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Abstract
The application of frequency scanning interferometry to long-range (∼10 m) high-speed (upwards of 105 coordinates s−1) absolute distance measurement is currently impractical at reasonable cost due to the extremely high modulation frequencies (typically 100 GHz or more). A solution is proposed here based on an adaptive delay line architecture, in which the reference beam passes through a series of N switchable delay lines, with exponentially-growing delays. The benefits include a reduction by a factor of 2N in the required signal sampling rate, in the size of dataset to be processed, and in minimum allowable source coherence length, thus paving the way for the use of fast sweeping sources such as vertical-cavity surface-emitting lasers (VCSELs) and Fourier-domain mode-locked (FDML) lasers for long-range lidars. The validity of the principle has been demonstrated experimentally by means of a three-switch prototype.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Optical techniques for absolute distance measurement have been developed in many branches of science and engineering. Those based on a tunable laser source find applications over length scales from the sub-mm in the form of swept source Optical Coherence Tomography (OCT), to tens of m or more with Frequency Scanning Interferometry (FSI, also commonly termed Frequency Modulated Continuous Wave, or FMCW, lidar) [1,2].
Such techniques involve combining the light reflected or scattered from a target (the object wave) with a local reference wave. The mixing of the two at the photodetector results in an electrical signal at a frequency f that is proportional to $\Lambda$, the optical path difference (OPD) between the two waves. For a linear frequency ramp and non-dispersive medium, $f$ is given by [3]:
where $f_s$ is the laser scan repetition rate, $\Delta \lambda$ is the tuning range and $\lambda _c$ is the centre wavelength for that $\Delta \lambda$. The resolution of $\Lambda$ varies inversely with $\Delta \lambda$.Current state-of-the-art tunable laser sources such as VCSELs [4] and FDML lasers [5] can produce scan rates of 100s of kHz to several MHz, respectively, combined with $\Delta \lambda$ values exceeding 100 nm at $\lambda _c = 1.0, 1.3$ or 1.5 $\mu$m. Since each scan provides the data for one coordinate, and the large $\Delta \lambda$ can measure surface location to sub-$\mu$m resolution, such sources therefore open-up high-accuracy long-range distance measurement at rates in the range $10^5-10^6$ s$^{-1}$ [2]. These rates offer significant potential for dimensional quality control on production lines, automated assembly and robotic path guidance and are 2-3 orders of magnitude higher than current commercial FSI-based instruments (e.g., Nikon MV331/351). However, there are at least four significant challenges that need to be overcome. The first is the extremely high sampling rates required of the data acquisition board (DAQ). For example, with $\Delta \lambda = 100$ nm, $\lambda _c = 1.3$ $\mu$m, $f_s = 100$ kHz, Eq. (1) shows that $f\sim 12$ GHz at a distance $z$ of 1 m ($\Lambda =2z=2$ m for coaxial illumination and observation directions), and an order of magnitude higher still for a 10 m range. Minimum sampling rates are twice these values, requiring DAQ hardware with sampling rates greater than 100 GS s$^{-1}$. Typical digital storage scopes with 70 GHz bandwidth, single channel and 200 GS s$^{-1}$ cost over $ \$ $300k. Secondly, processing in real-time such high-speed data streams is non-trivial. Thirdly, the coherence length of these laser sources is not well characterized and may pose limitations for long $\Lambda$ [6]. Finally, Fourier domain peak broadening and splitting due to imperfect frequency ramps increase in severity with increasing $\Lambda$ [7,8].
In this article we propose a solution to all four problems, based on the concept of a so-called Adaptive Delay Line (ADL). The ADL is introduced into the reference beam and can reduce $\Lambda$ to the point at which the modulation frequency drops to levels that can be dealt with by standard DAQs ($\sim 1$ GS s$^{-1}$) whilst simultaneously reducing data throughput, removing the need for a long coherence length source, and reducing Fourier domain peak broadening effects.
2. Method
The operating principle of the solution is shown in Fig. 1 where, in this example, the reference beam passes through $N=3$ optical switches S0, S1 and S2 in series. Each switch, which may be mechanically, optically or electronically controlled, selects one of two optical paths to the next switch: the path indicated with a solid line. At the final stage, the last two paths are recombined at the coupler (CPL) and the length-adjusted reference beam proceeds to the rest of the interferometer where it interferes with the object wave. Curved paths are shown here since an ADL could be implemented with optical fibres in a thermally-stabilized enclosure, or wave-guides on a photonic integrated circuit (PIC). A recent example of a PIC-based FMCW lidar is described in [9]; low-loss waveguides up to 5 m long (giving an OPD of $\sim$ 20 m in air) can be produced on a single 12 $\times$ 6 mm$^{2}$ die [10].
Fig. 1. ADL diagram featuring $N=3$ switches, allowing the selection of one of $2^N = 8$ equally spaced optical path lengths.
The state of the $j^{th}$ switch may be specified by a single bit, $b_j$, with 1 indicating that the longer path is selected, and 0 the shorter. By choosing the OPD ($\Lambda _j$) between two possible paths for successive switches to follow an exponential sequence, i.e. $\Lambda _j = 2^jd_0$ where $d_0$ is the optical path difference for the first switch, a single optical path length from a comb of $2^N$ discrete and uniformly spaced values with increment $d_0$ can be selected. Take for example the case $N = 10$ and $d_0 = 10$ mm. The resulting 1024 steps defined by the bit pattern ${B} = {b}_{{N}-1} {b}_{{N}-2} \cdots {b}_{1} {b}_{0}$ through which the imbalance between the reference and the object arms can be adjusted, cover the range 0 to $\sim 10$ m whilst the maximum required sampling frequency is reduced by 1024$\times$, to that for a $\Lambda$ of 10 mm. As a specific example, for a target with $\Lambda = 8.003$ m, the byte B = 1100100000 shifts the zero-$\Lambda$ surface (i.e., the surface on which a scattering point results in equal optical path lengths for object and reference waves) to 8.000 m while the remaining 3 mm are detected at a correspondingly much lower frequency. In general, for a given DAQ hardware, each additional switch in the chain doubles either the maximum range or the coordinate acquisition rate. The restriction on the source coherence length ($l_c\geq 2^Nd_0$), which places an upper limit on measurement range, is relaxed by a factor $2^N$ to $l_c\geq d_0$.
A similar switching architecture has been used in different fields: for telecoms time division multiplexing (TDM) [11], for reflectometry with a broadband source [12], and for Fourier Transform Spectroscopy [13]. However, to the best of our knowledge, its application to absolute distance measurement with a swept monochromatic source has not been previously proposed.
3. Optical setup
To test the concept, proof-of-principle experiments were carried out using the optical setup from Fig. 2. Although an eventual deployment of ADLs in an industrial context would most likely use electro-optic switches so as to achieve sufficiently high switching speeds, mechanically activated switches were used here due to the availability of the component parts. The demonstrator incorporates a 3-bit ADL with mechanical switching performed by rotation of achromatic half wave plates (HWP) in front of polarizing beam splitters (PBS). If the incoming state of polarization (SOP) to a given HWP is horizontal (P), the beam passes straight through the PBS to the next switch. When all three HWPs are in this orientation, thus implementing the 000 bit configuration, the reference beam follows the blue path and the OPD for the interferometer is the difference in optical path between the red and blue lines. Rotation of the HWP by $45^{\circ }$ causes a $90^{\circ }$ rotation in SOP (S), thereby directing the beam once around the loop formed by two pairs of beam-folding gold mirrors (M-M). The translation stages (TS) allow fine adjustment of the delay lengths, which took the values $d_0\sim 240$ mm, $d_1\sim 490$ mm, $d_2\sim 830$ mm. An additional HWP and PBS prior to the ADL act as a variable ratio beam splitter. The half-wave plates had a manufacturer’s stated retardance of $0.49$ ${\displaystyle \pm }$ $0.01$ over the full tuning range of the laser. The minimum extinction ratio of the PBSs was $180$ over the same wavelength range.
Fig. 2. Proof-of-principle experimental optical setup. Light paths are colour coded as follows: object beam is red, straight-through reference beam is blue, additional loops within the ADL are green.
The tunable laser source (TL) used was a SANTEC TSL-510 with $\Delta \lambda = 100$ nm, $l_c\sim 1.8$ (Coherence Control ON) to 300 m (Coherence Control OFF) and $\lambda _c = 1.3$ $\mu$m, operated in free running mode. As such, lack of a reference interferometer meant that laser repeatability errors will manifest themselves as large errors in $z$ [14]. The light beam is delivered to the interferometer by means of a single-mode, polarization-maintaining (SM PM) fibre and is subsequently collimated using a reflective collimator (RCL) prior to being split into the reference and object beams.
The two linear polarizers (LNP) on two sides of the final beam splitter (BSCPL) ensure interference between matching SOPs is detected at the auto-balanced photodetector (ABPD). Light is delivered to the ABPD by a pair of SM PM fibres using fibre couplers with achromatic doublets. The ABPD signal is then digitized by a storage oscilloscope (Tektronix MSO54, 500 MHz, 6.25 GS s$^{-1}$). The captured data sequences are transferred to a PC for subsequent processing. Finally, the target gold mirror (TM) was mounted on a rail assembly (not shown here) that allows manual movement of TM over a range of approx. 1 m and a corresponding round trip of $\sim 2$ m.
4. Results
4.1 Frequency down-shift
To illustrate the ability of the system to down-shift the interference signal frequency ($f$), TM was placed a few tens of mm beyond the maximum delay length of the 3-bit ADL ($\sim 780$ mm), achieved with the 111 bit configuration. The laser scan parameters were: $\Delta \lambda = 10$ nm, starting wavelength $\lambda _1 = 1.33$ $\mu$m and average laser scan-speed of d$\lambda$ / d$t = 10$ nm s$^{-1}$, while the sampling rate was set to 1.25 MS s$^{-1}$, giving a record length of $1.25 \times 10^6$ points. Of these, 9000 points were processed corresponding to a $\Delta \lambda <1$ nm. The reduced bandwidth was used to minimize the errors in $z$, owing to the combined effect of dispersion and fluctuations in d$\lambda$ / d$t$ over the full $\Delta \lambda$ ranges, and which would otherwise be impossible to decouple without proper wavelength referencing [15] and linearization techniques [16,17].
The interference signals over a 7 ms scan sub-section for all 8$\times$ bit patterns are shown in Fig. 3. This illustrates the gradual reduction in frequency as the imbalance between the reference and object arms is reduced through selection of the 8$\times$ bit configurations, with the 111 bit configuration giving the lowest frequency as expected. The modulus squared of the Fourier transforms of the eight signals are shown in Fig. 4. The frequency for each peak location was estimated to sub-pixel resolution by means of a Newton-Raphson iterative procedure [18], giving values 9.89, 8.21, 6.73, 5.23, 4.84, 3.13, 1.67 and 0.13 kHz for the 000 through to 111 bit configurations, respectively.
Fig. 3. Normalised time signals $I(t)$ corresponding to the eight ADL bit configurations for a target at $\sim 825$ mm from BSR.
The question of how to select the correct bit pattern, i.e. the one that minimizes $\Lambda$ and hence $f$, now arises. Consider first the general case where the object, whose range is to be measured, lies at some arbitrary point within the measurement volume. Each bit pattern can be applied to the ADL in turn. For sources with short $l_c$, the highest signal modulation will occur for the bit pattern with the shortest $\Lambda$. In the case of a source with long $l_c$, a low pass filter (LPF) can be introduced at the output of the photodetector, or indeed by choosing a photodetector with a low bandwidth. Only the shortest $\Lambda$ bit configurations will then produce significant signal, and this will be within the Nyquist limit for the DAQ hardware, provided $d_0$ has been chosen to be sufficiently small. All $2^N$ configurations could be explored during a single frequency scan, followed by the detailed $\Lambda$ measurement at the selected fixed bit configuration on the subsequent scan. For example, for the case $N = 10$ and a scan rate of $10^5$ Hz , switching events should take place every 10 ns ($1/(2^Nf_s)$), which is within the capabilities of fibre switches. For the less demanding case of a quasi-continuous surface, the search can be accelerated by only exploring bit patterns near to the one established for the previous measurement, with the system slowing down only in the presence of a large $z$-discontinuity. Alternatively, a low-cost time-of-flight lidar working in parallel with the FSI could be used to determine the integer part of $z$, and thus instruct the ADL which tackles the more demanding precision part of the measurement.
4.2 ADL sign determination
There remains, however, one additional source of ambiguity: how to distinguish between positive and negative deviations in $\Lambda$ from the zero-$\Lambda$ surface that gives the lowest modulation frequency. In the earlier example, the target at $z = 8.003$ m would produce the same signal frequency as the case with the target at $z = 7.997$ m. This ambiguity could be resolved by incorporating phase information (e.g. through I/Q detection), since the frequencies of the Fourier domain peaks would then have opposite signs for the two cases. When I/Q detection is not available, modulation frequencies measured with one or both of the two neighbouring bit configurations will allow the ambiguity to be overcome. For example, suppose $B_{\nu}$ is the bit configuration that minimizes the modulation frequency, denoted here $f_{B_{\nu}}$. $B_{\nu-1}$ and $B_{\nu+1}$ are the bit configurations that select the nearest neighbour zero-$\Lambda$ surfaces. Assuming identical increments in $\Lambda$ between adjacent surfaces, the sign $s_{B_{\nu}}$ of $f_{B_{\nu}}$ is recovered as:
Fig. 5. (a) Power spectrum of detected frequencies and (b) filtered signals in the presence of an LPF: cut off frequency at 1.8 kHz (dashed line).
4.3 ADL calibration
As with any FSI system, calibration is required to convert the measured modulation frequency to distance. There is, however, an additional step for an N-bit ADL-based FSI system, namely determining the N additional delay lengths, or equivalently the frequency shifts introduced by those delays. The latter approach was adopted here: with the TM fixed a few mm beyond the 111 zero-$\Lambda$ surface, eight signals corresponding to the eight bit configurations of the ADL were recorded and their frequencies calculated using the method described earlier.
By performing a least squares straight-line fit to the measured frequencies versus known distance data, $z_R$, the conversion factor can be extracted from the gradient of the best-fit line as shown in Fig. 6(a). This was calculated to be 0.01157 kHz mm$^{-1}$ with a root-mean-square (RMS) residual of 0.095 kHz. The latter, whilst high for FSI systems, arose from the temporal variation in scan rate for the particular laser used and was still sufficiently low to demonstrate the principle of the proposed method.
Fig. 6. (a) Least squares fit for frequency to distance conversion. (b) Comparison of range measured by the ADL FSI system and the reference interferometer, with superimposed best straight-line fit. Additional measurements with fast VCSEL source, and corresponding best-fit line, are shown in red [20].
As final validation of the method and data processing procedures described above, one further experiment was carried out to compare distances measured using the FSI to that measured by the Renishaw interferometer. A new set of measurements was taken with the TM placed in a set of six locations that were independent of those used for calibration. A graph of range measured by FSI versus that measured by the Renishaw interferometer is shown in Fig. 6(b). The graph has a gradient of 1.005 $\pm$ 0.015, demonstrating (within experimental error) the expected 1:1 correspondence between the two systems. The RMS residual about the best-fit line was 3.00 mm.
The large measurement uncertainty has been addressed in a recent study with the same ADL demonstrator and a fast VCSEL source, albeit over a restricted $z$ range due to the high modulation frequencies from the large $d_0$ value in this setup [20]. Twelve measurements from two bit configurations are shown superimposed on Fig. 6(b). The RMS of the residuals with respect to the best-fit line was 0.6 $\mu$m, a factor of 5000$\times$ lower than with the SANTEC TSL-510 laser, thus demonstrating that the limited accuracy was due to the laser source and not due to the Adaptive Delay Line itself. The main factors contributing to the improved performance can be summarised as (a) intrinsically better repeatability, (b) wider utilized tuning bandwidth (40 nm versus $\sim 1$ nm), and (c) the introduction of a reference interferometer in [20] to linearize the frequency scans. The experimental datasets presented here are available from Ref. [21].
5. Summary and conclusions
In summary, we have proposed Adaptive Delay Lines as a method to allow Frequency Scanning Interferometry to be used for very high coordinate measurement rates (upwards of $10^5$ s$^{-1}$), over long ranges (tens of m), with standard data acquisition hardware (maximum sampling rate $\sim 1$ GS s$^{-1}$). The optical system consists of a series of N switchable delay lines with exponentially-growing delays. The benefits include a reduction by a factor of $2^N$ in required sampling rate, dataset size and minimum allowable source coherence length that are of particular importance for dynamic FSI measurements [22]. The validity of the principle has been demonstrated by means of a low-speed 3-bit prototype.
Funding
Engineering and Physical Sciences Research Council, Future Metrology Hub (EP/P006930/1).
Disclosures
All three authors are co-authors of a current patent application in this area.
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