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An alternative method for evaluating subsurface damage (SSD) in ground fused silica is presented. The method can acquire the knowledge of depth and morphology of subsurface damage at the same time. The fundamental support lent to the method is the fact that the depth of field reduces as the numerical aperture (NA)/magnification increases in optical microscopes. Large depth of field without undermining NA is preferred in most applications while the narrow range of focus depth is desired for our method. Using this method, we experimented on fused silica which was ground with bound-abrasive diamond wheels and the results show good agreement with the traditional method. The consistency indicates that the proposed method is practicable and effective in inspecting the subsurface damage in optical components.
©2010 Optical Society of America
1. Introduction
Subsurface damage (SSD) is of great importance in material processing, because it is a critical factor influencing the strength of materials and the usage of components. Subsurface damage is incurred due to material fracture in the machining of brittle materials such as glasses and ceramics. The fracture will be generated when brittle material is subjected to extreme pressure such as exerted by fine abrasives, for instance, silicon carbide, alumina, and diamond, etc. which are widely used, at present, for loose abrasive lapping or bound abrasive grinding of glasses [1–3]. The SSD must be eliminated in order to improve the performance and lifetime of optical components by means of polishing techniques [4,5]. Polishing is time-consuming and not cost-effective compared to grinding process. Therefore, the less the material to be removed the better in polishing process. The material that needs to be removed should not be less than the depth of SSD left by loose/fixed abrasive grinding. Therefore it is necessary to measure subsurface damage so as to minimize the cost and time to fabricate an optical component.
A number of methods are available to assess subsurface damage in glass and ceramics nowadays [6–10]. Generally speaking, these methods can be grouped into two general categories: destructive and nondestructive evaluation [6,10]. Destructive techniques are more explicit and reliable whilst nondestructive ones will not make samples unusable. Because the equipment for nondestructive testing is usually very expensive and the mechanism is fairly complicated, the destructive methods are preferable to evaluating SSD in optical workshop. To measure subsurface damage, a profiler (e.g. TalySurf by Taylor Hobson) is typically utilized in conjunction with an optical microscope in conventional testing processes [11–14]. The ground surface of fused silica is at first wedged or spotted with a polishing machine and etched in chemical solutions (usually containing hydrofluoric acid or fluoride) to open cracks, then profiled with a stylus profilometer along the wedge or the centerline of the spot and inspected with the aid of an optical microscope. At last, the results from profilometer and microscope are compared in order to gain knowledge of subsurface damage (e.g. depth of SSD, morphologies at varied depths below the ground surface). The above procedure requires that the area scanned with the microscope correspond to the area profiled with the profilometer, which maybe bring about repositioning errors. In addition, the essential instrument profilometer can be as expensive as several hundred thousand dollars like the Form Talysurf PGI-1240, Taylor Hobson. More recently, a convenient approach was put forward by J. Neauport et al. to determine the subsurface damage of ground fused silica without the need for optical microscopy and pre-polishing to expose the SSD [15,16]. However, the surface to be measured undergoes chemical etching together with profiling several times so that the variation in surface roughness with the etching time/thickness can be obtained. The profilometer is a key apparatus to this technique, too. It is not necessarily time-saving to implement this technique in comparison with the traditional method. Most importantly, the results of the method strongly depend on the tip of the profilometer’s stylus [17–19]. Theoretically speaking, the sharper the tip is, the closer to actual value the measurements are. As a result, this technique underestimates the actual depth of subsurface damage.
Here we proposed an alternative to the classical testing method. The preparation of samples is the same as the conventional method whereas the differences exist in the observation and measurement of subsurface damage. A laser displacement sensor (less than ten thousand dollars) far more inexpensive than the Form Talysurf is combined with an optical microscope to simultaneously acquire the information on depth and density of subsurface damage. The repositioning error is obviated since there is no need for the transportation of the sample from microscopes to profilers or inverse operation. The detailed description of the system is presented and followed by discussion on the properties of measuring system. Finally, a comparison in measuring results between the new method and traditional one is given.
2. The basic science of the proposed method and the configuration of measuring system
As it is well known, each objective lens in a microscope has characteristic numerical aperture (NA), focus distance and depth of field (DOF). Greater magnification will be accompanied by larger NA and smaller DOF as well as shorter working distance (focal length). The depth of field in an optical microscope decreases as magnification increases. In most cases, both large NA and DOF/working distance (focal length) are preferred. Much effort has been made to increase the NA whilst maintaining long working distance and large DOF [20]. However, small DOF rather than large DOF is desirable in our method, because the DOF dominates the resolution of the proposed method which is based on the fact that the cracks out of focus are blurred and only when located in the range of depth of field the cracks can be clearly observed. When there exist cracks at Z1 & Z2, one can first focus the objective onto the location Z1 (Fig. 1 ). Moving the stage under the sample or the objective and adjusting the objective lens to focus the lens onto Z2, the difference is the depth of Z2 from Z1 once the values of Z1 & Z2 can be known and the cracks at Z1 & Z2 can be imaged as well. If Z1 is located on the surface of a ground fused silica sample, the difference between Z1 and Z2 is the depth of subsurface damage when the last traces of SSD is situated at Z2. Varying the Z2, one can collect a series of morphologies at various depths under the ground surface. This way the SSD depth and morphology of SSD at a certain depth can be obtained at the same time.
According to the abovementioned principle, a measuring system was set up. This set-up is composed of an optical microscope (Leica DM4000M, Germany), a laser displacement sensor (Keyence LK-G10, Japan), a motorized translation stage capable of moving in 3-direction independently (i.e. X, Y, Z axes) and a computer for displaying the images of cracks, controlling the movement of the stage and processing data (Fig. 2 ). The microscope was equipped with 5 types of objective lens with 5 × , 10 × , 20 × , 50 × , 100 × magnification, respectively, as well as a 10 × eyepiece. However, only two objectives (largest and smallest magnification lens) were frequently used in our experiments; the 100 × lens was applied to measure the depth of SSD and the other 5 × lens was employed to assist in approximately positioning the area to be examined and locating the last trace of SSD due to its relatively wide field of view (2620.3µm × 1965.2µm). The laser displacement sensor with a resolution of 0.1μm plays a part in registering the displacement in Z direction, the detecting beam of which is red laser light of 650nm in wavelength. The translation stage driven by a motor can travel in three directions independently with steps of 0.1mm, 0.1mm and 0.1μm in X-, Y-, and Z-axis, respectively. Two screws are designed to guarantee a horizontal stage or surface to be tested.
Fig. 2 Sketch of apparatus for measuring subsurface damage of ground substrates. The translation stage is capable of moving along X, Y and Z directions.
The resolution of the measuring system is influenced by many factors, among which the depth of field is the most important. The depth of field usually relates to numerical aperture (NA) and magnification of the objective. Provided that the sample lies within the range of the depth of field (DOF), the viewgraph will be clear. In our experiments, the small DOF facilitated the resolution of the system; as a result, the large NA/magnification objective lens(100 × ) was selected. The DOF of some commonly used objectives are tabulated in Table 1 [21], including the measured range out of which the images were apparently dimmed. The range is the distance between lower and upper position beyond which the images of cracks are obviously vague.
Table 1. The magnification and numerical aperture (NA) of common-use objective lens and corresponding depth of field (DOF).
3. Experiments and results
We experimented on ground fused silica with the set-up and made comparison between the measurements of the proposed setup and the conventional method. Two fused silica samples with diameter of 50mm, 10mm thick were ground with D91 (grit size: 75~90μm) and D7 (grit size: 5~10μm) diamond wheels (Winter Diamond Tools, Saint-Gobain Diamantwerkzeuge GmbH & Co., Germany). Following that, the samples were spotted with a commercial magnetorheological finishing (MRF) machine (Q22-400X, QED Technologies, USA) at 3, 6, 9 and 12 o’clock positions. Afterwards the substrates were etched for 15 minutes in HF solution (wt.1%HF, wt.10%NH4F) at room temperature 20°C so as to open cracks for the ease of observation. Then the subsurface damage was evaluated with the new system and classical approach (the profilometer used was the Form Talysurf PGI-1240, Taylor Hobson, UK).
Shown in Table 2 are the measurements of subsurface damage for two samples. The results agree well with each other, indicating the new technique is applicable to the measurement of SSD depth. The distribution of SSD was also investigated and the images are presented in Fig. 3 of cracks at varied depths from the ground surface. All the images were taken at 1000 × magnification (100 × objective lens), with the real size (i.e. field of view) of 131.0µm (length) × 98.3 µm (width). It is evident that the number of cracks decreases as the depth from the surface increases and the cracks disappear totally when the depth exceeds a certain value. These images were processed so that the change, at least the trend, in density can be reflected quantitatively. Here, we followed other researchers to adopt image processing technique as a makeshift measure for evaluating the density of SSD [22–24]. First, the image was converted to a binary picture. Then the size of cracks was calculated based on pixels. Finally, the crack density was represented as a percentage of the pixels of full images. The correlation of density with the depth into bulk material is plotted in Fig. 4 . The density/number of cracks exponentially decays as the depth increases. The density sharply diminishes within the top layer of first microns; thereafter, the diminution in crack density slows down and the cracks disappear at last beyond a finite depth. The reduction of crack density is more significant for D7 ground surface than for D91 diamond wheel. These results are consistent with earlier researches [13,23–25].
Table 2. The last traces of SSD in ground fused silica with D91 and D7 diamond wheels. The results using traditional and proposed methods agree well with each other.
Fig. 3 Typical subsurface cracks in ground optical substrates by D91 diamond wheel: (a)-(f) and D7 diamond wheel: (g)-(l). The value at upper left corner is the depth below the original ground surfaces where the image was taken.
Fig. 4 The relationship between subsurface crack density and the depth from ground substrate surface. The crack density drops exponentially with increasing the depth. The density by D7 diamond wheel drops much faster than that by D91 diamond wheel.
4. Conclusions
We have demonstrated a practical method that can concurrently measure the depth of subsurface damage and acquire the morphology of subsurface damage in ground optics. This method is put forward based on the fact that the depth of field decreases with increasing the magnification/numerical aperture (NA) in optical microscopes. In addition, the method incorporates a laser displacement sensor into an optical microscope other than a stylus profilometer, which makes the testing of SSD more convenient. The laser displacement sensor can precisely and non-contactly gauge the depth of subsurface damage. Compared to the conventional technique, both the cost and time needed to inspect subsurface damage in ground optical components are saved. The experimental results evidence that the SSD depth evaluated with the proposed method is in rather good agreement with the conventional technique.
Acknowledgements
The authors appreciate valuable expert comments and advice on the manuscript from all anonymous reviewers. This work was financially supported by the Foundation of China Academy of Engineering Physics (Grant No. 2007A08001).
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