With the advantages of simple structure, low-cost, large field of view, and high image quality, the transmission optical system is widely used in detection system, microscope, telescope, etc. However, the research on the illumination distribution law in the focal plane of transmission optical system is rarely reported. In this paper, this issue is studied. During the study on the first-order scattered light distribution law in the focal plane of the transmission optical system, the limitations of the two-parameter Harvey bi-directional scatter distribution function (BSDF) scattering theory are found, namely in the condition of small scattering angle, the two-parameter Harvey BSDF theory cannot accurately describe the scattering properties of the optical surface material. So the scattering model of the transmission optical system under small scattering angle is established by introducing parameter l, and the accuracy of the new theoretical model is verified experimentally. This model complements the two-parameter Harvey BSDF scattering model and broadens the application scope of the Harvey BSDF scattering model so that it can better explain the imaging law of scattered light spot in the focal plane of transmission optical system. At a small scattering angle, the conclusions can be drawn from the new theoretical model as follows. 1) The irradiance of the final image plane increases linearly with the increase of the incident optical power. 2) In the transmission optical system, the contribution of each optical surface with the same scattering properties to scattered spot irradiance in the final image plane can be expressed by a Gaussian function. 3) The irradiance of scattered spot in the final image plane can be expressed as the superposition of n Gaussian functions, where n is the number of optical surfaces with different scattering properties in the transmission optical system.%透射光学系统由于结构简单、成本低、视场大、成像质量高等优点,广泛应用于探测、显微、望远等实际应用中,但目前关于该类系统像平面散射光斑分布规律的研究却鲜见报道.本文对透射光学系统焦平面散射光照度分布规律展开研究,以Harvey双向散射分布函数散射理论为基础,建立了小散射角条件下透射光学系统一阶表面散射光在像平面的高斯函数分布规律的理论模型,该模型能与实验数据很好地符合.
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