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Extending single-molecule microscopy using optical Fourier processing.

Backer AS, Moerner WE - J Phys Chem B (2014)

Bottom Line: A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope.Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane.Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computational and Mathematical Engineering and ‡Department of Chemistry, Stanford University , Stanford, California 94305, United States.

ABSTRACT
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

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Dual-polarization/4foptical processing system. Adapted from ref (69) with permission. (a) Schematicdiagram of experimental setup. EP and ES denote P- and S-polarized electric fields withrespect to the beamsplitter, which subsequently are separated into ET and ER, the fields presentin the transmitted and reflected polarization channels, respectively.(b) Plot of the phase function defining the quadrated pupil. Axisalong which incident light is polarized is also sketched. (c) Geometryof our setup ensures that both the R and T channels are polarizedalong a single axis, so that the SLM can properly modulate all lightemitted by the specimen.
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fig5: Dual-polarization/4foptical processing system. Adapted from ref (69) with permission. (a) Schematicdiagram of experimental setup. EP and ES denote P- and S-polarized electric fields withrespect to the beamsplitter, which subsequently are separated into ET and ER, the fields presentin the transmitted and reflected polarization channels, respectively.(b) Plot of the phase function defining the quadrated pupil. Axisalong which incident light is polarized is also sketched. (c) Geometryof our setup ensures that both the R and T channels are polarizedalong a single axis, so that the SLM can properly modulate all lightemitted by the specimen.

Mentions: Figure 5 depicts our experimental apparatus.Using a polarizing beamsplitter, fluorescence exiting the microscopeis separated into a reflected (R) and transmitted (T) channel, respectivelycontaining S- and P-polarized light, as defined relative to the surfaceof the beamsplitter. Using the 4f optical processing configuration,the electric fields associated with the two polarization channelsare Fourier transformed and projected onto an SLM using a pyramidalmirror (Figure 5a,c). The geometrical arrangementof our setup ensures that both the T and R channels will be polarizedalong the x-axis, defined relative to the SLM surface.This configuration is desirable because our liquid crystal SLM iscapable of modulating only one polarization of incident light. Afterthe SLM imparts a phase function ψ(x,y), another set of lenses performs a second Fourier transformand images the T and R emission channels onto separate regions ofan electron multiplication charge coupled device (EMCCD) detector.The SLM is programmed with a pyramidal phase function (Figure 5b) consisting of four linear phase ramps:27The constant C0 is setby the dynamic range of the SLM (∼6π), and C = C0/ρmax, where ρmax is the radius of the region in whichintensity may be nonzero, as enforced by the numerical aperture, magnification,and the focal lengths of the lenses used in the 4f system. Intuitively,the function of this phase mask is as follows: Light falling intoa given quadrant of the phase mask will be shunted into one of fourseparate points at the image plane. Because each polarization channelis independently phase modulated and imaged on a separate region ofthe EMCCD, fluorescence from a single molecule will appear as a totalof eight separate “spots” on the detector. Because thedistribution of intensity at the back focal plane will depend upona given molecule’s orientation, the intensity distributionamong each of the eight spots on the image sensor will also vary.(When isotropic emitters, such as fluorescent beads, are imaged, eachof the image points will contain equal intensity.)


Extending single-molecule microscopy using optical Fourier processing.

Backer AS, Moerner WE - J Phys Chem B (2014)

Dual-polarization/4foptical processing system. Adapted from ref (69) with permission. (a) Schematicdiagram of experimental setup. EP and ES denote P- and S-polarized electric fields withrespect to the beamsplitter, which subsequently are separated into ET and ER, the fields presentin the transmitted and reflected polarization channels, respectively.(b) Plot of the phase function defining the quadrated pupil. Axisalong which incident light is polarized is also sketched. (c) Geometryof our setup ensures that both the R and T channels are polarizedalong a single axis, so that the SLM can properly modulate all lightemitted by the specimen.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4317050&req=5

fig5: Dual-polarization/4foptical processing system. Adapted from ref (69) with permission. (a) Schematicdiagram of experimental setup. EP and ES denote P- and S-polarized electric fields withrespect to the beamsplitter, which subsequently are separated into ET and ER, the fields presentin the transmitted and reflected polarization channels, respectively.(b) Plot of the phase function defining the quadrated pupil. Axisalong which incident light is polarized is also sketched. (c) Geometryof our setup ensures that both the R and T channels are polarizedalong a single axis, so that the SLM can properly modulate all lightemitted by the specimen.
Mentions: Figure 5 depicts our experimental apparatus.Using a polarizing beamsplitter, fluorescence exiting the microscopeis separated into a reflected (R) and transmitted (T) channel, respectivelycontaining S- and P-polarized light, as defined relative to the surfaceof the beamsplitter. Using the 4f optical processing configuration,the electric fields associated with the two polarization channelsare Fourier transformed and projected onto an SLM using a pyramidalmirror (Figure 5a,c). The geometrical arrangementof our setup ensures that both the T and R channels will be polarizedalong the x-axis, defined relative to the SLM surface.This configuration is desirable because our liquid crystal SLM iscapable of modulating only one polarization of incident light. Afterthe SLM imparts a phase function ψ(x,y), another set of lenses performs a second Fourier transformand images the T and R emission channels onto separate regions ofan electron multiplication charge coupled device (EMCCD) detector.The SLM is programmed with a pyramidal phase function (Figure 5b) consisting of four linear phase ramps:27The constant C0 is setby the dynamic range of the SLM (∼6π), and C = C0/ρmax, where ρmax is the radius of the region in whichintensity may be nonzero, as enforced by the numerical aperture, magnification,and the focal lengths of the lenses used in the 4f system. Intuitively,the function of this phase mask is as follows: Light falling intoa given quadrant of the phase mask will be shunted into one of fourseparate points at the image plane. Because each polarization channelis independently phase modulated and imaged on a separate region ofthe EMCCD, fluorescence from a single molecule will appear as a totalof eight separate “spots” on the detector. Because thedistribution of intensity at the back focal plane will depend upona given molecule’s orientation, the intensity distributionamong each of the eight spots on the image sensor will also vary.(When isotropic emitters, such as fluorescent beads, are imaged, eachof the image points will contain equal intensity.)

Bottom Line: A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope.Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane.Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computational and Mathematical Engineering and ‡Department of Chemistry, Stanford University , Stanford, California 94305, United States.

ABSTRACT
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

Show MeSH
Related in: MedlinePlus