We propose a spectrum analyzer based on the properties of a hologram recorded with the field transmitted by a Fabry–Perot etalon. The spectral response of this holographic Fabry–Perot spectrometer (HFPS) is analytically investigated in the paraxial approximation and compared with a conventional Fabry–Perot etalon of similar characteristics. We demonstrate that the resolving power is twice increased and the free spectral range (FSR) is reduced to one-half. The proposed spectrometer could improve the operational performance of the etalon because it can exhibit high efficiency and it would be insensible to environmental conditions such as temperature and vibrations. Our analysis also extends to another variant of the HFPS based on holographic multiplexing of the transmitted field of a Fabry–Perot etalon. This device increases the FSR, keeping the same HFPS performance.
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