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A novel computational method is used to calculate the modes of an optical resonator. The method is a computer simulation of the physical experiment of exciting a resonator externally and adjusting its length to resonate the various modes; the output at each resonance is purified by means of mode filters consisting of suitably adjusted resonators in tandem. The method is powerful and useful, and is applicable to resonators of arbitrary configuration. Calculated results for a Fabry-Perot resonator with a Fresnel number of ten are presented.