Montero Orille, CarlosPrieto Blanco, XesúsCouce, B.Fuente Carballo, Raúl de la2024-04-092024-04-092006-10-02X. Prieto-Blanco, C. Montero-Orille, B. Couce, and R. de la Fuente, "Analytical design of an Offner imaging spectrometer," Opt. Express 14, 9156-9168 (2006)1520-8532http://hdl.handle.net/10347/33462We present the analytical design of an imaging spectrometer based on the three-concentric-mirror (Offner) configuration. The approach presented allows for the rapid design of this class of system. Likewise, high-optical-quality spectrometers are obtained without the use of aberration-corrected gratings, even for high speeds. Our approach is based on the calculation of both the meridional and the sagittal images of an off-axis object point. Thus, the meridional and sagittal curves are obtained in the whole spectral range. Making these curves tangent to each other for a given wavelength results in a significant decrease in astigmatism, which is the dominant residual aberration. RMS spot radii less than 5 µm are obtained for speeds as high as f/2.5 and a wavelength range of 0.4–1.0 µm. A design example is presented using a free interactive optical design tool.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Diffraction gratingsSpectrometers and spectroscopic instrumentationAberration compensationOptical systems designjournal article10.1364/OE.14.009156open access