Defocused imaging of single molecules and quantum dots

Defoused images of single CdSe/ZnS quantum dots.

There are several techniques for determining the three-dimensional orientation of single molecules and quantum dots. A powerful one is defocused imaging. The core idea of is to obtain information about the angular distribution of a single fluorophore's emission by ?deteriorating? the image of the molecule either by introducing aberration, by defined image defocusing, or by imaging the collected fluorescence light with a Bertrand lens. In all cases, the intensity distribution of the blurred image contains information about the molecule?s emission dipole orientation. This concept can be applied to image surface-bound molecules using a conventional CCD-imaging epi-fluorescence microscope with laser wide-field illumination. It is easy to implement and allows for fast screening of single molecule orientations, without the necessity of scanning, excitation modulation or multiple channel detection. Thus, it is useful for applications where three-dimensional orientations of single molecules constitute an important measurement parameter. Knowing the optical parameters of the imaging system, in particular the numerical aperture of the objective, magnification of imaging, extent of defocusing, as well as pixel size of the imaging CCD, one can calculate exactly the defocused images of single molecules or quantum dots with more complex emission behavior. We have developed a special Matlab based uitility with a graphics user interface (GUI) for easy calculation and display of defocused images. For using the GUI, one has to download the files QDControl.fig and QDControl.m and to install them into a directory which is included in the local Matlab search path. The program is started by typing in Matlab QDControl.

The tool calculates the defocused image for a complex emitter with three perpendicular emission dipoles of different emission strengh or a degenerate elliptic dipole emitter plus a perpendicular linear dipole emitter. The parameters that can be input are: the numerical aperture, the defocusing of the objective in micrometers, the imaging magnification, and the Euler angles Omega, Psi, and omega, as shown in the subsequent figures (in the GUI, the large Omega is denoted by Theta):

Additionally, one can chose between a model of three perpendicular dipoles (left image) or an elliptic dipole (xy-plane) plus a perpendicular dipole (z-axis). For defining the emission strength ratios of the different dipoles, one inputs the parameter kappa defining the ratio of the emission strength of the x- to the y-dipole as Ix/Iy = (1-kappa)/(1+kappa), and the ratio R of the emission strength of the z-dipole to the combined x/y-dipoles as R*Iz + (1-R)*(Ix+Iy). In case of the elliptic emitter, Ix/Iy is the ratio of the ellipse half axes. The program assumes that the emitters are immobilized in air on a glass surface. Pixel size of the imaging CCD camera is assumed to be 6.45 by 6.45 square micrometers (change the magnification value correspondingly if you need a different pixel size). A screenshot of the GUI indicating the relation between the input windows and the gerometrical parameters as defined in the above figures is shown below.

Examplary view of the GUI. Displayerd is the defocused image of a simple dipole (Ratio = 1, i.e. no x or y components) with its axis within the air/glass interface (Omega alias Theta = 90), and turned within this plane by 30° (Psi = 30).