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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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Related in: MedlinePlus

Root-mean-square error (points) in ML point-source depth estimation, using the standard deviation between the ML estimate of z and taking the translation stage position (z) as ground truth. The points thus show the depth-measurement accuracy achieved. The curves show experimental sharpness-calibration measurements in each of the three images (arb. units), (a) data recorded using an Olympus IX71, (b) data recorded using our optical-bench assembled microscope [24]. Particularly in (b) note that the accuracy is generally lower for z-values corresponding to the sharpness peak in any diffraction order and that the accuracy decreases for z-values significantly outside the volume between the extreme in-focus image planes. Objective NA was 1.4 for (a) and 1.3 for (b). The wider sharpness curves in (a) appear to be due to directional ‘beaming’ from the nano-hole source, leading to underfilling the objective. The sample was damaged while trying to make AFM measurements to verify that conclusion.
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RSIF20100508F3: Root-mean-square error (points) in ML point-source depth estimation, using the standard deviation between the ML estimate of z and taking the translation stage position (z) as ground truth. The points thus show the depth-measurement accuracy achieved. The curves show experimental sharpness-calibration measurements in each of the three images (arb. units), (a) data recorded using an Olympus IX71, (b) data recorded using our optical-bench assembled microscope [24]. Particularly in (b) note that the accuracy is generally lower for z-values corresponding to the sharpness peak in any diffraction order and that the accuracy decreases for z-values significantly outside the volume between the extreme in-focus image planes. Objective NA was 1.4 for (a) and 1.3 for (b). The wider sharpness curves in (a) appear to be due to directional ‘beaming’ from the nano-hole source, leading to underfilling the objective. The sample was damaged while trying to make AFM measurements to verify that conclusion.

Mentions: Schematic of the DOE-based three-dimensional imaging attachment. An off-axis Fresnel lens positioned at a distance of one focal length from the secondary principal plane of an imaging system produces three images, each focused on a different specimen plane and all recorded with equal magnification. The in-focus plane separation increases with increasing curvature of the lines in the DOE. Crossing two such gratings delivers nine different in-focus z-planes. Inserts show the DOE structure and images of a nano-hole from three DOE diffraction orders (inverted contrast and saturated to show image structure when the nano-hole is positioned well away from focus, at z = −2.1 µm in figure 3a). The schematic represents a unit-magnification relay system attached to the microscope camera port. The microscope camera would normally be located at the position of the letter B on the left-hand side of the figure. An aperture or slit is located at B to prevent overlap of the images of the different z-planes on the camera, which is now located on the right-hand side.


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)

Root-mean-square error (points) in ML point-source depth estimation, using the standard deviation between the ML estimate of z and taking the translation stage position (z) as ground truth. The points thus show the depth-measurement accuracy achieved. The curves show experimental sharpness-calibration measurements in each of the three images (arb. units), (a) data recorded using an Olympus IX71, (b) data recorded using our optical-bench assembled microscope [24]. Particularly in (b) note that the accuracy is generally lower for z-values corresponding to the sharpness peak in any diffraction order and that the accuracy decreases for z-values significantly outside the volume between the extreme in-focus image planes. Objective NA was 1.4 for (a) and 1.3 for (b). The wider sharpness curves in (a) appear to be due to directional ‘beaming’ from the nano-hole source, leading to underfilling the objective. The sample was damaged while trying to make AFM measurements to verify that conclusion.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSIF20100508F3: Root-mean-square error (points) in ML point-source depth estimation, using the standard deviation between the ML estimate of z and taking the translation stage position (z) as ground truth. The points thus show the depth-measurement accuracy achieved. The curves show experimental sharpness-calibration measurements in each of the three images (arb. units), (a) data recorded using an Olympus IX71, (b) data recorded using our optical-bench assembled microscope [24]. Particularly in (b) note that the accuracy is generally lower for z-values corresponding to the sharpness peak in any diffraction order and that the accuracy decreases for z-values significantly outside the volume between the extreme in-focus image planes. Objective NA was 1.4 for (a) and 1.3 for (b). The wider sharpness curves in (a) appear to be due to directional ‘beaming’ from the nano-hole source, leading to underfilling the objective. The sample was damaged while trying to make AFM measurements to verify that conclusion.
Mentions: Schematic of the DOE-based three-dimensional imaging attachment. An off-axis Fresnel lens positioned at a distance of one focal length from the secondary principal plane of an imaging system produces three images, each focused on a different specimen plane and all recorded with equal magnification. The in-focus plane separation increases with increasing curvature of the lines in the DOE. Crossing two such gratings delivers nine different in-focus z-planes. Inserts show the DOE structure and images of a nano-hole from three DOE diffraction orders (inverted contrast and saturated to show image structure when the nano-hole is positioned well away from focus, at z = −2.1 µm in figure 3a). The schematic represents a unit-magnification relay system attached to the microscope camera port. The microscope camera would normally be located at the position of the letter B on the left-hand side of the figure. An aperture or slit is located at B to prevent overlap of the images of the different z-planes on the camera, which is now located on the right-hand side.

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