008).
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Nat. Methods (4)

A. G. York, S. H. Parekh, D. Dalle Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, C. A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9(7), 749–754 (2012).
[Crossref] [PubMed]

P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt, and E. H. Stelzer, “Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy,” Nat. Methods 7(8), 637–642 (2010).
[Crossref] [PubMed]

E. Papagiakoumou, F. Anselmi, A. Bègue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
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M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281(7), 1796–1805 (2008).
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Opt. Express (7)

Opt. Lett. (4)

PLoS One (1)

M. A. Lauterbach, E. Ronzitti, J. R. Sternberg, C. Wyart, and V. Emiliani, “Fast Calcium Imaging with Optical Sectioning via HiLo Microscopy,” PLoS One 10(12), e0143681 (2015).
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Proc. SPIE (1)

E. Y. S. Yew, H. Choi, D. Kim, and P. T. C. So, “Wide-field two-photon microscopy with temporal focusing and HiLo background rejection,” Proc. SPIE 7903, 79031O (2011).
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Science (1)

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S. L. Hahn, Hilbert Transforms in Signal Processing (Artech Print on Demand, 1996).

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Supplementary Material (1)

NameDescription
» Visualization 1       TFFM imaging results of fluorescently labeled glomeruli and convoluted tubules samples (mouse kidney) “without” and “with” the SLI algorithms, i.e., RMS and two-snapshot methods, from -6 µm to 6 µm.

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Figures (7)

Fig. 1
Fig. 1

Principles of generating structured images in a TFFM based on a DMD: (a) DMD disperses the laser pulses along the optical path until the objective lens (OBJ) recombines the spectral components, achieving temporal focusing at the focal region, where the shortest pulse is formed; CL: collimating lens; FFP: front focal plane; (b) illustration of pulse widening effect outside the focal region due to temporal focusing; (c) sinusoidal fringe patterns are formed in the focal plane by the interference of the 0th and ± 1st order diffractions; the characteristics of the fringes can be controlled by the vertical stripes on the DMD. The right image shows measured in-focus fluorescence emissions encoded with sinusoidal patterns. Note that in (a) and (c), the CL and OBJ form a 4-f system.

Fig. 2
Fig. 2

Processing steps of the two-snapshot SLI algorithm: (a) flowchart of the two-snapshot SLI algorithm; (b) test object: image of the cameraman, i.e., S( r ); (c) structured fringe pattern, 1+mcos( 2π p θ r + φ n ), n = 1 or 2; (d) generation of the raw structured image described in Eq. (1), i.e., the image is simulated by convolving the modulated test object image with the PSF of the optical system; (e) identification of the skew angle, θ, of the spatial frequency vector, p θ , in reciprocal space via local maxima detection; (f) rotation of the structured images by π/2θ to align the fringe pattern parallel to the y-axis, described in Eq. (2); image padding is performed before rotation to avoid the generation of artifacts. The region of interest is indicated by the white box; (g) image subtraction to remove the D p2 ' ( r ) term, described in Eq. (3); (h) result of parallel Hilbert transform, where s 1D vectors are reshaped as a 2D image; (i) amplitude demodulation result for the rotated in-focus image, described in Eq. (9); and (j) reconstructed in-focus image, i.e., S( r ) I 0 2 ( r ).

Fig. 3
Fig. 3

Schematics of the DMD-based SLI TFFM system. Laser: regenerative laser amplifier; HWP: half-wave plate; PBS: polarizing beam splitter; M1 - M3: mirrors; CL: collimating lens; DM: dichroic mirror; BPF: band pass filter; OBJ: objective lens; ZL: zoom lens.

Fig. 4
Fig. 4

Generation of π phase-shifted sinusoidal fringe patterns via a DMD. (a) and (b): binary fringe patterns programmed to the DMD of opposite states; the period of the stripe pattern is ten pixels (2.70 µm); (c) and (d): imaging results of the Rh6G sample at the focal plane when applying DMD patterns of (a) and (b) respectively; (e) measured fluorescent intensity profiles across the red and blue lines in (c) and (d) respectively. The circles and solid lines represent the raw data and the least-squares fitting results, which have a 180° phase shift; (f) Fourier transform of the fluorescent intensity profiles in (e), where the 1st and 2nd order peaks can be clearly observed.

Fig. 5
Fig. 5

Axial resolution characterization via the thin Rh6G sample; the red and blue circles represent the measured fluorescent intensities of the TFFM “without” and “with” the two-snapshot algorithm.

Fig. 6
Fig. 6

TFFM imaging results of a pollen grain at three different depths. (a) - (c) cropped optical cross-sections of the pollen at 0 µm, 6 µm, and 12 µm respectively; (d) - (f) two snap shots reconstructed images of the same pollen grain at 0 µm, 6 µm, and 12 µm respectively, where one may clearly observe the enhanced axial resolution and effect of out-of-focus fluorescent emission rejection in (c) and (f); (g) normalized intensity profiles along the red and blue dashed line in (c) and (f). The scale bar is 10 μm. All raw images are collected at 20 ms.

Fig. 7
Fig. 7

TFFM imaging results of fluorescently labeled glomeruli and convoluted tubules samples (mouse kidney) “without” and “with” the SLI algorithms at five different depths, i.e., −6 μm, −3 μm, 0 μm, 3 μm and 6 μm from left to right; each column corresponds to the same depth and field of view. All raw images are collected at 20 ms exposure time. (a) - (e) raw images captured by the TFFM, (f) - (j) reconstructed images based on the RMS algorithm; (k) - (o) reconstructed images based on the two-snapshot algorithm; the scale bar is 20 μm.

Equations (9)

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D( r )=S( r ) { I 0 ( r )[1+mcos(2π p θ r +φ)]} 2 H( r )+ D p2 ( r ).
D n ' ( r )= S ' ( r ) I 0 '2 ( r ){1+ m 2 2 +2mcos(2π| p θ |x+ φ n ) + m 2 2 cos[2(2π| p θ |x+ φ n )]}H( r )+ D p2 ' ( r ).
D d ' ( r ) S ' ( r )[ I 0 '2 ( r )cos(2π| p θ |x+ φ 1 )]H( r ).
V k ( e k ) S ' ( e k )[ I 0 '2 ( e k )cos(2π| p θ |x+ φ n )]H( r ).
V A k ( e k )= V k ( e k )+iV H k ( e k ).
V H k ( e k ) S ' ( e k ) I 0 '2 ( e k )sin(2π| p θ |x+ φ n )]H( r ).
V A k ( e k ) S ' ( e k ) I 0 '2 ( e k )[cos(2π| p θ |x+ φ n )+isin(2π| p θ |x+ φ n )]H( r ).
| V A k ( e k ) | S ' ( e k ) I 0 '2 ( e k )H( r ).
S ' ( r ) I 0 '2 ( r ) [| V H 1 ( e 1 ) | | V H 2 ( e 2 ) |, ..., | V H s ( e s ) |] T .

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