Normalized differential cross section for measurement of refractive ray distribution and focusing quality of a spherical lens: A probability model

IF 3.1 3区物理与天体物理 Q2 Engineering

Optik Pub Date : 2025-03-07 DOI:10.1016/j.ijleo.2025.172288

Wanguo Liu

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Abstract

From the viewpoint of statistical physics, the characteristics of macroscopic matter are dictated by the probability distribution of numerous random micro-states. Drawing a parallel in geometric optics, we consider the focusing effect of a spherical lens as a statistical outcome of a vast number of randomly incident rays. We propose the concept of the normalized differential cross section (NDCS), which we interpret as the probability density for the deflection angle of a random ray, to describe the angular distribution of refracted rays. When an optical screen is positioned behind the lens, the NDCS can provide an analytical solution for the brightness distribution on the screen, allowing for the assessment of the lens's focusing quality. To validate this probability model, we have derived distribution laws and numerical characteristics for the deflection angles of rays passing through a Luneburg lens and a half Maxwell fish-eye lens. The analytical results align perfectly with simulations. Our theory circumvents the cumbersome computation of the diffraction field, particularly for gradient-index (GRIN) lenses, and sets a precedent for employing probability to analyze the distribution of refracted rays and focusing effects.

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来源期刊

Optik 物理-光学

CiteScore

6.90

自引率

12.90%

发文量

1471

审稿时长

46 days

期刊介绍： Optik publishes articles on all subjects related to light and electron optics and offers a survey on the state of research and technical development within the following fields: Optics: -Optics design, geometrical and beam optics, wave optics- Optical and micro-optical components, diffractive optics, devices and systems- Photoelectric and optoelectronic devices- Optical properties of materials, nonlinear optics, wave propagation and transmission in homogeneous and inhomogeneous materials- Information optics, image formation and processing, holographic techniques, microscopes and spectrometer techniques, and image analysis- Optical testing and measuring techniques- Optical communication and computing- Physiological optics- As well as other related topics.