Comprehensive modelling and optical analysis of single-lens telescopes

Abstract

Classical refractors require at least two lenses, an objective and an eyepiece, to achieve image magnification and focusing. In this study, a minimalistic telescope design consisting of a single lens and a small aperture (the single-lens telescope) is examined. The design exploits the angular limiting properties of the aperture to achieve approximate image focusing, at the expense of image brightness. An analytical geometrical optics model is first presented to explore the fundamental optical properties of such a system, alongside a numerical ray-tracing framework; a more general Fourier optics theory unifying both diffractive and geometrical regimes is also developed. Extensive experimental validation of theoretical results across angular magnification, angular resolution, and image intensity profiles is demonstrated, and optimum aperture sizes for varying magnifications and irradiance wavelength are derived. The mechanical simplicity of such telescopes indicates good applicability as a simple and low-cost instrument for beginner astronomy or ad-hoc fieldwork.