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Quantitative scheme for full-field polarization rotating fluorescence microscopy using a liquid crystal variable retarder
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Image of FIG. 1.

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FIG. 1.

Experimental schematic of the polarization rotator. S and F denote the slow axis and fast axis of the quarter-wave plate, respectively. Fluorescent lipid analogs, DiI-PC and Bodipy-PC, are shown schematically inserted into a lipid vesicle situated in the focus of the polarization rotation microscope. DiI-PC is assumed to be oriented tangentially to the membrane surface whereas Bodipy-PC is represented perpendicular to the surface. The arrows indicate the directions of the absorption dipoles. DM represents a dichroic mirror.

Image of FIG. 2.

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FIG. 2.

Calibration data of polarization angle vs. applied peak-to-peak voltage to the LCVR. (a) A calibration map of peak-to-peak voltage vs. polarizer angle was used to determine the linear polarization output of the polarization rotator as a function of the applied voltage. This calibration map can be used to calculate the Stokes parameters for the incident light. (b) Four cross sections of intensity vs. voltage for four analyzing polarizer angles from A.

Image of FIG. 3.

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FIG. 3.

Plots showing the collected fluorescence intensity for two different locations on the CA46 cell membrane labeled with DiI-PC. The polarization state of the excitation light was rotated between 0° and 180° in a 5° increment. The emitted fluorescence signal agrees well with a cosine squared fit shown as a red line. The offset of the cosine square function should theoretically agree with the average dipolar orientation. If the fit and the data points are closely examined, there are systematic deviations from the ideal cosine squared behavior. These deviations most likely arise from residual ellipticity in the polarization state of the light, and are a justification for the need of a calibration procedure to provide quantitative results. (a) The fluorescence intensity (units normalized by the background reference signal) of the location between the dipoles identified as 6 and 7 of the DiI labeled CA46 cell in Fig. 6(b). (b) The fluorescence intensity (arbitrary units) of the location marked by dipole number 1 of the DiI labeled CA46 cell in Fig. 6(b).

Image of FIG. 4.

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FIG. 4.

DiI molecules, which lie tangential to the membrane surface, are excited optimally when the polarization angle (indicated by the arrows) is aligned with the absorption dipoles of the DiI dyes. The panels in the left column ((a), (c), (e), and (g)) represent a simulation of DiI molecules oriented tangentially to the membrane of a circular liposome. The emission of fluorescence is proportional to the angle between the polarization of the incident light and the orientation of the DiI absorption dipole. The panels in the right column ((b), (d), (f), and (h)) represent the detected fluorescence from a typical single CA46 cell labeled with DiI-PC. There is a general agreement with the simulated data. However, the DiI dye distribution is non-uniform in the CA46 cell, affecting the fluorescence distribution. The polarizations in the CA46 images represent the polarized beams shown in Fig. 2(b). As such they need to be corrected for incident elliptical polarized light by using the Stokes parameters for the light characterized at those analyzer angles.

Image of FIG. 5.

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FIG. 5.

Mueller matrix parameter images of a simulated liposome and a real CA46 cell labeled with DiI-PC molecules. The left column represents the simulated DiI-PC labeled liposome from Fig. 4 using the simple calculations possible with perfect linear polarized light. The right column represents the algebraically reconstructed Mueller matrix parameters. (a) The F11 intensity image calculated from either Fig. 4(a) plus Fig. 4(e) or Fig. 4(c) plus Fig. 4(g). (b) The F11 image for the CA46 cell calculated with the algebraic reconstruction. (c) The F12 image for the simulated liposome showing the difference in response to 0° and 90° polarized light. (d) The F12 image for the CA46 cell showing the difference in response to 0° and 90° pure polarized light. (e) The F13 image for the simulated liposome showing the difference in response to 45° and −45° polarized light. (f) The F13 image for the CA46 cell showing the difference in response to 45° and −45° pure polarized light.

Image of FIG. 6.

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FIG. 6.

(a) The DOLE image for the simulated circular liposome with tangentially aligned DiI molecules. The double arrows represent the DiI dipole orientation and the angles where taken from panel (c). (b) The experimentally measured DOLE image for the CA46 cell. The cell membrane shows DOLE contrast whereas the internal cellular structures show no change with linear polarization and have zero DOLE signal. Dipoles represented as double arrows are plotted along the cell membrane and the orientations were taken from panel (d). (c) The angular orientation image for the simulated liposome image. The corresponding areas where the DOLE signal is zero due to ensemble averaged fluorescence emission from multiple dyes with randomized orientations. (d) The angular orientation image for the CA46 cell. The net orientation angles can be taken from the regions where the DOLE is non-zero.


Generic image for table

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Table I.

The dumbbells represent the 2D orientations of single dye molecules with the rotation angle denoted at the right of the table. The 0, 45, 90 and −45° polarization signals represent incident light polarized at those angles. The relative polarized intensity (normalized to a maximum value of 1) collected from the fluorescent molecule depends on the angle between the molecule and the polarized light as cos 2(δ − θ) where δ represents the polarization angle of light and θ represents the 2D molecular orientation. The Mueller matrix components for the excitation of fluorescence with linear polarized light, the DOLE, and the rotation angle are found by combining the detected fluorescent intensities of the rotated molecules with different polarizations algebraically. If multiple molecules are present in a region or if the molecule rotates during the collection time, the time integrated signal can be used to measure the linear polarization response of the sample as is shown schematically with the samples with two dumbbells.


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We present a quantitative scheme for full-field polarization rotating fluorescence microscopy. A quarter-wave plate, in combination with a liquid crystal variable retarder, provides a tunable method to rotate polarization states of light prior to its being coupled into a fluorescence microscope. A calibration of the polarizationproperties of the incident light is performed in order to correct for elliptical polarization states. This calibration allows the response of the sample to linear polarization states of light to be recovered. Three known polarization states of light can be used to determine the average fluorescent dipole orientations in the presence of a spatially varying dc offset or background polarization-invariant fluorescence signal. To demonstrate the capabilities of this device, we measured a series of full-field fluorescencepolarizationimages from fluorescent analogs incorporated in the lipidmembrane of Burkitts lymphoma CA46 cells. The fluorescent lipid-like analogs used in this study are molecules that are labeled by either a DiI (1,1-Dioctadecyl 3,3,3,3-Tetramethylindocarbocyanine) fluorophore in its head group or a Bodipy (4,4-difluoro-4-bora-3a,4a-diaza-s-indacene) molecule in its acyl chain. A spatially varying contrast in the normalized amplitude was observed on the cell surface, where the orientation of the DiI molecules is tangential to the cell membrane. The internally labeled cellular structures showed zero response to changes in linear polarization, and the net linear polarization amplitude for these regions was zero. This instrument provides a low cost calibrated method that may be coupled to existing fluorescence microscopes to perform investigations of cellular processes that involve a change in molecular orientations.


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Scitation: Quantitative scheme for full-field polarization rotating fluorescence microscopy using a liquid crystal variable retarder