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Abstract
We propose “the external reflectance versus height conversion (ERHC) method” for measuring the full-field three-dimensional surface topography of a sample height from one micron to 100 micrometers. It is similar to the camera method, capturing images reflected and/or not from a prism by using a lens and a CCD. The reflectance of a point in the image can be converted to the height of the point. The method can obtain large-area full-field real-time three-dimensional measurement results and has the advantages of simple operation, low cost, and easy assembly. The measurement area is in the range of a few square millimeters for each time. The lateral and vertical resolutions are 2 and 0.1 micrometers, respectively, and the error is about 1% compared with the confocal microscope.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Methods for surface tomography measurement from 1 micron to 100 micron height are stylus profiler [1], laser triangulation profilometer [2–4], confocal profilometry [5–6], white light interferometer [7–9], fringe projection profilometry (or pattern projection profilometry) [10–17], and digital holographic metrology [18–20], etc., where the contact type method is the stylus profiler (for example Dektak XT) and others are the non-contact type methods. Stylus profilers [1] use a probe to detect the surface, physically moving a probe along the surface to acquire the surface height. The vertical resolution is determined by the amount of torque of the probe against the surface, and the lateral resolution is limited by the stylus size and shape. The changes in the vertical position of the arm holder can then be used to reconstruct the surface. However, the probe may be sensitive to soft surfaces, and the stylus can destruct or/and contaminate the specimen. Since the measuring speed of a stylus profilometer is limited by the speed of the 3-axis platform, the method is slower than typical non-contact techniques.
One of the non-contact methods, namely the laser triangulation profilometer [2–4], is based on the principle of triangular geometry and measuring the spot position to achieve the surface height. The method can scan a larger area with a deeper height, but the vertical and lateral resolutions are lower than other non-contact methods.
Confocal profilometry [5–6], is a point scanning optical technique used to image the sample surface. If the test surface is on the focal plane, the highly focused light is projected through a small aperture. If the surface departs from the focal plane, the light intensity will be reduced. Therefore, the amount of light intensity can determine the defocus distance. The optical probe scans up and down above the surface until a bright spot is observed. Once a bright spot is observed, the vertical position of the probe can determine the surface height of the test point. Scanning along the surface laterally while maintaining a bright spot, it can reconstruct the 3-D surface profile.
For white light interferometer (WLI) [7–9], the light source has multiple wavelengths and the interference occurs when the lengths of two arms are exactly equal. Typically, one mirror of the two arms is moved to record the positions of the interference fringes of different colors. Thus, the surface height of each point of the object can be calculated. In white light interferometry, an individual wavelength’s interference pattern is analyzed much like a laser interferometer, but in combination with many other wavelengths to increase the sensitivity. However, the optics involved are much more complex than a standard laser interferometer and the software reconstruction is also complex.
One of the optical profilometry methods is the fringe projection profilometry (or pattern projection profilometry) [10–17], which works by projecting a known pattern onto the sample and comparing the projected pattern to what is reflected by the sample. By comparing these two patterns, the surface information can be reconstructed by proper calculation. The imaging system uses a camera or a zoom microscope for measuring different surface area. Although the measurement speed can be relatively high, the lateral and vertical resolutions are still lower than that of a white light interferometer and confocal profilometer.
For digital holographic metrology [18], The technique uses a tunable laser and optical fibers to set up a near equal optical path interferometer and steps though multiple phases by using a fiber based phase shifter, and generates a digital hologram for the 3D surface measurement. Its vertical resolution is better than 1 micron over large surfaces. The digital holography without magnifying optics or lateral scanning can be suitable for rapid large-area surface topography measurements [19–20].
The above methods have their advantages. However, the measurement speed is still not fast enough. This paper proposes the external reflectance versus height conversion (ERHC) method for increasing the measurement speed. The method is simple and there is no need to scan, similar to taking pictures. Such a method can quickly measure a larger area within 100${\; }({\mu m} )$ in height for each process. But the limits of technique are 40° sample slope maximum and the test area is limited by the size of CCD and the magnification.
2. Principles
2.1 Relationship between height difference and reflection angle [21–22]
As we know that the tilt of the surface of the object will cause the reflected light to shift by twice the angle. As shown in Fig. 1, we assume that the distance between two object points to be tested is $\Delta x{\; }$. The corresponding pixel size of the CCD is $\Delta X$ and the optical magnification is M. The height difference $\Delta h$ between the two points can be written as:
2.2 Relationship between the reflectivity and reflection angle
For different cases of the internal reflection and external reflection, the reflectance curves of the s- and p-polarizations versus the incident angle are shown in Fig. 2, respectively.
Fig. 2. the reflectance curves of the s- and p-polarizations versus the incident angle in the internal and external reflections.
In order to obtain a larger angle measurement, we use the external reflectance method to measure the surface topography of the object. The method of internal reflectivity is suitable for small angle measurement, such as 3D microscope surface measurement [21–22]. But it is not suitable for use in large areas with large angles. In order to avoid the occurrence of zero in the reflectivity at Brewster angle that may cause serious errors in the height difference measurement, we use the s-polarization light and select the appropriate angle of incidence in external reflectance as a reference. This reference angle of incidence can be used as a reference for the starting height.
2.3 External reflection method
From Fig. 3, it is assumed that the s-polarization light is incident perpendicularly to the first side of the $30^\circ{-} 60^\circ{-} 90^\circ $ prism, and then passes through the second side and normally incident to the sample and is then reflected back to the prism. Finally, the object will be imaged on a CCD camera through the reflection of the prism and a lens. The difference in reflection angle due to the difference in height will cause the reflectivity of the prism to be different. The image contains the reflectivity inside, which means that it contains the height of the message inside. Through the conversion of reflectance to height (including the conversions of the reflectance to angle and the angle to height), we can estimate the height of every point of the object from the light intensity value in the image.
3. Experimental setup and results
The experimental structure of the three-dimensional external-reflection type surface topographer is shown in Fig. 4. The red LED light source passes through a beam expander (BE) (including an objective lens (OL), a spatial filter (SF) and a lens (L1)) to turn the beam into parallel beam that is enlarged and filtered out the noise.
We use an iris to select the size of the test beam and ensure a more even light intensity distribution. The beam reflected from a polarization beam splitter (PBS) and normally incident into the first surface of a $30^\circ{-} 60^\circ{-} 90^\circ $ prism (P) is the s-polarization light. The light transmits in the prism and will be normally incident at the sample. The reflected light from the sample is split into two paths by a beam splitter (BS). The light reflected from BS passes through the lens (L2) and is then imaged on CCD1. This image can be used as a reference image or the incident image before the reflection of the prism. Another transmitted light from BS returns to the prism and is imaged on CCD2 by another lens (L3). This image is the test image that contains the entire height difference messages. These two images have the same magnification. By overlapping the two images, using the matrix algorithm, the light intensity of the corresponding pixel is divided ($\frac{{{I_{CCD2}}}}{{{I_{CCD1}}}}$), and the reflectance $R$of each point can be obtained. When the reflectance matrix is obtained, substituting the value into the relationship between the reflectivity and the incident angle ($\theta (R )={-} 5 \times {10^4}{R^{10}} + 2.7 \times {10^5}{R^9} - 6.5 \times {10^5}{R^8} + 8.9 \times {10^5}{R^7} - 7.9 \times {10^5}{R^6} + 4.7 \times {10^5}{R^5} - 1.9 \times {10^5}{R^4} + 5.1 \times {10^4}{R^3} - 9.5 \times {10^3}{R^2} + 1.2 \times {10^3}R - 12$; unit: degree) would determine the corresponding angle deviation ($\Delta {\theta _n} = {\theta _n} - {\theta _0}$), where ${\theta _0}$ is initial incident angle for the initial height ${h_0} = 0$, n is the column number of CCD. And the height difference $\Delta {h_n} = {h_n} - {h_{n - 1}} = \frac{{\Delta X}}{M}tan\left( {\frac{{\Delta {\theta_n}}}{2}} \right)\; $ in one row and its tilt angle $\Delta {\alpha _n} = {\raise0.7ex\hbox{${\Delta {\theta _n}}$} \!\mathord{\left/ {\vphantom {{\Delta {\theta_n}} 2}} \right.}\!\lower0.7ex\hbox{$2$}}$. Finally, the three-dimensional surface profile of the test sample can be obtained by
The $30^\circ{-} 60^\circ{-} 90^\circ $ prism’s material is BK7. The wavelength of red LED is 631nm. The Optical magnification is 2. The size of the CCD is $1288 \times 964$ pixels. The pixel size is 3.75$\mu m \times 3.75\mu m$. 8 bits image can be divided into gray levels from 0 to 255. Therefore, the available area to be measured is $2.4mm \times 1.8mm$. The experimental results are shown in Fig. 5, where Figs. 5(a) and 5(b) show the images of CCD2 and CCD1, respectively. Figures 5(c) and 5(d) show the calculation results of 3D and 2D surface profiles. The averages of height, spacing, and full-width half-maximum (FWHM) of the lenticular lens measured by this ERHC method are 12.97$,\; 108,\; and\; 26\; \mu m$, respectively. To prove the feasibility of the method, we used the Laser Scanning Confocal Microscope (LSCM) (Keyence VKX-100) and Alpha-Step (Dektak XT) to measure the same sample, and the results are shown in Fig. 6(a) and Fig. 6(b). The average height, spacing, and FWHM measured by the LSCM are 12.91, 108.17, and 27 $\mu m$, and those of results from Alpha-Step are 12.89, 108, and 26.5 $\mu m$, respectively. Compared with the height measurement results between this method and the LSCM, the error is 1.05%. From the above observation, the results obtained by this method are quite close to the results of LSCM and Alpha-Step, so these can prove the practicability and feasibility of the method. In the ERHC method, the standard deviation of 10-times measurement for the FWHM of 26 $\mu m$ is 0.06 $\mu m$.
Fig. 5. The measurement results of a lenticular lens by using the ERHC method: (a) the image measured by CCD1; (b) the image measured by CCD2; (c) the 3D profile results; (d) the 2D profile results.
Furthermore, we only use the CCD2 single image system to measure, regardless of the CCD1 image, and use a plane measurement as a reference image, the measurement results are almost the same as the two CCD measurements. For example, we use a hair as a sample to measure the diameter or height of the hair. In order to improve the accuracy, we continuously shoot 50 images of CCD2 for the average light intensity. The result of the hair width measurement is 97.63 $\mu m$ is shown in Fig. 7(a) and Fig. 7(b). Using the same hair sample, the LSCM and Alpha-Step measuring the hair width results are 96.65 $\mu m$ and 86.9$\mu m$, and are shown in Fig. 7(c) and 7(d), respectively.
Fig. 7. A hair width measurement: (a) the 2D and (b) 3D measurement results by ERHC method; (c) the 2D measurement results by LSCM; (d) the 2D measurement results by Alpha-Step (Dektak XT))
The error of this result in comparison with the LSCM result is about 1%. We can thus conclude that the proposed method has almost the same accuracy as the confocal microscope and the cost is about 1% of the confocal microscope.
4. System analysis
4.1 Lateral resolution
Taking this system as an example, the image lens has a diameter of 5cm and a focal length of 10cm, thus the lateral resolution is 1.54$\mu m$ according to the formula of ${R_l} = {\raise0.7ex\hbox{${1.22\lambda f}$} \!\mathord{\left/ {\vphantom {{1.22\lambda f} D}} \right.}\!\lower0.7ex\hbox{$D$}}$. and because the optical magnification is twice the size of the pixel on the CCD, which is 3.75 $\mu m,\; $we can actually get a lateral resolution of 2 $\mu m$.
4.2 Vertical resolution
The surface height depends on the changes in the intensity of the imaged light. So, the vertical resolution is affected by the stability of the light source and the dark current of CCD itself. Therefore, we can measure the minimum amount of light intensity to determine the vertical resolution of the surface height. That is, within 1 minute, at a fix time internal, continuously measuring the light intensity of each pixel on the CCD2 would be able to obtain the standard deviation of light intensity. The standard deviation of reflectance is 0.0000207, which is much smaller than the amount of change between gray levels on the CCD (1/255 = 0.00392). Therefore, the standard deviation of light intensity still depends on the value of grayscale of the CCD. By taking this grayscale value variation into the relationship between the reflectance versus the angle and the angle to the surface height, we can draw the minimum surface height variation. The curve of vertical resolution versus the reflectance is shown in Fig. 8. From Fig. 8, the best vertical resolution is about 0.1$\mu m$ in the reflectance range of 0.05 to 0.55.
5. Conclusion
The external reflectance versus height conversion (ERHC) method for measuring the three-dimensional surface topography is proposed. The method adopts two CCDs or only one CCD to measure the reflectance or light intensity to convert the external reflectance to the surface height. The measurable height range is from 1 to 100 microns. The measuring area range is within a few millimeters square, and the best vertical and horizontal resolutions are 2.0 and 0.1 microns, respectively. The accuracy can be compared with confocal microscopes, and it is more convenient and easy to use. In addition, there are advantages of simple, fast, and large-area measurement for general industrial applications. Although the results from using only one CCD is similar to the use of two CCDs, but the one CCD method is limited for measuring samples of the same material only. The proposed method of ERHC is applicative for measuring the specular surfaces at the present stage.
Funding
Ministry of Science and Technology, Taiwan (MOST 107-2637-E-150-006, MOST 108-2112-M-006-005).
Acknowledgements
This study was supported in part by the MOST in Taiwan under contract numbers: MOST 107-2637-E-150-006 and MOST 108-2112-M-006-005.
Disclosures
The authors declare no conflicts of interest.
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