## Abstract

We introduce a novel optical propagation delay measurement scheme for distance estimation. It is based on a ring oscillator in which the oscillation signal is replaced by the clock information contained in optical data. A clock-and-data recovery can recover the oscillation signal at the receive end. Correlation of the received pattern with the transmitted pattern and a measurement of the bit duration by a frequency counter allow to determine the distance. The scheme has been realized at 1550 nm wavelength, using an externally modulated laser, a commercial 155.52 Mb/s clock-and-data recovery and a field-programmable gate array. Short-term repeatability is <10 µm at an equivalent free-space distance of 72 m. Measurement interval is 0.1 s. At 3 km distance the relative repeatability is 8·10^{−8}. The readout can be corrected with measured temperature data.

© 2009 Optical Society of America

## 1. Introduction

Optical distance measurement is attractive because the distant object is not touched and the principle works not only in air but also in vacuum. A wide choice of distance measurement instruments is on the market. Broadband or white-light interferometry yields ultimate precision [1], but a reference path must be scanned until coincidence is found. Narrowband interferometry is plagued from ambiguities. In [2] a 2 µm accuracy for a 50 m distance was achieved with a femtosecond frequency comb laser and a moving reference arm. These disadvantages are avoided in time-of-flight measurements. This widely employed method yields much lower accuracies [3–5]. It is advantageous to send binary optical sequences and to correlate the signals which are received after distant reflection with the transmitted signal [6-7]. The correlation peak occurs for a time delay which corresponds to the roundtrip delay. Using this principle, a resolution of 0.2 mm has been achieved [6]. Delays which are fractions of a bit duration are difficult to measure because interpolation is usually not strictly linear. Furthermore, power-greedy analog-to-digital converters are needed. In space applications this is cumbersome.

We present here a novel time-of-flight measurement principle which does not suffer from the mentioned difficulties. Section 2. describes the principle, achievable accuracy and distance range limits imposed by phase-locked loops of the clock frequency. Section 3. reports an implementation at 155.52 Mb/s data rate and 1550 nm wavelength, including measurement results. Distances are derived from time-of-flight measurements with help of the speed of light in free space or the (slightly different) group velocity in air [8] for industrial and other terrestrial ranging purposes.

## 2. Theory

#### 2.1 Operation principle

The overall principle consists in placing an integer number of optical data pulses in the ring transmitter – measurement path – receiver – transmitter. To this purpose the clock frequency of the optical data pulses is controlled, using standard clock-and-data recovery and MUX/DEMUX ICs for optical communication and a field-programmable gate array (FPGA). The recovered receiver clock signal serves as transmitter clock signal. The whole ring can be regarded as an oscillator with long roundtrip delay. It is as if the oscillation frequency were the clock frequency, although the clock signal doesn’t show up directly in most of the ring. An error-tolerant comparison in the FPGA between transmitted data and received data determines how many data pulses the ring contains. The clock impulses are counted within a quartz-stable counting time interval to determine how long the data pulses are. Propagation delay changes of optics an electronics can be eliminated by a calibration with a short reference path and other means.

An oversimplified block diagram is given in Fig. 1
, a detailed one in Fig. 2
. Figure 1 is simply **a ring oscillator where the ring length determines the oscillation frequency**. A coarse bandpass filter has been inserted in order to enforce oscillation at a high frequency where the total phase shift in the ring including amplifiers equals a high integer number *p* times 2π. The oscillation period is *T*. Oscillation occurs at that of many possible values of *p* where the transmission through the bandpass filter is highest in magnitude, but the frequency is mainly determined by the ring length, only little by the bandpass filter. **Counting the oscillation frequency allows to determine the ring length with high precision and linearity.** In this ring oscillator the switch is always in the lower position. Note that a large part of the ring is optical, to make it usable for optical distance measurement. In the ring the oscillation frequency or clock frequency propagates. If we knew *p* we could precisely determine the ring length.

For that purpose we use Fig. 2. Instead of the clock signal we could as well transmit, say, short pulses which indicate the positive zero crossing of the clock signal. So, we don’t really need to transmit the clock signal. One just needs to transmit a signal which somehow contains the clock phase information. We do this in Fig. 2 as follows: **In most of the ring the clock signal, i.e. the oscillation signal, is replaced by a data signal having the ring oscillation frequency as clock frequency.** The function therefore remains the same as that of Fig. 1. The clock signal occurs no longer in the optical path, only in part of the transmitter, part of the receiver and in an FPGA in which a number of other building blocks are implemented. Yet the oscillation occurs at the same frequency as in Fig. 1 because the clock signal is recovered at the receive end from the data signal, just as if the clock signal were transmitted instead of the data signal. The data signal carries in it the (average) clock signal phase information.

A clocked code generator transfers the clock phase information onto data bits. The clock-and-data recovery extracts not only data but also the clock signal and its phase information from the data signal. The clock signal is a rectangular or sinusoidal signal, the frequency of which is that at which the data pulses are clocked. **Transmitting data instead of the clock allows to determine the integer number p of bits or clock frequency periods T inside the ring.** The total roundtrip time in the ring is

*pT*.

An oscillator does not need an analog-to-digital converter, which is an advantage because ADCs have linearity problems and consume a lot of power. So, the principle of measuring the oscillation frequency in a closed loop is advantageous compared to the well-known measurement of the phase delay of a fixed frequency in an open loop. (In fact the open loop is not a loop.) There is no fundamental sensitivity advantage for one or the other method. Only the ring-oscillator based scheme greatly eases the linearity issue and as a consequence lowers the power consumption. With the usual digital bang-bang clock phase detector of a clock-and-data recovery the system reminds the principle of a 1-bit ΣΔ ADC.

While an oscillator starts oscillating all by itself we must help to start the particular one in Fig. 2, where the oscillation signal is replaced by a data signal in most of the ring. For this purpose a clock generator initially provides the clock signal for a Gold code generator, or pseudo-random bit sequence (PRBS) generator. A multiplexer (MUX) which combines several parallel bit streams may be used to achieve a higher optical line rate than achievable in the FPGA. The MUX contains a phase-locked loop which multiplies the clock frequency of the code generator to a multiple, which is used for optical transmission. The optical bit duration equals *T*. It is the same as the oscillation period in the equivalent setup of Fig. 1. The data drives a laser or a modulator behind it. The optical data signal is sent to and received from a reflecting object. A photoreceiver converts the received optical signal into an electrical one. A clock-and-data recovery with a phase-locked-loop (PLL) recovers clock and data. The data may be demultiplexed down to FPGA data rates. Once the clock is correctly received the original clock signal is replaced by the recovered clock signal, using a switch. Initially there may be a clock phase error of up to ± π. In an open loop this error would be measured, using an ADC. In the ring oscillator the clock phase error will be made equal to zero by an (automatic) adjustment of the oscillation frequency ( = clock frequency). Since the switch is flipped over instantly, clock phase jumps occur initially upon switching. But they will be smoothed out by the PLL after a number of revolutions in the ring. Fine tuning of the clock generator or insertion of a tunable delay inside the FPGA may be useful or necessary in order to limit large clock phase jumps to smaller values. The recovered clock frequency, corresponding to a period *T*, is measured by a clock frequency counter. It is gated with long counting time intervals ${T}_{m}$ which are generated by a counting interval generator, and the counting yields *n* impulses, with ${T}_{m}=nT$. The counting interval generator and the clock generator may but need not use a common reference signal. A word detector at the transmitter detects the occurrence of a characteristic word in the Gold code. The characteristic word is any finite sequence of bits which occurs only once in the code. A similar word detector exists in the receiver, but that one must be error-tolerant. Therefore the word length in the receiver must be longer than *N* if 2* ^{N}* − 1 is the code length. As an example, the occurrence of a word may be indicated if at least 25 bits out of an expected sequence of 32 bits are correct. This is necessary because the clock-and-data recovery will not always recover correct data when light power is low. The occurrence of a certain word in the transmitter starts, and its occurrence in the receiver stops a symbol counter that is clocked by the recovered clock. That counting result

*p*means the number of symbols which travel in the ring. With the knowledge of clock frequency 1/

*T*and symbol delay number

*p*a calculator can easily provide the object distance. The relative accuracy can become very high if one counts the clock frequency in multiple counting time intervals. It depends only on the stability of a stable external quartz oscillator. The necessary absolute accuracy, which is impaired for example by temperature change induced electrical propagation delay changes, can (hopefully) be achieved by comparing the measured propagation delay to that of a short reference path. In order to avoid optical switches, the splitter may be used to permanently feed the reference path, and a second photoreceiver recovers the data. First and second photoreceiver output signals are selected by an electrical switch (see also Fig. 5 ). The left part of Fig. 2 can be implemented with an FPGA. Also the remaining electronics are low-cost standard electronics.

In the alternating presence of measurement and reference paths it holds

#### 2.2 Clock oscillation stability

The delay in the measurement path and the number of PLLs in the ring compromise and limit oscillation stability. The phase transfer function of a PLL with angular resonance frequency ${\omega}_{r}$ and damping factor *ξ* equals

Here *ω* is the offset from the clock frequency, and oscillation is desired at zero offset, $\omega =0$. The phase transfer function of the measurement path with delay *τ*equals

There may be one PLL (PLL1) in the receiver clock-and-data recovery and another (PLL2) in the transmitter MUX, where we assume that their behavior is normalized to the same frequency, say, the optical line rate 1/*T*. The open-loop transfer function is then

*T*. The

**oscillation condition**in the stable state is ${H}_{o}\left(j\omega \right)=1$ (unity gain and integer number of 2π phase shifts in the ring), and we expect it to be fulfilled for $\omega =0$ but for no other $\omega \ne 0$. If for another frequency ${H}_{o}\left(j\omega \right)\ge 1$ is valid, stable oscillation at $\omega =0$ cannot be expected. It may even happen that several modes (= frequencies) oscillate simultaneously, like in a multimode laser. So, ${H}_{o}\left(j0\right)=1$ and $\mathrm{Re}\left({H}_{o}\left(j\omega \right)\right)<1$ for $\omega >0$ form a sufficient condition for stable oscillation on one mode at $\omega =0$ only.

Clock phase detection noise $x\left(t\right)$ with spectrum $X\left(j\omega \right)$ is added in the PLL to the oscillator phase. For the spectrum $Y\left(j\omega \right)$ of the detected clock phase $y\left(t\right)$, which is fed back in the oscillator through the open-loop transfer function ${H}_{o}\left(j\omega \right)$, is

$H\left(j\omega \right)$ is the closed-loop clock phase error transfer function. One can understand an oscillator output signal to be the (usually thermal) noise of the oscillator, filtered by an ultranarrow bandpass filter. The PLL(s) must be able to generate a certain non-zero VCO input signal even for vanishing clock phase error noise. So the closed-loop gain should reach $\left|H\left(j\omega \right)\right|\to \infty $ for $\omega \to 0$. This is indeed fulfilled since ${H}_{o}\left(j\omega \right)=1$ for $\omega =0$.

#### 2.3 Quantization error

Let the one-way object distance be *d*. The measurement path delay is $\tau =2d/c$. The quantization error, determined by the counting accuracy, is easily evaluated. If each optical clock pulse with frequency 1/*T* is counted then the quantization error equals

#### 2.4 Examples

We assess the achievable measurement range in a few examples. A counting interval ${T}_{m}$ of 0.1 s is assumed.

Initially there be no MUX or DEMUX or PLL2, only PLL1. Clock frequency and optical line rate are 155.52 MHz. Already for this low bit rate it holds ${\sigma}_{d,q}=6.5\cdot {10}^{-7}\text{m}$ for *d* = 35 m. For PLL it holds ${\omega}_{r,1}=2\pi \cdot 130kHz$. Figure 3
shows PLL behavior for damping factors 5, 2, 1, 0.7, 0.5, 0.3.

Open-loop and closed loop transfer functions are shown in Fig. 4 , for zero (A) and 35 m object distance (B), both with a damping factor of 5. Even with 35 m object distance, stability is quite good. But it is clear that object distance cannot rise extremely. Stability is improved by a reduction of the damping factor to 0.7, exemplified in (C) for 35 m and in (D) for 500 m object distance. Above 700 m of distance (not shown) there exists a secondary point with $\mathrm{Im}\left({H}_{o}\left(j\omega \right)\right)=0$, $\mathrm{Re}\left({H}_{o}\left(j\omega \right)\right)>1$ for $\omega >0$. Instability (multimodedness or mode hopping?) may be expected there.

The resonance frequencies of commercial clock-and-data recovery PLLs scale roughly proportional to bitrates. Measurement accuracy increases proportional to bitrate, but measurement range is limited by the inverse bitrate. A way to increase accuracy without sacrificing measurement range is, as mentioned before, the use of two PLLs. We assume the PLL1 which should be part of a 16:1 MUX component (155.52 MHz to 2.48832 GHz) to have ${\omega}_{r,1}=2\pi \cdot 130kHz$, ${\xi}_{1}=0.7$. At the receive end there be a 2.48832 GHz clock-and-data recovery with ${\omega}_{r,2}=2\pi \cdot 2MHz$, ${\xi}_{2}=0.7$ and subsequent 1:16 DEMUX. As can be seen in Fig. 4(E), this configuration allows to support measurement ranges of 500 m. Note that compared to examples (A) to (D), measurement accuracy is increased by a factor of 16, to ${\sigma}_{d,q}=4\cdot {10}^{-8}\text{m}$. Equal resonance frequencies ${\omega}_{r,1}={\omega}_{r,2}=2\pi \cdot 130kHz$ perform worse than example (E).

We notice that stable oscillation in one mode can always be achieved if one PLL has a time constant which is much longer than the propagation delay *τ* and the time constant of any other PLL. Locking to a third or more PLLs with yet lower resonance frequencies is of course possible to accommodate drastically larger measurement ranges.

## 3. Experiment

#### 3.1 Setup

The actual distance measurement setup is shown in Fig. 5. A commercial development board housed a Xilinx Virtex-II Pro FPGA. A multiphase (8-phase) fixed clock generator operating at 310 MHz was implemented in order to increase counting accuracy although data rate was just on the order of 155 Mb/s.

The counting interval generator specified the counting interval as equal to a high predefined integer number of bit periods.

The 8 individual numbers of fixed clock pulses registered during the counting interval were added up to give a more accurate measure of the bit period *T*.

The changed counting scheme of Fig. 5 compared to Figs. 1, 2 means indeed that not the clock frequency 1/*T* but its inverse, the bit duration *T*, is counted or measured.

Clock switching for loop closure turned out to introduce unstable phase delays in this FPGA. Therefore an external data and clock unit (EDCU) was constructed with ECL components, containing a clock switch and a D-flip-flop for data retiming. The switch was controlled by the FPGA. The loop clock, either fixed at 155 MHz for loop filling or variable near 155 MHz as given by the ring oscillation, was fed back into the FPGA for code and counting interval generation. Data was modulated by means of a driving amplifier (not shown) onto a 1550 nm DFB laser with integrated electroabsorption modulator (externally modulated laser, EML). Output power was about several 100 µW, but this value was uncritical.

The design goal was to measure the distance of an object about 35 m away in a measurement interval of 100 ms. For lack of a suitable optical free-space path an available, roughly 100 m long single-mode fiber was inserted as the measurement path. This fiber reel, and a 1:1 fiber coupler for signal separation into a measurement and reference paths, were (coarsely) temperature-stabilized. The two paths were terminated into two identical 2.5 Gb/s photoreceivers, with twisted input fibers of equal lengths. An electronic switch, likewise controlled by the FPGA, allowed to select one or the other front end output signal for regeneration in a commercial clock-and-data recovery with a PLL resonance frequency on the order of 160 kHz (according to the data sheet). The voltage controlled oscillator (VCO) tuning range was more than ±5%. The inverse of the tuning range specifies the minimum needed reference path length for coverage of all possible additionally inserted measurement path lengths. Our reference path (fiber and coaxial cable, expressed as equivalent free-space distance) was about 7.3 m.

For increased accuracy the measurement interval was subdivided into 32 periods, each 3.125 ms long. In these the reference and measurement paths were inserted alternately. Counting started after a short guard interval. Tuning range overflow in PLL and VCO was prevented by periodic insertion of short loop filling periods with fixed 155 MHz clock signal during these guard intervals.

#### 3.2 Results

Figure 6 shows the measured equivalent free-space distance difference (about 72 m) as a function of time, in 1000 samples or 100 s in total. The delays expressed as a number of symbols were ${p}_{ref}=10$, ${p}_{meas}=85$. The clock frequencies were of course different for reference and measurement paths and allowed to calculate the length difference according to Eq. (2). Figure 7 is a logarithmic histogram of the (short-term) measurement errors. The standard deviation is 6.7 μm.

Table 1
details the results of other measurement paths which resulted in other values of ${p}_{meas}$. The various fiber patchcords and reels were inserted by means of connectors. The standard deviation was < 5 μm for the short paths d_{11} and d_{12}.

Path d_{34}, about 3 km long, features a relative repeatability (standard deviation divided by mean) of only 8·10^{−8}. Path d_{4} ≈ 5.9 km, where relative repeatability drops to 3·10^{−5}, indicates instability. However, note that the stable range (3 km) is about 4 times longer than theoretically predicted (700 m).

Fiber length is equivalent free-space distance times 2 divided by the group refractive index 1.4679.

Three (*i* = 1, 2, 3) path quartets (d* _{ij}*) have been characterized. Due to proper combination of paths (see nominal inserted distance values, which stand for specific fibers) one always expects d

_{i}_{1}+ d

_{i}_{4}– d

_{i}_{2}– d

_{i}_{3}= 0. But the practically calculated values, between −35 mm and +9 mm, differ from zero. Part of this is probably caused by a power-dependence of the group delay in the clock-and-data recovery.

Indeed, for the (only roughly, but not exactly) 100 m long fiber (path d_{21}, equivalent to 72 m of free space) the readout varied by a bit more than 2 mm for optical powers between 100 and 350 µW. Therefore an automatic power control was realized. The sum of frontend photocurrents was measured and compared to a constant. The difference was integrated and added to the nominal laser current. In the range of nominal laser current where the automatic power control was able to add the missing laser current portion the distance variation dropped to just 10 µm.

In Fig. 8 we see the measured equivalent free-space distance difference variation for the 100 m long fiber measured during $2\cdot {10}^{5}$ s (a weekend). The temperature of the aluminum ground plane (around +35°C) where the boards were mounted was also recorded. Three cooling phases (nights) and two weak heating phases (daytime) are visible. At the end, fast heating starts very early on Monday morning. A strong correlation between temperature drift and distance difference drift is apparent. Total distance drift was 1.2 mm, temperature variation was 1.1°C. The correlation coefficient between distance and temperature was 0.992, almost unity! A linear temperature dependence of the distance was therefore introduced and fitted to the data of Fig. 8. This reduced the total length drift to 270 µm, with a standard deviation of only 34 µm (Fig. 9 ). It seems reasonable to assume that a temperature stabilization to 0.1 K or a compact setup with uniform temperature and more accurate temperature measurement can reduce the standard deviation in this case to 10 µm or so. The delay drift of the measurement path alone, with distance of about 79 m, was ~14 ps/K, and that of the reference path alone, with distance of about 7.3 m, was ~6 ps/K, in both cases including electronics.

All measurements were conducted with a Gold code of length ${2}^{11}-1$. The measurement range was therefore uncertain modulo $c({2}^{11}-1)/\left(2\cdot 155MHz\right)\approx 1980m$. Later we changed to other maximum-length sequences, namely a Gold code of length ${2}^{13}-1$ and PRBS of lengths ${2}^{11}-1$, ${2}^{13}-1$, ${2}^{15}-1$. The ${2}^{15}-1$ pattern increased the unambiguous range to 32 km. None of these changes influenced repeatability significantly.

## 4. Discussion and conclusion

The presented ring oscillator distance measurement scheme avoids the need for an elaborate analog-to-digital converter and exploits instead the 1-bit clock phase detection capability of a commercial clock-and-data recovery. With a differential measurement repeatability <10 µm (standard deviation) for 72 m distance, a relative repeatability down to 8·10^{−8} and a maximum distance of at least 3 km it is attractive for a wide range of distance measurement tasks, including space applications. Drawbacks are the temperature and power dependence of the readout and the discontinuity of the measurement introduced by different values of ${p}_{meas}$ due to different path lengths.

## Acknowledgements

This work was funded by the Raumfahrt-Agentur des Deutschen Zentrums für Luft- und Raumfahrt e.V. with financial means from the german Bundesministerium für Wirtschaft und Technologie due to a vote of the Deutscher Bundestag with funding code 50 RR 0902. The authors alone are responsible for the contents. We acknowledge fruitful discussions with Hartmut Jörck from EADS Astrium GmbH in Friedrichshafen, Germany.

## References and links

**1. **C. Yang, A. Wax, R. R. Dasari, and M. S. Feld, “2π ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer,” Opt. Lett. **27**(2), 77–79 (
2002). [CrossRef]

**2. **M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. M. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. **34**(13Issue 13), 1982–1984 (
2009). [CrossRef] [PubMed]

**3. **A. Nemecek, K. Oberhauser, C. Seidl, and H. Zimmermann, “PIN-Diode Based Optical Distance Measurement Sensor for Low Optical Power Active Illumination”, Sensor, 2005 IEEE, Oct. 30 2005 - Nov. 3 2005, pp. 861-864, DOI 10.1109/ICSENS.2005.1597836. [CrossRef]

**4. **R. Lange, “3D time-of-flight distance measurement with custom solid-state image sensors in CMOS/CCD-technology”, Dissertation at the Univ. Siegen, Germany, 08.09.2000, http://dokumentix.ub.uni-siegen.de/opus/volltexte/2006/178/pdf/lange.pdf.

**5. **D. Van Nieuwenhove, W. Van der Tempel, R. Grootjans, and M. Kuijk, “Time-of-flight Optical Ranging Sensor Based on a Current Assisted Photonic Demodulator”, Proceedings Symposium IEEE/LEOS Benelux Chapter, 2006, Eindhoven, pp. 209-212, http://leosbenelux.org/symp06/s06p209.pdf.

**6. **J. M. Kovalik, W. H. Farr, C. Esproles, and H. Hemmati, “Optical Communication System with Range and Attitude Measurement Capability”, IPN Progress Report 42-161, pp. 1-6, May 15, 2005 http://tmo.jpl.nasa.gov/progress_report/42-161/161Q.pdf.

**7. **J. Morcom, United States Patent US6753950, June 22, 2004, http://www.freepatentsonline.com/6753950.pdf.

**8. **P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express **17**(11Issue 11), 9300–9313 (
2009), http://www.opticsinfobase.org/oe/viewmedia.cfm?uri=oe-17-11-9300&seq=0. [CrossRef] [PubMed]