A heating control method is provided for a multi-stage heating system including a heating circuit having a compressor, a condenser and an evaporator. The circuitry includes, in part, first and second flip-flops, as well as a one-shot block. Thereby, overheating of the filter catalyst is prevented. A determination is made whether the request is for a commodity part or device or for a non-commodity part or device. If the reservation is possible, it performs the reservation operation. The index light passes through the barrier filter, includes a wavelength range different from the fluorescence wavelength range, and can pass through a filter having a wavelength range different from a filter which transmits fluorescence through the most among the tri-color separation filter.