Telecentricity-governed analytical framework and deterministic initial design of wide-field Offner-type imaging spectrometers

Wide-field imaging spectrometers require simultaneous control of imaging aberrations and spectral-spatial distortions, yet dedicated initial-layout generation strategies that explicitly address wide-field performance remain limited. Here, a Fermat-principle-based analytical framework reveals how telecentricity governs these behaviors through the chief-ray-dependent optical path and image mapping mechanisms in Offner-type spectrometers. The derived telecentric conditions are translated into explicit structural-parameter constraints, forming a deterministic initialization method for wide-field Offner-type imaging spectrometers. A design based on GF-5/AHSI specifications generates a high-quality initial layout from one prescribed set of inputs. Compared with a well-established engineering design approach, which requires six rounds of experience-guided structural refinement in this case, the proposed method achieves comparable performance without repeated manual refinement. The initial and optimized configurations remain highly consistent, with most structural parameter deviations below 0.6% and a maximum deviation of 1.39%. These results demonstrate that telecentricity can be elevated from a passive optical property to an active structural constraint, enabling physics-constrained deterministic initialization with potential extension to wide-field optical systems incorporating freeform surfaces.