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An asymmetric polarization-based frequency scanning interferometer is proposed using the asymmetric polarimetric method. The proposed system controls the polarization direction of the beam using a polarizer and wave plate, along with a conventional interferometer system. By controlling the wave plate, it is possible to asymmetrically modulate the magnitude of the object and reference beam, which are divided by the polarizing beam splitter. Based on this principle, if the target object consists of both transparent and opaque parts with different polarization characteristics, each part can be measured. After a fast Fourier transform of the acquired interference signal, the shape of the object is obtained by analyzing its spectrum. The proposed system is evaluated in terms of measurement accuracy and noise robustness through a series of experiments to show the effectiveness of the system.
© 2015 Optical Society of America
1. Introduction
A recent trend in semiconductor chip manufacturing technology, electronics, and various areas of mechanical technology is miniaturization. As a result, products using micro-processing technology have become more complicated. Because of the miniaturization of electronic and mechanical components, the need for accurate 3D measurements, for the purposes of reducing the defect rate and fulfilling the customer’s demand, has increased [1]. And compact and high-accuracy miniaturization has traditionally limited to certain industrial sectors, but this technology has been recently applied to smart phones, tablets, the electronic control of automobiles, etc. As a result, there is a growing tendency for the high-precision inspection of various characteristics of miniaturized objects.
The use of transparent membranes/films is currently increasing with the growth of specialized technologies, such as a thin-film coatings and flexible displays. Moreover, as a result of advances in semiconductor packaging technology, high-accuracy measurements of the height of certain metal objects, fluxes, or adhesives are now required. However, the optical characteristics of transparent objects, such as a film or flux, and commonly used metals are different. Therefore, it is necessary to develop equipment that can measure surface profiles of objects with various surface characteristics.
In order to fulfill these requirements, various 3D measurement technologies are currently being researched [2–7]. Among them, interferometry has the advantage of being able to measure the object accurately based on optical interference characteristics without bringing the measuring instrument into contact with the object. General interferometry techniques can be classified into three types: phase shifting interferometry (PSI), white-light scanning interferometry (WLSI), and frequency scanning interferometry (FSI).
The PSI system uses a single-wavelength laser [8,9]. The phase of the interference signal is altered by moving the reference mirror, which allows the height to be measured. The PSI system exhibits a high-accuracy, but has a limited range of heights that can be measured due to the use of single wavelength lasers. Alternatively, the WLSI system uses white light that has a short coherence length [8]. It generates interferogram signals within the coherence length when the optical path differences (OPDs) between reference and optical arms are the same. Due to the characteristics of white light, the available area from which the interference signal can be generated is quite limited. Accordingly, the required measuring time due to its z-axis scanning mechanism is increased in proportion to height range being measuring. Furthermore, since the reference mirror is moved by mechanical actuators, this hardware is relatively unreliable [10]. Lastly, the FSI system generates interference by changing the wavelength of the light continuously. The required measurement time is independent of the object’s height range, and the observable range can be changed by adjusting the amount of wavelength change interval [11–15]. However, the FSI system, as it currently exists, struggles to measure objects with complicated surface characteristics.
In the case of conventional interferometers, the reference beam and object beam are divided evenly using a beam splitter (BS) or a polarizing beam splitter (PBS). If the reflexibility of the measured object is not similar to the reflexibility of the reference mirror, the contrast of the interference fringes is low. Moreover, if the measured object is a diffuse object, the polarization direction of the beam before being reflected from the object, and after being reflected, are different. If the polarization direction of the object beam is changed, the reflected beam cannot reach the image sensor, ultimately preventing interference fringes from being created.
In light of these observations, we investigate an FSI-based system that is capable of providing high-accuracy measurements even for objects with a variety of surface characteristics. More specifically, we propose the FSI system based on asymmetric polarized light applying a polarimetric analysis method with polarizer and wave plate to the conventional interferometer. We show that it is possible to obtain a clear image of interference fringes by controlling the wave plate and asymmetrically manipulating the magnitude of the reference beam and the object beam, which are separated by a polarizing beam splitter (PBS). We calculate the optical path difference (OPD) from the obtained interference signal, which allows us to measure the height of the object, along with the error associated with that measurement.
2. Polarization-based frequency scanning interferometer
2.1 FSI system using polarization analysis
Figure 1 shows the design schematics and a prototype of the polarization-based frequency scanning interferometer (PFSI) implemented for the use of in-line inspection. A tunable laser is used to continuously change the frequency of the output light source. The output light from the laser diode passes through the collimation lens, and is diffracted from the grating. The diffracted light is reflected to the mirror and, goes to the grating. Then, it returns to the laser diode again. While the process is repeated, the light is amplified, and becomes the output light of the tunable laser. At this time, the wavelength of output light is varied by angular changes of the mirror. Here, the galvano mirror is used in order to enhance the changing speed of the wavelength of output light. The galvano mirror is the mirror attached to the galvano motor. In order to get the linearity of the wavelength changes, the calibration process is performed to make the angle changes of the galvano mirror proportional to the wavelength changes.
Fig. 1 Optical hardware setup for polarization-based frequency scanning interferometer (PFSI). (a) Schematic diagram. (b) Image of the actual setup.
The light output from the fiber is expanded through the beam-expanding optical device, passes through the polarizer and the λ/2 wave plate, and is finally split in the PBS. One of the split beams travels toward the object, while the other travels toward the reference mirror. The two beams reflected from the object and from the reference mirror interfere at the PBS. After the interfered signal passes the polarizer, it is finally captured on the image sensor. The surface height of the object is measured relative to the physical plane of the reference mirror, so that half of the OPD between the two beams is equal to the height.
Generally, the interference fringe generated by the two beams is expressed as [16]:
According to the OPD of the two beams, the value of will change. Therefore, the total constructive/destructive interference is generated by the value of . The contrast of the interference fringe must be maximized in order to achieve precise height measurements. Since the cosine function takes on the values from 0 to 1 in this context, maximum and minimum values of the brightness of interference fringes are as follows:That is, when the value of is a maximized, the difference between Imax and Imin is also maximized. Since the light from tunable laser is divided by the PBS, the sum of I1 and I2 is always fixed. If the sum of two positive numbers is fixed, then their product is maximized when they are equal. So, the interference effect becomes maximized when the intensities of light reflected from the reference mirror and from the measurement object are equal. Assume that Er and Eo represent light reflected off the reference mirror and the object, respectively. The reflectivity of the reference mirror is nearly 1, because of reflecting the incident light mostly. However, for the case of the measurement object, the reflectivity is some arbitrary value between 0 and 1. If the reflectivity of the measurement object is r, the intensity of light reflected from the measurement object is rEo. The conventional interferometer system equally divides the intensity of light into 50:50 using the BS or PBS. If the reflectivity of the measurement object is not the same as that of the reference mirror, then the ratio of intensity between the reference beam and the object beam will be 1:r, and the contrast of the interference fringes will decrease.
The polarization direction of incident light can be changed by controlling the half wave plate. In this way, P-polarization and S-polarization are controlled, and the light is divided by the PBS according to the polarization direction. In addition, if the quarter wave plate, located between the PBS and measurement object, is rotated, the diffuse surface or the mirror surface can be selectively emphasized. Figure 2 shows two cases: in the first case Fig. 2(a), the optical axis of the quarter wave plate is parallel the polarization direction of the incident beam from the PBS; in the second case Fig. 2(b), that angle is increased to roughly 45°.
Fig. 2 Change in polarization according to the wave plate rotation. (a) The optical axis of the wave plate set as 0°. (b) The optical axis of the wave plate of wave plate set as 45°.
There is no diffuse reflection in the area of the measurement object with mirror surface, denoted by “c” in Fig. 2. There is only specular reflection, meaning that the polarization of the beam is maintained. However, in case of the area denoted by “d” with diffuse surface, the polarization is lost due to 100% diffuse reflection.
In the scenario depicted in Fig. 2(a), the reflected beam at area “d” becomes diffuse. It has a component that passes by the PBS. As a result, an interference fringe is generated in the charge-coupled device (CCD) sensor. On the other hand, because the optical axis of the quarter wave plate is aligned with the polarization direction of the beam, the reflected beam at area c maintains its linear polarization. Thus, it is reflected on the inside of the PBS and it goes toward the input laser side. It doesn’t generate any interference fringe. In other words, the diffuse surface of the measurement object generates the fringe.
Concerning Fig. 2(b), the reflected beam at area “d” passes the PBS and generates an interference fringe. For the beam reflected at area “c,” the polarization direction of the beam is rotated about 90° over, passing back and forth through the quarter wave plate, thereby generating the fringe in the CCD. At this time, the fringe from surface of the mirror is more emphasized, since the amount of light reflected at area “c” is greater than that of area “d.” The point worth noting here is that the diffuse surface and the mirror surface can be selectively emphasized by appropriately rotating the optical axis of the quarter wave plate.
Figure 3 displays an image yielded by the proposed PFSI system. The object is the printed circuit board (PCB), in which a copper foil circle is arranged on the surface and a transparent film is attached. The dotted line indicates where the transparent film is attached at a side. In the case of (a), the optical axis of the quarter wave plate is same the as the polarization direction of the incident beam, whereas in (b) the optical axis is rotated by about 45°. As described above, it can be clearly seen that the transparent film and PCB surface are selectively emphasized.
Fig. 3 The resulting images from the polarization-based frequency spanning interferometer (PFSI). (a) The optical axis of the quarter wave plate is in line with the polarization of the incident beam. (b) The optical axis is rotated by roughly 45°.
2.2 The algorithm of the frequency scanning interference system
The interference signal can be represented as a function of k:
where k represents the modulated term of the wave number, and h represents the height of the object. Δφ can be measured, which represents the change in φ(k;x,y) that results from modulating k. The amount by which the phase of the interference signal changes can be expressed by the wave number shift Δk.The height of the object, h(x,y), can be obtained from the Δk (previously known) and Δφ, which is the result of measurement:
Figure 4 is the diagram of overall signal processing. A set of images of interference fringes captured by camera is loaded, and the image data is rearranged along each pixel point. To calculate accurate frequencies, some preprocessing is needed on the arranged interference signal. First, the average of the interference signal is subtracted to eliminate the DC components of the signal. Second, the length of the data of the interference signal is expanded through zero padding to improve the resolution of the frequency. Third, after padding, the noise of the frequency is eliminated by multiplying a Gaussian window on the signal. When the preprocessing is over, a fast Fourier transform (FFT) is performed on the filtered signal. Through the FFT, the frequency of the interference signal is analyzed, and the peaks of the frequency spectrum are extracted. They are proportional to height information of the target object, thereby yielding a measurement of the height [17–20].
In the case of measuring an opaque object, one peak position is generally observed in the signal spectrum after the FFT. On the other hand, in case of a transparent object, multi-layer reflections are generated because the object is usually located on an opaque object (e.g., PCB). Therefore, in the transformed signal spectrum for a transparent object, multiple peaks can be distinguished. By selecting one of the peaks, the height of the transparent object or its underside can be obtained.
As shown in Fig. 5, in the case of measuring a transparent object, the multi-layer reflections are generated from the top surface and the underside of the object. Spectral response in Fig. 5 is generated by FFT of the interference signals. Three interference signals are mainly observed when a transparent object is deposited on the PCB surface. Signal A results from interference between the reflected light from the reference mirror and the reflected light from the transparent object’s surface; signal B results from the interference of the reflected light from the reference mirror and the reflected light from the transparent object’s underside; and signal C results from the interference between the reflected light from the transparent object’s surface and the reflected light from the transparent film’s underside. When input light penetrates the transparent object, signal A and signal B have different polarization characteristics. By controlling the polarization of the system, the height of the transparent object and the height of the object’s underside may be measured simultaneously or separately.
Fig. 5 Frequency spectrum for a multi-layer reflection signal. Peak A and B are generated by the interference between reference signal from mirror and reflection signals from the top of film and the top of mirror, respectively. Peak C is induced by self-interference between two reflections from film and mirror.
3. Experiments
To illustrate the utility of the proposed PFSI system, we perform several kinds of experiments [21]. These consist of measurements of opaque objects, transparent films, and complex objects.
In this experimental setup, the wavelength of light generated in tunable laser can be scanned from 760 nm to 794 nm with a minimum variation of wavelength of 0.02 nm. For the components of tunable laser, the laser diode is EYP-RWE-0780-02000-1300-SOT12-0000 model by Eagleyard Photonics., and galvanomirror is 6210H model by Cambidge Technology. Diffraction grating is GH25-24V by Thorlabs. For experiments, the wavelength of incident light is changed 99 times from 765 nm to 784.8 nm with a 0.2 nm step during the measuring object. After acquiring a series of images, they are used to calculate the height of the measuring object. The resolution of camera used is 2048 × 2048 (4M) pixels. And the frame rate is 180 fps (SEN TECH Co., STC-CMB4MCL). Therefore, almost half second is needed to take 100 images. Current optical setup provides the maximum size of possible measuring area with 25 mm × 25 mm. It is dependent upon optical qualities of the camera lens and beam expander. To increase the measuring area, it is needed that numerical aperture (NA) of camera lens is larger and the beam expander also has to output the laser light on the wide area uniformly. NIR cube PBS and polarizers and wave plates are made by Edmund Optics. In the wavelength tuning range of laser, the extinction ratio of the polarizer is 30 dB.
3.1 The height of an opaque object
The opaque target used for height measurement is VLSI SHS-50.0 in Fig. 6, which is a product of VLSI Standards Inc. This target is generally used for equipment calibration. On the target, letters and patterns are engraved with a 50 μm step height. The product information states that the step height is 48.811 ± 0.262 μm.
Figure 7(a) is a sample image of interference fringes acquired from the CCD camera. Figure 7(b) is a 3D graph generated from the height calculation results on a VLSI standard target. It shows that letters and patterns can be successfully resolved from the proposed hardware and algorithm. Analyzing a one-directional line-profile of the target, the step height is measured as 48.726 μm, which is only 0.085 μm smaller than the number listed above. This error value is within the ± 0.262 μm associated with the product. To measure the reliability of the PFSI system, experiments on the VLSI target are performed in the same environment five times, and the step height of the same area is monitored. The results are arranged in Table 1.
Table 1. Results of repeatability experiment
3.2 The height of a transparent film
The height of a transparent film is measured according to the same method listed in Sect. 3.1. The target used in this experiment is made by attaching a 30 μm transparent film onto a mirror. Matching gel is used between the transparent film and the mirror. We measure the step height between the top surface of the transparent film and the top surface of the mirror.
Figure 8(a) is 3D model image of the target used in the experiment, while (b) is a sample of the interference fringes observed from this experiment. It shows that the interference fringe pattern is changes from the region with the film attached to the region without the film. The height is calculated from a set of 100 images of interference fringes.
Figure 9 is a graph of the one-directional line-profile, marked as a section ‘A-B,’ of the calculated height map on the target in Fig. 8(b). It shows that the height difference between top (film surfaces) and bottom (mirror surfaces) is 29.419 μm. The thickness of the transparent film is 30 μm, so the measurement error is 0.581 μm. Figure 10 is the result of the height measurements of the transparent film surface and the mirror surface under the transparent film on a same area. As previously described in Fig. 5, the multi-peaks are detected in the interference signal which is made by lights reflected from multi-layered object in an overlapped area. Using this method, the height map of top of transparent film and one of top of mirror surface are calculated separately. Figure 10(a) is the measurement of the transparent film surface (red color) with detecting the peak A in the overlapped area and mirror surface (blue color) in the other area. Figure 10(b) is the measurement of the mirror surface under the transparent film with detecting the peak B in the same area.
Fig. 10 Reconstructed height map of the object according to selective peaks. (a) Surface of transparent film. (b) Surface of mirror.
3.3 The surface of a complex object
In this section, an experiment is performed to measure the surface shape of an object that consists of various materials with different optical characteristics. For this purpose an electronic component was selected as a target object, which is a laser diode of consisting of various kinds of materials with different optical properties in Fig. 11. The surface of the diode is blocked with transparent glass in order to protect the electronic components from external dust or moisture. A metallic ring houses all of these components. The height of laser diode without the connect pins is 6.05 mm, and the diameter of cylindrical base frame is 9.0 mm. First, the outer surface shape of a laser diode is measured, and its inner shape is secondly tested after that.
If light is exposed to the part blocked with the transparent glass, some light is reflected while the remainder penetrates the glass and is reflected by the internal components. Generally, the intensity of light reflected from the internal components is higher than light reflected from the transparent glass. Therefore, it is difficult to measure the surface of this transparent glass with conventional interferometry techniques. However, as previously described in Fig. 2, the proposed system makes the measurements of external part covered with glass and internal part with electric components possible by controlling the wave plate located in front of object, using the proposed system.
Figure 12 is the 3D reconstruction of the shape being measured. As described in Fig. 2, Fig. 12(a) depicts a measurement of surface height when light reflected from transparent glass is emphasized. On the other hand, the image in Fig. 12(b) is the result when light reflected from the internal components is emphasized. The complex shapes of the internal electronic components are clearly visible in this image.
Fig. 12 Images of the laser diode measurements. (a) Outside the laser diode. (b) Inside the laser diode.
As the electronic components and the metal housing have optical characteristics of diffuse surface, the angle of wave plate is initially set to 0° to get the image of Fig. 12(b). When the angle of wave plate is 0°, reflected light from transparent glass maintains the linear polarization. After the reflection at the PBS, it goes toward the input laser side, and results in no interference fringe. However, reflected light from internal components passes through the PBS, and generates the interference fringe with reflected lights from reference mirror.
Conversely, as the glass part does one of smooth surface, the angle of wave plate is set to an appropriate angle to weaken the reflected light from internal components and to strengthen the reflected light from the glass with getting the interference signal from the metal housings. If the wave plate is rotated with the appropriate angle, reflected light from the glass is changed into the circular polarization while it passes through the wave plate. Then, it can pass through the PBS, and generates the interference fringe with reflected lights from reference mirror. It finally results in getting Fig. 12(a).
In this way, the light of a particular polarization direction can be emphasized and measured by controlling the quarter wave plate. Additionally, although multiple reflection signals from smooth surface and rough surface are somehow mixed, the strongest peak based on FFT spectrum analysis can be selected according to the user’s purpose.
4. Conclusion
The use of transparent objects has increased owing to the advanced manufacturing technologies of semiconductor and the display industries. The need for high-precision inspection equipment has grown as a result. The PFSI system is proposed for measuring the height of objects with varied surface characteristics.
The proposed interference system utilizes the polarimetric analysis method. Even in the case of measuring a complex object with a smooth surface and a diffuse surface, a selectable high-precision height measurement is possible. A series of experiments has confirmed that the PFSI system can selectively measure the height of either the transparent surface or the mirror surface. For this purpose, height can be measured by modifying the polarization direction of incident light and reflected light. However, additional experimentation is needed to get high reliability on various cases of objects with complex surfaces.
In future, we will study how the time taken to achieve the interference signal images can be reduced by reducing the wavelength change rate of input light of the interferometry system. Reducing the time needed to achieve the interference signal images while simultaneously maintaining the accuracy of previous interferometry devices is the purpose of this research.
Acknowledgment
This research was supported by Kyungpook National University Research Fund, 2014.
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