# Quantitative Evaluation of Subsurface Damage by Improved Total Internal Reflection Microscopy
## 1 Introduction  
Ultra-smooth and high-damage-threshold optics is largely demanded in high power laser systems (such as NIF in the U.S., or the SG-III Facility in China) [1; 2]. However, researches indicate that the subsurface damage (SSD) generated during grinding and polishing plays a key role in reducing the laser-induced damage threshold (LIDT) [3; 4; 5; 6]. It leads to having the service life of optical elements to decrease notably. Lawrence Livermore National Laboratory adopts an optics recycling loop strategy to maintain NIF operation. They have developed the capability to sustain UV-fused silica optic recycling rate of 40 optics per week [7]. In order to control and eliminate SSD, a variety of methods have been put forward to measure and evaluate this SSD. Generally, these methods are classified into two categories: Destructive and non-destructive measurement. Destructive measurement methods mainly include ball dimpling [8], magnetorheological finishing (MRF) wedge or MRF spot technique [9; 10; 11], and HF etching [12; 13]. The first two ways involve exposing the SSD by a supposed non-invasive polishing process. Cracks are opened by acid etching. Then, an optical microscope is applied to measure the SSD depth by scanning the wedge surfaceor spot. In HF etching techniques, there are also two kinds. One method is that the peak-to-valley (PV) roughness and root-mean-square (RMS) roughness of the surface are measured at each etching stage. The surface roughness increases initially and reaches its peak value, then subsequently drops smoothly. The first peak position is the SSD's depth. The other way is that a small amount of barium is added inside the grinder coolant fluid. After grinding, the sample is etched progressively with controlled quantities. The barium concentration of etchant solution after each etching is analyzed by an Inductively Coupled Plasma-Atomic Emission Spectrometer. Then the relation curve between SSD depth and barium concentration is built. These destructive measurements are more explicit and reliable. However, the element surface is destroyed irreversibly. The depth by polishing or etching is much larger than that of the SSD, therefore more processing time may be needed. In addition, to ensure measurement accuracy, the polishing or etching process, influenced by many factors, must be carefully controlled. In view of this, non-destructive measurement techniques are widely studied, such as predictive methods [14; 15], confocal fluorescence microscopy [16; 17], optical coherence tomography (OCT) [18; 19], and total internal reflection microscopy (TIRM) [20; 21; 22], etc. Considering the formation of SSD in optical glasses based on the indentation fracture mechanics, [PERSON] et al. proposed an explicit equation to predict SSD depth. Furthermore, they also put forward a relationship between SSD depth and the size of abrasive grains through many experiments on glasses and ceramics. With an excitation at the wavelength of 405 nm, subsurface features of grinded or polished fused silica glasses are observed in fluorescence confocal mode, and not observed in the reflection mode. OCT is applied to detect subsurface defects in ceramics. As is reported in Ref.18, its depth and lateral resolutions are 10 \(\upmu\)m and 4 \(\upmu\)m, respectively. Equipment for these two methods is always expensive, and the mechanism is complicated. Compared with the former two means, TIRM, proposed firstly by [PERSON], takes advantages of simple apparatus and low cost. However, because of surface and subsurface defects imaged simultaneously, it is difficult to differentiate SSD from surface flaws. [PERSON] et al. [23] obtained the surface image (A) using differential interference contrast lighting and a TIRM image (B) at the same site. The surface image is inverted and superimposed on top of the TIRM image (i.e., B-A). Surface information could not be removed completely, due to blooming of the saturated CCD and misalignment of the images caused by vibration and air turbulence.