The results in this sections are well-known and can be found in different forms in standard textbooks [1, 5-7]. For completeness, we summarize the key results used in our analysis.

In this supplementary material, we present additional details of the proposed Flare7K dataset and experimental settings and show more results. Figure 1: Illustration of a simplified lens system. In the lens and aperture plane, the light passes through the dirty aperture and lens system, leaving a scattering flare on the image plane. In this section, we use a simplified Fourier optics model to illustrate how different kinds of scattering flares occur. A basic lens system can be viewed as a combination of one convex lens, one aperture, and an image plane as shown in Figure 1. We set the optical center as the origin of a coordinate system. Then, the light source's position is (x0,y0, z0). It is a combination of aperture function eAλ(x,y) and a lens function eTL(x,y). Supposing the focus of the lens is f and the lens is ideal. After adjusting the origin of x1 and x2, Equation (11) can be viewed as a standard Fourier transformation. Thus, the point spread function (PSF) which is the square of the amplitude of the image plane's optical field can be written as: PSFλ = |F{eAλ(x,y)}|2. Since stains with depth may bring phase shift for the aperture function, the PSFλ may vary with the wavelength λof the light source.

Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and ground-truths. Ensemble learning, as a powerful machine learning technique, aims to address these deviations by combining the predictions of multiple base models.

A three-Dimensional Look-up Table (3D LUT) is often used to transform one set of colors into another.