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Optical detection and spectroscopy of single molecules has become an indispensable tool in biological imaging and sensing. Its success is based on fluorescence of organic dye molecules under carefully engineered laser illumination. In this paper we demonstrate optical detection of single molecules on a wide-field microscope with an illumination based on a commercially available, green light-emitting diode. The results are directly compared with laser illumination in the same experimental configuration. The setup and the limiting factors, such as light transfer to the sample, spectral filtering and the resulting signal-to-noise ratio are discussed. A theoretical and an experimental approach to estimate these parameters are presented. The results can be adapted to other single emitter and illumination schemes.