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Three-dimensional evaluation of subsurface damage in optical glasses with ground and polished surfaces using FF-OCT

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Abstract

Subsurface damage (SSD) induced during conventional manufacturing of optics contributes mainly to a reduction in the performance and quality of optics. In this paper, we propose the application of full-field optical coherence tomography (FF-OCT) as a high-resolution and nondestructive method for evaluation of SSD in optical substrates. Both ground and polished surfaces can be successfully imaged, providing a path to control SSD throughout the entire optics manufacturing process chain. Full tomograms are acquired for qualitative and quantitative analyses of both surface and SSD. The main requirements for the detection of SSD are addressed. Data processing allows the removal of low-intensity image errors and the automatic evaluation of SSD depths. OCT scans are carried out on destructively referenced glass samples and compared to existing predictive models, validating the obtained results. Finally, intensity projection methods and depth maps are applied to characterize crack morphologies. The experiments highlight differences in crack characteristics between optical glasses SF6 and HPFS7980 and illustrate that wet etching can enhance three-dimensional imaging of SSD with FF-OCT.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Microcracks induced during the conventional optic manufacturing process are known as subsurface damage (SSD) [1,2]. Due to many iterative processes, a nearly SSD-free optical surface can be obtained for the final polishing steps. Even after chemical–mechanical polishing, small cracks remain below a small polishing layer called the Beilby layer [3]. SSD reduces the overall performance of optics, including imaging quality [3,4], laser induced damage threshold (LIDT) [59], and breaking strength [10,11]. Due to an increasing demand in high-performance optics, the urgency to expand existing measurement methods for SSD rises. In EUV lithography, surface requirements in the nanometer range [12] can be realized only on SSD-free substrates. High-power laser facilities such as the National Ignition Facility (NIF) [13] also rely on SSD-free optics to realize high LIDTs for laser operation. In the laser fluence regime below ${10}\; {\rm J}/{\rm cm}^2$, fracture surfaces have been identified as the main damage precursors for the initiation of laser induced damage [14]. Especially, ultraprecision optics with long operating times need long optimizing loops leading to high manufacturing costs. This urges the need for a nondestructive measurement procedure to control SSD along the process chain.

Both destructive and nondestructive methods can be applied to characterize SSD [4,8,10,1539]. In the industry, destructive methods related to the taper polishing technique [2,15] are common. A taper is polished into the surface to generate a cross section throughout the SSD layer. Chemical etching is used to reveal SSD hidden below the closed Beilby layer. The SSD depth is determined by observing the polished wedge under a microscope and subsequent image analysis. Instead of polishing a wedge, a cross section can be realized by other means, e.g., by using the ball-dimple technique [16] or by polishing a sphere [34]. The main drawbacks of destructive SSD evaluation are long processing times and the incapability to measure inline at multiple and specific locations. In combination with laboratory analytical tools, Menapace et al. [40] used taper polishing with a magnethorhelogical polishing tool called the MRF wedge technique [18] to investigate the three-dimensional (3D) structure of fractures, but this destructive procedure is time consuming and not applicable in industrial process monitoring. For the nondestructive characterization of SSD, there exist several imaging methods, but they suffer individual drawbacks as analyzed in [4144]. Most recently, Liu et al. [39] proposed dark field confocal microscopy (DFCM) for 3D evaluation of surface and subsurface defects and listed successful measurements of SSD located underneath a polished surface with individual scattering surface defects. SSD with up to a three- to four-fold lower signal intensity compared to the surface reflection is acquired. The question remains as to whether DFCM is suitable for detecting SSD on highly scattering, rough samples as well as for materials other than the examined neodymium glass. As far as our experience goes, no universal nondestructive measurement technique is available for the optics manufacturing industry.

To understand the difficulty of imaging SSD, it is important to know some key characteristics of the microcracks. The cracks measure only a few micrometers or less in the smallest dimension [45]. They reach a depth of 100 µm and deeper under the surface during pre-grinding and are reduced to only a few micrometers prior to polishing [41]. In the literature, a three-layered model is widely known to describe the structure of the damaged glass, as shown in Fig. 1. The refractive index of the cracks varies and often only slightly differs from the surrounding bulk material [46]. Up to now, SSD reflection and scatter efficiency has been quantified as small as ${R_{{\rm{SSD}}}} = {10^{- 6}}$ [22].

 figure: Fig. 1.

Fig. 1. Three-layer model of SSD in polished optical glass after Hed et al. [2]

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2. EXPERIMENTAL SETUP

In recent literature, optical coherence tomography (OCT), an optical measurement method based on short coherence interferometry, successfully captured surface defects [47], laser induced damage [48,49], as well as SSD [28,35]. OCT was first mentioned by Huang et al. [50] in 1991. Its current main application is the 3D imaging of tissue in biomedicine. A broad overview of OCT is given elsewhere [51]. The two main versions of OCT, time domain (TD) and Fourier domain (FD) OCT, acquire depth information either by axial scanning (TD) or analysis of the spectral signal (FD). TD-OCT generally allows a higher lateral resolution than FD-OCT [5254]. By refocusing over the axial scanning range, the trade-off between axial scanning range and lateral resolution can be minimized in TD-OCT. Contrary to previous measurements of SSD using OCT that were limited in resolution and in one case restricted to SSD beneath polished surfaces [35], we focus on a special form of TD-OCT called full-field OCT (FF-OCT). FF-OCT was first described by Beaurepaire et al. [55]. Besides its various applications in biomedicine, FF-OCT has already been implemented in different areas of nondestructive testing, e.g.,  to reveal pointlike defects on the interfaces inside a multilayer multidielectric structure [56] or to analyze paints in the automotive sector [57]. Through parallelized acquisition on a camera chip, an increased acquisition speed compared to conventional TD-OCT is achieved. In FF-OCT, single sagittal two-dimensional (2D) slices (C-scans) are acquired with phase shifting interferometry and stacked together to realize a full 3D scan. The use of immersion objectives with a high numerical aperture (NA) as well as focus shifting for subsequent C-scans [58] results in an ultrahigh lateral resolution for FF-OCT. High axial resolution is achieved by use of broadband, spatially incoherent light sources for illumination, e.g.,  thermal sources, fluorescence-based sources, and broadband light emitting diodes (LEDs) [59]. Normally, in OCT, axial resolution quickly declines with increased imaging depth due to dispersion mismatch in both interferometer arms [60]. In our FF-OCT setup, dispersion mismatch is minimized due to a symmetrical interferometer setup and the use of immersion and index matching (IM) fluids. To summarize, we circumvent main limitations of previous works for SSD detection with OCT, comprising a general low resolution and/or a strong reduction in both lateral and axial resolution over the imaging depth as stated by Wu et al. [35]. New challenges due to image errors arising with the use of FF-OCT for low-signal SSD imaging are addressed in this paper.

 figure: Fig. 2.

Fig. 2. Sketch of experimental setup with FF-OCT from LLTech.

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 figure: Fig. 3.

Fig. 3. Schematic representation of a tomographic OCT dataset and application of different projection methods. Intensity values for voxels range from zero (black) to one (white).

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The optical setup of the commercial FF-OCT system from LLTech used in our experiments consists of a Linnik interference microscope, as seen in Fig. 2, combining a Michelson interferometer with identical microscope objectives in each interferometer arm—a setup widely used in FF-OCT [6164]. Key components of the device include its broadband LED, which has a central wavelength of 565 nm and spectral bandwidth of 104 nm, two identical $10 \times$, 0.3 microscope immersion objectives, as well as a CMOS camera with 2 million pixels and a framerate of 300 Hz. The resulting field of view covers an area of $1.26\;{\rm{mm}} \times 1.26\;{\rm{mm}}$ with one pixel representing 0.875 µm. When combining multiple C-scans to a 3D dataset as depicted in Figs. 2 and 3, each acquired camera pixel now represents a 3D voxel. The voxel size in $z$ corresponds to the C-scan spacing during acquisition, which was set to 0.5 µm in our experiments.

For visualization and evaluation of the 3D data, projection methods are essential to reduce the vast amount of data and highlight relevant areas. The average intensity projection (AIP) is computed by calculating the average intensity of each voxel column in one direction, as illustrated for one exemplary voxel column in Fig. 3. Maximum intensity projection (MIP) works the same way, but instead of calculating the mean value of each voxel column, their maximum value is taken as a representative value. The resulting projections are 2D and thus easily evaluable. At the same time, they contain information from the whole 3D dataset.

 figure: Fig. 4.

Fig. 4. Sketch of destructively referenced glass sample with OCT measurement positions (1–7) and position marks (L-shapes). (a) Sagittal view; (b) lateral view; (c) image of a sample ($40 \times 40 \times 12\;{\rm mm}^3$).

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Tables Icon

Table 1. Predictions for Maximum Crack Depths ${c_{{\max}}}$ Based on Surface Roughness ${Rt}$

3. MATERIALS AND METHODS

The experiments are carried out with samples of optical glass Schott SF6 (SF6) and Corning Fused Silica HPFS7980 5F (FS), as shown in Fig. 4(c). Six samples per material are prepared starting from sawn-cut semi-finished parts with a cuboid shape of $40 \times 40 \times 12\;{\rm mm}^3$. A first preprocessing step consists of grinding a circular area with chamfer on a five-axis grinding machine (DMG ultrasonic linear 20) to improve the contact zone between the workpiece and a concave, spherical polishing tool later to be used for our reference method called spherical polishing [34,65]. To evaluate our SSD measurement method with OCT, a process chain is designed to ensure that a significant amount of SSD remains in the material. SSD is intentionally induced by a conventional loose-abrasive grinding process on an eccentric lapping machine with coarse grit size F230 (average grit size ${\bar d_{{\rm{F}}230}} = 53 \pm 3\;{{\unicode{x00B5}{\rm m}}}$ [66]), followed by a second grinding step with a finer grit size F800 (average grit size ${\bar d_{{\rm{F}}800}} = 6.5 \pm 1\;{{\unicode{x00B5}{\rm m}}}$ [66]). The material removal of the second grinding step is set to a minimum to only partly remove deeper SSD originating from the first grinding step and at the same time, allow for subsequent surface polishing. Silicon carbide is used for both grinding [SIC BW plus (black), Pieblow & Brandt GmbH] and polishing (CERI 900 Q, Pieblow & Brandt GmbH). The initial roughness after each grinding step is given in Table 1 for a better placement of the SSD depths, measured using a stylus profilometer Form Talysurf i5. An aluminum polishing tool with a polyurethane foil and a radius of 2 m is employed to create a cross section reaching around 100 µm below the ground surface, as depicted in Fig. 4(a). Polishing is carried out with a pressure of $7.5\;{\rm{N/c}}{{\rm{m}}^{{2}}}$ at 200 rotations per minute and a slurry temperature regulated between 23°C and 25°C, using the above-mentioned silicon carbide with average grit size ${\bar d_{{\rm{Ceri900Q}}}} = \,2.5\;{{\unicode{x00B5}{\rm m}}}$ at a concentration of 25% in the polishing slurry. Afterwards, the sample surface is etched using hydrofluoric acid (HF) (20%, 30 s) for FS and HF (10%, 10 s) for SF6. On the etched surface area, digital microscopy (DM) and subsequent image processing are used to determine reference depths for SSD; results are summarized in Table 2. Images are taken on random positions on the etched part of the wedge. Surface profiles of the spherical wedge are acquired with the profilometer for registering the images to their positions. The acquired data are analyzed by means of automated image processing developed by Seiler et al. [34], eliminating any operator influence.

Tables Icon

Table 2. Metrics for Local Maximum Crack Depths ${c_{{\max}}}$

For the FF-OCT measurements, our distinctive surface positions are labeled with ultra-short-pulsed (USP) laser radiation on one sample per material. This allows the allocation of FF-OCT images to stitched DM images of the wedge. Fourteen different locations were imaged with FF-OCT between the four labeled positions (L-shaped marks at positions 1 and 7) on each sample, as shown in Fig. 4(b), ranging from ground to polished state. Four stitched DM images (FS e/ne and SF6 e/ne) with corresponding OCT results combined with multilayer TIFF files can be found in Dataset 1, Ref. [67], Dataset 2, Ref. [68], Dataset 3, Ref. [69], and Dataset 4, Ref. [70].

Raw data acquisition is performed with a commercial FF-OCT device, namely, the biopsy scanner from LLTech introduced in Section 2, which offers an isotropic resolution of 1 µm. The penetration depth in the range of millimeters exceeds the maximum depths of SSD of around 100 µm. In addition to the resolution, sensitivity is another key requirement to detect SSD in transparent materials due to the low reflectivity of the cracks. IM is carried out with a silicone oil (${n_{\rm d}} = 1.40$) for SF6 (${n_{\rm d}} = 1.81$) and a saline solution (0,9% NaCl, ${n_{\rm d}} = 1.33$) for FS (${n_{\rm d}} = 1.46$) to reduce scattering and reflectivity at the sample surface with the help of an IM fluid, as illustrated in Fig. 2. This enhances the measurement of both highly scattering rough surfaces as well as reflecting polished surfaces. C-scan averaging is used to further improve sensitivity. The minimum resolvable reflectivity ${R_{{\min}}}(N)$ is inversely proportional to the sensitivity of FF-OCT and depends on the number of averaging steps $N$ [71] for the acquisition of one C-scan; see Eq. (1) derived from Dubois et al. [61]. ${R_{{\min}}}(10) = 1.5 \cdot {10^{- 8}}\, \approx - 78\,{\rm{dB}}$, given by the device manufacturer, is in good agreement with ${R_{{\min}}}(10) = - 81\,{\rm{dB}}$, derived from our experiments. The setup used theoretically reaches a minimum reflectivity ${R_{{\min}}}(100) = 1.5 \cdot {10^{- 9}}\, \approx - 88\,{\rm{dB}}$ with 100-times averaging, which is confirmed in the experiments:

$${R_{{\min}}}(N) = \frac{{{R_{{\min}}}(10)}}{{10 \cdot N}}.$$

Raw FF-OCT images contain multiple image errors that impede good visualization and evaluation of the datasets. In this context, image errors denote pixel defects, noise, as well as measurement artifacts. For characterization of SSD, those image errors are highly relevant, as OCT signals generated by SSD are in general low in intensity due to the small size and low reflectivity of the cracks. For data preprocessing, one-dimensional (1D) deconvolution using the axial point spread function (PSF) of the OCT system was applied to remove signal sidelobes related to the non-Gaussian spectral shape of the LED and enhance axial image contrast. The PSF was measured on a flat mirror with a reflectivity of 0.23 at 565 nm, being placed in the sample holder and immersed with silicone oil. Deconvolutions are computed in MATLAB using a Lucy–Richardson algorithm [72,73]. Strongly visible signal sidelobes originating from the sample surface as well as their removal are depicted in Fig. 5. Additionally, in FF-OCT, pixel defects leave an imprint on each C-scan. So-called hot pixels showing high intensities without illumination as well as small differences in the individual pixel sensitivity lead to artifacts during evaluation and visualization (Fig. 5), as data processing with low thresholds is needed with regard to SSD. This paper presents a novel image processing method to tackle low-intensity image errors in FF-OCT images. The method operates without additional measurements, using the 3D datasets already acquired for SSD imaging. 3D data are merged into one 2D image ${\rm{imgInt}}$ by the summation of $n$ C-scans ${\rm{im}}{{\rm{g}}_i}$ via AIP as described by Eq. (2) and shown in Fig. 3:

$${\rm{imgInt}} = \sum\limits_{i = 1}^n {\frac{{{\rm{im}}{{\rm{g}}_i}}}{n}} .$$
 figure: Fig. 5.

Fig. 5. Detailed lateral view of a defect captured in FF-OCT scan SF6 4 ne, displayed in SSD dynamic range. (a) Local MIP without deconvolution or defective pixel correction. i: Signal sidelobes from surface signal; ii: defective pixel artifacts. (b) Local MIP with defective pixel correction and deconvolution; iii: removed signal sidelobes resulting in a darkened area.

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As offsets and slightly higher sensitivities of erroneous pixels sum up, they appear as bright spots on the integral image. Binarizing is applied to map defective pixels and correct the image stack with a multi-step approach, leading to the improvement observable in Figs. 5(a) and 5(b). A total of 2295 erroneous pixels on the image sensor are identified, corresponding to 0.11% of the total.

Another image error is the noise floor, which is inherent to OCT imaging. Figure 6(a) shows log–log histograms of FF-OCT scans for polished and ground surfaces as well as for a dataset containing only noise, highlighting the difficulty in extracting relevant image information. SSD signals with both low intensity and minor spatial dimensions are masked by noise. Noise with a mean intensity of 25 for 10-times averaging is reduced by a factor of 2.3 with 100-times averaging, leading to the sensitivity improvement predicted by Eq. (1). For automatic SSD characterization, the 3D data are binarized using a global threshold of 78 for 10-times averaging and 44 for 100-times averaging. After binarization, 3D filtering removes erroneously binarized noise using an anisotropic area filter, as cracks tend to be three-dimensionally connected in the lateral direction contrary to uniformly distributed and separated binarized noise artifacts. The binarized and filtered data are evaluated by counting voxels for each C-scan. The resulting area-depth function shows an exponential decline in crack area with increasing depth below the surface, as can be seen in Fig. 6(b), which corresponds to area-depth functions captured along the wedge using destructive methods [34]. To allow a comparison of the SSD detection sensitivity between the used destructive reference method of spherical polishing and FF-OCT, an identical crack area threshold of 0.001% is used to deduce maximum SSD depths. In FF-OCT, the threshold corresponds to 20 voxels and a crack area of ${16}\;\unicode{x00B5}{\rm m}^2$ per field of view. For calculation of the crack depths ${c_{{\max}}}$, the surface position of each OCT scan is determined by locating the maximum area value of the area-depth function. One disadvantage and source of uncertainty of destructive methods lies in the separate acquisition of SSD positions and SSD depth [36]. The latter is inherently eliminated with the proposed evaluation method.

 figure: Fig. 6.

Fig. 6. (a) Histogram of FF-OCT scans with 10-times averaging. Red: noise only; green: polished; blue: ground. (b) Area-depth functions of FF-OCT scans along the taper. Green: polished; cyan: partly polished; blue: ground. Maximum of area density corresponds to surface position. SSD threshold indicated by dashed line in magenta.

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4. THEORETICAL PREDICTIONS

As existing measurement methods are time consuming and mostly destructive, one focus in SSD research over the past decades has been to establish and continuously improve prediction models for SSD [2,10,19,31,7495]. In general, the use of prediction models is fast and cheap, but they lack in either precision or universality. Models rely on relationships between SSD characteristics and linked parameters that are easier to measure. Surface roughness, normal load applied on a single grit, grit size, as well as breaking strength have been identified as suitable correlating parameters. In general, SSD depths increase with increasing surface roughness, grit size, and applied load, as well as with decreasing breaking strength. Models are created empirically or with the semi-empirical approach introduced by Lambropoulos et al. [76] by deriving SSD depth formulas from crack mechanics. Especially, semi-empirical models rely on a good understanding of crack morphology, as prevailing crack types such as lateral and radial cracks are described by different crack mechanics [11]. Earlier, models were based on the assumption that maximum SSD depths are dominated by radial cracks. In recent research [89,92,96], this relationship is questioned, and it is shown that SSD depth is more likely to be dominated by lateral cracks. High-resolution 3D evaluation of crack morphology based on FF-OCT may provide a new tool to correct and improve predictive models and to get a better understanding of SSD formation. In this paper, to validate experimental results, existing predictive models for grit size and surface roughness are applied as a “rule-of-thumb” to get an estimate of SSD depths to be expected.

For predictive models based on grit size, Suratwala [92] summarizes different studies with lower and upper boundaries ${c_{{\max}}} = 3.5 \cdot \;{(\bar d - 15)^{0.5}} \ldots \;7.5 \cdot {\bar d^{0.5}}$. For our experiments, this results in lower and upper estimates for the SSD depth of 20.7 µm and 5.1 µm for grit size ${\bar d_{{\rm{F}}230}}$. For the finer grit size ${\bar d_{{\rm{F}}800}}$ used to create a polishable surface, only an upper boundary can be calculated with 20.5 µm, as the lower boundary is mathematically restricted to grit sizes over 15 µm. SSD depth measurements for the iteratively prepared sample are expected to end up in between the values predicted for both grit sizes.

Correlations of SSD depth and surface roughness are described by either linear [2,10,19,7577,7981,84,86,87,89] or nonlinear [31,78,80,83,85,89,91,93,95] relationships with ${c_{{\max}}} \sim Rt^{3/4} \ldots \;{Rt}$. Empirically determined corrective factors $K$ span from one to 49, depending on the material and processes used, and are even strongly varying for one same material as emphasized by Suratwala [3,81]. When applying linear models closely related to the process and materials in our experiments, predictions according to Table 1 can be made.

5. RESULTS AND DISCUSSION

Various metrics for local maximum crack depths ${c_{{\max}}}$ are listed in Table 2, summarizing in total 24 OCT scans. Measurements at positions 1 and 7 (Fig. 4) containing USP laser written labels as well as three measurements at position 4 of SF6 containing interference artifacts were excluded from quantitative analysis. Both measurement methods, the destructive reference method of spherical polishing and the proposed nondestructive FF-OCT approach roughly correspond to each other with depths spanning from 14 µm to 67 µm. As expected, depth predictions from Table 1 based on the surface roughness as well as the grit size of the final grinding step (grit size F800) lead to significantly smaller SSD depths compared to measured results. One main reason for the discrepancy is suspected to be the two step-preparation procedure, as roughness was reduced in a second grinding step to achieve a polishable surface with only minor material and SSD removal. To some extent, maximum SSD depth is still related to the first grinding step with coarse grit size F230 and the resulting intermediate surface roughness of ${Rt} = 36.9\;{{\unicode{x00B5}{\rm m}}}$ for SF6 and ${Rt} = 13.5\;{{\unicode{x00B5}{\rm m}}}$ for FS. As material removals were not recorded during the experiments, a more detailed assessment of the influence of both grinding steps on SSD depth must be omitted at this point. Nonetheless, as enforced in our experiments, possible discrepancies between SSD prediction in multi-step processes and measured SSD depth, as well as the broad range of correlating factors, highlight the difficulty in transferring and applying predictive models on industrial processes.

For the measurements, it is shown that maximum SSD depths obtained by FF-OCT scans are up to 6.4 µm higher for SF6 and 9.4 µm higher for FS than maximum SSD depths obtained by the reference method. Mean values from OCT only slightly differ from reference measurements for both materials, thus validating FF-OCT as a representative measurement method. Low minimum crack depths for FF-OCT indicate that multiple scans are needed to reliably capture deeper cracks and get representative mean values. It must be mentioned that the standard deviation $\sigma$ in FF-OCT is higher than for the reference method. OCT scans of etched samples result in higher minimum and slightly higher maximum depths and thus a smaller standard deviation compared to OCT scans without etching. It can be deduced that the detection of deep cracks in FF-OCT is related to the spatial distribution of deep cracks as well as an optimized sensitivity for detecting SSD.

Besides a quantitative evaluation using binarizing, dynamic ranging and projection methods on the grayscale 3D data help to visualize relevant image information in 2D. Lateral projections are generated using MIP and sagittal projections using AIP, as depicted in Fig. 3. In sagittal projections, surface or subsurface features appear, depending on the chosen dynamic range. For intensities from 500 to 2000, images of the glass surface comparable to the DM result [Figs. 7(e)–7(h)]. SSD visualization is optimized in a lower signal regime with intensities from 15 to 100. In lateral slices and projections, the optic surface and underlying cracks appear in a side view, as depicted in Fig. 8. For further visualization of crack shapes and crack distribution in 2D, color-coded depth maps (CCDMs) are generated by evaluating the binarized image stacks [Figs. 7(a)–7(d)]. Detected SSD beneath a closed, polished surface can be identified in Fig. 7(a). Figure 7(c) shows a homogeneous distribution of SSD over the whole field of view of 1.58 mm2 in etched fused silica, compared to only a few unevenly distributed SSD in SF6 [Fig. 7(d)].

 figure: Fig. 7.

Fig. 7. Images with magnified sections of four FF-OCT scans in two different visualization modes. Color indicates depth relative to ground surface. (a)–(d) Sagittal view, CCDM; (e)–(f) sagittal view, AIP. (a), (e) FS 1 ne; (b), (f) SF 6 ne; (c), (g) FS 4 e; (d), (h) SF6 4 e. Overviews with all FF-OCT scans can be found in Dataset 1, Ref. [67] for FS e, Dataset 2, Ref. [68] for FS ne, Dataset 3, Ref. [69] for SF6 e, and Dataset 4, Ref. [70] for SF6 ne.

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For the validation of automatically registered crack depths, an algorithm is used to output lateral views at the centroids of crack segments contained in the C-scan correlating to the calculated SSD depth. Lateral views for validation are created using local MIP in a restricted area of 31 B-scans, the procedure depicted in Fig. 3. The obtained lateral images reveal crack shapes as well as corresponding surface characteristics as visible in Figs. 8(a)–8(c). Especially for FS, we observe that crack morphology is dominated by complex crack systems induced by the intersection of multiple lateral cracks, supporting recent theories that lateral cracks are a main cause of SSD depths [89,92,96].

By evaluating the local MIP images for all measurements taken as well as by analyzing the AIP and CCDM images, it can be deduced that severe SSD is in most cases linked to significant surface defects. This supports observations from Suratwala et al. that deepest cracks are caused by a few rogue particles [82], as rogue particles are commonly related to surface defects in optics manufacturing. In future work, crack and scratch forensics [97] in combination with the presented visualization methods may therefore be used to identify damage sources in the manufacturing chain.

 figure: Fig. 8.

Fig. 8. Images of FF-OCT scan FS 4 e. (a) Lateral view, global MIP; (b) lateral view, local MIP; (c) lateral view, slice. The horizontal black bar beneath the surface is an artifact originating from deconvolution.

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6. CONCLUSION

In summary, FF-OCT can be adapted to image surface topography as well as the remaining SSD layer of ground and polished glass samples locally and nondestructively in three dimensions. Difficulties in visualizing and evaluating SSD arise from the low signal intensity of SSD vanishing beneath the noise floor, as depicted in Fig. 6. A combination of methods is proposed to tackle this issue: (1) the reduction of scattering and reflection at the sample surface by IM, (2) increasing the sensitivity by using a high number of averaging steps during image acquisition, (3) using data processing to eliminate image artifacts related to OCT, and (4) through a sophisticated data evaluation and visualization toolset. The measurement method may provide new insights for SSD and LIDT research. As a first result, we were able to observe that deep cracks are often linked to main surface irregularities, and we found different crack characteristics in FS and SF6. Indicated by small cracks vanishing below the noise floor, the minimum reflectivity of SSD can be even smaller than the minimum detectable reflectivity ${R_{{\min}}}(100) = 1.5 \cdot {10^{- 9}}$ achieved in the experiments, exceeding previous figures for the reflectivity of SSD by three orders of magnitude. This further promotes the use of OCT for SSD detection due to its sensitivity advantage by imaging interference fringes instead of mean intensities. An automated quantitative evaluation using binarizing to create an area-depth function was successfully applied to FF-OCT. For equivalent threshold parameters, the comparison with a conventional, destructive reference method, yields to comparable average SSD depths in FF-OCT. Measured SSD depths correspond roughly to predictive models for the coarse grinding step, which tends to dominate SSD depth in the so-designed experimental process chain. Applying lower thresholds as well as further improvements in sensitivity, e.g.,  by using FF-OCT in a dark field configuration [98], will qualify FF-OCT as an even more precise SSD evaluation tool compared to conventional wedge polishing. This further emphasizes the use of FF-OCT as an inline tool for optimization and quality control in the optics manufacturing process. In future work, various other manufacturing processes and process parameters will be analyzed for further validation of FF-OCT. OCT scans on etched surfaces reveal slightly increased SSD depths compared to scans on raw surfaces. It also has been demonstrated that etching with the parameters given allows a better visualization of crack geometry for 3D imaging with OCT, as would have suggested similar observations by Preston in microscopy [1]. Further investigation is needed to quantify the influence of etching on the detection of SSD with OCT and evaluated SSD depths. In the future, high-resolution OCT measurements with high sensitivity can be a powerful research and quality inspection tool to reveal 3D characteristics of even the smallest SSD. We have shown that based on OCT images, crack morphology can be conveniently analyzed, which helps to improve existing predictive models for SSD.

Funding

Bundesministerium für Bildung und Forschung (13FH003IA6).

Acknowledgment

We thank LLTech SAS and especially Émilie Benoit for providing raw images taken with their FF-OCT biopsy scanner and information on the FF-OCT system. We also thank Dietmar Gräfe, Sebastian Henkel, and Lukas Tianis from EAH Jena for preprocessing and referencing the samples.

Disclosures

The authors declare no conflicts of interest.

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2020 (7)

J. Yin, Q. Bai, H. Haitjema, and B. Zhang, “Two-dimensional detection of subsurface damage in silicon wafers with polarized laser scattering,” J. Mat. Proc. Tech. 284, 116746 (2020).
[Crossref]

J. Liu, J. Liu, C. Liu, and Y. Wang, “3D dark-field confocal microscopy for subsurface defects detection,” Opt. Lett. 45, 660–663 (2020).
[Crossref]

J. Ogien, O. Levecq, H. Azimani, D. Siret, J.-L. Perrot, and A. Dubois, “Line-field confocal optical coherence tomography: technology and application in dermatology,” Proc. SPIE 11359, 113590F (2020).
[Crossref]

P. Li, S. Chen, H. Xiao, Z. Chen, M. Qu, H. Dai, and T. Jin, “Effects of local strain rate and temperature on the workpiece subsurface damage in grinding of optical glass,” Int. J. Mech. Sci. 182, 105737 (2020).
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D. Lv, M. Chen, Y. Yao, Y. Zhao, G. Chen, Y. Peng, and Y. Zhu, “Prediction of subsurface damage depth in rotary ultrasonic machining of glass BK7 with probability statistics,” Int. J. Adv. Manuf. Technol. 107, 1337–1344 (2020).
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T. I. Suratwala, R. A. Steele, N. Shen, N. Ray, L. A. Wong, P. Miller, and M. Feit, “Lateral cracks during sliding indentation on various optical materials,” J. Am. Ceram. Soc. 103, 1343–1357 (2020).
[Crossref]

E. Auksorius and C. Boccara, “High-throughput dark-field full-field optical coherence tomography,” Opt. Lett. 45, 455–458 (2020).
[Crossref]

2019 (6)

A. Solhtalab, H. Adibi, A. Esmaeilzare, and S. M. Rezaei, “Cup wheel grinding-induced subsurface damage in optical glass BK7: an experimental, theoretical and numerical investigation,” Precis. Eng. 57, 162–175 (2019).
[Crossref]

T. I. Suratwala, W. A. Steele, L. A. Wong, and G. C. Tham, “Subsurface mechanical damage correlations after grinding of various optical materials,” Opt. Eng. 58, 092604 (2019).
[Crossref]

W. Liu, L. Zhang, Q. Fang, and J. Chen, “A predictive model of subsurface damage and material removal volume for grinding of brittle materials considering single grit micro-geometry,” Int. J. Adv. Manuf. Technol. 69, 161 (2019).
[Crossref]

F. Hou, M. Zhang, Y. Zheng, L. Ding, X. Tang, and Y. Liang, “Detection of laser-induced bulk damage in optical crystals by swept-source optical coherence tomography,” Opt. Express 27, 3698–3709 (2019).
[Crossref]

M. Seiler, L. Tianis, J. Bliedtner, M. Berlinger, and S. Gürtler, “Approaches for a destructive measurement method of subsurface damages,” EPJ Web. Conf. 215, 8001 (2019).
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F. Lakhdari, N. Belkhir, D. Bouzid, and V. Herold, “Relationship between subsurface damage depth and breaking strength for brittle materials,” Int. J. Adv. Manuf. Technol. 102, 1421–1431 (2019).
[Crossref]

2018 (4)

C. J. Trum, C. Vogt, S. Sitzberger, R. Rascher, and O. Faehnle, “Filled-up-microscopy (FUM): a non-destructive method for approximating the depth of sub-surface damage on ground surfaces,” Proc. SPIE 10829, 11 (2018).
[Crossref]

J. Yin, Q. Bai, and B. Zhang, “Methods for detection of subsurface damage: a review,” Chin. J. Mech. Eng. 31, 385 (2018).
[Crossref]

A. Dubois, O. Levecq, H. Azimani, A. Davis, J. Ogien, D. Siret, and A. Barut, “Line-field confocal time-domain optical coherence tomography with dynamic focusing,” Opt. Express 26, 33534–33542 (2018).
[Crossref]

H. Xiao, Z. Chen, H. Wang, J. Wang, and N. Zhu, “Effect of grinding parameters on surface roughness and subsurface damage and their evaluation in fused silica,” Opt. Express 26, 4638–4655 (2018).
[Crossref]

2017 (6)

2016 (6)

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mat. Proc. Tech. 229, 785–794 (2016).
[Crossref]

J. Luo, H. Huynh, C. G. Pantano, and S. H. Kim, “Hydrothermal reactions of soda lime silica glass—revealing subsurface damage and alteration of mechanical properties and chemical structure of glass surfaces,” J. Non-Cryst. Solids 452, 93–101 (2016).
[Crossref]

X. Wu, W. Gao, and Y. He, “Estimation of parameters for evaluating subsurface microcracks in glass with in-line digital holographic microscopy,” Appl. Opt. 55, A32–A42 (2016).
[Crossref]

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large optics for the National Ignition Facility,” Fusion Sci. Technol. 69, 295–351 (2016).
[Crossref]

J. Ogien and A. Dubois, “High-resolution full-field optical coherence microscopy using a broadband light-emitting diode,” Opt. Express 24, 9922–9931 (2016).
[Crossref]

Z. Dong and H. Cheng, “Developing a trend prediction model of subsurface damage for fixed-abrasive grinding of optics by cup wheels,” Appl. Opt. 55, 9305–9313 (2016).
[Crossref]

2015 (1)

2014 (6)

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
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H. Liu, X. Ye, X. Zhou, J. Huang, F. Wang, X. Zhou, W. Wu, X. Jiang, Z. Sui, and W. Zheng, “Subsurface defects characterization and laser damage performance of fused silica optics during HF-etched process,” Opt. Mater. 36, 855–860 (2014).
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W. Liao, Y. Dai, X. Xie, and L. Zhou, “Microscopic morphology evolution during ion beam smoothing of Zerodur surfaces,” Opt. Express 22, 377–386 (2014).
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H. Aida, H. Takeda, S.-W. Kim, N. Aota, K. Koyama, T. Yamazaki, and T. Doi, “Evaluation of subsurface damage in GaN substrate induced by mechanical polishing with diamond abrasives,” Appl. Surf. Sci. 292, 531–536 (2014).
[Crossref]

A. Esmaeilzare, A. Rahimi, and S. M. Rezaei, “Investigation of subsurface damages and surface roughness in grinding process of Zerodur glass–ceramic,” Appl. Surf. Sci. 313, 67–75 (2014).
[Crossref]

Z. Dong, H. Cheng, X. Ye, and H.-Y. Tam, “Subsurface damage of fused silica lapped by fixed-abrasive diamond pellets,” Appl. Opt. 53, 5841–5849 (2014).
[Crossref]

2013 (2)

2012 (2)

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[Crossref]

Z. Yao, W. Gu, and K. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,”J. Mat. Proc. Tech. 212, 969–976 (2012).
[Crossref]

2011 (3)

Y. Lee, J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. Rapid Publ. 6, 1 (2011).
[Crossref]

B. Ma, Z. Shen, P. He, Y. Ji, T. Sang, H. Jiao, H. Liu, D. Liu, Z. Zhai, and Z. Wang, “Subsurface quality of polished SiO2 surface evaluated by quasi-Brewster angle technique,” Optik 122, 1418–1422 (2011).
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B. Ma, Z. Shen, P. He, F. Sha, C. Wang, B. Wang, Y. Ji, H. Liu, W. Li, and Z. Wang, “Evaluation and analysis of polished fused silica subsurface quality by the nanoindenter technique,” Appl. Opt. 50, C279–C285 (2011).
[Crossref]

2010 (5)

2009 (6)

S. Labiau, G. David, S. Gigan, and C. Boccara, “Defocus test and defocus correction in full-field optical coherence tomography,” Opt. Lett. 34, 1576–1578 (2009).
[Crossref]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X (2009).
[Crossref]

F. Elfallagh and B. J. Inkson, “3D analysis of crack morphologies in silicate glass using FIB tomography,” J. Eur. Ceram. Soc. 29, 47–52 (2009).
[Crossref]

J. Neauport, P. Cormont, P. Legros, C. Ambard, and J. Destribats, “Imaging subsurface damage of grinded fused silica optics by confocal fluorescence microscopy,” Opt. Express 17, 3543–3554 (2009).
[Crossref]

C. Wang, A. Tian, H. Wang, B. Li, and Z. Jiang, “Optical subsurface damage evaluation using LSCT,” Proc. SPIE 7522, 75226K (2009).
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J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17, 20448–20456 (2009).
[Crossref]

2008 (2)

T. Suratwala, R. Steele, M. D. Feit, L. Wong, P. Miller, J. Menapace, and P. Davis, “Effect of rogue particles on the sub-surface damage of fused silica during grinding/polishing,” J. Non-Cryst. Solids 354, 2023–2037 (2008).
[Crossref]

S. Li, Z. Wang, and Y. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mat. Proc. Tech. 205, 34–41 (2008).
[Crossref]

2007 (3)

W. Lu, Z. J. Pei, and J. G. Sun, “Non-destructive evaluation methods for subsurface damage in silicon wafers: a literature review,” Int. J. Mach. Machinability Mater. 2, 125 (2007).
[Crossref]

G. Guss, I. L. Bass, R. Hackel, C. Mailhiot, and S. G. Demos, “High-resolution 3D imaging of surface damage sites in fused silica with optical coherence tomography,” Proc. SPIE 6720, 67201F (2007).
[Crossref]

S. N. Shafrir, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage and microstructure development in precision microground hard ceramics using magneto rheological finishing spots,” Appl. Opt. 46, 5500–5515 (2007).
[Crossref]

2006 (2)

T. I. Suratwala, L. A. Wong, P. Miller, M. D. Feit, J. A. Menapace, R. A. Steele, P. A. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[Crossref]

W. Y. Oh, B. E. Bouma, N. Iftimia, S. H. Yun, R. Yelin, and G. J. Tearney, “Ultrahigh-resolution full-field optical coherence microscopy using InGaAs camera,” Opt. Express 14, 726–735 (2006).
[Crossref]

2005 (4)

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44,2241–2249 (2005).
[Crossref]

J. A. Menapace, P. J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599103 (2005).
[Crossref]

J. A. Menapace, P. J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “Utilization of magnetorheological finishing as a diagnostic tool for investigating the three-dimensional structure of fractures in fused silica,” Proc. SPIE 5991, 599102 (2005).
[Crossref]

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik 116, 288–294 (2005).
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2004 (2)

D. A. Lucca, C. J. Wetteland, A. Misra, M. J. Klopfstein, M. Nastasi, C. J. Maggiore, and J. R. Tesmer, “Assessment of subsurface damage in polished II–VI semiconductors by ion channeling,” Nucl. Inst. Meth. Phys. Res. B 219-220, 611–617 (2004).
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A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, “Ultrahigh-resolution full-field optical coherence tomography,” Appl. Opt. 43, 2874–2883 (2004).
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2003 (1)

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264 (2003).
[Crossref]

2002 (4)

1999 (2)

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, and J. L. Ruckman, “Noncontact estimate of grinding-induced subsurface damage,” Proc. SPIE 3782, 41–50 (1999).
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J. C. Lambropoulos, S. D. Jacobs, and J. L. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).
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1997 (1)

J. Lambropoulos, S. D. Jacobs, and B. Gillman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

1994 (1)

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[Crossref]

1991 (1)

D. Huang, E. A. Swanson, C. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, and C. Puliafito, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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1987 (1)

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745 (1974).
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1972 (1)

1946 (1)

F. S. Jones, “Latent milling marks on glass,” J. Am. Ceram. Soc. 29, 108–114 (1946).
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1922 (1)

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Agrawal, A.

Aida, H.

H. Aida, H. Takeda, S.-W. Kim, N. Aota, K. Koyama, T. Yamazaki, and T. Doi, “Evaluation of subsurface damage in GaN substrate induced by mechanical polishing with diamond abrasives,” Appl. Surf. Sci. 292, 531–536 (2014).
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Ambard, C.

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D. S. Anderson and M. E. Frogner, “A method for the evaluation of subsurface damage,” in Technical Digest of the Optical Fabrication and Testing Workshop (1985).

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H. Aida, H. Takeda, S.-W. Kim, N. Aota, K. Koyama, T. Yamazaki, and T. Doi, “Evaluation of subsurface damage in GaN substrate induced by mechanical polishing with diamond abrasives,” Appl. Surf. Sci. 292, 531–536 (2014).
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P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large optics for the National Ignition Facility,” Fusion Sci. Technol. 69, 295–351 (2016).
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Auksorius, E.

Azimani, H.

J. Ogien, O. Levecq, H. Azimani, D. Siret, J.-L. Perrot, and A. Dubois, “Line-field confocal optical coherence tomography: technology and application in dermatology,” Proc. SPIE 11359, 113590F (2020).
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A. Dubois, O. Levecq, H. Azimani, A. Davis, J. Ogien, D. Siret, and A. Barut, “Line-field confocal time-domain optical coherence tomography with dynamic focusing,” Opt. Express 26, 33534–33542 (2018).
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Bai, Q.

J. Yin, Q. Bai, H. Haitjema, and B. Zhang, “Two-dimensional detection of subsurface damage in silicon wafers with polarized laser scattering,” J. Mat. Proc. Tech. 284, 116746 (2020).
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J. Yin, Q. Bai, and B. Zhang, “Methods for detection of subsurface damage: a review,” Chin. J. Mech. Eng. 31, 385 (2018).
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P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large optics for the National Ignition Facility,” Fusion Sci. Technol. 69, 295–351 (2016).
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Bao, W.

Barut, A.

Bass, I. L.

G. Guss, I. L. Bass, R. Hackel, C. Mailhiot, and S. G. Demos, “High-resolution 3D imaging of surface damage sites in fused silica with optical coherence tomography,” Proc. SPIE 6720, 67201F (2007).
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Baxamusa, S.

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
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Beaurepaire, E.

Belkhir, N.

F. Lakhdari, N. Belkhir, D. Bouzid, and V. Herold, “Relationship between subsurface damage depth and breaking strength for brittle materials,” Int. J. Adv. Manuf. Technol. 102, 1421–1431 (2019).
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Benattar, L.

Berlinger, M.

M. Seiler, L. Tianis, J. Bliedtner, M. Berlinger, and S. Gürtler, “Approaches for a destructive measurement method of subsurface damages,” EPJ Web. Conf. 215, 8001 (2019).
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Bliedtner, J.

M. Seiler, L. Tianis, J. Bliedtner, M. Berlinger, and S. Gürtler, “Approaches for a destructive measurement method of subsurface damages,” EPJ Web. Conf. 215, 8001 (2019).
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Boccara, A. C.

Boccara, C.

Börret, R.

M. Sergeeva, K. Khrenikov, T. Hellmuth, and R. Börret, “Sub surface damage measurements based on short coherent interferometry,”J. Eur. Opt. Soc. Rapid Publ. 5, 1–5 (2010).
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R. Börret, D. Wiedemann, and A. Kelm, “Detection of subsurface damage in optical transparent materials using short coherence tomography,” in 58th Ilmenau ScientificColloquium, (2014).

Bouma, B. E.

Bouzid, D.

F. Lakhdari, N. Belkhir, D. Bouzid, and V. Herold, “Relationship between subsurface damage depth and breaking strength for brittle materials,” Int. J. Adv. Manuf. Technol. 102, 1421–1431 (2019).
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Brinksmeier, E.

G. Schnurbusch, E. Brinksmeier, and O. Riemer, “Influence of cutting speed on subsurface damage morphology and distribution in ground fused silica,” Inventions 2, 15 (2017).
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Bude, J.

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
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Bude, J. D.

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
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P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X (2009).
[Crossref]

Carr, W.

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
[Crossref]

Catrin, R.

Chang, W.

D. Huang, E. A. Swanson, C. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, and C. Puliafito, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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Chen, G.

D. Lv, M. Chen, Y. Yao, Y. Zhao, G. Chen, Y. Peng, and Y. Zhu, “Prediction of subsurface damage depth in rotary ultrasonic machining of glass BK7 with probability statistics,” Int. J. Adv. Manuf. Technol. 107, 1337–1344 (2020).
[Crossref]

Chen, J.

W. Liu, L. Zhang, Q. Fang, and J. Chen, “A predictive model of subsurface damage and material removal volume for grinding of brittle materials considering single grit micro-geometry,” Int. J. Adv. Manuf. Technol. 69, 161 (2019).
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Chen, M.

D. Lv, M. Chen, Y. Yao, Y. Zhao, G. Chen, Y. Peng, and Y. Zhu, “Prediction of subsurface damage depth in rotary ultrasonic machining of glass BK7 with probability statistics,” Int. J. Adv. Manuf. Technol. 107, 1337–1344 (2020).
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Chen, S.

P. Li, S. Chen, H. Xiao, Z. Chen, M. Qu, H. Dai, and T. Jin, “Effects of local strain rate and temperature on the workpiece subsurface damage in grinding of optical glass,” Int. J. Mech. Sci. 182, 105737 (2020).
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Chen, X.

Chen, Z.

Cheng, H.

Cheng, J.

J. Cheng, J. Wang, J. Hou, H. Wang, and L. Zhang, “Effect of polishing-induced subsurface impurity defects on laser damage resistance of fused silica optics and their removal with HF acid etching,” Appl. Sci. 7, 838 (2017).
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Corbineau, T.

Cormont, P.

Cross, D.

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
[Crossref]

Dai, H.

P. Li, S. Chen, H. Xiao, Z. Chen, M. Qu, H. Dai, and T. Jin, “Effects of local strain rate and temperature on the workpiece subsurface damage in grinding of optical glass,” Int. J. Mech. Sci. 182, 105737 (2020).
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Dai, Y.

Darbois, N.

David, G.

Davis, A.

Davis, J.

P. P. Hed, D. F. Edwards, and J. Davis, “Sub-surface damage in optical materials: origin, measurement, and removal,” in Sub-Surface Damage in Glass (1989).

Davis, P.

T. Suratwala, R. Steele, M. D. Feit, L. Wong, P. Miller, J. Menapace, and P. Davis, “Effect of rogue particles on the sub-surface damage of fused silica during grinding/polishing,” J. Non-Cryst. Solids 354, 2023–2037 (2008).
[Crossref]

Davis, P. A.

T. I. Suratwala, L. A. Wong, P. Miller, M. D. Feit, J. A. Menapace, R. A. Steele, P. A. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[Crossref]

P. Miller, T. I. Suratwala, L. A. Wong, M. D. Feit, J. A. Menapace, P. A. Davis, and R. A. Steele, “The distribution of subsurface damage in fused silica,” in Boulder Damage Syposium (2005).

Davis, P. J.

J. A. Menapace, P. J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “MRF applications: measurement of process-dependent subsurface damage in optical materials using the MRF wedge technique,” Proc. SPIE 5991, 599103 (2005).
[Crossref]

J. A. Menapace, P. J. Davis, W. A. Steele, L. L. Wong, T. I. Suratwala, and P. E. Miller, “Utilization of magnetorheological finishing as a diagnostic tool for investigating the three-dimensional structure of fractures in fused silica,” Proc. SPIE 5991, 599102 (2005).
[Crossref]

de Martino, A.

Demos, S. G.

G. Guss, I. L. Bass, R. Hackel, C. Mailhiot, and S. G. Demos, “High-resolution 3D imaging of surface damage sites in fused silica with optical coherence tomography,” Proc. SPIE 6720, 67201F (2007).
[Crossref]

Deng, Y.

Destino, J.

T. I. Suratwala, R. A. Steele, L. A. Wong, P. Miller, J. Destino, E. Feigenbaum, N. Shen, N. Ray, and M. Feit, “Predictive models for grinding & polishing of various optical materials,” in Optical Design and Fabrication (Freeform, OFT) (OSA, 2019), paper OT1A.3.

Destribats, J.

Ding, L.

Ding, Z.

Doi, T.

H. Aida, H. Takeda, S.-W. Kim, N. Aota, K. Koyama, T. Yamazaki, and T. Doi, “Evaluation of subsurface damage in GaN substrate induced by mechanical polishing with diamond abrasives,” Appl. Surf. Sci. 292, 531–536 (2014).
[Crossref]

Dong, Z.

Drévillon, B.

Drexler, W.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2015).

Dubois, A.

Duparré, A.

M. Trost, T. Herffurth, D. Schmitz, S. Schröder, A. Duparré, and A. Tünnermann, “Evaluation of subsurface damage by light scattering techniques,” Appl. Opt. 52, 6579–6588 (2013).
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T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Light scattering to detect imperfections relevant for laser-induced damage,” Proc. SPIE 8530, 85301B (2012).
[Crossref]

Edwards, D. F.

P. P. Hed and D. F. Edwards, “Relationship between surface roughness and subsurface damage,” Appl. Opt. 26, 4677–4680 (1987).
[Crossref]

P. P. Hed, D. F. Edwards, and J. Davis, “Sub-surface damage in optical materials: origin, measurement, and removal,” in Sub-Surface Damage in Glass (1989).

Elfallagh, F.

F. Elfallagh and B. J. Inkson, “3D analysis of crack morphologies in silicate glass using FIB tomography,” J. Eur. Ceram. Soc. 29, 47–52 (2009).
[Crossref]

Esmaeilzare, A.

A. Solhtalab, H. Adibi, A. Esmaeilzare, and S. M. Rezaei, “Cup wheel grinding-induced subsurface damage in optical glass BK7: an experimental, theoretical and numerical investigation,” Precis. Eng. 57, 162–175 (2019).
[Crossref]

A. Esmaeilzare, A. Rahimi, and S. M. Rezaei, “Investigation of subsurface damages and surface roughness in grinding process of Zerodur glass–ceramic,” Appl. Surf. Sci. 313, 67–75 (2014).
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Faehnle, O.

C. J. Trum, C. Vogt, S. Sitzberger, R. Rascher, and O. Faehnle, “Filled-up-microscopy (FUM): a non-destructive method for approximating the depth of sub-surface damage on ground surfaces,” Proc. SPIE 10829, 11 (2018).
[Crossref]

Fan, Z.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik 116, 288–294 (2005).
[Crossref]

Fang, Q.

W. Liu, L. Zhang, Q. Fang, and J. Chen, “A predictive model of subsurface damage and material removal volume for grinding of brittle materials considering single grit micro-geometry,” Int. J. Adv. Manuf. Technol. 69, 161 (2019).
[Crossref]

Feigenbaum, E.

T. I. Suratwala, R. A. Steele, L. A. Wong, P. Miller, J. Destino, E. Feigenbaum, N. Shen, N. Ray, and M. Feit, “Predictive models for grinding & polishing of various optical materials,” in Optical Design and Fabrication (Freeform, OFT) (OSA, 2019), paper OT1A.3.

Feit, M.

T. I. Suratwala, R. A. Steele, N. Shen, N. Ray, L. A. Wong, P. Miller, and M. Feit, “Lateral cracks during sliding indentation on various optical materials,” J. Am. Ceram. Soc. 103, 1343–1357 (2020).
[Crossref]

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
[Crossref]

T. I. Suratwala, R. A. Steele, L. A. Wong, P. Miller, J. Destino, E. Feigenbaum, N. Shen, N. Ray, and M. Feit, “Predictive models for grinding & polishing of various optical materials,” in Optical Design and Fabrication (Freeform, OFT) (OSA, 2019), paper OT1A.3.

Feit, M. D.

P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. 35, 2702–2704 (2010).
[Crossref]

P. E. Miller, T. I. Suratwala, J. D. Bude, T. A. Laurence, N. Shen, W. A. Steele, M. D. Feit, J. A. Menapace, and L. L. Wong, “Laser damage precursors in fused silica,” Proc. SPIE 7504, 75040X (2009).
[Crossref]

T. Suratwala, R. Steele, M. D. Feit, L. Wong, P. Miller, J. Menapace, and P. Davis, “Effect of rogue particles on the sub-surface damage of fused silica during grinding/polishing,” J. Non-Cryst. Solids 354, 2023–2037 (2008).
[Crossref]

T. I. Suratwala, L. A. Wong, P. Miller, M. D. Feit, J. A. Menapace, R. A. Steele, P. A. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352, 5601–5617 (2006).
[Crossref]

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264 (2003).
[Crossref]

P. Miller, T. I. Suratwala, L. A. Wong, M. D. Feit, J. A. Menapace, P. A. Davis, and R. A. Steele, “The distribution of subsurface damage in fused silica,” in Boulder Damage Syposium (2005).

T. I. Suratwala, P. E. Miller, M. D. Feit, and J. A. Menapace, Scratch Forensics (2008).

Fine, K. R.

K. R. Fine, R. Garbe, T. Gip, and Q. Nguyen, “Non-destructive real-time direct measurement of subsurface damage,” in Optical fabrication and testing, Québec, Canada, June18, 2000 (OSA, 2000), pp. 105.

Flotte, T.

D. Huang, E. A. Swanson, C. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, and C. Puliafito, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Frogner, M. E.

D. S. Anderson and M. E. Frogner, “A method for the evaluation of subsurface damage,” in Technical Digest of the Optical Fabrication and Testing Workshop (1985).

Fujimoto, J. G.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2015).

Funkenbusch, P. D.

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, and J. L. Ruckman, “Noncontact estimate of grinding-induced subsurface damage,” Proc. SPIE 3782, 41–50 (1999).
[Crossref]

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[Crossref]

Gao, W.

Garbe, R.

K. R. Fine, R. Garbe, T. Gip, and Q. Nguyen, “Non-destructive real-time direct measurement of subsurface damage,” in Optical fabrication and testing, Québec, Canada, June18, 2000 (OSA, 2000), pp. 105.

Gigan, S.

Gillman, B.

J. Lambropoulos, S. D. Jacobs, and B. Gillman, “Subsurface damage in microgrinding optical glasses,” LLE Rev. 73, 45–49 (1997).

Gip, T.

K. R. Fine, R. Garbe, T. Gip, and Q. Nguyen, “Non-destructive real-time direct measurement of subsurface damage,” in Optical fabrication and testing, Québec, Canada, June18, 2000 (OSA, 2000), pp. 105.

Golini, D.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, and A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[Crossref]

Gregory, K.

D. Huang, E. A. Swanson, C. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, and C. Puliafito, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Grieve, K.

Gu, W.

Z. Yao, W. Gu, and K. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,”J. Mat. Proc. Tech. 212, 969–976 (2012).
[Crossref]

Guo, Y.

Y. Lee, J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. Rapid Publ. 6, 1 (2011).
[Crossref]

Y. Li, H. Huang, R. Xie, H. Li, Y. Deng, X. Chen, J. Wang, Q. Xu, W. Yang, and Y. Guo, “A method for evaluating subsurface damage in optical glass,” Opt. Express 18, 17180–17186 (2010).
[Crossref]

Gürtler, S.

M. Seiler, L. Tianis, J. Bliedtner, M. Berlinger, and S. Gürtler, “Approaches for a destructive measurement method of subsurface damages,” EPJ Web. Conf. 215, 8001 (2019).
[Crossref]

Guss, G.

J. Bude, P. E. Miller, N. Shen, T. Suratwala, T. Laurence, W. Steele, S. Baxamusa, L. Wong, W. Carr, D. Cross, M. Monticelli, M. Feit, and G. Guss, “Silica laser damage mechanisms, precursors and their mitigation,” Proc. SPIE 9237, 92370S (2014).
[Crossref]

G. Guss, I. L. Bass, R. Hackel, C. Mailhiot, and S. G. Demos, “High-resolution 3D imaging of surface damage sites in fused silica with optical coherence tomography,” Proc. SPIE 6720, 67201F (2007).
[Crossref]

Hackel, R.

G. Guss, I. L. Bass, R. Hackel, C. Mailhiot, and S. G. Demos, “High-resolution 3D imaging of surface damage sites in fused silica with optical coherence tomography,” Proc. SPIE 6720, 67201F (2007).
[Crossref]

Haitjema, H.

J. Yin, Q. Bai, H. Haitjema, and B. Zhang, “Two-dimensional detection of subsurface damage in silicon wafers with polarized laser scattering,” J. Mat. Proc. Tech. 284, 116746 (2020).
[Crossref]

Han, J.

Y. Lee, J. Wang, Y. Li, J. Han, Q. Xu, and Y. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. Rapid Publ. 6, 1 (2011).
[Crossref]

Hawley, R. A.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large optics for the National Ignition Facility,” Fusion Sci. Technol. 69, 295–351 (2016).
[Crossref]

He, H.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik 116, 288–294 (2005).
[Crossref]

He, P.

B. Ma, Z. Shen, P. He, Y. Ji, T. Sang, H. Jiao, H. Liu, D. Liu, Z. Zhai, and Z. Wang, “Subsurface quality of polished SiO2 surface evaluated by quasi-Brewster angle technique,” Optik 122, 1418–1422 (2011).
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B. Ma, Z. Shen, P. He, F. Sha, C. Wang, B. Wang, Y. Ji, H. Liu, W. Li, and Z. Wang, “Evaluation and analysis of polished fused silica subsurface quality by the nanoindenter technique,” Appl. Opt. 50, C279–C285 (2011).
[Crossref]

He, Y.

Hed, P. P.

P. P. Hed and D. F. Edwards, “Relationship between surface roughness and subsurface damage,” Appl. Opt. 26, 4677–4680 (1987).
[Crossref]

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T. I. Suratwala, R. A. Steele, N. Shen, N. Ray, L. A. Wong, P. Miller, and M. Feit, “Lateral cracks during sliding indentation on various optical materials,” J. Am. Ceram. Soc. 103, 1343–1357 (2020).
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Supplementary Material (4)

NameDescription
Dataset 1       Digital microscopy image with co-registered OCT-images on a ground fused silica sample (HPFS7980, wet etched, HF 20%, 30 s), polished with a wedge by spherical polishing. TIFF-Stack. Layer 1: DM; Layer 2: DM+AIP; Layer 3: DM+CCDM. Colormap in La
Dataset 2       Digital microscopy image with co-registered OCT-images on a ground fused silica sample (HPFS7980, not etched), polished with a wedge by spherical polishing. TIFF-Stack. Layer 1: DM; Layer 2: DM+AIP; Layer 3: DM+CCDM. Colormap in Layer 3 ranges f
Dataset 3       Figital microscopy image with co-registered OCT-images on a ground optical glass sample (SF6, wet etched, HF 10%, 10 s), polished with a wedge by spherical polishing. TIFF-Stack. Layer 1: DM; Layer 2: DM+AIP; Layer 3: DM+CCDM. Colormap in Layer
Dataset 4       Digital microscopy image with co-registered OCT-images on a ground optical glass sample (SF6, not etched), polished with a wedge by spherical polishing. TIFF-Stack. Layer 1: DM; Layer 2: DM+AIP; Layer 3: DM+CCDM. Colormap in Layer 3 ranges from

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Figures (8)

Fig. 1.
Fig. 1. Three-layer model of SSD in polished optical glass after Hed et al. [2]
Fig. 2.
Fig. 2. Sketch of experimental setup with FF-OCT from LLTech.
Fig. 3.
Fig. 3. Schematic representation of a tomographic OCT dataset and application of different projection methods. Intensity values for voxels range from zero (black) to one (white).
Fig. 4.
Fig. 4. Sketch of destructively referenced glass sample with OCT measurement positions (1–7) and position marks (L-shapes). (a) Sagittal view; (b) lateral view; (c) image of a sample ( $40 \times 40 \times 12\;{\rm mm}^3$ ).
Fig. 5.
Fig. 5. Detailed lateral view of a defect captured in FF-OCT scan SF6 4 ne, displayed in SSD dynamic range. (a) Local MIP without deconvolution or defective pixel correction. i: Signal sidelobes from surface signal; ii: defective pixel artifacts. (b) Local MIP with defective pixel correction and deconvolution; iii: removed signal sidelobes resulting in a darkened area.
Fig. 6.
Fig. 6. (a) Histogram of FF-OCT scans with 10-times averaging. Red: noise only; green: polished; blue: ground. (b) Area-depth functions of FF-OCT scans along the taper. Green: polished; cyan: partly polished; blue: ground. Maximum of area density corresponds to surface position. SSD threshold indicated by dashed line in magenta.
Fig. 7.
Fig. 7. Images with magnified sections of four FF-OCT scans in two different visualization modes. Color indicates depth relative to ground surface. (a)–(d) Sagittal view, CCDM; (e)–(f) sagittal view, AIP. (a), (e) FS 1 ne; (b), (f) SF 6 ne; (c), (g) FS 4 e; (d), (h) SF6 4 e. Overviews with all FF-OCT scans can be found in Dataset 1, Ref. [67] for FS e, Dataset 2, Ref. [68] for FS ne, Dataset 3, Ref. [69] for SF6 e, and Dataset 4, Ref. [70] for SF6 ne.
Fig. 8.
Fig. 8. Images of FF-OCT scan FS 4 e. (a) Lateral view, global MIP; (b) lateral view, local MIP; (c) lateral view, slice. The horizontal black bar beneath the surface is an artifact originating from deconvolution.

Tables (2)

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Table 1. Predictions for Maximum Crack Depths ${c_{{\max}}}$ Based on Surface Roughness ${Rt}$

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Table 2. Metrics for Local Maximum Crack Depths ${c_{{\max}}}$

Equations (2)

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$${R_{{\min}}}(N) = \frac{{{R_{{\min}}}(10)}}{{10 \cdot N}}.$$
$${\rm{imgInt}} = \sum\limits_{i = 1}^n {\frac{{{\rm{im}}{{\rm{g}}_i}}}{n}} .$$

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