Three-dimensional profilometry for tool wear area using modulation-based structured illumination microscopy

A new approach named modulation-based structured-illumination microscopy (MSIM) is presented in this paper to reconstruct the three-dimensional (3D) topography of the tooltip, which can be used to evaluate the degree of wear. In MSIM, the modulation estimation of the reflected patterns characterizes the surface profile. This technique can reconstruct the 3D profile precisely and something that conventional computer vision and imaging analysis cannot achieve. Importantly, an ordinary objective lens is used in the measurement system to take the image of the sample. So, the measurement system is simple and cheap. The theoretical analysis and experiments conducted on the tooltip are presented. The measurement repeatability can reach 500 nm. This method holds promise for applications in tool wear monitoring, wear mechanism analysis, and micromachining.


Introduction
Tool wear can lead to a decrease in machining accuracy, increase machining costs, and reduce the quality of parts processing.The widespread characterization of tool wear is an increasingly demanding and interesting field, as it always has an important influence on the machined parts' quality [1].The poor imaging quality caused by the extremely rough characteristics of the tool wear makes it difficult to determine the three-dimensional (3D) topography effectively.Currently, most laboratories and research departments that perform wear analysis utilize ordinary microscopes to observe the twodimensional (2D) images of the wear.However, the 3D morphology of the wear area contains richer wear information which is significant for precisely studying the wear mechanism.So far, various technologies have been proposed to monitor tool wear, among which computer vision, confocal scanning microscopy, and interferometry are the most widely used.
Previously, techniques based on machine vision were proposed to detect tool wear in the manufacturing field due to the advantages of high efficiency and a simple measurement system.For example, TG.Kim uses a computer vision sensor module to measure the lateral wear of drilling tools, which features a zoom lens, a CCD camera, and intelligent image processing algorithms [2].The drawback is that these methods can only detect the two-dimensional topography of the tool wear area.The 3D topography of the worn area is almost absent.In addition, the threshold needs to be manually selected to remove the noise of the image in most cases.In that case, the image processing of the measurement is complex and time-consuming.In addition to image processing methods, methods based on interferometry are also established for precise contour measurement of engineering surfaces, especially microstructures [3].In these methods, the phase information of the interferogram is extracted to reshape the 3D profile.However, when these methods are applied on extremely rough surfaces, the the interferogram will be distorted and difficult to accurately evaluate.Therefore, these methods are not suitable for surfaces with sudden phase transitions, such as specimens with extremely rough surfaces or large step heights.
To solve the problem of rough morphology measurement, techniques based on focus detection are developed.For example, laser confocal is a typical measurement method based on focus detection and can be used to evaluate the rough surface contours [4].In confocal microscopy, the location of the maximum signal intensity is extracted to evaluate the 3D shape.For example, Y. Takaya evaluated the tool geometry precisely using confocal fluorescence microscopy with sub-micron accuracy.However, to obtain a whole field profile, this method needs to scan the sample using a moving platform which will be time-consuming.
To overcome the drawbacks described above, a novel method named modulation-based structured illumination (MSIM) for 3D tool wear detection is proposed.In this method, a sinusoidal image produced by a projector is illuminated on the sample.Then, the modulation of the strip images which depends on the surface topography of the sample is used to characterize the 3D shape.The measurement can be achieved with high adaptability since it directly exploits the distribution of the light field to achieve the measurement.Furthermore, this technique can achieve a three-dimensional profile with high accuracy, which is impossible for conventional computer vision and imaging analysis.In addition, the system is relatively simple as the three-dimensional observation of images can be achieved under ordinary optical microscopy.This method holds promise for applications in tool wear monitoring, wear mechanism analysis, and micromachining.

measurement system and principle
Figure 1 is the schematic diagram.In this measurement system, the function of digital micromirror devices (DMD) is to generate stripe images.The produced strip images are transmitted onto the sample through the imaging system, which is composed of a splitter mirror, two tube lenses, and an objective lens.The reflected patterns from the sample are transmitted through the imaging system and are finally captured by a camera.

modulation evaluation
A detailed explanation of the principle of modulation evaluation will be introduced in this section.
Here, the phase shift algorithm is used to calculate the modulation.When a sinusoidal pattern is projected on the sample, the expression of the intensity of the captured image is (1) where f is the spatial frequency, I0(x, y) indicates the background intensity and its value is a constant, ϕ0 is the initial phase, and M(x, y) is the modulation.
To calculate the modulation distribution from Equation (1), the pattern needs to be shifted by a predetermined phase.Assuming that the total phase-shift steps are L, the intensity can be denoted by (2) where i is the i-th phase-shift image and its value is i = 1, 2, ..., L. (3)

Three-dimensional reconstruction
After calculating the modulation from the captured pattern, the focal position needs to be determined.According to the analysis by P. A. Stokseth, the relationship between the distance from the focal plane and the modulation satisfies Gaussian distribution [5][6], and its expression can be denoted by To detect the focal position from Equation ( 4), the existing algorithms mainly include the curve fitting technique, the centroid algorithm, and the maximum point method.Among them, curve fitting is the most accurate focus detection technique.So, several points need to be extracted around the maximum point, and then the Gaussian curve fitting technique based on least squares is performed to detect the accurate focal position, as shown in Figure 2. The height information H can be described as <√ as H ZZ (5) where Zs is the vertical scanning distance for each step.

Measurement results
Experiments were conducted based on the above theory.The experimental setup is shown in Figure 3, A broadband LED lighting tool sample is used with a central wavelength of 533 nm, a projector (1024 × 768 pixels, TI), a PZT scanning table with a resolution of ±0.5 nm, a CCD camera (WAT-902H), and a microscope (20 X, NA = 0.4, Nikon).In the experiment, the tip of a worn tool is utilized as the measured object.

Discussion and conclusion
A novel way is provided in this paper to obtain the surface topography of the tool wear area.First, the modulation distribution is determined by the phase shift algorithm.Then, a Gaussian fitting based on the least square technique is used to detect the focus position.Finally, the 3D shape can be determined by the focus position and step pace.The proposed method can provide precise 3D profiles of the tool wear area and something that conventional computer vision and imaging analysis cannot achieve.The system is relatively simple as the 3D observation of images can be achieved under ordinary optical microscopy.The contact measuring system is easy to cause damage to the sample at the microscopic level, while the non-contact measuring system has no damage to the measured sample and can continuously and automatically measure the sample.With the continuous progress of science and technology, the direction of precision measurement technology is developing toward polarization, super-size precision measurement, and micro-size precision measurement.Many disciplines, such as mechanics, electronics, materials, and mechanics, analyze and study samples at the microscopic level.This method holds promise for applications in tool wear monitoring, wear mechanism analysis, and micromachining.

Figure 1 .
Figure 1.Schematic diagram of the MSIM system for tool wear measurement.

3
where Mmax represents the modulation value of the focal position, z is the distance from the focal plane, za shows the precise focal position, and FWHM is the abbreviation for half maximum full width.

Figure 2 .
Figure 2. Determining the focal position based on Gaussian curve fitting.The height information H can be described as
Figure 4(a) shows the image of the sample.The fringe pattern loaded on the DMD is set to 16 pixels per period.The scanning range and the step pace are set as 58 μm and 0.5 μm, respectively.Figure 4 (b) shows the images of different scanning positions.For each position, eight patterns are captured and the modulation is achieved by the eight-step phase shift algorithm.Figure 4(c) illustrates the modulation curve at the position of (X = 400, Y = 500).

Figure 4 .
Figure 4. (a) The measured object (a worn tool).(b) The images captured by camera.(c) The modulation curve (x=400, y=500).Then, the focal position is detected by the curve fitting technique.The 3D shape can be determined through Equation (5).

Figure 5 .
Figure 5. (a) The reconstructed 3D map.(b) The profile (Y = 350) of Figure 5(a).Five repeated measurement experiments were conducted in this paper to evaluate the measurement accuracy.The red line and blue line of Figure 6(a) illustrate the profile at the position (X = 400:500) of Figure 5(b), which is obtained from the first experiment and the second experiment, respectively.The repeatability is within 500 nm.