1. Introduction

Optical methods for non-contact dimensional measurement have significantly improved over the last few years and brought major changes in commercially available surface measuring technologies [1–3]. When it comes to high-quality manufacture of optical components – like aspheric lenses or, optical free forms- Laser interferometry is irreplaceable [4,5]. One of the common approaches to increase the resolution of phase measurement within an interferometer is through sinusoidal optical path length modulation using a Piezoelectric Transducer (PZT) [6]. The intensity distribution of a phase modulated interference pattern is,

The concept of interferometry with multiple wavelengths allows to overcome the problem of a short unambiguity range of simple interferometers by designing a synthetic wavelength (Λ) which corresponds to the spatial beat frequency of the two constituent wavelengths (λ₁, λ₂).

The commercial MWLI system in this study (presented in section 2), is currently being operated with four wavelengths ranging from ~1530 - 1630 nm with highest constructible unambiguity range up to 1.25 mm. This is almost ~1000 times larger than the range of a typical unambiguousness of single wavelength interferometer [9]. The obvious advantage of the system is its pure mathematical evaluation of beating interval by checking individual phases of each of the four nested wavelengths that ultimately allows absolute distance measurement with high accuracy. However, the dependency of the speed and precision of the MWLI system is entirely involved with the associated phase modulation technique [10]. For the current system phase modulation is performed mechanically using ~1µm back and forth movement of PZT with modulating frequency ~1.25 kHz. To speed up the measurement process, the PZT needs to be operated with higher driving frequency. However, the mechanical phase modulation suffers from some unavoidable limitations. The possibility for having faster measurement is hindered by the restricted value for the operating frequency of the PZT, as higher frequency can bring considerable amount of vibration in the system [11]. Also, the higher frequency is associated with higher heat dissipation in the system. Apart from that, the amount of voltage requirement is also comparatively high. Hence, the goal is to replace the mechanical phase modulation scheme of present MWLI system with a different type of modulation process which can overcome such limitations.

In this work, the potential of Electro-Optical (EO) phase modulation for replacing mechanical phase modulation has been investigated for realising an interferometric distance sensor which enables free beam propagation from sensor to target. However, the performance of EO modulation has been previously investigated for interferometric applications [12] but here we have demonstrated simultaneous modulation of four different wavelengths using linear EO effect in an MWLI setup and to our knowledge, it has not been reported earlier. To activate the linear EO phase modulation a lithium niobate (LiNbO₃) crystal with Titanium (Ti) indiffused waveguides was placed in the path of the test/target beam (illustrated in section 3). Initial measurement confirmed the phase modulation ability of the EO distance sensor which showed equivalent efficiency like in the present system (given in section 4.1). The interferometric distance and displacement measurements have also been tested suggesting its applicability for absolute distance measurement using MWLI (discussed in section 4.2). The performance on phase modulation at higher modulating frequency ~5 kHz has been monitored for both EO and current PZT based setup (demonstrated in section 4.3). The results justify the reason behind replacing the mechanical phase modulation with EO sensor to achieve higher measurement speed. Besides the advantages like lower driving voltage and acceleration of the measurement procedure with higher driving frequency, it can operate in a compact optical setup. Furthermore, it does not have the problem of high power dissipation or audible noise.

2. Current interferometer system configuration

Figure 1 shows the schematic diagram of the present PZT based mechanical phase modulation in the MWLI set-up. The working principle is related to Fizeau-homodyne interferometry and it is an entirely fibre based system. The light source is comprised of four diode lasers that are coupled by a 4 × 1 coupler and directed towards the sensor unit. After entering the sensor, containing the mechanical phase modulation system, the reference beam is separated by a partial back reflection from the end face of the fibre ferule. The other part of the light reaches the target, will be reflected, and coupled back into the sensor unit. The resultant interference patterns for all the four wavelengths are then detected individually by four highly sensitive photo diodes after being separated by Demultiplexer (DEMUX). The distance information is simultaneously analysed from the phase modulated interference signal using a Data Acquisition (DAQ) system interfaced with a computer for final data processing.

 

Fig. 1 Present MWLI system with PZT based mechanical phase modulation process.

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3. EO-distance sensor design

To implement an EO-sensor, experiments have been carried out using a z-cut LiNbO₃ crystal [13]. Waveguide channels were fabricated on LiNbO₃ by in-diffusion of Ti [14]. The half wavelength voltage (${\text{V}}_{\text{π}}$) for π-phase modulation under transverse configuration of a z cut LiNbO₃ crystal is defined as ${\text{V}}_{\text{π}}=\frac{\lambda }{n_e^3 \cdot r_{33}} \left(\frac{w}{l}\right)$. For LiNbO₃, the extra ordinary refractive index ($n_e$) is ~2.14, $r_{33}$ is the EO coefficient ~30.8 pm/V, $w$ and $l$ refer to the width and length of waveguide respectively [15]. The change of refractive index in response to the applied E-field is governed by the equation, $\Delta {\left(\frac{1}{n^2}\right)}_p={\displaystyle \sum }_{q=1}^3{r}_{pq}{E}_q$, where index $q$ runs from 1 to 3 representing x, y, z crystal axis and $r_{pq}$ is the EO coefficient matrix [16]. So, to access the $r_{33}$ coefficient the input light needs to be linear polarised along the z axis of the crystal. Here, for the experiments we started with LiNbO₃ having $l$ ~15 mm, electrodes separation ~50 µm. The ${\text{V}}_{\text{π}}$ for this configuration was around ~12-14 V, which is much lower than the necessary driving voltage of ~94-100V for a PZT based mechanical phase modulation as used in the present setup (Fig. 1).

The experimental set up is presented in Fig. 2. In comparison to the primary system in Fig. 1, changes have been made in the sensor unit by detaching the PZT from the sensor and placing the electrode connected LiNbO₃ crystal in the path of the target beam for phase modulation. Like the previous set up the driving voltage is provided by the MWLI unit for EO phase modulation. To avoid reflexes from the end facet of the waveguide the exit edge (i.e. crystal edge facing the target) has been cut slightly angled (~5°) so that the back reflected light follows a different path (indicated in green line within the schematic diagram of the LiNbO₃ waveguide in Fig. 2).

 

Fig. 2 Experimental set up with EO crystal LiNbO₃ using MWLI.

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4. Experimental results

The results obtained from the EO phase modulation have been compared with the current PZT based system under modulating frequencies 1.25 kHz and 5 kHz.

4.1 π- phase modulation using EO sensor

Figures 3(a) and 3(b) show the phase modulated interferometric signal governed by Eq. (1) from the PZT and EOM based systems, respectively at modulating frequency 1.25 kHz. These clearly depict the equivalent phase modulation ability of the EO crystal LiNbO₃ in comparison with the present PZT based process. The four colours represent the four source wavelengths of the MWLI system. The phase modulated signal confirms the capability of EO phase modulation for being applied as a replacement of PZT for absolute distance measurement.

 

Fig. 3 Intensity distribution of the π-phase modulated interferometric signal obtained from the photo-diode voltage during the experiment under (a) mechanical phase modulation; (b) EO phase modulation’.

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The comparative study on the stability in distance measurement over 1200 seconds, using PZT and EO phase modulation under modulating frequency 1.25kHz has been shown for a fixed target distance in Fig. 4. The drift in distance measurement for EOM was about ~40 nm and for PZT ~15 nm (inset of Fig. 4). For the PZT driven phase modulation of the current MWLI setup, the distance fluctuation range is comparatively low as the PZT has an established and compact setup. The EO phase modulation is under experiment stage which is more sensitive to environmental disturbances like slow environmental changes of the refractive index of air and thermal expansion of optical rails within the experimental setup. However, the result still shows that distance measurement is possible in the nanometer range using EO phase modulation.

 

Fig. 4 Comparative test on distance measurement sensitivity between PZT and EO driven phase modulation over 1200 seconds for a fixed target position.

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4.2 Displacement measurement test using EO sensor

Another test for comparing the displacement measurement under the same modulating frequency 1.25 kHz with the EO phase modulation and the established PZT phase modulation is shown in Fig. 5(a). The target mirror has been moved by introducing a controlled periodic mechanical oscillation using a Piezo. It was operated with a triangular voltage waveform from an external function generator with low driving frequency ~0.3 Hz (to avoid measurement sensitivity due to vibration in the setup). The piezo actuated positioning of the mirror has been first monitored with the current system using mechanical phase modulation and afterwards with the EO phase modulation to draw comparison between these two modulation techniques. The graph clearly shows that the EO phase modulation based system can measure the ~0.8 µm amplitude of target displacement driven with triangle voltage signal similar to that of PZT based phase modulation.

 

Fig. 5 Performance evaluation on measuring piezo actuated absolute positioning of the target (a) comparison on displacement measurement using PZT and EO phase modulation; (b) verifying displacement measurement by EOM with actual target movement measured by the current PZT based system.

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In Fig. 5(b) the target positions measured by the EO phase modulation have been plotted with corresponding target displacements. The fitted slope of the plot is: (1.0027 ± 0.00904) with the intercept: (−0.00289 ± 0.00634) which suggest that the data in Fig. 5(b) has a linear nature between the sequences of displacement measurement made by the EOM with varying amplitudes of Piezo actuated target movement. The result again ensures the ability of EO phase modulation for interferometric distance measurement.

4.3 Performance analysis at higher modulating frequency

Experiments have been carried out for checking the performance of EO phase modulation at higher modulating frequency ~5 kHz. Figure 6 shows the study on the stability in distance measurement for a fixed target position under both types of modulation processes. The result depicts a better system stability against initial temperature changes for EO based modulation process compared to the current PZT based setup. While the distance measurement using the EOM still contains mechanical noise due to external vibration, the influence of thermal drift is almost negligible compared to PZT which has shown ~300 nm distance change within 800 seconds.

 

Fig. 6 Comparison on interferometric stability at higher modulating frequency (~5 kHz) between PZT and EO phase modulation.

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The test on displacement measurement under periodic target movement with EO phase modulation has been repeated for 5 kHz and compared with the PZT system under the same operating condition. Figure 7(a) shows the ability of EO modulation to measure the ~0.8 µm Piezo activated target displacement (driven under triangle voltage signal with movement frequency ~0.3 Hz) at higher modulating frequency similar to that of current PZT based system. The EO system showed more stability during this measurement where the thermal drift experienced by the PZT (red curve in Fig. 7(a)) is visible in the plot. Measurement linearity between EO phase modulation and PZT has been shown in Fig. 7(b) [fitted slope: 0.98902 ± 0.00991 and intercept: −0.00962 ± 0.00799] for different amplitudes of target movement. Table1 summarises the results obtained from the test on measurement linearity between PZT and EO phase modulation at modulating frequencies 1.25 kHz and 5 kHz.

 

Fig. 7 Performance on measurement of piezo actuated periodic target displacement at higher modulating frequency ~5kHz (a) comparison on displacement measurement between PZT and EO phase modulation; (b) test on linearity between the measured values of target displacement by PZT and EO phase modulation.

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Table 1. Experimental results obtained from the test for verifying linearity between the measurements performed by PZT and EO phase modulation.

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5. Conclusions

The concept of EO phase modulation for absolute distance measurement using MWLI system has been proposed and tested in this study. First, the phase modulation has been achieved by EO phase modulation using Ti-indiffused LiNbO₃ waveguide and its modulation efficiency has been compared with the present PZT based system suggesting good compatibility for interferometric measurements. The input voltage requirement (${\text{V}}_{\text{π}}$~12-14 V) for EO phase modulation is even lesser than one-fourth of the driving voltage ~94-100 V necessary for present mechanical phase modulation. Second, the performance of interferometric distance measurement has been examined at modulating frequency 1.25 kHz under static target condition depicting equivalent efficiency of EO phase modulation. The capability on evaluating the precise positioning of the target has also been experimented under dynamic measurement condition when the target was made to execute periodic displacement with an external triangular voltage waveform. This confirms the suitability of EO phase modulation for absolute distance and displacement measurement. Third, the performance of both PZT and EO phase modulation for static and dynamic interferometric measurement has been experimented at higher modulating frequency ~5 kHz. The EO based system showed significantly better system stability when the mirror was kept fixed at a certain position where the PZT suffered from ~300 nm initial thermal drift which again justifies the suitability of EO phase modulation to achieve the goal of faster measurement. The result obtained from the displacement measurement at modulating frequency 5 kHz showed the better performance of EO phase modulation with considerably less amount of drift in measurement due to thermal changes compared to PZT. However, the distance drift at modulating frequency of 1.25 kHz, was found to be relatively higher for the EO phase modulation (about ~40 nm and for PZT ~15 nm) during static interferometric measurement due to air turbulence and ambient thermal fluctuation. The future task is to encapsulate the EO crystal with suitable sensor housing using photonic integrated circuit, for eliminating external influences to attain better measurement stability. The EO-interferometric sensor is expected to significantly improve the measurement speed of the commercial MWLI for performing absolute metrology.