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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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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.
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RSIF20100508F2: 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.

Mentions: For three-dimensional tracking tests, we used a nano-hole, illuminated from above with a laser, to represent a single unresolved and self-luminous ‘particle’. This particle, imaged through the microscope plus the DOE system described above, yields three images, each corresponding to a PSF that would have been recorded in a z-stack sequence and with about one-third of the detected flux in each image. If the total measurement time is equal to that required for the equivalent three-image z-stack, the flux in each of the three images is equal whether the DOE system or a z-stack is used. This system is illustrated schematically in figure 2, together with example out-of-focus particle images from a simultaneous three-image snapshot. The snapshot was recorded using a 100 × 1.4NA oil-immersion objective lens (UPLSAPO100XO/1.4), with an off-axis Fresnel lens of focal length 0.94 m in a unit magnification optical relay from the microscope focus to the CCD camera employing an achromatic compound lens of focal length 76.2 mm. The source is a nominally 210 nm diameter hole in an NiCr/Al/NiCr film approximately 90 nm thick, illuminated by a laser at 532 nm wavelength and mounted on a precision Mad City Labs (NanoView PDQ375/M) translation stage that provides z-displacement of the source under computer control (Micromanager) with sub-nanometre level accuracy and repeatability.Figure 2.


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)

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.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSIF20100508F2: 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.
Mentions: For three-dimensional tracking tests, we used a nano-hole, illuminated from above with a laser, to represent a single unresolved and self-luminous ‘particle’. This particle, imaged through the microscope plus the DOE system described above, yields three images, each corresponding to a PSF that would have been recorded in a z-stack sequence and with about one-third of the detected flux in each image. If the total measurement time is equal to that required for the equivalent three-image z-stack, the flux in each of the three images is equal whether the DOE system or a z-stack is used. This system is illustrated schematically in figure 2, together with example out-of-focus particle images from a simultaneous three-image snapshot. The snapshot was recorded using a 100 × 1.4NA oil-immersion objective lens (UPLSAPO100XO/1.4), with an off-axis Fresnel lens of focal length 0.94 m in a unit magnification optical relay from the microscope focus to the CCD camera employing an achromatic compound lens of focal length 76.2 mm. The source is a nominally 210 nm diameter hole in an NiCr/Al/NiCr film approximately 90 nm thick, illuminated by a laser at 532 nm wavelength and mounted on a precision Mad City Labs (NanoView PDQ375/M) translation stage that provides z-displacement of the source under computer control (Micromanager) with sub-nanometre level accuracy and repeatability.Figure 2.

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