Abstract

Spatiotemporal focusing, or simultaneous spatial and temporal focusing (SSTF), has already been adopted for various applications in microscopy, photoactivation for biological studies, and laser fabrication. We investigate the effects of aberrations on focus formation in SSTF, in particular, the effects of phase aberrations related to low-order Zernike modes and a refractive index mismatch between the immersion medium and sample. By considering a line focus, we are able to draw direct comparison between the performance of SSTF and conventional spatial focusing (SF). Wide-field SSTF is also investigated and is found to be much more robust to aberrations than either line SSTF or SF. These results show the sensitivity of certain focusing methods to specific aberrations, and can inform on the necessity and benefit of aberration correction.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13, 2153–2159 (2005).
    [CrossRef]
  2. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun. 281, 1796–1805 (2008).
    [CrossRef]
  3. D. Oron and Y. Silberberg, “Harmonic generation with temporally focused ultrashort pulses,” J. Opt. Soc. Am. B 22, 2660–2663 (2005).
    [CrossRef]
  4. D. Oron and Y. Silberberg, “Spatiotemporal coherent control using shaped, temporally focused pulses,” Opt. Express 13, 9903–9908 (2005).
    [CrossRef]
  5. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005).
    [CrossRef]
  6. E. Tal, D. Oron, and Y. Silberberg, “Improved depth resolution in video-rate line-scanning multiphoton microscopy using temporal focusing,” Opt. Lett. 30, 1686–1688 (2005).
    [CrossRef]
  7. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14, 12243–12254 (2006).
    [CrossRef]
  8. A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
    [CrossRef]
  9. E. Papagiakoumou, V. de Sars, D. Oron, and V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
    [CrossRef]
  10. E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express 17, 5391–5401 (2009).
    [CrossRef]
  11. E. Yew, C. J. Sheppard, and P. T. So, “Temporally focused wide-field two-photon microscopy: paraxial to vectorial,” Opt. Express 21, 12951–12963 (2013).
    [CrossRef]
  12. F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35, 1106–1108 (2010).
    [CrossRef]
  13. D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express 18, 24673–24678 (2010).
    [CrossRef]
  14. D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express 18, 18086–18094 (2010).
    [CrossRef]
  15. D. Kim and P. T. So, “High-throughput three-dimensional lithographic microfabrication,” Opt. Lett. 35, 1602–1604 (2010).
    [CrossRef]
  16. Y.-C. Li, L.-C. Cheng, C.-Y. Chang, C.-H. Lien, P. J. Campagnola, and S.-J. Chen, “Fast multiphoton microfabrication of freeform polymer microstructures by spatiotemporal focusing and patterned excitation,” Opt. Express 20, 19030–19038 (2012).
    [CrossRef]
  17. R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
    [CrossRef]
  18. M. J. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192, 90–98 (1998).
    [CrossRef]
  19. M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
    [CrossRef]
  20. A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18, 21090–21099 (2010).
    [CrossRef]
  21. A. Jesacher, G. D. Marshall, T. Wilson, and M. J. Booth, “Adaptive optics for direct laser writing with plasma emission aberration sensing,” Opt. Express 18, 656–661 (2010).
    [CrossRef]
  22. B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express 19, 9419–9425 (2011).
    [CrossRef]
  23. R. D. Simmonds, P. S. Salter, A. Jesacher, and M. J. Booth, “Three dimensional laser microfabrication in diamond using a dual adaptive optics system,” Opt. Express 19, 24122–24128 (2011).
    [CrossRef]
  24. P. Salter and M. Booth, “Focussing over the edge: adaptive subsurface laser fabrication up to the sample face,” Opt. Express 20, 19978–19989 (2012).
    [CrossRef]
  25. E. Hecht and A. Zajac, Optics (Addison-Wesley, 2002).
  26. U. Fuchs, U. Zeitner, and A. Tünnermann, “Ultra-short pulse propagation in complex optical systems,” Opt. Express 13, 3852–3861 (2005).
    [CrossRef]
  27. Y. M. Engelberg and S. Ruschin, “Fast method for physical optics propagation of high-numerical-aperture beams,” J. Opt. Soc. Am. A 21, 2135–2145 (2004).
    [CrossRef]
  28. A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18, 19645–19655 (2010).
    [CrossRef]
  29. O. Therrien, B. Aubé, S. Pagès, P. De Koninck, and D. Côté, “Wide-field multiphoton imaging of cellular dynamics in thick tissue by temporal focusing and patterned illumination,” Biomed. Opt. Express 2, 696–704 (2011).
    [CrossRef]
  30. L.-C. Cheng, C.-Y. Chang, C.-Y. Lin, K.-C. Cho, W.-C. Yen, N.-S. Chang, C. Xu, C. Y. Dong, and S.-J. Chen, “Spatiotemporal focusing-based widefield multiphoton microscopy for fast optical sectioning,” Opt. Express 20, 8939–8948 (2012).
    [CrossRef]
  31. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2010).
  32. P. Török, P. Varga, Z. Laczik, and G. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
    [CrossRef]

2014 (1)

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

2013 (1)

2012 (3)

2011 (3)

2010 (7)

2009 (1)

2008 (3)

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

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

E. Papagiakoumou, V. de Sars, D. Oron, and V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef]

2007 (1)

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

2006 (1)

2005 (6)

2004 (1)

1998 (1)

M. J. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

1995 (1)

Adams, D. E.

Aubé, B.

Backus, S.

Bellouard, Y.

Bhuyan, M.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Block, E.

Booker, G.

Booth, M.

Booth, M. J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2010).

Campagnola, P. J.

Chang, C.-Y.

Chang, N.-S.

Chen, S.-J.

Cheng, G.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Cheng, L.-C.

Cheng, Y.

Cho, K.-C.

Colombier, J.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Côté, D.

Cumming, B. P.

De Koninck, P.

de Sars, V.

Dong, C. Y.

Durfee, C. G.

Durst, M.

Durst, M. E.

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

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14, 12243–12254 (2006).
[CrossRef]

Emiliani, V.

Engelberg, Y. M.

Fuchs, U.

Gu, M.

He, F.

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2002).

Jesacher, A.

Johnson, A.

Kim, D.

Kleinfeld, D.

Laczik, Z.

Li, Y.-C.

Lien, C.-H.

Lin, C.-Y.

Marshall, G. D.

Mauclair, C.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Midorikawa, K.

Neil, M.

M. J. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

Ni, J.

Oron, D.

Pagès, S.

Papagiakoumou, E.

Ruschin, S.

Salter, P.

Salter, P. S.

Shank, C. V.

A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18, 19645–19655 (2010).
[CrossRef]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

Sheppard, C. J.

Shroff, H.

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

Silberberg, Y.

Simmonds, R. D.

So, P. T.

Squier, J. A.

Srisungsitthisunti, P.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Stoian, R.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Sugioka, K.

Tal, E.

Tang, J.

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

Therrien, O.

Török, P.

Tsai, P. S.

Tünnermann, A.

van Howe, J.

Varga, P.

Vaziri, A.

A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18, 19645–19655 (2010).
[CrossRef]

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

Velpula, P.

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Vitek, D. N.

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2010).

Xiong, H.

Xu, C.

Xu, H.

Xu, Z.

Yen, W.-C.

Yew, E.

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2002).

Zeitner, U.

Zhu, G.

Zipfel, W.

Appl. Phys. A (1)

R. Stoian, J. Colombier, C. Mauclair, G. Cheng, M. Bhuyan, P. Velpula, and P. Srisungsitthisunti, “Spatial and temporal laser pulse design for material processing on ultrafast scales,” Appl. Phys. A 114, 119–127 (2014).
[CrossRef]

Biomed. Opt. Express (1)

J. Microsc. (1)

M. J. Booth, M. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc. 192, 90–98 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (1)

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

Opt. Express (18)

G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13, 2153–2159 (2005).
[CrossRef]

M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14, 12243–12254 (2006).
[CrossRef]

D. Oron and Y. Silberberg, “Spatiotemporal coherent control using shaped, temporally focused pulses,” Opt. Express 13, 9903–9908 (2005).
[CrossRef]

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13, 1468–1476 (2005).
[CrossRef]

D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express 18, 24673–24678 (2010).
[CrossRef]

D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express 18, 18086–18094 (2010).
[CrossRef]

E. Papagiakoumou, V. de Sars, D. Oron, and V. Emiliani, “Patterned two-photon illumination by spatiotemporal shaping of ultrashort pulses,” Opt. Express 16, 22039–22047 (2008).
[CrossRef]

E. Papagiakoumou, V. de Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express 17, 5391–5401 (2009).
[CrossRef]

E. Yew, C. J. Sheppard, and P. T. So, “Temporally focused wide-field two-photon microscopy: paraxial to vectorial,” Opt. Express 21, 12951–12963 (2013).
[CrossRef]

A. Vaziri and C. V. Shank, “Ultrafast widefield optical sectioning microscopy by multifocal temporal focusing,” Opt. Express 18, 19645–19655 (2010).
[CrossRef]

Y.-C. Li, L.-C. Cheng, C.-Y. Chang, C.-H. Lien, P. J. Campagnola, and S.-J. Chen, “Fast multiphoton microfabrication of freeform polymer microstructures by spatiotemporal focusing and patterned excitation,” Opt. Express 20, 19030–19038 (2012).
[CrossRef]

U. Fuchs, U. Zeitner, and A. Tünnermann, “Ultra-short pulse propagation in complex optical systems,” Opt. Express 13, 3852–3861 (2005).
[CrossRef]

A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18, 21090–21099 (2010).
[CrossRef]

A. Jesacher, G. D. Marshall, T. Wilson, and M. J. Booth, “Adaptive optics for direct laser writing with plasma emission aberration sensing,” Opt. Express 18, 656–661 (2010).
[CrossRef]

B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express 19, 9419–9425 (2011).
[CrossRef]

R. D. Simmonds, P. S. Salter, A. Jesacher, and M. J. Booth, “Three dimensional laser microfabrication in diamond using a dual adaptive optics system,” Opt. Express 19, 24122–24128 (2011).
[CrossRef]

P. Salter and M. Booth, “Focussing over the edge: adaptive subsurface laser fabrication up to the sample face,” Opt. Express 20, 19978–19989 (2012).
[CrossRef]

L.-C. Cheng, C.-Y. Chang, C.-Y. Lin, K.-C. Cho, W.-C. Yen, N.-S. Chang, C. Xu, C. Y. Dong, and S.-J. Chen, “Spatiotemporal focusing-based widefield multiphoton microscopy for fast optical sectioning,” Opt. Express 20, 8939–8948 (2012).
[CrossRef]

Opt. Lett. (3)

Phil. Trans. R. Soc. A (1)

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

A. Vaziri, J. Tang, H. Shroff, and C. V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Natl. Acad. Sci. USA 105, 20221–20226 (2008).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2010).

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Lens focusing coordinate systems, pupil illumination, and focal intensity distribution (I=|E|2) for the line and wide-field focusing. (a) Coordinate systems in the pupil and focus. (b1), (b2) Line focusing generated by simultaneous spatial and temporal focusing (SSTF) and spatial focusing (SF). The variation in color in the pupil of (b1) shows schematically how the spectral components are distributed across the aperture. The white stripe in (b2) indicates that all spectral components illuminate equally a line in the pupil. (c) Wide-field focusing generated by SSTF, showing the spectral spread along a line in the pupil. The color bar shows the focal intensity, normalized to each plot.

Fig. 2.
Fig. 2.

Effects of aberration on the temporal focusing properties for line SSTF and line SF. In the images of the aberrated focus, the 150 fs pulsed laser light with a central wavelength of 790 nm is focused into diamond (refractive index 2.4) with a nominal focus depth of 25 μm. Each column is individually normalized. (a) Temporal intensity distribution (I=|E|2) of SSTF at the time of 1.5, 0, and 1.5 ps, as well as the time average profile. (b) Temporal intensity distribution of line SF at the time of 0.15, 0, and 0.15 ps, as well as the time average profile.

Fig. 3.
Fig. 3.

Effects of Zernike mode aberrations on line focus. Each profile is calculated as the time average of the squared intensity I2. (a)–(c) Simultaneous SSTF. (a) Comparison of the I2 yz profiles between the unaberrated case and with Zernike modes 5–11 aberrated cases [mode amplitude for central wavelength component equals to 1 rad (rms)]. The inset in the first profile is the pupil illumination, and the insets in the remaining profiles show the phase of the Zernike modes. (b) Normalized plot of the variation of Ip(z) (red curve). The black curve is the unaberrated case included for comparison. (c) Peak I2 changes with Zernike mode amplitude [radians (rms)] of the central wavelength. (d)–(f) The effects of Zernike modes on conventional SF. Each row indicates the same comparison as above.

Fig. 4.
Fig. 4.

Effects of refractive index mismatch on a line focus. The sample is diamond with the refractive index of 2.4. The light is focused by using a 1.4 NA oil immersion lens. The nominal focus depth is 50 μm. (a) Aberrated I2 yz profile for line SSTF. Insets are the pupil illumination (left) as well as the phase induced by the index mismatch (right, with defocus element removed). (b) Aberrated yz profile for line SF. (c) Comparison of the axial Ip(z) distribution for unaberrated and index mismatch aberrated SSTF and SF. Each curve is individually normalized. (d) Peak I2 changes with the nominal focus depth into the sample for line SSTF and SF. Each curve is individually normalized.

Fig. 5.
Fig. 5.

Effects of Zernike mode aberrations on wide-field SSTF. (a) Comparison of I2 xz profiles between unaberrated and Zernike mode 5–11 aberrated [central wavelength amplitude equals to 1 rad (rms)] wide-field SSTF. The inset in the first figure is the pupil illumination, and the insets in the aberrated figures are the Zernike modes phase plot in the pupil. (b) Normalized plot of the variation of Ip(z) (red curve). The black curve is the unaberrated version included for comparison. (c) Peak I2 changes with Zernike mode amplitude [radians (rms)] of the central wavelength.

Fig. 6.
Fig. 6.

Effects of refractive index mismatch on wide-field SSTF. The sample is diamond with the refractive index of 2.4. The nominal focus depth is 50 μm. (a) Unaberrated I2 xz profile for wide-field SSTF. (b) Aberrated I2 xz profile. Insets are the pupil illumination (left) as well as the phase induced by the index mismatch (right, with defocus element removed). (c) Comparison of axial I2 distribution for unaberrated and index mismatch aberrated wide-field SSTF. Each curve is individually normalized. (d) FWHM of the I2 distribution along axial direction versus nominal focus depth into the sample. (e) Peak I2 changes with the focusing depth into the sample for SSTF.

Fig. 7.
Fig. 7.

Effect of a coma aberration (mode 7) with different pulse widths. The graphic shows the peak I2 changes with Zernike mode amplitude [radians (rms)] of the central wavelength. Insets are the pupil illumination and aberrated I2 profile. (a) Line SSTF. (b) Wide-field SSTF.

Tables (1)

Tables Icon

Table 1. Zernike Polynomials k=5 to 11

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E(ω,x,y,zf)=ωi2πcfexp(ikf)exp[ikx2+y22f]×F[E(ω,px,py)],
I(t,x,y,z)=|E(t,x,y,z)|2=|F[E(ω,x,y,z)]|2.
E(ω,px,py)=E0exp[τ2(ωω0)24]exp[(pxpx0)2sBFP2]u(px,py),
u(px,py)={1,px2+py2R0,px2+py2>R,
E(ω,px,py)=E0exp[τ2(ωω0)24]exp[(pxpx0)2+py2sBFP2]u(px,py).
E(ω,px,py)=E0exp[τ2(ωω0)24]exp[px2sBFP2]u(px,py),
E(ω,px,py)=E(ω,px,py)ejϕ(ω,px,py).
ϕ(ω,ρ,θ)=k=1ck(ω)Zk(ρ,θ),
ck(ω)=ck(ω0)×ω/ω0.
ϕ(d,ρ)=k·d·NA(n22NA2ρ2n12NA2ρ2),
D(d,ρ)=k·d·NAn22NA2ρ2.
ϕ^(d,ρ)=ϕ(d,ρ)ϕ(d,ρ),D(d,ρ)D(d,ρ),D(d,ρ)D(d,ρ).
ϕ(d,ρ)=ϕ(d,ρ)1Nρϕ(d,ρ)D(d,ρ)=D(d,ρ)1NρD(d,ρ),
ϕ(d,ρ),D(d,ρ)=1Nρϕ(d,ρ)·D(d,ρ).

Metrics