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Abstract
Long-range shape measurement with high accuracy is needed for precision manufacturing of large-scale parts such as turbines, compressors, and trains. We have developed a high-accuracy ranging system based on frequency-modulated continuous-wave (FMCW) technology. Our system has two unique features. First, it achieves high-accuracy range measurement by directly modulating a low-cost vertical-cavity surface-emitting laser (VCSEL) at high sweep rates. The nonlinearity of the optical frequency sweep is compensated for by resampling through a reference interferometer. Second, an optical fiber with multiple fiber Bragg grating (FBG) structures is used for distance calibration. Ranging accuracy better than 10 μm is achieved at 2 m distance. Three-dimensional (3D) imaging of 10-cubic-meter volume has been obtained by combining the FMCW ranging with a galvanometer scanner.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Accurate shape measurement is important for quality control of precision mechanical parts [1]. Traditional methods (Vernier calipers, rulers) are time consuming, prone to errors, and difficult to scale up for large-scale objects such as compressors, turbines, and trains (Fig. 1). Their sizes are several meters in length and height, and machining precision must be better than 100 μm. A non-contact, high-speed automatic measurement method with ranges of several meters and accuracy less than 10 μm will be revolutionary for such industrial manufacturing.
Several laser-based optical metrologies of three-dimensional (3D) objects have been reported, including triangulation, time of flight (TOF), phase shift, and frequency-modulated continuous-wave (FMCW) methods [2–5]. The FMCW approach is particularly interesting because of its high accuracy at long ranges [6–10]. Previously, measurement precision up to 10 μm with a 10-m measurement range was achieved [11]. However, the optical frequency comb source they used to calibrate the range was expensive and may be difficult to use in the industrial field. In the medical field, swept-source optical coherent tomography (SS-OCT) have achieved resolution of tens of micrometers at a 1m range [12–17]. However, the swept frequency lasers were also expensive. Recently, low-cost vertical-cavity surface-emitting lasers (VCSEL) have been used for OCT, but their target range was limited to 0.1m [18]. In this paper, we report on a low-cost, high accuracy (10 μm) and long range (10 m) FMCW system using direct modulation of a low-cost commercial VCSEL. Distance calibration using fiber Bragg grating (FBG) is described.
2. Characterization of VCSEL performance
2.1 Optical frequency sweep range
We used a long-wavelength (1550 nm) single polarization VCSEL with an optical isolator in a TO can package (RC32xxx1-F, Raycan). The laser has a threshold current of 2 mA. Due to thermal effect, the lasing wavelength shifts from 1540 to 1549 nm when the current increases from 2 to 14 mA, with a total frequency shift of 1300 GHz, as shown in Fig. 2(a) and (b). The frequency shift is slightly nonlinear with the injection current. The optical output power is shown in Fig. 2(c). The maximum output power, 0.85 mW, is obtained at 8 mA. The output power decreases at higher current due to thermal effect. For FMCW experiments, we bias the laser at 8 mA and modulate it with a sinusoidal waveform with a current amplitude of 4 mA. A semiconductor optical amplifier (SOA) is used to boost up the output power to 10 mW, the maximum power allowed for a Class-1 laser at 1550 nm wavelength.
Fig. 2 Current response of VCSEL: (a) Wavelength response, (b) Optical frequency shift from the frequency with 2 mA injection current, and (c) Optical output power.
2.2 Frequency response of optical frequency sweep
The frequency modulation (FM) response of the VCSEL under a sinusoidal modulation with a 4-mA amplitude is shown in Fig. 3. The frequency range under modulation is measured with an optical spectrum analyzer (ANDO 6317B) with a resolution of 10 pm (1.2 GHz). The 3-dB bandwidth is 10 kHz, as expected for thermally induced frequency shift. The frequency sweep range at 10 kHz is 4.4 nm, or 550 GHz.
2.3 Coherence length
The coherence length of the laser, Lc, is related to its linewidth, , by [19]
where λ is the center wavelength. We measured the static linewidth of the laser at 8 mA bias current using a delayed self-heterodyne method [20]. The result is shown in Fig. 4. The full-width-at-half-maximum (FWHM) of the beat note is 10 MHz, corresponding to a coherence length of 13 m.3. Range measurement using resampling method
We used resampling method to obtain highly accurate distance measurements. The resampling method is often used in SS-OCT and FMCW [21, 22]. The VCSEL is biased at 8 mA and modulated with an 8-mApp sinusoidal waveform at 10 kHz. This allows us to acquire a range data in 100 μs. We compared the theoretical FMCW distance resolution with the resampling result under sinusoidal modulation. We also evaluated the measurement error when the sinusoidal modulation was not symmetric and when there was a timing delay between the reference and target beats signals. We evaluated the resampling method by both simulation and experiments.
3.1 Simulation model for resampling
The simulation model for resampling is shown in Fig. 5. The light from the VCSEL is split and sent to a reference and a target Mach-Zehnder interferometers (MZIs). The reference signal is resampled to linearize the frequency sweep. The target beat signal is resampled by the reference and the target distance is calculated by fast Fourier transform (FFT). In this simulation, we did not consider the change of optical power. Detailed experimental conditions (coupler’s splitting ratios, etc.) will be discussed in Section 4. Here, we only use the up ramp of the sinusoid for processing, as illustrated in Fig. 6. In principle, we can use both up and down ramps to measure both distance and velocity [10].
3.2 Resolution
The delays in both MZIs are both set to 1 m. The beat signals are sampled at 500 MS/s. The FFT for the target beat signal after resampling is shown in Fig. 7. The FWHM of point-spread function (PSF) is 0.33 mm. The theoretical resolution, , is calculated from the width of the optical frequency sweep, :
where λ is the center wavelength. With = 4.4 nm, △R is 0.24 mm. The simulation result is slightly larger than the theoretical resolution. We can obtain higher accuracy of the peak position by interpolating the PSF, as shown in the next section.3.3 Distance measurement accuracy
We calculate the distance accuracy by varying the delay in the target MZI from 0.1 m to 2.1 m. Since the optical frequency shift is not linear with current (Fig. 2(b)), the resulting optical frequency under modulation is not sinusoidal. To understand this effect, we performed the simulation with two optical frequency shift functions. The ideal function has a symmetric sinusoidal function, and the non-ideal function includes the actual transfer curve of Fig. 2(b), resulting in a non-symmetric sinusoid-like functions. The distance error is defined as the difference between the delay in the target arm and the extracted distance by FMCW resampling method. Figure 8 shows error signals versus the distance for (a) ideal sinusoidal frequency shift and (b) actual (non-symmetric sinusoid-like) frequency shift. For symmetric sinusoidal modulation, the error is less than 10 μm. However, for the non-symmetric sinusoid-like modulation, the error has a quadratic shape and has a maximum value of 25 μm. It is therefore important to calibrate the measured distance considering this nonlinear effect. We will discuss a novel calibration method using FBG fiber in Section 5.
Fig. 8 Simulated distance accuracy for (a) Symmetric sinusoidal modulation and (b) Non-symmetric sinusoid-like modulation of VCSEL.
3.4 Effect of optical delay between reference and target MZIs
In practical instrument, the measurement head containing the target MZI may be placed far away from the reference MZI. The delay between these two MZIs will cause a shift in resampling time. It is therefore important to investigate the impact of this delay on the error function. We added another delay (Delay Path 3) between the VCSEL and the target MZI in Fig. 5 and varied the delay length from 1 to 6 m. For each delay, we varied the target distance from 0.1 to 2.1 m.
The FFTs of the target beat signals vary significantly with this additional delay, as shown in Fig. 9. For a target distance of 0.1 m, the FFT exhibit a sharp peak even with a 6-m delay between the MZIs (Fig. 9(b)). However, when the target distance is increased to 2.1 m, the FFT peak broadens significantly with a reduced amplitude (Fig. 9(c)). The broader peak reduces signal to noise ratio and leads to increased errors in position accuracy. We can use the amplitude of the FFT peak as a proxy of this impact. Figure 9(a) shows the peak of the FFT versus the optical delay between the MZIs for various target distances. For short target distance, the two MZIs are well matched, and the calculated FFT is not affected by optical delay between the MZIs. However, with increasing target distance, the amplitude of the FFT peak starts to decrease significantly with increasing delay. The offset in resampling times of these two MZIs leads to significant errors in resampling. These results show that it is necessary to match the timing between the reference and target MZIs.
Fig. 9 (a) The amplitude of the FFT peak versus the optical delay between the reference and target MZIs for various target distances. (b) The FFT signal of P1 (target distance 0.1 m and optical delay 6 m). (c) The FFT signal of P2 (target distance 2.1 m and optical delay 6 m).
4. Experimental evaluation
4.1 Experimental setup
The experimental setup is shown in Fig. 10. The VCSEL is modulated by a sinusoidal current from a waveform generator. An isolator is inserted after the VCSEL to prevent back reflection. The output power is amplified by an SOA with 13 dB gain before splitting between the reference (10%) and target (90%) MZIs. In the target MZI, 90% of light is directed to the target port. The optical power at the target port is 10 mW, the maximum allowed for Class-1 laser at 1550 nm wavelength. An attenuator is inserted in the target arm to measure the dynamic range of the system. The beat signals at both MZIs are detected by coherent receivers with 1.6 GHz balanced detectors and then digitized by analog-to-digital converters (ADCs) with sample rates of 500 MS/s. The splitting ratios of all couplers are denoted in Fig. 10. The target distance is calculated from FFT of the resampled target beat signals. An optical attenuator is inserted in the target arm to measure the dynamic range of the FMCW system.
4.2 Experimental evaluation results
The FFT of the target beat signal after resampling is shown in Fig. 11. The FWHM of PSF is 0.36 mm, which matches very well with the simulation in Fig. 7. We calculate the peak position by interpolation and realize high accuracy measurement exceeding the resolution. To measure the dynamic range of the system, we measure the precision of the target distance while the target signal is attenuated by 50 to 90 dB. The precision is defined as the standard deviation of the measured distances over 50 measurements. Figure 12 shows the precision versus the attenuation of the target signal. Precision better than 1 μm is obtained with 60 dB attenuation, and 10 μm with 80 dB attenuation.
5. Calibration method using FBG fiber
5.1 Concept of calibration
From the resampling simulation shown in Fig. 8(b), the target distances calculated by resampling method have a quadratic error. The error depends on the degree of nonlinearity of the optical frequency shift in VCSEL. It can be calibrated to improve the accuracy. One calibration method is to use an interferometer with a moving target. Their measurements are accurate to sub-micrometer level. However, it is difficult to calibrate distance over a wide range using an interferometer.
We propose a simple calibration method using FBG. The experimental setup shown in Fig. 13(a) is similar to the FMCW system described earlier except a circulator is added in the target arm to collect the reflected signal from either an FBG fiber or a free-space target through a collimator. We used a fiber optic switch to toggle between these two targets. The FBG has an array of localized gratings at known locations, with each grating reflecting a few percent of light. The FBG allows us to generate the calibration data shown in Fig. 13(b) in one measurement. The calibration can be performed periodically as the nonlinear frequency sweep in VCSEL might change over time as the VCSEL ages.
Fig. 13 Calibration method using an FBG fiber: (a) Equipmental setup; (b) Schematic calibration curve. If measured distance is not linear with the true distance, we can use the calibration curve to deduce the true distance.
5.2 Calibration method using FBG length
The FBG fiber is designed to have seven precisely located reflection points over a length of 1.4 m. Each reflection point has a length of 0.1 mm, a reflectivity of 2%, and a reflection bandwidth of 8 nm in wavelength. We calibrate the distances between adjacent reflection points using a gauge block, as illustrated in Fig. 14. The length of the gauge block, which is already calibrated, is measured to determine the distance between reflection points A and B in FBG. The gauge block is 304.8 mm (12 inches) long. A second gauge block is attached at the end of the first gauge block by wringing. The length of the first gauge block is measured using a collimated laser beam illuminating both gauge blocks simultaneously. The FMCW is calibrated as the measured distance is made to match the gauge block’s calibrated length. Under the same condition, the distance between A and B in the FBG fiber is measured and calibrated. The distances between other grating reflectors (B and C, C and D, etc) be calibrated in a similar way.
5.3 Resampling optical delay effect between reference and target MZIs
As discussed in Section 3, an optical delay between the reference and target MZIs will affect the resampling points and thus the measurement results. We experimentally evaluated the effects of the optical delay using the FBG fiber. We inserted a 4-m-long optical fiber (6-m optical path length) between the FBG fiber and the optical switch in Fig. 13 as the optical delay. Figure 15 shows the FBG measurement results. Figure 15(b) and (c) show the expanded views of the area labelled W1 and W2 in Fig. 15(a). When the target distance is short (W1), the FFT peak is narrow. However, with large target distance, the FFT peak becomes significantly wider (W2). These match very well with the simulation results in Fig. 9. Therefore, it is necessary to match the timing between the reference and target MZIs. To illustrate this effect, we add a 4-m-long optical fiber before the reference MZI. Figure 16 shows the FBG measurement results after inserting the fiber. The FFT width remains narrow even at large target distance (Fig. 16(c)). In this experiment, we match the physical path lengths. Alternatively, we can delay the reference beat signal electrically before the ADC, or with software after the signal is digitized.
We also consider the effect of chromatic dispersion because the reference and target MZIs are not perfectly balanced. We use single mode fibers (SMF-28, Thorlabs) with a dispersion of 18 ps/nm/km. Our experiment uses a 5-nm wavelength sweep and a 4-m fiber delay. The resulting dispersion is 0.36 ps, which small compared to the modulation period of 100 μs.
For the distance measurements below, the FMCW system is calibrated without optical delay between the reference and target MZIs.
5.4 Distance measurement
We first measured the distance of a mirror on a stepping motor (TD206, Thorlabs) using a collimated beam in the target arm. The reflected light is collected by the same fiber through a circulator. Figure 17 shows the photograph of the experimental setup. The measured distance is compared with the position of the stepping motor. Since the range of stepping motor is limited to 20 mm, we placed the stepping motor at 0.5, 1, 1.5, and 2 m from the fiber collimator. Figure 18 shows the error between the stepping motor position and the FMCW measurement versus the stepping motor position at 0.5 m. The measurement was repeated two times, and the results were almost identical. The standard deviation of the error was 5.7 μm. The measurement results at other distances are summarized in Table 1. In all measurements, the standard deviations of the errors are less than 6.1 μm. This includes the position error of the stepping motor itself, which has a repeatability of 5 μm. The real error of the FMCW system is likely to be lower. More precise measurement can be obtained using an interferometer, which we plan to perform in the future.
Fig. 18 Measurement errors versus the stage position at 0.5 m from the collimator. The error is defined as the difference between the distance measured by the FMCW system and the stage position from the stepping motor readout.
Table 1. Summary of the measurement errors at various distances.
6. 3D Imaging
Three-dimensional (3D) imaging was performed by combining the FMCW range measurement with a galvanometer scanner. We use a pair of lenses (f = 30 mm, 100 mm) to focus light on various targets. The emitted optical power is 10 mW. We first imaged a coin (a US quarter) at a distance of 0.7 m. The photograph and the measurement results are shown in Fig. 19. The images contain 440 × 440 measurement points. The rendered 3D image and the height map are shown in Fig. 19(b) and (c), respectively. These results show the system is capable of measuring the surface of a coin with a height of ± 0.3 mm. Next we imaged an optical post (at 1.2 m) and a gas cylinder (at 1.5 m). The photograph and the 3D image are shown in Fig. 20. The 3D image consists of 290 × 630 measurement points.
To test the maximum distance of the FMCW system, we imaged a room with various objects at distances from 2 to 9 m. The 3D images with 450 × 600 measurement points are shown in Fig. 21. The maximum round-trip distance (18 m) is slighter larger than the coherence length of the VCSEL (13 m). The image volume is an order of magnitude larger than that in Ref [13].
7. Conclusion
A low-cost 3D imaging system with 10-cubic-meter imaging volume has been successfully demonstrated using a directly modulated vertical-cavity surface-emitting laser (VCSEL) as frequency-modulated continuous-wave (FMCW) source. A commercially available VCSEL is modulated at 10 kHz. It has a frequency sweep range of 4.4 nm (550 GHz) and a coherence length of 13 m. A resolution of 0.36 mm is obtained using resampling method. High accuracy measurement (5.7 μm) is achieved by using interpolation to extract the peak position. This is experimentally verified using a stepping motor with 5 μm repeatability. We have also proposed a new calibration method using a fiber with localized Bragg reflectors. This allows quick, periodic, and on-demand calibrations.
Three-dimensional (3D) imaging is achieved by combining the FMCW system with a galvanometer scanner. A wide range of 3D images were obtained, including large imaging volume (~10 cubic meter) and small target (e.g., a coin with ± 0.3 mm height variation). This 3D imaging system is simple, low cost but highly accurate, and can be used for 3D shape measurement of large-scale objects for precision industrial manufacturing.
Funding
Hitachi.
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