Limits...
Nanometric depth resolution from multi-focal images in microscopy.

Dalgarno HI, Dalgarno PA, Dada AC, Towers CE, Gibson GJ, Parton RM, Davis I, Warburton RJ, Greenaway AH - J R Soc Interface (2011)

Bottom Line: To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound.The approximations used in the analytical treatment are tested using numerical simulations.Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

View Article: PubMed Central - PubMed

Affiliation: Physics, SUPA/IIS, School of Engineering and Physical Sciences, Heriot-Watt University, , Edinburgh EH14 4AS, UK.

ABSTRACT
We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

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The line shows the MVB for sharpness ranging on a point source emitting an average of 768 detected photons distributed between the DOE diffraction orders and evaluated using equation (5.4) with α = 2. The axis labels in micrometres are correct for an objective of NA = 1.26 and wavelength 500 nm. The spacing of the in-focus planes is 0.6 µm and the Lorentzian half-width a = 0.334 µm. The MVB suggests that for the specimen volume between the outermost in-focus planes a measurement uncertainty of approximately 14 nm is obtainable with this level of detected flux. The local peaks in measurement uncertainty correspond accurately with the positions of the in-focus planes. The accuracy will scale inversely with the square of the numerical aperture, so the flux requirements will fall by about 20% for NA = 1.4. The crosses and dots represent r.m.s. errors (as in figure 3) for results from numerical simulations; the dots are taken from the movie data shown in figure 5.
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RSIF20100508F4: The line shows the MVB for sharpness ranging on a point source emitting an average of 768 detected photons distributed between the DOE diffraction orders and evaluated using equation (5.4) with α = 2. The axis labels in micrometres are correct for an objective of NA = 1.26 and wavelength 500 nm. The spacing of the in-focus planes is 0.6 µm and the Lorentzian half-width a = 0.334 µm. The MVB suggests that for the specimen volume between the outermost in-focus planes a measurement uncertainty of approximately 14 nm is obtainable with this level of detected flux. The local peaks in measurement uncertainty correspond accurately with the positions of the in-focus planes. The accuracy will scale inversely with the square of the numerical aperture, so the flux requirements will fall by about 20% for NA = 1.4. The crosses and dots represent r.m.s. errors (as in figure 3) for results from numerical simulations; the dots are taken from the movie data shown in figure 5.

Mentions: Using more than one in-focus plane resolves the singularity and provides a unique estimation of the depth of the source. Figure 4 shows the MVB estimated from equation (5.4) for three in-focus image planes (M = 3), α = 2 and mean flux of 768 photons (approx. 256 in each image). Note that the curve in figure 4 shows qualitative agreement with the high-flux experimental results in figure 3, in particular the variance minima correspond with the cross-over points in the sharpness curves and the local variance maxima correspond to the positions of the in-focus image planes.Figure 4.


Nanometric depth resolution from multi-focal images in microscopy.

Dalgarno HI, Dalgarno PA, Dada AC, Towers CE, Gibson GJ, Parton RM, Davis I, Warburton RJ, Greenaway AH - J R Soc Interface (2011)

The line shows the MVB for sharpness ranging on a point source emitting an average of 768 detected photons distributed between the DOE diffraction orders and evaluated using equation (5.4) with α = 2. The axis labels in micrometres are correct for an objective of NA = 1.26 and wavelength 500 nm. The spacing of the in-focus planes is 0.6 µm and the Lorentzian half-width a = 0.334 µm. The MVB suggests that for the specimen volume between the outermost in-focus planes a measurement uncertainty of approximately 14 nm is obtainable with this level of detected flux. The local peaks in measurement uncertainty correspond accurately with the positions of the in-focus planes. The accuracy will scale inversely with the square of the numerical aperture, so the flux requirements will fall by about 20% for NA = 1.4. The crosses and dots represent r.m.s. errors (as in figure 3) for results from numerical simulations; the dots are taken from the movie data shown in figure 5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3104330&req=5

RSIF20100508F4: The line shows the MVB for sharpness ranging on a point source emitting an average of 768 detected photons distributed between the DOE diffraction orders and evaluated using equation (5.4) with α = 2. The axis labels in micrometres are correct for an objective of NA = 1.26 and wavelength 500 nm. The spacing of the in-focus planes is 0.6 µm and the Lorentzian half-width a = 0.334 µm. The MVB suggests that for the specimen volume between the outermost in-focus planes a measurement uncertainty of approximately 14 nm is obtainable with this level of detected flux. The local peaks in measurement uncertainty correspond accurately with the positions of the in-focus planes. The accuracy will scale inversely with the square of the numerical aperture, so the flux requirements will fall by about 20% for NA = 1.4. The crosses and dots represent r.m.s. errors (as in figure 3) for results from numerical simulations; the dots are taken from the movie data shown in figure 5.
Mentions: Using more than one in-focus plane resolves the singularity and provides a unique estimation of the depth of the source. Figure 4 shows the MVB estimated from equation (5.4) for three in-focus image planes (M = 3), α = 2 and mean flux of 768 photons (approx. 256 in each image). Note that the curve in figure 4 shows qualitative agreement with the high-flux experimental results in figure 3, in particular the variance minima correspond with the cross-over points in the sharpness curves and the local variance maxima correspond to the positions of the in-focus image planes.Figure 4.

Bottom Line: To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound.The approximations used in the analytical treatment are tested using numerical simulations.Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

View Article: PubMed Central - PubMed

Affiliation: Physics, SUPA/IIS, School of Engineering and Physical Sciences, Heriot-Watt University, , Edinburgh EH14 4AS, UK.

ABSTRACT
We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

Show MeSH
Related in: MedlinePlus