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Kusumi Membrane Organizer Project, Exploratory Research for Advanced Technology Organization (ERATO/SORST), Japan Science and Technology Agency, Department of Biological Science, and The Institute for Advanced Research, Nagoya University, Nagoya, 464-8602, Japan
Correspondence: Address reprint requests to Dr. Akihiro Kusumi, Dept. of Biological Science, Nagoya University Chikusa-ku, Nagoya 464-8602, Japan. Tel.: 011-81-52-789-2969; Fax: 011-81-52-789-2968; E-mail: akusumi{at}bio.nagoya-u.ac.jp.
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ABSTRACT |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIX: DETAILS OF THE...SUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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; Iino et al., 2001; Schütz et al., 2000; Sheetz et al., 1989; Tardin et al., 2003). They have given researchers the ability to directly observe the motion and localization of individual single molecules in live cells. In particular, for signal transduction studies, they facilitate observations of the diffusion of individual receptor molecules in the plasma membrane (Lommerse et al., 2004; Sako et al., 2000; Suzuki et al., 2004, 2003) as well as the recruitment of each individual cytoplasmic signaling molecule to the plasma membrane (Lommerse et al., 2004; Mashanov et al., 2004; Murakoshi et al., 2004). However, for the single-molecule techniques to be truly useful for studies of the molecular processes in living cells, particularly the signal transfer processes in the plasma membrane, these technologies must be developed to allow direct observations of two molecules that are undergoing (transient) binding to each other and/or colocalization/correlated motion in the plasma membrane of living cells, because such interactions are the essence of many molecular functions.
Signal transduction in the plasma membrane often proceeds through the correlated actions of many signaling molecules. Classically, the interaction/binding of two molecular species was implied by the colocalization of the two molecular species, as observed through bulk, multicolor fluorescence microscopy (or by biochemical and molecular biological techniques, such as immuno-coprecipitation, pull-down assays, and two-hybrid results). However, conventional fluorescence microscopy can only visualize the assembly of two molecular species when many molecules of each species are recruited, whereas most signaling events involve only one or two molecules of a single species. Furthermore, even when many molecules of a single species may be involved, if the residency time of each recruited molecule is short, which may be common in many signaling pathways, then the detectability of molecular interactions will fall rapidly. Therefore, advanced technologies that allow us to observe dynamic processes, like the transient assembly of only a few signaling molecules, are required. With this goal in mind, we have developed a method to directly and simultaneously image two individual signaling molecules (each labeled with a different color) in living cells through simultaneous, dual-color, single-molecule fluorescence microscopy. In fact, such single-molecule methods, including the single-molecule fluorescence resonance energy transfer (FRET) technique recently developed by Murakoshi et al. (2004), might be the only ways to directly visualize the signal transfer process, by examining the recruitment of upstream and downstream molecules, and the possible involvement of scaffolding proteins in that process.
Instrumentally, in our laboratory, the specimen was illuminated with two individual laser beams, using objective-lens-type total internal reflection fluorescence (TIRF), and the emission signals from the sample were chromatically separated by a dichroic mirror and filtered into two detection arms terminating in high-sensitivity cameras. However, the real issue here is that, to study live cells at the molecular level, tracking colocalization and/or correlated motion requires extremely high levels of spatial precision in the superposition of the two split images obtained at video rate or faster, and until this is done, the usefulness of single molecule technologies may be limited.
Colocalization at the level of single or small groups of molecules has been explored by several other groups. Kinosita et al. (1991) proposed the capture of two images shifted laterally depending either on their polarization or emission wavelength onto a single camera, before the single-molecule era. This technique was applied to imaging the orientation along actin filaments (using polarization) and calcium influxes into a cell (using fluorescence). No description was given regarding the accuracy of the method. For the practical purpose of performing single-molecule, two-color, simultaneous observations, it is much easier to have two separate gain controls over each of two cameras, rather than trying to use a single camera. Trabesinger et al. (2001) evaluated the statistical coincidental overlap events in vitro, thus putting the determination of the probability of overlap from a single image on firm statistical grounds, but did not propose a method for correcting for inherent aberrations in the dual-color imaging technique. Schütz et al. (1998) proposed a method to take two-color images on a single camera by rapidly alternating two excitation laser light sources (every 5 ms), and thus eliminated most of the distortions, except for chromatic aberrations, to obtain 40-nm accuracy for two colocalized single molecules in two colors. Morrison et al. (2003) and Karakikes et al. (2003) developed a spatial correction method for images of fixed cells taken sequentially on a single camera. Their spatial correction technique relies on determining the optical center of the image and calculating the radial shift of the images from that center through a single parameter, but the accuracy was limited to 
300 nm. Lacoste et al. (2000) achieved an impressive 10-nm accuracy using bright fluorescent particles or quantum dots that can be excited with a single laser light and emit at separable wavelengths and through scanning the sample across a focused excitation laser. Though high in accuracy, this technique requires long times for image acquisition and, as described, is not applicable to imaging the motion of molecules in living cells.
In this research, we used a microscope with two detection arms equipped with high-sensitivity cameras working synchronously (at video rate or faster), to detect fluorescence signals chromatically separated by a dichroic mirror and filter sets. To achieve high precision in the colocalization of the two differently colored molecules in the two split images, the large systematic errors due to optical aberrations (like chromatic aberrations of the objective lens, and chromatic and other aberrations of the optics in the separate imaging paths) and camera-based effects must be corrected. We developed a method for spatially correcting the full video frame (covering all of the pixels in each frame) obtained on each arm, by first imaging a precise array of optical holes spanning the entire image in both observation paths (with optics used for the GFP-Alexa633 pair) using "white-light" bright-field transmission microscopy, and then performing a third-order spline fit across these arrays. Once the correction look-up table is made, the correction transformation is fast (12 s for 100 frames of 640 x 480 pixels or 
1/4 of the video rate, using a 2.8-GHz Intel-PC machine) and was usually used to correct the entire sequence of the full frame images. A practical method to detect the colocalization of single molecules is proposed, based on the accuracies in the overlay and the determination of each molecule's position. This method is also applicable to single-molecule FRET imaging data (Murakoshi et al., 2004) and to split images projected on a single camera (Kinosita et al., 1991).
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METHODS |
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) was modified. Fig. 1 shows a schematic diagram of the TIRF microscope we built to perform dual-color imaging at the level of single molecules. As the base, we used an Olympus IX-70 microscope with a modified mirror turret to allow the side entry of the excitation laser beams into the microscope. Excitation was performed through two laser beams steered into the microscope by a dual-color dichroic mirror (Chroma Technology, Rockingham, VT), to focus the beams at the back focal plane of the objective. We used an Olympus PlanApo 100x oil immersion objective with a numerical aperture of 1.4. For total internal reflection illumination, the incident laser beams were placed off the optical axis (but parallel to it) so that they would pass near the edge of the objective lens. Emission from the fluorophore was collected by the objective, past the dual-color excitation path dichroic, and was split into the two imaging systems by an observation path dichroic mirror. The image in each arm was projected on the photocathode of an image intensifier with a two-stage microchannel plate (C8600-03; Hamamatsu Photonics, Hamamatsu, Japan), which was lens-coupled to the camera. The cameras used were Hamamatsu electron bombardment charge-coupled device (EBCCD; C7190-23) or silicon intensified target (C2400-08) cameras. The cameras on the two detecting arms (side and bottom; two cameras of the same model number produced in the same batch were placed on each arm) were synchronized frame by frame by coupling the sync out of one camera to the trigger of the second (gen-locked). The camera images were stored on a digital video tape (PDV-184ME; Sony, Tokyo, Japan) for postexperiment spatial synchronization.
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Fluorescence intensity measurement
Alexa Fluor 633 carboxylic acid succinimidyl ester (Molecular Probes, Eugene, OR) conjugated to anti-CD59 Fab fragments (Alexa633-Fab; dye/protein = 0.3 by mol), and EGFP produced in Escherichia coli (BD Biosciences Clontech, Palo Alto, CA) were adsorbed on coverslips and covered with a layer of polyacrylamide gel (15%). They were simultaneously imaged at the level of single molecules by the two EBCCD cameras. Fluorescence images were digitized frame by frame, and the fluorescence signal intensities of 620 x 620 nm areas (8-bit images in 12 x 12 pixels) containing a single spot and the background intensities of the adjacent 620 x 620 nm areas were measured (Iino et al., 2001).
Analysis of the movement of single fluorescent molecules
The positions of these Alexa633-Fab and EGFP fluorescent spots fixed on coverslips were obtained and analyzed by a published method (Gelles et al., 1988; Kusumi et al., 1993; Sako et al., 1998). The positions (x- and y-coordinates) of each fluorescent spot were determined by software developed in our lab, based on the method of Gelles et al. (1988). The precision of the position determination for a single Alexa633-Fab or EGFP molecule was estimated using immobile Alexa633-Fab and EGFP molecules attached to the coverslip covered with 15% polyacrylamide gel.
Preparation of a standard sample for the determination of precision in two-color fluorescence imaging of single molecules in the cell
E-cadherin, a transmembrane protein responsible for the calcium-dependent cell-cell adhesion of epithelial tissues, was doubly labeled with GFP at its C-terminal cytoplasmic domain (Ecad-GFP) and with the Fab fragment of the anti-E-cadherin rat monoclonal antibody ECCD2 (Shirayoshi et al., 1986) conjugated with Alexa633 (Alexa-
Ecad-Fab). This doubly labeled protein was observed as a standard sample for simultaneous, two-color, observations of single molecules. L cells, which do not express endogenous E-cadherin, were transfected with the cDNA for Ecad-GFP, and those stably expressing Ecad-GFP were cloned and maintained in Dulbecco's modified Eagle's medium with 10% fetal bovine serum (Iino et al., 2001). These cells were plated on 12 mm-
coverslip-based dishes (Iwaki, Japan) and used two days later. The anti-E-cadherin antibody was digested with papain, and the anti-E-cadherin Fab fragments were purified by protein G column chromatography (Amersham, Buckinghamshire, UK) (Derrick and Wigley, 1994; Perosa et al., 1997). The anti-E-cadherin Fab fragments were conjugated with Alexa633, at an Alexa633/Fab molar ratio of 0.7 (Alexa-Ecad-Fab). For the observation of fixed cells, the Ecad-GFP molecules expressed on the cell surface were labeled with the Alexa-Ecad-Fab by incubating the cells with 5.4 nM Alexa-Ecad-Fab for 15 min at room temperature. The cells were then fixed with 4% paraformaldehyde in Hanks' medium buffered with 2 mM PIPES (pH 7.4, called Hanks' buffer) for 1.5 h at room temperature. For live cell observations, L cells stably expressing Ecad-GFP molecules on the cell surface were incubated with 20 nM Alexa-Ecad-Fab for 2 min at 37°C and the microscope observation was carried out without washing away the unbound probe molecules. The Ecad-GFP molecule on the cell surface bound by an Alexa-Ecad-Fab molecule provides a convenient colocalization marker for testing our protocol for detecting colocalized molecules.
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RESULTS AND DISCUSSION |
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The SIT camera has some level of retained image lag, so we often use an EBCCD camera for single fluorescent molecule observations. EBCCD cameras (or CCD cameras in general) have much less distortion as compared to SIT cameras, and the deviation of the displacement between two images of the same optically transparent hole without spatial correction was 66 and 42 nm (0.66 and 0.42 pixels) in the x- and y-directions, respectively, with EBCCD cameras (Fig. 4 C, left; each pixel corresponding to 100 nm on the sample plane). CCD cameras are often used for scientific measurements, and when they are used, the spatial distortion by the camera is often neglected. However, these results indicated the possibility that the measurements could include an error of over a half-pixel (standard deviation) and possibly over a pixel in a particular region of the camera (see the distribution in Fig. 4 C, left), if the distortions were not corrected. After spatial correction, the accuracies were improved to 25 and 20 nm for 100 nm/pixel (0.25 and 0.2 pixels; Fig. 4 C, right) or 13 and 10 nm for 50 nm/pixel (0.26 and 0.2 pixels; Fig. 4 D) in the x- and y-directions, respectively. Because our normal two-color colocalization experiments of single molecules are carried out with the pixel size of 50 nm, a superposition accuracy of 13 nm is probably generally achieved. These results indicate that the image superposition protocol developed here works well even for cameras with large distortions, like SIT tube cameras, and after the correction, the same levels of superposition accuracies can be achieved by the method described here.
Precision in position determination of single fluorescent molecules
The precision in the position determination of single fluorescent molecules in each image was evaluated under the conditions of simultaneous observations of two different fluorophores. For this purpose, Alexa633 conjugated to anti-CD59 Fab fragments (Alexa-Fab) and the recombinant GFP, produced in E. coli and purified, were attached to coverslips, which were and then covered with 15% polyacrylamide gel (thus immobilizing the molecules).
Typical images of these immobilized molecules (no averaging taken here) are shown in Fig. 5 A. The fluorescent spots are numbered in the order of integrated fluorescence intensity in each image, which will be related to the histograms in Fig. 5 C. Fig. 5 B shows typical single-molecule Alexa633 and GFP fluorescence intensities and the background intensities adjacent to the single-molecule spots, plotted as a function of time (video frames), showing the time-dependent fluctuations of the single-molecule fluorescence and the background signals. In Fig. 5 C, the distributions of the fluorescence intensities of the individual spots after background subtraction for each spot and the distributions of their background intensities (after subtracting the mean value) are shown for Alexa633 and GFP, respectively. (The fluorescence intensities of all of the observed spots in four independent images, like those shown in Fig. 5 A, were measured and plotted. In Fig. 5 A, only one quadrant of an image is shown.) The signal/noise (S/N) ratio for the single molecule fluorescent spot is given as
 | (1) |
is the signal intensity, 
is the background signal intensity, and 
and 
are their respective standard deviations (Cheezum et al., 2001). Based on Eq. 1, we found signal/noise ratios of 2.7 and 2.6 for Alexa633 and GFP, respectively, in our instrument set up for simultaneous observations of Alexa633 and GFP (Table 1). Because Eq. 1 is true only when the noise components for the signal and the background are independent, and because, some noise, like that due to fluctuations of the laser power and the camera gain, may actually be spatially and temporally correlated, the true S/N ratio may be slightly better.
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Definition of colocalization for two chromatically separated images of single molecules of two different species
In this section, we develop a working definition of colocalization for the visualization of single GFP and Alexa633 molecules. We consider the accuracy of locating each fluorophore in their respective images (Alexa633, 29 and 28 nm; GFP, 34 and 32 nm; for 50 nm/pixel images by EBCCD cameras) and the accuracy of overlaying these images (13 and 10 nm for 50 nm/pixel images by EBCCD cameras) (in the horizontal and vertical directions, respectively). We combine these three distributions to determine the overall standard deviations, 
, between the two fluorophores in the overlapped images, obtaining 
in the horizontal direction and 
in the vertical direction.
These results indicate that even after the spatial correction between the side and bottom ports, the Alexa633 and GFP colocalized at the molecular level may appear to be 47 and 44 nm (one standard deviation, 68% of the total distribution) apart for the x- and y-directions, respectively. For simplicity, we will use 45 nm as the standard deviation of the "displacement" for each direction and 64 nm as that of the "distance" between the two spots. Note that if fluorophores with higher signal levels, such as fluorescent beads and semiconductor nanocrystal quantum dots, could be employed, the colocalization accuracy would improve greatly.
To ascertain 90% probability that two colocalized molecules are in fact judged as colocalized, the definition of colocalization has to be loosened so that two molecules may be designated as being colocalized when they are within 1.65, i.e., within 74 nm in displacements in both the horizontal and vertical directions, or within 100 nm in distance after overlaying the spatially corrected images. As the definition becomes less strict, the chances of missing true colocalization decrease, but the chances of erroneously including a pair of molecules incidentally passing by each other increase. However, the latter possibility could be reduced, for example, by reducing the number of probe molecules in the image or by examining consecutive image frames. Although the value of 100 nm is 10–50-fold greater than the size of a protein, and this by itself may be insufficient for colocalization at the molecular level, for molecules in motion, colocalization could be defined much more precisely by including a time-dependent definition of colocalization. Because molecules can diffuse in the membrane with diffusion coefficients of 0.3–3 µm2/s (when viewed at 30 Hz) (Chang et al., 1981; Fujiwara et al., 2002; Kusumi et al., 1993; Murase et al., 2004; Sako and Kusumi, 1994; Tomishige et al., 1998; Vrljic et al., 2002), during one frame at the standard video rate, the molecules in the plasma membrane can cover an area with a radius of 200–700 nm. Therefore, if two molecules are located within 100 nm over several video frames after the corrections for spatial distortions proposed here, it is likely that an interaction or binding of these two molecules is occurring. Such a definition depends on the motion of individual molecular species, and has to be considered for each case.
Determination of the actual precision of colocalization of simultaneous, dual-color, fluorescence images of single molecules
The precision for colocalization of two single fluorescent molecules was estimated by attaching anti-E-cadherin Fab conjugated with Alexa633 (Alexa-Ecad-Fab) to E-cadherin-GFP (Ecad-GFP) expressed on the surface of L cells (fixed), and then by examining the distribution of the displacement between single molecules of Ecad-GFP and Alexa-Ecad-Fab (Fig. 6). Because E-cadherin molecules on the cell surface exhibit various levels of clustering (Iino et al., 2001), only the fluorescent spots with fluorescence intensities within the single molecule range in the histograms shown in Fig. 5 C were selected. All of these fluorescent spots were identified in eight independent images for each color, and between the synchronously obtained images, the distances of all of the possible pairs of GFP and Alexa633 were measured. We found 163 pairs of E-cad-GFP and Alexa-Ecad-Fab with distances within 100 nm of each other, and selected them as candidates for bound pairs. The distributions of the displacements between these candidate pairs are shown in the histograms shown in Fig. 6 B. The standard deviations of the displacements between these fluorophores were 44 and 50 nm in the x- and y-directions, respectively, indicating that the standard deviation of the distance between the pair was 67 nm, consistent with the prediction of 64 nm.
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Ecad-Fab/Ecad-GFP image as an example: the number of coincidental colocalizations is estimated by shifting one image (Ecad-GFP) by 1 µm with respect to the image from the other observation arm (Alexa-Ecad-Fab). As compared with top images of Fig. 6 A, which are correctly overlaid, we could find only one pair of Ecad-GFP and Alexa-Ecad-Fab molecules with distance within 100 nm. We investigated the six images of 240 x 260 pixel area where we found a total of five pairs of E-cad-GFP and Alexa-Ecad-Fab in the shifted, overlaid images, which can be compared to the 43 pairs found in the same images that were correctly overlaid. Therefore, we could estimate that the error of detection of colocalization under the threshold of 100 nm is 12% in this particular case. The error levels vary depending on the density and distribution of the fluorescent spots, and therefore the coincidental overlaps always have to be examined for all of the paired images captured simultaneously.
Note that the superposition accuracy of 64 or 100 nm is a factor of 3–6 smaller than the Rayleigh limit for resolving two points in a single image. This is not surprising, because the precision with which the single spots can be localized is much greater than the resolving limitation (Anderson et al., 1992; Gelles et al., 1988).
Demonstration of simultaneous, dual-color, fluorescence imaging of single molecules for the colocalization detection of membrane molecules diffusing in the plasma membrane of living cells
To demonstrate this technique in live cells for observing colocalization of two single molecules, we observed Ecad-GFP labeled on its extracellular domain with Alexa-Ecad-Fab, diffusing in the plasma membrane in live L cells. Simultaneous, dual-color, fluorescence video imaging of GFP and Alexa at the single-molecule level was carried out at 37°C (30 Hz, i.e., every 33 ms), and a series of synchronized raw images of Ecad-GFP and Alexa-Ecad-Fab (210 frames each for 7 s) were spatially corrected and superimposed by the method described in Fig. 3 (Fig. 7; also see Supplementary Material). As described previously (Iino et al., 2001), Ecad forms oligomers on the cell surface, and therefore, the fluorescent spots within single-molecule fluorescence intensities were selected and used for the examinations here.
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Ecad-Fab and a single molecule of Ecad-GFP were colocalized. Both of these spots diffused in a similar way, as shown in trajectories shown in Fig. 7, keeping their colocalization to each other (they were basically within 100 nm to each other, but see below). The problem of using live cell samples for single fluorescent molecule imaging is that the fluorescence intensities of single spots fluctuate much more greatly in live cells than in fixed cells. Therefore, a fluorescent spot representing a single molecule may occasionally become too dim for the calculation of its location or the distances between two fluorescent spots may become >100 nm. But, these tend to last only for a single observation frame. In this example, if these lasted only for a single frame, and if the signal intensity came back to the normal level or the colocalization of the two spots was recovered in the next fame, then they were counted as a part of the colocalization period. The spot that disappeared for a single frame was assumed to be present at the middle point between the two adjacent spots in the trajectory. To show the transient loss of colocalization for just a single frame in the trajectories shown in Fig. 7, the locations of the pair in such instances are displayed with open circles.
This particular pair shown in Fig. 7 exhibited colocalization until 2.00 s. In the next frame, the Ecad-GFP spot was gone, suggesting a single-step photobleaching, confirming that this Ecad-GFP represented a single molecule of Ecad-GFP. The Alexa spot disappeared in a single frame from 2.40 to 2.43 s, again confirming that this spot originated from a single Alexa-Ecad-Fab molecule. The diffusion coefficients in the time window of 67 267 ms averaged over this whole colocalization period were 0.047 and 0.037 µm2/s for Ecad-GFP and Alexa-Ecad-Fab, respectively, showing a reasonable agreement. These results indicate that the fluorescence single-molecules colocalization method developed here works well for membrane molecules in living cells.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIX: DETAILS OF THE...SUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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; however, for the practical purpose of performing complex single-molecule two-color simultaneous observations, it is much easier to have two separate gain controls over each of two cameras, rather than trying to use a single camera with the spatial or temporal shifts of images with two different colors). Our procedure for image correction, when applied to molecules diffusing in the membrane, will allow the extension of the definition of colocalization to include the probability that the two molecules, while diffusing in the membrane, stay within 100 nm of each other. This is a much more robust measure of colocalization, and work for including diffusion in colocalization detection is in progress in our laboratory.
As another approach for a higher degree of precision in determining molecular colocalization, one may be able to employ single-molecule FRET between the two molecules of interest (Murakoshi et al., 2004; Schütz et al., 1998). In this case, the image correction and overlay technique described here allows for the accurate determination of single-molecule FRET as well as the precise overlay of the fluorescent images, before, during, and after the occurrence of FRET. This allows the dynamics of the interaction to be fully explored (Murakoshi et al., 2004).
When the method developed here was applied to the observation of a doubly labeled E-cadherin molecule in the plasma membrane of a live cell, the signals from the two fluorophores were found to colocalize over several seconds even in the presence of the diffusion of the E-cadherin molecule. In fact, the register of the two molecules in the presence of diffusion further strengthens the definition of colocalization due to the fact that two independent diffusing molecules at 0.04 µm2/s will not stay within our defined 100 nm for such a long period of time (2 s). Therefore, this method will provide a powerful tool for studying interactions of signaling molecules at the level of single molecules in live cells, where the dynamics of the process can be functionally important. Such approaches will allow the critical testing of many current hypotheses in cell biology, as the interaction, binding, and colocalization of molecules are fundamental issues to be elucidated in the studies of a variety of cellular processes.
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APPENDIX: DETAILS OF THE SPATIAL CORRECTION OF THE IMAGES |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIX: DETAILS OF THE...SUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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50 nm/pixel. The positions of the points in the array on the raw image are 
where the upper indices refer to the position in the array at column m = 0...M – 1 and row n = 0...N – 1. These points are parameterized with respect to the horizontal pixel position of the corresponding point in the array in the corrected image, that is 
where p is the number of pixels between each point of the array in the corrected image (p=100 for 50 nm/pixel and 5 µm between points). For each row n, cubic spline interpolation is employed for both sets of 
and 
separately. From this, we can interpolate the position in the raw image, 
on row n, that corresponds to the pixel in row n at pixel position 
in the corrected image. The interpolation is done such that between two adjacent points of the array on any row, there are p equally spaced points (pixels). At this point, we have a corresponding location on the raw image for all of the pixels that reside between the points of the mask array on any row. To fill in the rest of the points, cubic spline interpolation is once again employed. Along the corresponding interpolated points in each row at a horizontal pixel position, 
and 
parameterized with respect to their vertical pixel location in the destination corrected image, a spline interpolation is performed to estimate the location on the raw image 
corresponding to the pixel 
on the destination corrected image. Thus, a mapping between the intensity found at location (determined by the nearest neighbor method) on the raw image and the intensity to be written to location 
in the corrected image is determined, and can be applied to all subsequent frames of the video. |
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ACKNOWLEDGEMENTS |
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Submitted on July 4, 2004; accepted for publication October 14, 2004.
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REFERENCES |
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/4, quarter-wave plate; L1 and L2, working as a 10x beam expander (L1, f = 150 mm; L2, f = 15 mm) for 488-nm excitation, or 4x beam expander (L1, f = 80 nm; L2, f = 20 mm) for 594-nm excitation; FD, field diaphragm; M, mirror, DM, dichroic mirror; L3, focusing lens (f = 35 mm); BP, band-pass filter. The two-color fluorescence emission signal is split by a dichroic mirror (DM3) and detected by two cameras at the side and bottom ports. TL, tube lens (1x or 2x); BF, barrier filter; PL, projection lens (2x); I.I, image intensifier.
