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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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Actual position (line) and ML solution spread to the 1σ level (grey area) for a simulated movie of a particle on a smoothed random trajectory. The ‘time’ axis represents 100 simulated frames of data with an average of 768 detected photons per frame distributed between the three in-focus images (approx. 256 per image). A total of 50 movies were simulated and no smoothing has been applied to the solutions, so the grey area represents the scatter on the ML z estimates obtained from single data frames. In real measurements, and in the smoothed trajectory used in the simulation, the particle depth in consecutive frames must be correlated at some level, thus smoothing the time sequence of z estimates could have been used to reduce the spread in solutions. The unsmoothed variance from these movies is shown by the dots in figure 4.
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RSIF20100508F5: Actual position (line) and ML solution spread to the 1σ level (grey area) for a simulated movie of a particle on a smoothed random trajectory. The ‘time’ axis represents 100 simulated frames of data with an average of 768 detected photons per frame distributed between the three in-focus images (approx. 256 per image). A total of 50 movies were simulated and no smoothing has been applied to the solutions, so the grey area represents the scatter on the ML z estimates obtained from single data frames. In real measurements, and in the smoothed trajectory used in the simulation, the particle depth in consecutive frames must be correlated at some level, thus smoothing the time sequence of z estimates could have been used to reduce the spread in solutions. The unsmoothed variance from these movies is shown by the dots in figure 4.

Mentions: 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.


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)

Actual position (line) and ML solution spread to the 1σ level (grey area) for a simulated movie of a particle on a smoothed random trajectory. The ‘time’ axis represents 100 simulated frames of data with an average of 768 detected photons per frame distributed between the three in-focus images (approx. 256 per image). A total of 50 movies were simulated and no smoothing has been applied to the solutions, so the grey area represents the scatter on the ML z estimates obtained from single data frames. In real measurements, and in the smoothed trajectory used in the simulation, the particle depth in consecutive frames must be correlated at some level, thus smoothing the time sequence of z estimates could have been used to reduce the spread in solutions. The unsmoothed variance from these movies is shown by the dots in figure 4.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSIF20100508F5: Actual position (line) and ML solution spread to the 1σ level (grey area) for a simulated movie of a particle on a smoothed random trajectory. The ‘time’ axis represents 100 simulated frames of data with an average of 768 detected photons per frame distributed between the three in-focus images (approx. 256 per image). A total of 50 movies were simulated and no smoothing has been applied to the solutions, so the grey area represents the scatter on the ML z estimates obtained from single data frames. In real measurements, and in the smoothed trajectory used in the simulation, the particle depth in consecutive frames must be correlated at some level, thus smoothing the time sequence of z estimates could have been used to reduce the spread in solutions. The unsmoothed variance from these movies is shown by the dots in figure 4.
Mentions: 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.

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