Blue Wedge : low-angle birefringent prism Green: Annular quarter wave plate

1. Nanometer Optical Imaging of Fluorescent Dyes Matthew Johns and Rolfe Petschek Dept of Physics CWRU 10900 Euclid Ave, Cleveland, OH, 44106 Blue Wedge:low-angle birefringent prism Green:Annular quarter wave plate Red: “ordinary” glass Orange:Quarter wave plate Abstract If a single fluorescent dye molecule is near the image plane of a far-field microscope, it is possible, by carefully analyzing the image of the particle in an ordinary light microscope, to find the position of the particle in the directions perpendicular to the axis of the microscope to accuracy significantly better than the wavelength of light that is the “Rayleigh limit.” We are examining theoretically how these limits can be improved by interfering light on different paths or with different polarizations, and then examining simultaneously the images that these interferences form. This work will be used to find which filter design will result in the best signal to noise ratio for various combinations of the 3-dimensional position of the particle and its orientation. Motivation The observation and measurement of single molecules has become an increasingly important and commonly used technique in the past 15 years, particularly for molecular biology and biophysics. These techniques offer the ability to detect a single molecule of the object of interest within a system, and provide insight into the heterogeneity and details on subpopulations of complex systems that ensemble averaging cannot provide. Current techniques, most notably fluorescent imaging with one nanometer accuracy (FIONA) and defocused orientation and position imaging (DOPI) can be employed to obtain reasonably accurate measurements of the position and orientation of fluorophores near the image plane. We believe that we can improve upon FIONA and DOPI by placing a series of filters in the microscope where the light is focused at infinity. This technique should not only yield more accurate measurements of 2-D position and orientation but also allow us to measure the depth of the molecule, which FIONA and DOPI can not do. Objectives We aim to improve the accuracy of microscopes that detect fluorescence from single dyes at or near the focal plane of a microscope. To do so we will design a series of filters which, when placed in the microscope where the light is focused at infinity, will allow for simultaneous measurement of 3-D position and orientation of a single fluorescent molecule. In order to accomplish that goal we will create a computer model that will simulate the image generated by a combination of filters with adjustable parameters for a variety of molecular positions and orientations. We will then design a statistical test to determine the viability and quality of each filter combination and find the optimal design. We believe that there may be many such “best” designs: the parameters we aim to measure are difficult to separate from each other in the far-field optics, thus the “best” design may depend on which parameters are deemed most important. Filter Design The blue prism acts to create two spots from each molecule, one from the polarized light and the other from the polarized light, after the effects of the other filters. It accomplishes this by adding a phase shift to the incident light that is dependent on , the wavevector perpendicular to the microscope axis, but is dif ferent for and polarized light. As a result, given a single point source of light, the light with polarization and the light with polarization at the prism will focus at two separate points on the image plane. The other filters imply that one of the two spots created by the blue prism will be a small, in-focus spot. The in-focus spot will be used to measure x and yas per FIONA. The other, more disperse “interferometer” spot is used to measure z the orientation. Combinations of the two will then be used to determine z. Geometry of the microscope. Object is at bottom: image plane is at top. Results Thus Far Before computational analysis and modeling can begin, we must first derive analytically equations for the electric and magnetic fields in the image plane. In order to accomplish this, we have been working with Hertz vectors, as per analyses done by Lukosz. Future Work Having derived equations for the electric and magnetic fields in absence of the filter design, we now need to determine how the addition of the filters will affect those equations. Once that is accomplished we can move foreward with the computational and statistical analyses described in our objectives. Where and Acknowledgements I would like to thank Prof. Rolfe Petschek for his assistance and support, as well as Professors Gary Chottiner and Ken Singer. The Hertz vectors can be written in the form are scalar functions corresponding to s- and p- polarized waves. e0 is the magnitude of the electric dipole moment, θ isthe angle of the dipole with respect to the z-axis, t is the Fresnel transmission coefficient, and z0is the depth of the molecule.