Muon rings are proving to be a powerful tool for calibrating telescopes at the Cherenkov Telescope Array Observatory (CTAO). A recent study, initiated as part of a bachelor's thesis at the Universitat Autònoma de Barcelona (UAB), has led to a new analytical method for calibrating dual-mirror Cherenkov telescopes using muon-generated light. The research addresses a long-standing challenge in the field: accurately determining how much of the Cherenkov light produced by a muon reaches the telescope camera, while accounting for the shadows cast by the secondary mirror and the camera itself. The study, published in The Astrophysical Journal Supplement Series, was conducted by Markus Gaug, a physics lecturer at UAB; Víctor Giráldez-Segalàs, a UAB physics graduate; and Fiona Redmen, a doctoral student. Cherenkov telescopes detect brief flashes of light in the atmosphere caused by particle cascades from gamma rays and cosmic rays. Among these particles are muons, which move faster than the speed of light in air, causing them to emit a blue glow known as Cherenkov radiation. When a muon passes near a telescope, this radiation forms a ring-shaped image on the camera. Because the amount of light emitted by a muon can be precisely calculated, these rings serve as a natural and continuous calibration source. By comparing the expected light with the light actually detected, scientists can assess the efficiency of the telescope's optical and detection systems. This is especially important for CTAO telescopes, which are not housed in protective domes and are thus exposed to environmental changes. The research began with Giráldez-Segalàs’s bachelor's thesis, supervised by Gaug, with the goal of adapting muon calibration methods from single-mirror telescopes to the more complex dual-mirror designs used in CTAO. In dual-mirror systems, the secondary mirror, its supports, light deflectors, and the camera itself can block part of the Cherenkov light. These shadows vary depending on the muon’s path and angle, making precise calculations essential. The new analytical method eliminates the need for time-consuming computer simulations, providing a more efficient way to calibrate the telescopes. The new method reveals that previous simplified models can differ from the actual amount of light detected by up to 40%, which is far beyond the 4% precision required by CTAO. The study also introduces corrections for single-mirror telescopes, including adjustments for the curvature of the primary mirror and the effect of coma aberration on muon ring images. These findings are critical for ensuring the accuracy of gamma-ray measurements and reducing systematic errors. The Cherenkov Telescope Array Observatory (CTAO) is set to become a leading facility in very-high-energy gamma-ray astronomy. It will operate two arrays: one in the Roque de los Muchachos Observatory on La Palma, Spain, and another in the Atacama Desert in Chile. More than half of the planned telescopes will use dual-mirror designs, including the Small-Sized Telescopes (SST), which offer wide fields of view and high image quality. The new analytical approach provides the tools needed to precisely calibrate these advanced instruments using muon rings, ensuring the accuracy and reliability of the data collected.