Abstract

We present a technique to systematically measure the change in the blurring function of an optical microscope with distance between the source and the coverglass (the depth) and demonstrate its utility in three-dimensional (3D) deconvolution. By controlling the axial positions of the microscope stage and an optically trapped bead independently, we can record the 3D blurring function at different depths. We find that the peak intensity collected from a single bead decreases with depth and that the width of the axial, but not the lateral, profile increases with depth. We present simple convolution and deconvolution algorithms that use the full depth-varying point-spread functions and use these to demonstrate a reduction of elongation artifacts in a reconstructed image of a 2μm sphere.

© 2007 Optical Society of America

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2006

2005

2004

2003

C. Preza and J. Conchello, "Image estimation accounting for point-spread function depth variation in three-dimensional fluorescence microscopy," in Proc. SPIE 4964, 135-142 (2003).
[CrossRef]

S. Mezouari and A. Harvey, "Phase pupil functions for reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003).
[CrossRef] [PubMed]

2002

M. Booth, M. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

A. Caspi, R. Granek, and M. Elbaum, "Diffusion and directed motion in cellular transport," Phys. Rev. E 66, 011916 (2002).
[CrossRef]

M. Lang, C. Asbury, J. Shaevitz, and S. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

A. Diaspro, F. Federici, and M. Robello, "Influence of refractive-index mismatch in high-resolution three-dimensional confocal microscopy," Appl. Opt. 41, 685-690 (2002).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

2001

2000

A. Pralle, E. Florin, E. Stelzer, and J. Hoerber, "Photonic force microscopy: a new tool providing new methods to study membranes at the molecular level," Single Mol. 1, 129-133 (2000).
[CrossRef]

1997

C. Sheppard and P. Torok, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

P. Török and P. Varga, "Electromagnetic diffraction of light focused through a stratified medium," Appl. Opt. 36, 2305-2312 (1997).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. Horber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

S. Wiersma, P. Török, T. Visser, and P. Varga, "Comparison of different theories for focusing through a plane interface," J. Opt. Soc. Am. A 14, 1482-1490 (1997).
[CrossRef]

1996

A. Boden, D. Redding, R. Hanisch, and J. Mo, "Massively parallel spatially-variant maximum likelihood restoration of Hubble Space Telescope imagery," J. Opt. Soc. Am. A 13, 1537-1545 (1996).
[CrossRef]

N. White, R. Errington, M. Fricker, and J. Wood, "Aberration control in quantitative imaging of botanical specimens by multidimensional fluorescence microscopy," J. Microsc. 181, 99-116 (1996).
[CrossRef]

B. Scalettar, J. Swedlow, J. Sedat, and D. Agard, "Dispersion, aberration and deconvolution in multi-wavelength fluorescence images," J. Microsc. 182, 50-60 (1996).
[CrossRef] [PubMed]

1995

1994

J. McNally, C. Preza, J. Conchello, and L. Thomas, Jr., "Artifacts in computational optical-sectioning microscopy," J. Opt. Soc. Am. A 11, 1056-1067 (1994).
[CrossRef]

T. Visser and J. Oud, "Volume measurements in three-dimensional microscopy," Scanning 16, 198-200 (1994).
[CrossRef]

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

1993

S. Hell, G. Reiner, C. Cremer, and E. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

1992

T. Visser, J. Oud, and G. Brakenhoff, "Refractive index and axial distance measurements in 3-d microscopy," Optik (Stuttgart) 90, 17-19 (1992).

1991

T. Visser, G. Brakenhoff, and F. Groen, "The one point response in fluorescence confocal microscopy," Optik (Stuttgart) 87, 39-40 (1991).

K. Carlsson, "The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy," J. Microsc. 163, 167-178 (1991).
[CrossRef]

P. Crilly, "A quantitative evaluation of various iterative deconvolution algorithms," IEEE Trans. Instrum. Meas. 40, 558-562 (1991).
[CrossRef]

S. Gibson and F. Lanni, "Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy," J. Opt. Soc. Am. A 8, 1601-1613 (1991).
[CrossRef]

1989

D. Agard, Y. Hiraoka, P. Shaw, and J. Sedat, "Fluorescence microscopy in three dimensions," Methods Cell Biol. 30, 353-377 (1989).
[CrossRef] [PubMed]

1988

1986

1984

D. Agard, "Optical sectioning microscopy: cellular architecture in three dimensions," Annu. Rev. Biophys. Bioeng. 13, 191-219 (1984).
[CrossRef] [PubMed]

1965

1963

J. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).

Abbondanzieri, E.

Agard, D.

B. Scalettar, J. Swedlow, J. Sedat, and D. Agard, "Dispersion, aberration and deconvolution in multi-wavelength fluorescence images," J. Microsc. 182, 50-60 (1996).
[CrossRef] [PubMed]

D. Agard, Y. Hiraoka, P. Shaw, and J. Sedat, "Fluorescence microscopy in three dimensions," Methods Cell Biol. 30, 353-377 (1989).
[CrossRef] [PubMed]

D. Agard, "Optical sectioning microscopy: cellular architecture in three dimensions," Annu. Rev. Biophys. Bioeng. 13, 191-219 (1984).
[CrossRef] [PubMed]

Andres, P.

Arlt, J.

E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Asbury, C.

M. Lang, C. Asbury, J. Shaevitz, and S. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Barakat, R.

Block, S.

K. Neuman, E. Abbondanzieri, and S. Block, "Measurement of the effective focal shift in an optical trap," Opt. Lett. 30, 1318-1320 (2005).
[CrossRef] [PubMed]

M. Lang, C. Asbury, J. Shaevitz, and S. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Block, S. M.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Boden, A.

Booth, M.

M. Booth, M. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Brakenhoff, G.

T. Visser, J. Oud, and G. Brakenhoff, "Refractive index and axial distance measurements in 3-d microscopy," Optik (Stuttgart) 90, 17-19 (1992).

T. Visser, G. Brakenhoff, and F. Groen, "The one point response in fluorescence confocal microscopy," Optik (Stuttgart) 87, 39-40 (1991).

Carlsson, K.

K. Carlsson, "The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy," J. Microsc. 163, 167-178 (1991).
[CrossRef]

Caspi, A.

A. Caspi, R. Granek, and M. Elbaum, "Diffusion and directed motion in cellular transport," Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Conchello, J.

Conchello, J.-A.

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

Crilly, P.

P. Crilly, "A quantitative evaluation of various iterative deconvolution algorithms," IEEE Trans. Instrum. Meas. 40, 558-562 (1991).
[CrossRef]

Diaspro, A.

Diaz, A.

Dressbach, K.

Elbaum, M.

A. Caspi, R. Granek, and M. Elbaum, "Diffusion and directed motion in cellular transport," Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Errington, R.

N. White, R. Errington, M. Fricker, and J. Wood, "Aberration control in quantitative imaging of botanical specimens by multidimensional fluorescence microscopy," J. Microsc. 181, 99-116 (1996).
[CrossRef]

Escobar, I.

Faisal, M.

Federici, F.

Florin, E.

A. Pralle, E. Florin, E. Stelzer, and J. Hoerber, "Photonic force microscopy: a new tool providing new methods to study membranes at the molecular level," Single Mol. 1, 129-133 (2000).
[CrossRef]

Florin, E. L.

E. L. Florin, A. Pralle, J. K. Horber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Fricker, M.

N. White, R. Errington, M. Fricker, and J. Wood, "Aberration control in quantitative imaging of botanical specimens by multidimensional fluorescence microscopy," J. Microsc. 181, 99-116 (1996).
[CrossRef]

Gibson, S.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Co., 2004).

Granek, R.

A. Caspi, R. Granek, and M. Elbaum, "Diffusion and directed motion in cellular transport," Phys. Rev. E 66, 011916 (2002).
[CrossRef]

Groen, F.

T. Visser, G. Brakenhoff, and F. Groen, "The one point response in fluorescence confocal microscopy," Optik (Stuttgart) 87, 39-40 (1991).

Hain, M.

Hanisch, R.

Harvey, A.

Hell, S.

H. Jacobsen and S. Hell, "Effect of the specimen refractive index on the imaging of a confocal fluorescence microscope employing high aperture oil immersion lenses," Bioimaging 3, 39-47 (1995).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, and E. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

Hiraoka, Y.

D. Agard, Y. Hiraoka, P. Shaw, and J. Sedat, "Fluorescence microscopy in three dimensions," Methods Cell Biol. 30, 353-377 (1989).
[CrossRef] [PubMed]

Hoerber, J.

A. Pralle, E. Florin, E. Stelzer, and J. Hoerber, "Photonic force microscopy: a new tool providing new methods to study membranes at the molecular level," Single Mol. 1, 129-133 (2000).
[CrossRef]

Horber, J. K.

E. L. Florin, A. Pralle, J. K. Horber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Hossack, W.

E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Houston, A.

Jacobsen, H.

H. Jacobsen and S. Hell, "Effect of the specimen refractive index on the imaging of a confocal fluorescence microscope employing high aperture oil immersion lenses," Bioimaging 3, 39-47 (1995).
[CrossRef]

Jansson, P.

P. Jansson, Deconvolution With Applications in Spectroscopy (Academic, 1984).

Juskaitis, R.

M. Booth, M. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Knittel, J.

Lancis, J.

Lang, M.

M. Lang, C. Asbury, J. Shaevitz, and S. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Lanni, F.

Lanterman, A.

Markham, J.

Martínez-Corral, M.

McNally, J.

Mezouari, S.

Mills, J.

Mo, J.

Neil, M.

M. Booth, M. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Neuman, K.

Ojeda-Castafieda, J.

Ojeda-Castaneda, J.

Oud, J.

T. Visser and J. Oud, "Volume measurements in three-dimensional microscopy," Scanning 16, 198-200 (1994).
[CrossRef]

T. Visser, J. Oud, and G. Brakenhoff, "Refractive index and axial distance measurements in 3-d microscopy," Optik (Stuttgart) 90, 17-19 (1992).

Pralle, A.

A. Pralle, E. Florin, E. Stelzer, and J. Hoerber, "Photonic force microscopy: a new tool providing new methods to study membranes at the molecular level," Single Mol. 1, 129-133 (2000).
[CrossRef]

E. L. Florin, A. Pralle, J. K. Horber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Preza, C.

Qian, F.

F. Qian, "Combining optical tweezers and patch clamp for studies of cell membrane electromechanics," Rev. Sci. Instrum. 75, 2937-2942 (2004).
[CrossRef] [PubMed]

Redding, D.

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

Richter, H.

Robello, M.

Rohrbach, A.

Saavedra, G.

Scalettar, B.

B. Scalettar, J. Swedlow, J. Sedat, and D. Agard, "Dispersion, aberration and deconvolution in multi-wavelength fluorescence images," J. Microsc. 182, 50-60 (1996).
[CrossRef] [PubMed]

Sedat, J.

B. Scalettar, J. Swedlow, J. Sedat, and D. Agard, "Dispersion, aberration and deconvolution in multi-wavelength fluorescence images," J. Microsc. 182, 50-60 (1996).
[CrossRef] [PubMed]

D. Agard, Y. Hiraoka, P. Shaw, and J. Sedat, "Fluorescence microscopy in three dimensions," Methods Cell Biol. 30, 353-377 (1989).
[CrossRef] [PubMed]

Shaevitz, J.

M. Lang, C. Asbury, J. Shaevitz, and S. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Shaw, P.

D. Agard, Y. Hiraoka, P. Shaw, and J. Sedat, "Fluorescence microscopy in three dimensions," Methods Cell Biol. 30, 353-377 (1989).
[CrossRef] [PubMed]

Sheppard, C.

C. Sheppard and P. Torok, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

Snyder, D.

Somalingam, S.

Stankovic, S.

Stelzer, E.

A. Pralle, E. Florin, E. Stelzer, and J. Hoerber, "Photonic force microscopy: a new tool providing new methods to study membranes at the molecular level," Single Mol. 1, 129-133 (2000).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, and E. Stelzer, "Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index," J. Microsc. 169, 391-405 (1993).
[CrossRef]

Stelzer, E. H.

E. L. Florin, A. Pralle, J. K. Horber, and E. H. Stelzer, "Photonic force microscope based on optical tweezers and two-photon excitation for biological applications," J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Svoboda, K.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Swedlow, J.

B. Scalettar, J. Swedlow, J. Sedat, and D. Agard, "Dispersion, aberration and deconvolution in multi-wavelength fluorescence images," J. Microsc. 182, 50-60 (1996).
[CrossRef] [PubMed]

Theofanidou, E.

E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Thomas, L.

Thompson, B.

Torok, P.

C. Sheppard and P. Torok, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

Török, P.

Tschudi, T.

Tsujiuchi, J.

J. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).

Varga, P.

Visser, T.

S. Wiersma, P. Török, T. Visser, and P. Varga, "Comparison of different theories for focusing through a plane interface," J. Opt. Soc. Am. A 14, 1482-1490 (1997).
[CrossRef]

T. Visser and J. Oud, "Volume measurements in three-dimensional microscopy," Scanning 16, 198-200 (1994).
[CrossRef]

T. Visser, J. Oud, and G. Brakenhoff, "Refractive index and axial distance measurements in 3-d microscopy," Optik (Stuttgart) 90, 17-19 (1992).

T. Visser, G. Brakenhoff, and F. Groen, "The one point response in fluorescence confocal microscopy," Optik (Stuttgart) 87, 39-40 (1991).

White, N.

N. White, R. Errington, M. Fricker, and J. Wood, "Aberration control in quantitative imaging of botanical specimens by multidimensional fluorescence microscopy," J. Microsc. 181, 99-116 (1996).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the optical-trapping deconvolution microscope. Excitation light from a xenon light source is coupled into the microscope via dichroic mirror D2, which reflects the excitation light but transmits the fluorescence emission wavelengths. The optical-trapping laser is injected via dichroic mirror D1, which reflects the IR laser but transmits visible wavelengths. Lenses L1 and L2 are set up in a one-to-one telescope such that L1 images the back aperture of the objective onto L2. Lens L2 is mounted on a three-axis stage with a motorized control along the optical axis, which allows for 3D steering of the optical trap in the object plane (see Section 3). The trapping light is transmitted through the objective and condenser lenses (O, C) and projected onto a position-sensitive detector imaged in the back-aperture of the condenser by lens L3. The specimen is mounted to a three-axis nanopositioning piezo stage (S).

Fig. 2
Fig. 2

Variation in the PSF with depth. Lateral and axial medial sections of an optically trapped 170 nm bead are shown at four different depths relative to the coverglass. Images are 4.2 μ m × 2.8 μ m . Images have been corrected for the measured focal shift before display. A logarithmic scale (Section 4) was used to enhance visualization of the low-amplitude regions of the image.

Fig. 3
Fig. 3

Lateral and axial line profiles of the PSF at different depths. As the depth of the optically trapped bead is increased from 0 (solid curve) to 3 μ m (dotted curve) the width of the central peak remains constant in a, the lateral dimensions but increases in b, the axial direction. The amplitude of the PSF scales with the axial width such that the total collected intensity at each depth remains constant.

Fig. 4
Fig. 4

Intensity of the PSF decreases with depth. The maximum measured intensity for a measured PSF is normalized by the value at the surface. The depth axis has been corrected for the measured focal shift.

Fig. 5
Fig. 5

Axial, but not lateral, PSF width increases with depth. The FWHM of the axial (solid circles) and lateral (open circles) line profiles of the measured PSFs is displayed. The depth axis has been corrected for the measured focal shift.

Fig. 6
Fig. 6

Deconvolution of a 2 μ m fluorescent sphere. Lateral (top row) and axial (bottom row) medial sections are displayed. Raw data from a, the wide-field fluorescence stack, and reconstructed images using b, the 3D and c, the DV deconvolution algorithms (see Section 6). Lateral sections are 3.8 μ m × 3.8 μ m . Axial sections are 3.8 μ m × 5.3 μ m . All images have been corrected for the measured focal shift before display.

Fig. 7
Fig. 7

Axial line profiles of the reconstructed fluorescent sphere images. The raw data (dotted curve), 3D deconvolution (gray curve) and DV deconvolution (solid black curve) are shown. Line profiles are an average of a 5 × 5   pixel beam extending axially through the center of each bead image.

Equations (3)

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s ( x o ) = z Z s z ( x o ) ,
s z ( x o ) = { s ( x o ) for z o = z 0 otherwise } ,
g ( x i ) = z Z ( x o O h z ( x i x o ) s z ( x o ) ) ,

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