# Calibration and Image Reconstruction in a Spot Scanning Detection System for Surface Defects
## 1 Introduction  
The detection of surface defects is one of the main items of surface quality evaluation for optical elements. In optical systems, scattering induced by surface defects will reduce the utilization efficiency of energy or even lead to severe damage to those with high-energy lasers, such as the inertial confinement fusion system (ICF) [1; 2; 3]. With the wide application of the optical elements and the development of manufacturing technology, the requirements for defect detection become higher. On the one hand, sufficient detection sensitivity for small-size defects is required to ensure the effectiveness and safety of optical elements for use. On the other hand, to obtain a comprehensive evaluation report containing hazard assessment and cause analysis of defects, the ability of quantitative detection, including defect size metrology and defect classification, has become increasingly significant. Various detection approaches for surface defects of optical elements have been studied. Commercial microscopes, such as atomic force microscope (AFM) and scanning electron microscope (SEM), are used to detect and characterize the surface defects on fine optics [4; 5]. These methods have high detection accuracy and sensitivity but require long inspection times. Because of the advantages of non-destructiveness and high throughput, optical inspection techniques have gained more and more attention. For example, [PERSON] et al. [6] proposed a defect inspection method which obtains defect images using the photo-thermal reflectance technique. [PERSON] et al. [7] adopt the total internalreflection (TIR) technique with back and edge illuminations to detect both the surface defects and sub-surface damages of large optical elements. At present, the most common detection approaches for surface defects are based on the dark-field scattering technique [8; 9; 10]. On this basis, a surface defect evaluation system (SDES) has been proposed and established from our previous works [11; 12; 13]. It employs subaperture scanning, image stitching, and image processing methods to finally realize the quantitative inspection of surface defects down to micrometer-level dimension. The measuring aperture can reach the order of a meter. However, because the SDES uses a zoom microscope with a long working distance, the numerical aperture of the objective is relatively low. As a result, only a small amount of scattered light induced by defects can be collected, and therefore, especially for small-size defects (such as shallow scratches), the defect signal acquired by the image sensor will be weak [14]. Hence, the detection sensitivity is limited. Moreover, the SDES lacks the ability to distinguish the defects that exhibit similar features in the acquired image [15]. In detection approaches based on dark-field scattering techniques, enhancing the defect scattering signal is an effective way to improve the detection sensitivity [16]. For this purpose, a spot scanning surface defect evaluation system (SS-SDES) is established in this paper. A short-wavelength laser beam is focused on the optical surface to form an illuminated spot, and a positioning system is used to bring the spot onto each portion of the surface along a spiral trace. In each illuminated spot, the scattered light caused by defects will be collected by a large solid-angle ellipsoidal mirror, and then detected by a high-sensitivity photomultiplier (PMT), thus improving the intensity of the acquired defect scattering signal. Additionally, the SS-SDES incorporates a polarization measurement channel, which is capable of measuring the polarization characterization of defects for classification. Due to the use of the spot scanning technique, the SS-SDES cannot, like an image sensor-based system, acquire a defect image directly. Therefore, before defect extraction and analysis, the SS-SDES needs to perform image reconstruction on the acquired intensity signals.