Research Article

Vol. 29, No. 19 / 13 Sep 2021 / Optics Express 30727

Doppler velocimeter and vibrometer FMCW
LiDAR with Si photonic crystal beam scanner
S ANEYUKI S UYAMA , H IROYUKI I TO, RYO K URAHASHI , H IROSHI A BE ,AND T OSHIHIKO B ABA *Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai,
Hodogaya-ku, Yokohama 240-8501, Japan* baba-toshihiko-zm@ynu.ac.jp

Abstract: In this paper, we propose and demonstrate a frequency-modulated continuous-wave
light detection and ranging (LiDAR) with a Si photonic crystal beam scanner, simultaneously
enabling scanning laser Doppler measurements. This nonmechanical solid-state device canreduce the size of conventional scanning laser Doppler vibrometers, making LiDAR a multimodal
imaging sensor, which can measure the distributions of distance, velocity, and vibration frequency.
We fabricated this device using Si photonics process and confirmed the expected operations.
Distance and velocity resolutions were less than 15 mm and 19 mm/s, respectively. The detection
limit of the vibration amplitude determined by the signal-to-noise ratio was 2.5 nm.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1.

Introduction

Light detection and ranging (LiDAR) is a three-dimensional (3D) imaging sensor, applicable toself-driving vehicles, robotics, drones, mapping, and so on [1]. LiDAR is usually comprised of alaser source, beam scanner and photodiode. In recent years, optical phased array (OPA) [2–8],
focal plane array (FPA) [9–11], and slow light grating (SLG) [12,13], which are fabricated by
Si photonics technology, have been actively studied as compact and nonmechanical solid-state
beam scanners. Additionally, integrated LiDAR incorporating many of these components on asingle chip have been demonstrated [11]. We have also demonstrated wide-angle, high-resolution
solid-state beam scanning using SLG based on photonic crystal waveguides (PCWs).
Time of flight (ToF), which measures the round-trip delay of an optical pulse, is commonlyused as the ranging method in commercial LiDAR systems. When Si photonics, particularly with
Si waveguides, is applied to LiDAR, two-photon absorption occurs even at telecom wavelengths
and strongly constrains the pulse intensity and, thus, the LiDAR sensitivity. Consequently,
many studies have employed the frequency-modulated continuous-wave (FMCW) method, which
does not use an optical pulse, but FMCW light. The range information is obtained from thebeat frequency between round-trip light and reference light via coherent homodyne detection.
In principle, this method provides shot-noise-limit high sensitivity and high-range resolution
determined by the frequency modulation bandwidth and does not interfere with ambient lightand other LiDARs.
A more significant feature of the FMCW method is that the velocity of objects can also
be obtained by detecting Doppler shifts [6,11,14]. If the range and velocity are acquired
simultaneously in two dimensions (2D), it will be quite useful for exactly analyzing high-speed
moving objects, such as self-driving vehicles and drones, to predict subsequent motions and, thus,increase their safety. Combining the principle of scanning laser Doppler vibrometer (SLDV)[15–17] with the FMCW, the vibration distribution of objects can also be visualized. SLDV
is used to inspect vibrating equipment, infrastructure, and human health conditions [18,19].
Currently, its large size and expense limit its applications. If an on-chip FMCW LiDAR isrealized by Si photonics, a multimodal imaging sensor will evolve, which will function as a#438453
Journal © 2021

https://doi.org/10.1364/OE.438453
Received 21 Jul 2021; revised 27 Aug 2021; accepted 1 Sep 2021; published 8 Sep 2021

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velocimeter and vibrometer beyond the capability of standard ToF LiDARs and acquire further
applications.
In this study, we demonstrated the operation of such a multimodal LiDAR with an SLG
beam scanner. In Section 2 of this paper, we briefly summarize the theory of the velocimeterand vibrometer combined with the FMCW LiDAR. Subsequent sections describe the setupof the experiment and then present the experimental results of each function, followed by theconclusions.
2.

TheoryThe FMCW LiDAR measures the frequency difference (beat frequency f b ) between reflectedsignal light and reference light and obtains the range R to the target object by the following
equation [20]:
cT
R=
fb .
(1)
2B
where c is the speed of light in the environment, T is the frequency sweep period, and B is thefrequency sweep bandwidth, assuming linear frequency sweep as the frequency modulation. The
range resolution ∆R is given from the sampling theorem, ∆f b = 1/T, and is expressed as
∆R =

c
.
2B

(2)

For example, ∆R = 15 mm for B = 10 GHz.
When the target object has a velocity component v in the direction of light travel, f b is
Doppler-shifted by f D , resulting in frequencies of f up = f b + f D and f down = f b – f D for a triangularfrequency sweep. For the wavelength λ of light, v is given asv=(fup − fdown )λ fD λ
=
.
4
2

(3)

The velocity resolution ∆v is given under the condition f b = f D , then
∆v =

λ
.
2T

(4)

For example, ∆v = 19 mm/s for T = 40 µs and λ = 1550 nm.
When the target is displaced by x(t) along the direction of light travel with respect to time t,
the FMCW beat signal S is given as [21–23]
S ∝ cos2 [2πfb t + ϕ(t)] , ϕ(t) = 2k0 x(t)(5)

where k0 is the wavenumber in the environment. When the target is vibrating sinusoidally withthe amplitude ∆X and frequency f v , which is,x(t) = ∆X sin(2π fv t).

(6)

2
⎡
(︂
)︂ ∑︁
(︂
)︂ ⎡⎢ cos 2π{fb − (2k − 1)fv }t ⎤⎥ ⎤⎥
n
⎢
⎢
⎥ ⎥
⎢ J0 4π∆X−
J2k−1 4π∆X
⎢
⎥ ⎥
λ
λ
⎢
k=
1
⎢
⎥ ⎥
−
cos
2π{f
−
(2k
+
1)f
}t
S∝⎢
b
v
⎣
⎦ ⎥
(︂
)︂
⎢
n
∑︁
⎢ +
⎥
J2k 4π∆X
{cos
2π(f
−
2kf
)t
+
cos
2π(f
+
2kf
)t}
⎢
⎥
b
v
b
v
λ
⎣ k= 1⎦(7)

Equation (5) is expanded asResearch Article

Vol. 29, No. 19 / 13 Sep 2021 / Optics Express 30729

This equation indicates that sidebands with integer multiple frequencies of f v are generated
around f b . The spectral intensity ratio of f b + f v to f b is given as
|︁ (︃
)︃
(︃
)︃|︁2
|︁
4π∆X
4π∆X |︁|︁
(8)
S1 /S0 = |︁|︁J1
/J0
|︁ .
λ
λ
For example, ∆X = 2.5 nm for S1 /S2 = −40 dB and λ = 1550 nm.
3.

Setup

Figure 1 shows the measurement setup used. Output light from a bench-top tunable laser(Santec TSL-550) was modulated by LiNbO3 in-phase/quadrature-phase modulator (IQ MOD,
Thorlabs LN86-14-P-A-A). A frequency swept signal of 1–11 GHz (B = 10 GHz) generated
by an arbitrary waveform generator (Keysight M9502A) was used for the modulation, which
determined the range resolution ∆R = 15 mm. Frequency-modulated light with a suppression ratioof 20 dB for unwanted frequency components was obtained. This was amplified by erbium-doped
fiber amplifiers (EDFA, Thorlabs EDFA 100P, Alnair Labs HPA-200CL-30-PM-FA-FA) and a
bandpass filter (Alnair Labs CNF220CL) and was split into signal and reference light at a ratio of
99:1. The signal light with polarization controlled to transverse electric was launched at the beamscanner chip. We have reported details of the chip in [24]. A 5-µm-wide channel waveguide wasfabricated on a 210-nm-thick Si slab with a square array of perforated holes with a lattice constanta = 380 nm and a diameter 2r = 345 nm, which we refer to as a bulk photonic crystal waveguide(BPCW). A shallow grating with a 10 nm depth, 300 nm width, and the period of 2a was formed
on of the Si slab to emit the guided mode to the free space. The wavelength sweep was used toscan the emitted beam in the θ direction along the BPCW. To couple the light into the chip, weused a lensed fiber and an end-fire spot size converter. The emitted light was collimated by acylindrical plano-convex lens of 50 mm focal length, because the emitted beam was fan-shaped
and expanded in the direction across the BPCW (ϕ direction). Another plano-convex lens of
700 mm focal length was placed 300 mm from the BPCW to reduce the slight divergence inthe θ direction. Reflected light from the object was received by the same BPCW through thereverse path of transmission, mixed with the reference light through the circulator, detected by
an InGaAs balanced photodiode (Discovery Semiconductors DSC710-39-FC), and analyzed bya spectrum analyzer (Rohde & Schwarz, FSW 43). In this experiment, we used these external
components, but it is possible to integrate all of these components except for the laser, EDFA,
and spectrum analyzer by using Si photonics technology. Although we used a combination of the
BPCW, wavelength sweep, and plano-convex lenses for convenience of the experiment, it is also
possible to use a standard PCW with a built-in thermo-optic heater for faster beam scanning anda prism lens for wide-angle collimation.

Fig. 1. Measurement setup and a confocal laser micrograph of BPCW for optical beamscanning, transmission, and reception.

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Velocity measurement

The velocity was measured on the sidewall of a turntable (diameter D = 330 mm), as shown in
Figs. 2(a) and 2(b). To enhance reflected light intensity toward the BPCW, a retroreflective sheet(ORALITE AP1000) was pasted on the sidewall. The distance from the BPCW to the sidewall,R, was approximately 4.08 m. The laser wavelength was swept in the range from 1535–1553 nm,
and the beam was scanned in the range of θ ≈ ±1.25°. In the ϕ direction, the offset against theplano-convex lens tilted the beam, and thus 2D beam scanning was obtained. Figure 2(a) also
shows the scanned beam shining on the sidewalls, which was observed by an InGaAs camera.
When a triangular modulation with T = 40 µs was used for the frequency sweep, the beat spectrum
was measured, as shown in Figs. 2(c) and 2(d). Without rotating the turntable, the beat spectrum
appeared at 17.4 MHz, with a full width at half maximum (FWHM) of 20 Hz (determined by the
resolution of the spectrum analyzer setting) and a signal-to-noise ratio (S/N) of 65 dB.

Fig. 2. Measurement of range and velocity of turntable. (a) Schematic of measurement
setup and InGaAs camera image of the collimated beam shining on the turntable sidewalls.
(b) Parameters of the beam (arrow) and turntable (circular arc). (c) Measured beat spectra at
θ = –0.25°. Upper and lower panels show those without and with the rotation of turntable,
respectively. (d) Measured spectra with the rotation for different θ changed by the wavelength
λ. (e) Comparison between measured velocity (open circle) and theoretical value (solid line).

Further, the turntable was rotated at 45 rpm (tangential velocity vt = 0.78 m/s), and thewavelength was swept for linear beam scanning. At λ = 1554 nm, the beam shone on the center of
the turntable at normal incidence (θ = 0°). At this wavelength, the Doppler shift did not occur due
to the absence of velocity components in the direction of light travel. At other wavelengths, thebeam was shone on a position other than the center of the turntable, and the Doppler shift clearly
appeared, exhibiting the split of the beat frequency into f up and f down . The spectral FWHM
expanded to ∼10 kHz, and the peak intensity decreased by 30 dB due to jitter, which might becaused by slight eccentricity of the turntable. Figure 2(e) shows the velocity v on the optical axis;
the circular plots were measured from the spectral split and the solid line was calculated fromResearch Article

Vol. 29, No. 19 / 13 Sep 2021 / Optics Express 30731

the relation v = vt sin (θ + θt ), where θt = sin˘1 [(D/2R) sin θ]. The θt at the edge point was 30°,
and the corresponding v was calculated to be 0.40 m/s. The measure value agreed well with thisvalue. The maximum error estimated from the difference between the circular plots and the solidline was 29 mm/s, which is reasonable, considering the range resolution ∆R and the eccentricity.
Figure 3 shows the off-line point cloud image created by calculating the range and velocity from
Eqs. (1) and (3), respectively. The simultaneous imaging of range and velocity was confirmed.
The step-like profile of the fixed pedestal was caused by the range resolution ∆R.

Fig. 3. Point cloud image of range and velocity obtained from mean value and split of thebeat spectra.

5.

Vibration measurement

For the vibration measurements, we used the same measurement setup shown in Fig. 1, but
employed a sawtooth modulation signal with T = 4 µs. As shown in Figs. 4(a), speakers (SLP
Limited LSE77-20R of 78 mm diameter and 15 kHz cutoff frequency) with reflective sheets(ORALITE AP1000) pasted on the front were used as target objects. The beam spot on thissheet was approximately 10 mm in diameter. Figure 4(b) shows the beat spectrum measured
when the speakers were vibrated at various f v . At this time, the speakers were driven at 8 Vp−p ,exhibiting maximum sidelobe levels, by a function generator (Agilent 33220A). The noise floor
determined by the used setup did not change when the signal generator drove the speakers. As
expected from Section 2, sidebands clearly appeared with a frequency spacing of f v around thebeat frequency. At f v < 5 kHz, the spectral intensity distribution is complicated, reflecting higher
order sidebands in Eq. (7). In each panel, the vibration amplitude ∆X obtained from Eq. (8) was
noted together with the vibration frequency. Figure 4(c) summarizes the relation between ∆Xand the applied voltage at f v = 5 kHz. The response was linear up to the rated voltage of 7.5
Vp−p . Since the used voltage of 8 Vp−p for Fig. 4(b) was higher than this value, the vibration
might include harmonic components. We consider that such components were larger for lower f v
and generated extraordinary envelope profiles of the spectra. Even in these situations, we could
estimate ∆X as the vibration amplitude of the fundamental frequency from Eq. (8). At f v = 3 kHz
and 20 kHz, the intensity ratios in Eq. (8) were 3.5 dB and 35 dB, respectively, which indicatedthat ∆X = 140 nm and 4.4 nm. When S/N was higher than 40 dB, the detection limit of ∆X was
2.5 nm.
Then, three speakers at different ranges were driven at f v = 1.5 kHz, 2 kHz, and 2.5 kHz,
respectively. The beam was scanned in 2D, and the beat spectrum was measured at each resolution
point. Figure 5 shows the off-line point cloud image created from the calculated range andmeasured vibration frequency. The center and right speakers were placed perpendicular to thebeam, whereas the left speaker was tilted slightly. Each f v was represented as a color plot. The
measurement error in f v was simply determined by the spectrum analyzer and was no larger than
10 Hz. Figure 5 also shows the distribution of ∆X for Speaker 1. It is observed that the amplitude
was larger at the circular edge of the speaker, to which the retroreflective sheet was attacheddirectly.

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Vol. 29, No. 19 / 13 Sep 2021 / Optics Express 30732

Fig. 4. Measurement of range and vibration distribution. (a) Schematic of the measurement
setup and an InGaAs camera image of the collimated beam shining on three speakers. (b)Beat spectrum with sidelobes at different f v . Estimated ∆X from the sidelobe intensity isalso shown. (c) Relation between ∆X and the applied voltage at f v = 5 kHz.

Fig. 5. Point cloud image of range and vibration frequency, which were estimated from thebeat spectrum. Upper panel shows the amplitude distribution on Speaker 1 obtained fromthe sidelobe intensity.

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Conclusion

We demonstrated the simultaneous measurement of distance, velocity, and vibration in a FMCW
LiDAR setup, including a Si photonic crystal beam scanner. In this experiment, the range
resolution and velocity resolution were estimated to be 15 mm and 19 mm/s, respectively. The
maximum measurement error of the velocity was 29 mm/s, and the detection limit of the vibration
amplitude was 2.4 nm. The range resolution could be improved by increasing the frequency
bandwidth B. However, the external modulation frequency used was already as high as 10 GHz,and a wider bandwidth becomes a constraint on the system. For this purpose, direct modulationof the laser will be more effective, although it needs some compensation for the nonlinearity.
The velocity error might be caused by the eccentricity of the turntable, and the theoretical limitof 19 mm/s will be obtainable for a more accurate target. The resolution can be improved byincreasing the period T. The detection limit of the vibration amplitude is determined by the S/Nof the beat signal. In this experiment, a retroreflective sheet improved S/N. Without this sheet,
the S/N drops by more than 20 dB, and the detection limit is degraded comparably. To ensure
similar S/N for arbitrary targets, it will be effective to reduce the fiber coupling loss, improve theupward emission from the BPCW by optimizing its structure, and increase the aperture of thecollimator lens.
In this experiment, external components were used except for the beam scanner, but using
Si photonics technology, on-chip integration is possible, except for the laser and EDFA. In the
future, it is expected that a multimodal FMCW LiDAR with SLDV functionality will be realized
on a fingertip-sized chip.
Funding. Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values(JPMJAC1603) of Japan Science and Technology Agency (JST). Innovation Strategy Formulation Project of The
Mechanical Social Systems Foundation.
Disclosures. The authors declare no conflicts of interest.
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may
be obtained from the authors upon reasonable request.

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