Distortion of ultra-wide-angle lenses over an angular field extending to a hemisphere

Subject of study. This study investigates the process of distortion variation across an angular field in object space extending to a hemisphere in ultra-wide-angle optical systems composed of spherical surfaces. Aim of study. This study aims to determine the dependence of distortion on variations across the angular field extending to a hemisphere in ultra-wide-angle optical systems composed of spherical surfaces. Method. The proposed method employs a polynomial representation of distortion as a power-law function of the field angle in object space, obtained from combinations of various image-formation laws with the isolation of distortion as the only aberration under consideration. Main results. This study demonstrates, for the first time, that the derived analytical relations enable estimation of both the direction and rate of distortion variation across the angular field in object space for optical systems with accuracy up to the nineteenth and higher orders of aberration. These results confirm the potential universality of the proposed approach. A comparison of the analytically obtained results with numerical values demonstrated a high degree of agreement for different image-formation laws. The maximum error of the analytical determination of distortion relative to the numerical calculations ranges from approximately 13.69% to 32.66%, depending on the image-formation law. Practical significance. In addition to its theoretical significance, the proposed approach offers substantial practical value for the design of ultra-wide-angle optical systems. The method enables preliminary prediction of the possible magnitude of distortion and corresponding focal length of the optical system under development without unnecessarily increasing the angular field to fit the format of the receiving device.