We have improved on our technique for observing individual fluorescent molecules in solution based on two-photon excitation (TPE). A mode-locked laser beam is focused into the solution, thereby defining a TPE volume localized in 3 dimensions. Molecules diffusing in and out of this volume produce fluorescence bursts which are detected with a high signal-to-background ratio. The theoretical foundations for the technique have been derived which enable us to optimize excitation parameters (focal volume, intensity, pulse width, etc.) to maximize the fluorescence the signal. These are supported by experimental results obtained for rhodamine~B in various solvents.
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