Super-dense point clouds acquired by an ultralight 10 g solid-state single photon LiDAR

Domain: physics
Published: 2025-12-29
Editorial outcome: minor_revision

Abstract
Integration of photogrammetry and light detection and ranging (LiDAR) algorithms has garnered attention to enhance visual fidelity and geometric accuracy in three-dimensional (3D) modeling. Here we show an ultralight 10 g solid-state single-photon LiDAR that minimizes photon cost per measurement. Achieving a maximum indoor distance of 25 m and a point cloud density of ~3.16 Mpps, the LiDAR provides geometric fidelity, while maintaining fine structure information challenging for conventional LiDAR. Key embedded components include a Q-switching semiconductor laser, which emits a 50-ps pulse-width tail-free laser using bandgap renormalization. A four-channel time-to-digital converter achieves a 3 ps timing jitter per channel and features real-time time-walk error correction for Poisson-distributed photon counts. A low-Q two-dimensional (2D) MEMS mirror with a 20 mm2 mirror size and precisely controlled feedforward-driven frequency enables non-repetitive scanning and super-dense point cloud generation. We present 3D modeling using the colored point clouds and discuss its characteristics and challenges.

Introduction
In recent years, interest in realistic three-dimensional (3D) modeling has surged, accompanied by significant advancements in algorithms that utilize multiple photographs, such as photogrammetry1, neural radiance field (NeRF)2, and 3D Gaussian splatting (3DGS)3,4. These technologies have driven innovations in virtual production and game development, particularly for background assets5. However, absolute coordinates cannot be determined from photographs alone, making ground control points or additional modalities essential for accurate georeferencing6,7. The integration of light detection and ranging (LiDAR) has garnered significant attention for enhancing geometric fidelity and improving 3D models8–10. LiDAR is particularly valuable in scenarios where generating a point cloud via structure-from-motion (SfM) is impractical, such as for objects beneath dense canopies or those with limited distinctive features11. However, insufficient point cloud density often poses a challenge for dense reconstruction12.

Recently, algorithms integrating physical models of nature with 3DGS have been explored13. Interest in 4D Gaussian splatting, driven by augmented reality (AR) and virtual reality (VR) applications, is also growing14. Therefore, the integration of LiDAR is expected to play a crucial role in handling dynamic objects. This could lead to a need for higher point cloud density corresponding to higher frame rates. Drones have become essential tools for scalable 3D modeling, particularly in inaccessible environments for photogrammetry. However, integrating photogrammetry with LiDAR is often limited to large aircraft owing to payload constraints. Therefore, miniaturizing LiDAR technology is also key to enhancing the versatility and applicability of these systems.

While algorithms for photogrammetry–LiDAR fusion continue to evolve, LiDAR systems used for 3D modeling were primarily intended to advance driver-assistance systems (ADAS)15 or unmanned aerial vehicles (UAVs)16. In these applications, characteristics such as long-range detection and a wide field of view (FoV) are prioritized; however, the point cloud density and geometric fidelity required for high-quality 3D modeling are frequently lacking. Typical single-photon LiDAR (SPL) systems are used in aerospace17 and aviation applications18,19, where they are capable of measuring distance with a single photon per shot. The fundamental principle of SPL—achieving the lowest photon cost per measurement point and excelling in capturing fast motion—is critical for 3D modeling, as it supports high point cloud density and motion tracking while maintaining compact size and low power consumption. However, improving distance precision from a single shot requires the temporal precision of both the light source and the timer to match the levels found in SPL systems used in space and aviation applications.

The purpose of this study is to resolve the trade-offs among dense point clouds, distance precision, ultra-miniaturization, and low cost in LiDAR systems. Therefore, we introduce an ultralight solid-state SPL (SS-SPL) system comprising the following devices, each addressing specific conventional issues: a pulsed semiconductor laser enhanced by bandgap renormalization (BGR) provides low beam quality factors (M²), which was difficult to achieve with conventional high-intensity pulsed semiconductor lasers20–23, and contributes to improved angular resolution of point clouds. A large-aperture two-dimensional (2D) micro-electro-mechanical system (MEMS) mirror achieves more than twice the figure of merit (FoM) compared to conventional devices24–26. As a result, it provides the FoV required for 3D modeling, while being more compact than traditional mechanical optical systems. A proposed feedforward frequency control using an up-down direct digital synthesis (UD-DDS) eliminates the beam trajectory instability caused by changes in the resonant frequency in conventional feedback methods27–29, thereby improving the positional accuracy and spatial filling rate of point clouds. A high-precision time-to-digital converter (TDC) reflects a state-of-the-art architecture with picosecond-level accuracy30,31, unlike the conventional TDCs with around 100 ps resolution typically used in LiDAR systems32. This contributes to improved distance precision and also shows that such advanced architecture exhibits sufficient electrical noise tolerance.

In this work, the SS-SPL, reflecting the features of the introduced devices and maintaining a high optical efficiency carried by the principle of SPL, solves the critical issues discussed above, such as insufficient point cloud density for 3D modeling and payload limitations in drone applications. To demonstrate the capabilities of SS-SPL, we compare the ground truth target with the corresponding point clouds and present colored 3D models obtained by fusing the super-dense point clouds generated by SS-SPL with camera data. The demonstration suggests new possibilities for introducing LiDAR into a wider range of fields, such as 3D modeling and compact drones that represent rapidly growing and large-scale markets, with applications spanning industries including entertainment, sports, construction, logistics, and other sectors.

Results
Concept
The ranging principle of SS-SPL is illustrated in Fig. 1a. A single short pulsed laser beam is directed at an object, and weak light scattered by the object is detected by a silicon photomultiplier (SiPM). The detected light corresponds to photons ranging from a single to several tens, which can be converted into quantized weak electrical pulses. This occurs because the SiPM consists of thousands of single-photon avalanche diode (SPAD) elements connected to a common cathode and a common anode, resulting in a linear output for weak signals33,34. If the temporal resolution of both the pulsed laser and the SiPM is sufficiently high, a single electrical pulse can exhibit quantized levels, as illustrated in the figure. These weak electrical pulses are usually buried in common mode noise. However, these electrical pulses can be extracted by employing a replica of the SiPM to cancel out only the common mode noise. The rising edge timing detection is performed using a threshold voltage corresponding to the quantized number of photoelectrons. A time of flight (ToF) is measured from the difference between the reference rising edge timing and the rising edge timing of the round trip from the SS-SPL to the object. Since the single short-pulse laser beam is continuously scanned in two dimensions (Fig. 1b), measurements at each beam position are performed in a single shot. A schematic illustration of the SS-SPL system is shown in Fig. 1c.

The Q-switching semiconductor laser chip and a dedicated complementary metal-oxide semiconductor (CMOS) driver were die-bonded onto a compact 0.033 cc half-cavity package (Fig. 1d). A tail-free laser pulse with an energy of 0.2 nJ and a width of ~50 ps was output from a window. The emitted beam was collimated, passed through a perforated freeform mirror with a 2.3 mm diameter hole (equivalent to a 4.15 mm2 TX aperture), and was incident on a 2D MEMS mirror with a large reflection area of 20 mm2 at an angle of 30°. Scattered light from an object irradiated by the beam passed through an RX aperture of 13.17 mm2, formed by the perforated freeform mirror in a coaxial optical path.

A timer to measure the ToF was designed based on 40 nm CMOS technology and consisted of four two-stage TDCs, each incorporating a differential amplifier, a comparator, and a low-voltage differential signaling (LVDS) output. The rising edge detection threshold voltages for the stop terminals of channels Ch-1, Ch-3, and Ch-4 were Th-1, Th-3, and Th-4, respectively, while that for the common start terminals as the reference was Th-ref. The TDC provided a temporal resolution of ~2 ps and a single-shot timing jitter of 3 ps. To mitigate erroneous signals such as ambient sunlight or dark count of the SiPM, the TDC provided multiple acquisition modes: single-photon mode (SP-mode), double-photon mode (DP-mode), and triple-photon mode (TP-mode). Furthermore, it captured both the first and second events by switching to Ch-2 from Ch-1. Real-time time-walk error correction and vector operations on the point cloud were performed by the external field-programmable gate array (FPGA).

Finally, the ultralight module, which integrated all of the aforementioned components—including voltage regulators, folded circuit boards, and a resin body—achieved a total weight of 9.97 g (inset image in Fig. 1e).

Q-switching semiconductor laser
Performance requirements for semiconductor lasers in SS-SPL are unique, as they necessitate the coexistence of pulse widths on the order of several tens of picoseconds, nJ-class pulse energies, tail-free pulse shaping, and low two-axis M2 values. It is challenging for conventional semiconductor lasers to possess all of them. Building upon an edge-emitting platform that inherently provides low M2 values, we adopted a Q-switching structure to achieve the remaining three stringent requirements. Fifty-two pairs of alternately arranged gain and Q-switch regions are laterally electrically isolated within a 4-mm-long cavity, and both regions are actively driven, as illustrated in Fig. 2a, b.

The characteristics of the laser beam emitted outside the module, as a function of the pulse width controlled by the low-side driver NMOS (denoted as Δt lsd), are shown in Figs. 2c–f. The value of Δt lsd was estimated through simulation. In Fig. 2c, the color scale image represents the linear intensity measured using a streak camera (Hamamatsu Photonics C5680). For each condition, the timing of the PMOS and NMOS driving the anode of the Q-switch was individually optimized to minimize the laser pulse tail. The laser waveform at Δt lsd = 5.22 ns is shown in Fig. 2d. A peak power of 3.04 W, a pulse width of 48.7 ps (defined as full width at half maximum, FWHM), and a 289-ps delay between the main laser pulse and its tail were observed. The peak power, average power, and pulse width are illustrated in Fig. 2e. A clear lasing threshold was observed at Δt lsd = 2.70 ns; the peak power increased while the laser pulse width decreased with increasing Δt lsd. The center wavelength of the laser pulse red-shifted rapidly as the peak power increased, then shifted more gradually when Δt lsd exceeded 4 ns, while the tail transitioned to a shorter wavelength, as shown in Fig. 2f. At Δt lsd = 5.22 ns, the wavelength difference between the laser pulse and the tail reached 5.02 nm (equivalent to 9.2 meV). The ratio of the tail to total pulse energy decreased with increasing Δt lsd, as shown in Fig. 2f. Further details are shown in Supplementary Notes 1.

The red-shift and the 289 ps delay between the laser pulse and its tail were attributed to high carrier density in BGR35–37 and its associated recovery time36. The recovery time provided a temporal margin to turn off the active Q-switch, allowing the low-side driver to be deactivated and the Q-switch anode to return to the ground state. Therefore, the laser pulse peak power was maximized while simultaneously suppressing the pulse tail. The temporal waveform measured in single-shot mode using an oscilloscope with a 256 GSa s−1 sampling rate is shown in Fig. 2g. The pulse jitter, including the trigger timing jitter, was calculated as 43 ps from the temporal waveform. An example of the beam quality (M2) of a similar semiconductor laser not integrated into the module is presented in Fig. 2h. The M2 value was calculated using the D4σ method, based on the second moment of the intensity distribution. The M2 values perpendicular (fast) and parallel (slow) to the semiconductor layers were 1.3 and 1.15, respectively. While BGR has been widely studied, its transient response has not been exploited in semiconductor laser operation; here, we demonstrate a device that utilizes this regime.

A comparison among different types of semiconductor lasers20–23 is provided in Supplementary Notes 3. Although some other semiconductor laser emits a higher-power laser pulse, none of the conventional semiconductor lasers satisfy all four characteristics required for SS-SPL, such as the pulse width on the order of several tens of picoseconds, the nJ-class pulse energy, the tail-free pulse, and the low two-axis M2 values.

2D laser beam scanner
In beam steering for the SS-SPL, priority is given to capturing more photons, while also ensuring a wider FoV, uniform scanning across the entire FoV, and a compact size. Beam steering methods can be categorized into mechanically driven motor systems, MEMS mirrors, and fully solid-state nanophotonics with no moving parts38,39. In this study, we designed a low-Q resonant 2D MEMS mirror that operates in air due to three fundamental advantages. It consists of a single gold-coated mirror, resulting in minimal optical loss. It scans the entire FoV within a short period by employing a relatively higher slow-axis frequency. It possesses superior robustness against electrical noise due to its mechanical inertia, in comparison with other linear scanners. From these advantages, the risk of missing the target in dynamic 3D modeling applications can be reduced, and uniform non-repetitive scanning of the entire FoV can be achieved with only stable frequency control due to the inertia when the exposure time is increased. The trajectory generated by the two-axis resonant MEMS mirror forms a Lissajous pattern (Fig. 1b), as described in the Methods section.

We prioritized feedforward controllability at the desired frequency over energy efficiency in the design of the low-Q 2D MEMS mirror with the mirror area of 20 mm2 and Pb-free piezoelectric actuators40. The frequency dependences of the optical scan full angle when driven independently in the vertical (fast) and horizontal (slow) directions are shown in Fig. 3a, b, respectively. The resonance amplitude decay plot is presented in Fig. 3c. The black lines represent fitted results, with Q values of 172 (fast) and 112 (slow).

We propose an UD-DDS system (Fig. 3d) that uses a high-precision reference clock f sys of 20 MHz from a crystal oscillator. To achieve the desired step, the number of counter bits, denoted N c, is set to 27. An output frequency is defined as: f out = f sys * Count inc / 2 N c. Since the MEMS mirror resonates only near specific frequencies, harmonic components of the MEMS driving wave exert minimal influence. Therefore, the number of bits required for DAC (denoted as N d in Fig. 3d) can be relatively low, and is estimated to be 9 bits. In standard DDS, storing N d-bit DAC values for each counter value (2 N c addresses) requires 1.2 billion bits (N d * 2 N c = 9 * 2 27). However, when DAC inputs change gradually and not by multiple bits at once as shown in Fig. 3e, the LUT capacity can be significantly reduced to levels comparable to the DDS equipped with a computational unit by storing the DAC threshold values (timing of bit transitions) in the LUT instead of the waveform shape. Despite this minimal LUT storage, single-shot noise below 0.2 Hz in bandwidth was achieved at a reference clock f sys of 20 MHz, as shown in Fig. 3f. Non-repetitive scanning at 2075.0 Hz and repetitive scanning at 2075.5 Hz along the vertical axis are shown in Fig. 3g, h, respectively. The optical scanning full angles reached 42° horizontally and 26° vertically. Since the piezoelectric actuators in the proposed MEMS mirror were shared between vertical and horizontal drives, the 2D scanning angles were smaller than those in the 1D cases, as shown in Fig. 3a, b. Although the trajectory changed significantly with only a 0.5 Hz frequency shift, the proposed UD-DDS system enabled stable feedforward control.

The shock robustness42,43 of the MEMS fixed to the resin frame exceeded 2771G during operation, as discussed in Supplementary Notes 2 and demonstrated in Supplementary Video 1. Since no hysteresis was observed in the resonant spectrum as shown in Fig. 3a, b, the Lissajous trajectories remained after the impact.

Supplementary Notes 3 show a comparison of 2D large MEMS mirrors. An FoM44,45 of the MEMS mirror is more than twice as high as that of conventional ones24–26 operating at atmospheric pressure, and is more than half that of those operating in a vacuum46.

High functional time-to-digital converter
The TDC integrated into the SS-SPL module required precise measurement under a common-mode noise environment of up to several hundred millivolts and supported advanced functionalities such as time–walk error correction based on the number of incident photons. The two-stage TDC was implemented, comprising an inverter ring operating at ~1.1 GHz for coarse timing and the pulse-shrinking gated buffering ring (PSGBR) architecture30,47, which provided ~2 ps of pulse shrink per buffer stage, for fine timing. A relatively strong signal waveform measured at the node between the isolation transfer and the differential amplifier is shown in Fig. 4a. The signal pulse width was estimated to be 920 ps. The base-level voltage increased gradually over the first ~20 ns and stabilized thereafter, which suppressed erroneous measurements caused by stray laser light. The distributions of time differences between Ch-1 and Ch-3, Ch-1 and Ch-4, and Ch-3 and Ch-4, with standard deviations of σ TDC(ch3-ch1) = 4.2 ps, σ TDC(ch4-ch1) = 4.7 ps, and σ TDC(ch4-ch3) = 4.8 ps, respectively, are shown in Fig. 4b. Since each channel operated independently, the standard deviation for each channel was obtained from these time-difference distributions, which represented the convolution of the noise distribution from each channel. Accordingly, the estimated standard deviations were σ TDC(ch1) = 2.9 ps, σ TDC(ch3) = 3.1 ps, and σ TDC(ch4) = 3.6 ps. The resulting single-shot noise levels were significantly low to allow estimation of the number of incident photons based on inter-channel correlations.

Three detection modes, single-photon (SP-mode) (m=1), double-photon (DP-mode) (m=2), and triple-photon (TP-mode) (m=3), were incorporated, and their thresholds (Th-1, Th-3, and Th-4) were set to m, m+1, and m+2 photoelectrons, respectively. When m or m+1 photoelectrons were obtained as output from the SiPM, the number of photoelectrons could be determined because only Ch-1 or Ch-1 and Ch-3 operated. When Ch-4 was measured, more than m+2 photoelectrons were obtained as output from the SiPM. The probability P(x≥k, N RX) of detecting more than k photons, depending on the distance to the target for SP-mode (circular), DP-mode (triangle), and TP-mode (rhombus), is illustrated in Fig. 4c. The dashed lines were calculated by the Poisson distribution as: P(x≥k) = 1 - Σ i=0 k-1 (N RX i / i!) * e^-N RX (1), where N RX denotes the expectation of the detected number of photons, D is the distance to the target, and α is a constant throughout the measurement. As the base level voltage was low at short distances, more photoelectrons were required for the signal to exceed the threshold. However, the probability of detection did not significantly decrease owing to the increased number of returned photons.

The time–walk error caused by the weak SiPM output introduced considerable time delays, thereby requiring corrections even in real-time usage. As reflected in the waveform in Fig. 4a, the time–walk error increased as the difference of detection timing between Ch-4 and Ch-3 increased. For example, red dots in Fig. 4d show the raw data of the detection timing of Ch-4 versus the difference of detection timing between Ch-4 and Ch-3 under the condition that the distance to the target was 6.486 m. By applying the estimated correction value induced by the quantized photon number, the raw data were corrected, as shown by blue dots.

The distance precision of a single-shot after the time–walk error correction is shown in Fig. 4e. The standard deviations were ~7 mm (47 ps) at a distance of 3 m or less, where the signal of more than m+2 photoelectrons was dominant, as shown in Fig. 4c. At distances longer than 3 m, the standard deviations increased with the distance owing to the number of photoelectron reduction to m or m+1. The value approached the lines with open circles. Each line represented the standard deviation extracted for m, where only Ch-1 operated. The distance precision at 25 m is discussed in the next subheading of LiDAR. The distance accuracy of the single-shot after the time-walk error correction was within 5 mm, as shown in Fig. 4f.

The performance of the built-in TDC is compared with that of conventional ones30,31 in Supplementary Notes 3. The obtained results based on 40 nm technology fell between those of the introduced 180 nm and 28 nm technologies in terms of both precision and FoM. The commonly used FoM did not include precision, but in LiDAR applications, designing both with a good balance is crucial.

Light detection and ranging (LiDAR)
Geometric accuracy was verified using a stepped target as the ground truth (Fig. 5). The divergence angles of the laser beam were 0.44 mrad and 1.2 mrad in fast and slow directions, respectively. As shown in Fig. 5a, the fast-slow axis of the laser beam was 60° counterclockwise from to the x–y axis. A point cloud that clearly reproduced the ground truth was obtained at a distance of 3 m. At the distance of 25 m, the point cloud shape became smoother due to the beam divergence; however, the outline of the ground truth, derived from the distribution of the counted number of points per an anisotropic voxel, showed good agreement. The standard deviations of the distances at 3 m and 10 m were nearly the same as the results shown in Fig. 4e. At 25 m, they were 47.7 mm (x) and 45.8 mm (y), which lie on the extended trend line of the SP-mode results for m=1, from 5 to 10 m shown in Fig. 4e.

The characteristics of SS-SPL are summarized in Table 1. The laser pulse output from the module PE TX was 0.2 nJ, which corresponds to the transmit laser energy per point for single-shot measurements. The TX aperture A TX was 1.25 mm2, which was smaller than the optical component limit of 4.15 mm2. This was due to the insufficient expansion of the slow beam width by the anamorphic optical components, resulting in the increased divergence angle. The RX aperture A RX was 13.17 mm2, realized by the relatively large MEMS mirror and the coaxial optical system. The expected number of photons to be detected is expressed as: N RX = (PE TX / E 0) * ρ * η RX * (A RX / π * D 2) (3), where E 0 is photon energy, ρ is the reflectance of the target, and η RX is the total optical efficiency of RX, including the PDE of SiPM. A probability of detection of wrong signal induced by the dark count of the SiPM is defined by P WS = 1 - e^-R DC * 2 * c * D (4), where R DC is the dark count rate of the SiPM. For example, the expected number of photons N RX is 0.273 with the parameters of E 0 = 2.41 * 10^-19 J, PE TX = 2 * 10^-10 J, ρ = 0.7, η RX = 0.07, D = 25 m, R DC = 7 * 10^5 cps. The probability of detection more than single photon (1 - P WS) * P(X≥1, 0.273) = e^-R DC * 2 * c * D * (1 - e^-N RX) = 0.213 (5). The results show good agreement with those illustrated in Fig. 4c. The SS-SPL operates at nearly the lower limit of transmit laser energy required for distance measurement with single photons.

Table 1 also includes the pioneering frequency modulated continuous wave (FMCW) LiDAR based on the silicon photonics platform48. The transmit laser energy per point of 200 nJ and the distance precision of 3.1 mm were demonstrated. Notably, they discussed in the article that scalability of point cloud density in FMCW LiDAR can be achieved by increasing the output power and pixel count, and further suggested that ~200 μm precision is feasible with the use of 50-GHz. The difference between the FMCW LiDAR and the SS-SPL is that the transmit laser energy per point is smaller by a factor of 1/1000 to 1/100, which allows photon efficiency to enable flexible allocation between point cloud density and precision. Additionally, since TDCs and pulse lasers have achieved high temporal resolution, improving the RX’s temporal resolution leads to a direct enhancement of distance precision without the need to allocate photon efficiency to it.

From an alternative perspective, traditional direct ToF systems require averaging processes, such as histogramming, to improve distance precision, which consumes optical output. In contrast, FMCW LiDAR benefits from enhancements in laser linewidth and chirp bandwidth characteristics, while SS-SPL benefits from improvements in device temporal precision, both of which directly contribute to enhanced distance precision.

Miniaturization of LiDAR systems mounted on UAVs has been progressing16. As shown in Table 2, SS-SPL enables significant weight reduction compared to these LiDAR systems, even when the FPGA board is included.

3D modeling
We also expect that the number of photographs required for fusion will decrease by introducing super-dense point clouds substitute for the initial processing in 3D modeling, making it easier to acquire the data necessary for 3D modeling in the future. We propose a fusion system based on super-dense point clouds with high geometric fidelity and a single-view full-color photograph instead of performing advanced fusion using multiple photographs in post-processing, and visualize the expressive power of the resulting colored point clouds. Table 3 summarizes conversion parameters used for the fusion system in this study. The point clouds acquired by the non-repetitive scanning with a 20-s exposure were post-processed by filtering and averaging within 0.2 mrad grids as shown in Fig. 6. The maximum number of points per grid before the filtering was ~3 (at the center of FoV) and ~7 (average of the entire FoV). The camera’s FoV encompassed that of the SS-SPL, enabling full-color data acquisition at approximately 0.1 mrad grid intervals. Consequently, roughly one-fourth of the full-color pixel data within the SS-SPL’s FoV after distortion correction using Zhang’s algorithm49 were assigned to the unique point clouds. All processes were performed in real time.

A meticulously stitched 3D model of a restaurant floor (Fig. 7a–e) obtained by the fusion system demonstrated geometric accuracy in global coordinates, including scenes with less texture information and sufficient density to project fine textures (Fig. 7e). Cherry blossom trees captured by the fusion system from a single viewpoint for several conditions are shown in Fig. 7f–k, Supplementary Notes 5, and Supplementary Video 2. The front and side views were aligned with the shooting direction and perpendicular to the shooting direction, respectively. The petals and branches behind were captured through the gaps between the petals, representing a typical scene demonstrating the advantages of the coaxial optical system in the SS-SPL. A dynamic view of basketball shot acquired by the SS-SPL without the fusion is shown in Fig. 7l and Supplementary Video 3 to illustrate another interest: how the dense point clouds model dynamic scenes. The point clouds continuously acquired along the Lissajous trajectory were packed into a frame every 60 Hz to reproduce the motion of the shooter and the trajectory of the ball.

Methods
Key criteria for pulsed semiconductor laser design
As in optical discs and optical communication technologies, semiconductor lasers are considered optimal compact light sources. Since class-1 laser safety at near-infrared wavelengths is evaluated at the same pulse energy for the irradiation time of 10 ps to 5 μs, introducing shorter pulse widths within this range reduced timing jitter. For two-axis laser beam scanning, achieving a low M2 (beam quality) factor is essential to improve angular resolution.

Q-switching technique is widely employed to generate short-pulse laser beams for semiconductor lasers. Notable examples include narrow-stripe edge-emitting lasers (EEL) with the 18.6 ps pulse width61, bowtie lasers with 15 ps pulse width and 100 pJ pulse energy62, bowtie lasers with 45 ps pulse width and 39 pJ pulse energy63, broad-stripe EELs comprising asymmetric thick cladding layers with 80 ps pulse widths and 35 W peak power21,64, and photonic-crystal surface-emitting laser (PCSEL) with pulse width less than 30 ps and 200 W class peak power65. In conventional EELs, the output power increases with the propagation mode area, whereas M2 increases owing to the generation of higher-order transverse modes. In contrast, PCSELs offer increased beam cross-section while maintaining low M2, which is a significant breakthrough.

For accurate ranging using single-photon detection in a single shot, both the absence of laser pulse tail and a short pulse width are necessary. However, eliminating laser pulse tails is challenging owing to the longer current injection time compared with the laser pulse width. We propose a laser pulse tail suppression technique based on the following mechanism: First, suppressing amplified spontaneous emission (ASE) achieves high carrier density, following which BGR is induced before Q-switching laser pulse generation. Second, BGR disappears after Q-switching laser pulse generation, reducing gain in conjunction with the transient response of the disappearance. Third, a dedicated circuit rapidly changes the Q-switch state to a low level during the transient response. This method was applied to the narrow-stripe EEL with reliable process reproducibility.

Structure of the Q-switching semiconductor laser and operation
The schematic cross-section of the semiconductor laser along the 4 mm cavity is shown in Fig. 2a. The front section comprises 51 pairs of 21 μm Q-switch and 42 μm gain regions, and the rear end includes 200 μm Q-switch and 100 μm gain regions. These p-doped gain and Q-switch regions above the active layer, comprising an n-type AlGaAs single quantum well (SQW), were electrically isolated by 4 μm n-doped grooves. A composition ratio of the active layer was adjusted to achieve a wavelength of approximately 820–830 nm, where the photon detection efficiency of the SiPM is relatively high. Transverse modes were weakly confined by an 8 μm ridge stripe created via dry etching. All gain and Q-switch regions were connected to the one gain region anode and the one Q-switch region anode. The Q-switch region anode was driven by independently controlled PMOS and NMOS, and the cathode was low-side-driven by NMOS. They were driven precisely by a pulse signal generator embedded in the CMOS driver-controlled timing with an LSB of approximately 100 ps. The gain region anode was adjusted between 4.45 and 5.04 V to keep the cathode voltage within the CMOS drive voltage of 5 V. This applied voltage is significantly lower than that of conventional Q-switching semiconductor lasers, and minimizing common-mode noise and reducing power consumption in the compact module is crucial. During the current injection into the gain region before Q-switching, the NMOS for Q-switch remains on. The drain voltage caused by the on-resistance of the low-side driver negatively biases the Q-switch region. In this state, the high absorption coefficient of the Q-switch region disrupts the propagation mode. Spontaneous emission from the gain region is rapidly absorbed either into the Q-switch region or the substrate via leakage. Therefore, ASE is more effectively suppressed in shorter gain regions due to the rapid absorption and limited amplification of spontaneous emission.

Bandgap renormalization in a quantum well
The redshift induced by BGR was observed in GaAs/AlGaAs quantum wells via photoluminescence35,36 and current injection37. Specifically, Bobrysheva et al. investigated GaAs/AlGaAs multiple quantum wells (MQW) employing photoluminescence spectra at high-level picosecond excitation. They observed that the e–h plasma-stimulated luminescence line red-shifted due to BGR, with a recovery time of 300 ps as the plasma density decreased36. Comparing the previous results with those of the present study indicated that BGR plays a significant role in laser pulse formation in semiconductor lasers.

Silicon photomultiplier (SiPM)
MPPC® S15369-1325PS, manufactured by Hamamatsu Photonics, was used. It consisted of 2120 SPAD elements. We designed a dedicated CMOS driver that was controlled by the FPGA.

Lissajous trajectory of resonant 2D micro-electro-mechanical system mirror
The optical scanning angle of the 2D MEMS mirror, featuring a fast beam on the inner circumference and a slow beam on the outer circumference as shown in Fig. 1b, can be expressed as: R(θ) = [1 0 0; 0 cosθ -sinθ; 0 sinθ cosθ] (6), R(φ) = [cosφ 0 -sinφ; 0 1 0; sinφ 0 cosφ] (7), n = R(φ)R(θ)n 0 (8), r = s - 2(s*n)n (9), where R(θ) and R(φ) are the rotation matrices, n 0 represents the normal of the fixed MEMS mirror, n represents the normal during rotation, s denotes the direction of laser incidence, and r denotes the direction of laser reflection. The trajectory is referred to as a Lissajous curve.

Up-down direct digital synthesis in micro-electro-mechanical system mirror driver
Because Lissajous trajectories varied significantly with frequency shifts even by 1 Hz, frequency control must be maintained in steps of 0.2 Hz or less. Conventional MEMS mirrors with high FoM typically exhibit Q values exceeding several thousands27–29. The resonant frequency of MEMS is temperature-dependent; hence, a phase-locked loop (PLL) is typically used to align the driving frequency with resonance. However, for uniform spatial scanning employing Lissajous trajectories, maintaining a fixed frequency ratio between horizontal and vertical scans is preferable. Considering the recent advances in piezoelectric devices47, we designed a low-Q MEMS mirror, prioritizing feed-forward controllability at the target frequency over energy efficiency.

When stabilizing and fixing the frequency of the low-Q MEMS mirror, direct digital synthesis (DDS)66 is preferred over PLLs used in the high-Q MEMS mirror. However, typical DDS implementations require larger LUTs to store waveform information for achieving precise frequency control. To address this issue, incorporating a computational unit into the DDS and storing coefficients in the LUT instead of waveform information significantly reduced the size of the read-only memory (ROM)41. We propose an up-down-DDS (UD-DDS) system equipped with a high-precision reference clock f sys of 20 MHz from a crystal oscillator as shown in Fig. 3d. To achieve the desired step, the number of counter bits, denoted N c, is set to 27. An output frequency is defined as: f out = f sys * Count inc / 2 N c (10), where Count inc determines the maximum frequency. Since the MEMS mirror resonates only near specific frequencies, harmonic components of the MEMS driving wave exert minimal influence. Therefore, the number of bits required for DAC (denoted as N d in Fig. 3d) can be relatively low, and is estimated to be 9 bits. In standard DDS, storing N d-bit DAC values for each counter value (2 N c addresses) requires 1.2 billion bits (N d * 2 N c = 9 * 2 27). However, when DAC inputs change gradually and not by multiple bits at once as shown in Fig. 3e, the LUT capacity can be significantly reduced to levels comparable to the DDS equipped with a computational unit by storing the DAC threshold values (timing of bit transitions) in the LUT instead of the waveform shape. The architecture where the up or down DAC input values are generated when the counter value crosses the threshold from the LUT is denoted as If block, in Fig. 3d. The number of bits stored in the LUT of the UD-DDS is 1.4 thousand (N c * 2 N d = 27 * 2 9), storing the threshold values of N c bits for each DAC value (2 N d addresses). In recent years, digital components, which strongly benefit from advances in semiconductor process miniaturization, and the analog components, which benefit from conventional stable processes, are implemented on separate chips. In these cases, the UD-DDS offers a reduced baud rate between chips to 2-bit/9-bit.

Key criteria for time-to-digital converter architecture selection
Timers in LiDAR are classified into time-dependent single-photon counting and rise-time measurement. The latter timer, which directly measures ToF, is used for SPL as it can be measured in a single shot. In a coaxial optical system, a high-precision TDC with a relatively large core unit area can be introduced because measurements are processed sequentially for each point. Several types of fine-TDC were reported, such as vernier buffer ring31,67, pulse shrinking buffer ring68, and PSGBR30,47. The fine-TDC was combined with the coarse-TDC to create the two-stage TDC, thereby expanding the measurable range30. To further support long-range operation, the stable clock from TCXO was introduced directly or via t ref.50. In addition, the TDCs designed for laser rang-finder applications were verified50–52. The temporal resolution of the PSGBR is determined by the difference in gate sizes of closely arranged paired inverters within the buffer. This architecture offers superior tolerance to manufacturing variations and electrical noise. In developing the two-stage TDC embedded in the SS-SPL based on the PSGBR, the layout of the 40 nm CMOS process was carefully designed to ensure the TDC usability in environments with several hundred milliwatts of common-mode noise.

The operation of the two-stage TDC with PSGBR is as follows. The coarse-TDC is initiated by inputting the start signal and is stopped by detecting the first counting-up of the inverter ring immediately following the stop signal input. An initial pulse width, which is a time difference between the stop signal input and the coarse-TDC stop, is determined by counting the number of gates traversed before the pulse disappears. The time difference between the start and stop signals is obtained by subtracting the estimated period of the fine-TDC from that of the coarse-TDC.

Estimation of the timing jitter of the time-to-digital converter
The TDC was evaluated in its integrated state within the module. During testing, the semiconductor laser embedded was active, and the MEMS mirror remained stationary. To analyze TDC performance, the rise timing distributions were obtained for Ch-1, Ch-3, and Ch-4. The start signal was input by the laser pulse, the stop signal was generated by a synchronized electrically strong waveform instead of the ToF, and the thresholds of the stop signal were set significantly above the baseline noise. The coarse count was 176, which corresponded to a time duration of 158 ns. The standard deviations were σ ch1 = 42.28 ps, σ ch3 = 43.22 ps, and σ ch4 = 42.34 ps, respectively. Subsequently, as shown in Fig. 4b, the standard deviation of each channel was calculated from the measured value of the standard deviation of the time difference between the channels. Notably, the standard deviation for single-photon measurements was increased from 229 ps at 10 m to 311 ps at 25 m, corresponding to a coarse count difference of 111. This difference between the cases of the reproducible strong electrical signal sequence and the actual ToF signals suggests that the coarse TDC is influenced by the stability of the input signal across the entire FoV.

Time-work error correction
Time-walk errors, which must be corrected to improve distance precision, were reported to primarily occur within the SPAD elements and the electrical readout circuitry51,52,69. By sufficiently expanding the cross-sectional area of the light illuminating the SiPM, as shown in Fig. 1c, the probability of two or more photons simultaneously arriving at a single SPAD element is minimized, thereby suppressing the occurrence of the former time-walk error. However, similar to an avalanche photodiode (APD)51, the time-walk error of several hundred picoseconds, caused by the slope of the output pulse waveform, was observed. In the configuration, time–walk error caused by variations in SiPM output intensity was corrected through dedicated signal processing that leveraged slight differences in rise timing across channels with different threshold voltages. The multi-threshold approach was adopted in APD-based systems51,52. In this study, the threshold voltage difference corresponded to the signal difference generated by a single photoelectron. For example, in the SP-mode, single-photon, two-photon, and three-photon or more detections can be distinguished based on the responding channels. Particularly for the case of three-photon or more detections, the nonlinear time walk error correction value was retrieved from the LUT containing the correction factor determined from the calibration and the time difference between Ch-4 and Ch-3. As shown in Fig. 4d, the measured single-shot timing jitter of 3 ps was sufficient to correct the time–walk errors on the order of several hundred picoseconds.

Equipment and post processing
The measurement system comprises the SS-SPL module housed in a die-cast shell, a circuit board equipped with the FPGA, and a 12 V AC adapter. The circuit board and a GPGPU-equipped PC are connected via USB 3. Multiple buck converters are mounted on the circuit board, whereas low-dropout regulators and boost converters are embedded inside the module. The time difference data outputs from the four-channel TDC are input to the FPGA for rearrangement, noise filtering, time-walk-error correction, and conversion to position vectors. The PC displays the point cloud in real-time from the received position vectors and reconstructs them after accumulating data for approximately 20 s. Timestamps can be inserted at arbitrary intervals between position vector data for synchronization or analysis purposes. By fixing the SS-SPL to the digital camera (Sony ILX-LR1), an RGB image can be acquired simultaneously to create a colored point cloud by projecting the points onto the RGB image70. Although photo brightness and tint must be adjusted as needed, parameters must remain constant across the measurement for the stitched point clouds. Ambient illumination is measured by orienting an instrument toward the zenith. For point cloud stitching, the digital camera and SS-SPL are mounted on a gimbal where polar coordinates are controlled by the PC.

The stitched 3D model of the restaurant by the fusion system
A meticulously stitched 3D model was constructed from colored point clouds captured from 114 distinct viewpoints and locations, as shown in Fig. 7a–e. All measurements were taken at a height of 1.58 m and in the SP-mode. The point clouds above 3 m in height from the floor were filtered out (Fig. 7a). Initially, mid-range point clouds up to 25 m were stitched together, followed by the alignment of finer short-range point clouds. No significant geometric mismatches were observed between the point clouds, confirming the achievement of geometric fidelity in the 3D model. The ground truth (photograph) of the restaurant’s interior and the corresponding stitched point clouds are illustrated in Fig. 7d, highlighting clear visibility of kitchen utensils and the neon lights of the logo. Even the structure of the dark ceiling was captured within the point cloud data. Furthermore, Fig. 7e presents the ground truth (photograph) of the text on the white wall and the naturally patterned concrete walls, alongside their corresponding stitched point clouds. Certain objects posed challenges for point cloud acquisition, such as the mirror-surfaced metal enclosure and the black couch with low reflectivity.

The stitched super-dense point cloud contained a large volume of data, such as 2.15 GB in point cloud data format for the case shown in Fig. 7a. Voxelization compressed the data to 345 MB at 10 mm voxel size and to 90 MB at 20 mm voxel size. Adaptive voxelization is expected to further compress the data while preserving fine structural details. Unfortunately, at substantially high point cloud densities, CICP failed to perform effectively, requiring manual stitching of all segments.

The 3D model of cherry blossom by the fusion system
The colored point clouds of cherry blossoms acquired by the first event in SP-mode, DP-mode, and TP-mode are shown in Fig. 7f–k. Following a 20-s exposure from a single viewpoint, the post-process reconstruction was performed. At 2500 lx in SP-mode, the tree trunk (7 m ahead) was visible, while cherry blossoms and branches up to 8 m ahead could be captured from the gap between the petals of the cherry blossoms. At 30,000 lx, the point cloud density decreased throughout the space, reflecting the increase in the point cloud noise caused by sunlight as discussed in Supplementary Notes 4. Particularly, the bush in front of the tree disappeared considerably. In the DP-mode, visibility farther than the tree trunk (7 m away) was low. Minimal change in the point cloud density was observed, attributed to the difference in environmental illumination. In TP-mode, the visible distance became shorter, but the point cloud density was not affected by environmental illumination. The point cloud of cherry blossom, obtained by DP-mode from a slightly closer distance and processed to remove points farther than 5 m, is shown in Supplementary Notes 5. Detailed cherry blossoms could be captured, even though it was acquired from the single viewpoint. Supplementary Video 2 shows an omnidirectional view of a 3D model acquired by SP-mode under environmental illumination of 2500 lx.

The dynamic 3D model of basketball shot by the solid-state single-photon light detection and ranging
The basketball shot was captured by the SS-SPL under conditions including SP-mode, the first event, ambient illumination of 500 lx, and a single viewpoint on an indoor court. A noise filter was applied during post-processing, but no reconstruction was performed. The front view was nearly coaxial with the shooting direction of the SS-SPL, and the top and side views were obtained from the same point cloud at different angles (Supplementary Video 3). Colors were added subsequently to highlight the movement and were not the actual colors. Walls and other structures behind the basketball goal were eliminated using an area filter during post-processing.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The author has developed a compact, ultra-light single-photon LiDAR capable of super-dense point clouds acquisition at\ndistances up to 25m. The system is eye-catching and the experimental results are solid. The compact design and the\nminimization engineering is impressive. Overall, I believe the results are of high quality, which fits the high criteria of a high\nimpact journal.\nHowever, the manuscript focuses on the hardware without adequately introducing the scientific details, such as its potential\napplication scenarios, the specific problems it solves and its advantages over existing technologies. Therefore, before\nmaking a decision, I would like to raise the following questions.\n1. What are the potential application scenarios for the author's ultra-light single photon LiDAR? What are the existing\nsolutions in these scenarios, and what problems do they suffer from? Which practical problems does the proposed device\nsolve?\n2. The manuscript lacks a detailed collection of systematic parameters, and comparisons with existing LiDAR systems.\nIndices such as imaging frame rate, lateral resolution, and ranging error beyond 10m are not provided. The system's main\ncapabilities and parameters are scattered throughout the text, making direct comparison with other LiDARs difficult. Also,\nexplicit comparisons (like size and weight) with other LiDARs (e.g., the one in Ref.[1] and those cited in Ref.[2]) would better\ndemonstrate the value of the author's achievement.\n3. The paper describes the author's work on the laser, 2D MEMS, and TDC. What improvements do these components offer\ncompared to existing corresponding components? Can these developments be generalized and applied to other LiDARs?\n4. The experimental scene presented in the manuscript is overly complex, making it difficult for readers to intuitively\nunderstand the LiDAR's performance. It is suggested to use 3D resolution test targets or construct a simple scene where\ndimensions can be quantified. Comparing the results with ground truth would more effectively show the system's\ncapabilities. Some quantitative analyses for reconstruction performance are needed.\n5. There are some writing errors in the paper. In Fig. 4, the x-axis labels for the last two plots should be \"Wavelength\" instead\nof \"Time\". The multiplication symbol should be \"×\" instead of the letter \"x\".\n6. What are the perspectives for the proposed LiDAR to work or contribute to longer ranges? Like the one used in self-driving\ncars, or the one for ultralong ranges [3].\n[1] Rogers, C., Piggott, A.Y., Thomson, D.J. et al. A universal 3D imaging sensor on a silicon photonics platform. Nature 590,\n256–261 (2021).\n[2] N. Li, C. P. Ho, J. Xue, L. W. Lim, G. Chen, Y. H. Fu, L. Y. T. Lee, A Progress Review on Solid-State LiDAR and\nNanophotonics-Based LiDAR Sensors. Laser Photonics Rev 2022, 16, 2100511.\n[3] Li, Z. P., Ye, J. T., Huang, X., Jiang, P. Y., Cao, Y., Hong, Y., ... & Pan, J. W. (2021). Single-photon imaging over 200 km.\nOptica, 8(3), 344-349.", "reviewer_2": "While I think this is a good paper, I find it confusing. It should be clearer. If this paper highlights fusion between a high\ndensity single photon lidar and a passive sensor each sensor should be described in a clear manner. One or two tables with\nsensor parameters could be used to assist this description.\nThis paper does provide a description of a light weight, small, high density lidar, but the description of the Lidar is not clear.\nThe range resolution of this lidar is very good. 50 psec pulse width can result in a range resolution of 7.5 mm.\nIt is possible to develop range information from stereo images, but wide angles and excellent angle resolution are required.\nThis is applicable to short range systems. The lidar only has a 25 m range.\nThis study introduces an ultralight 71 solid-state SPL (SS-SPL) system comprising a newly designed semiconductor laser, a\n72 5 time-to-digital converter (TDC), and a MEMS mirror.\nLine 93 – “detected by the silicon photomultiplier (SiPM) 93 via a coaxial optical path. As the SiPM comprised thousands of\nsingle-photon avalanche 94 diode (SPAD) elements, its output corresponded to the number of simultaneously incident 95\nphotons16, 17.”. I’d be interested in knowing more about the detector. Is this a photo multiplier tube? Is it an array of solid\nstate SPAD detectors? It was not clear to me. The lack of a good description is characteristic of this paper.\nMain point is this lidar is very small, and has high 3D point density.\nLine 219 – “precisely using Lissajous trajectories”. Why Lissajous trajectories? With Risley prisms I am aware scanning\nusually uses Lissajous patterns, but I was not aware MEMs scanning uses Lissajous trajectories. Can this paper include an\nexplanation why this lidar uses Lissajous scanning?\nFor dynamic situations, can you comment if there are any issues with the MEMs scanning? For an auto lidar using MEMs\nwhen a stone hits the vehicle there could be a resonance. In this case that may not apply.\n320 – “distance to the target of white paper for SP-mode (black), DP-“ should have or instead of “of” before white paper.\nI missed how narrow the filter is. In the discussion on sky brightness how narrow the filter is, is important. It is probably there,\nbut should be highlighted when sky background is decisioned. Also the wavelength of operation should be discussed.\nThis discusses the fusion of lidar and visible imagery. Sometimes it could be clearer whci hsensor is being discussed.\nA table with the Lidar parameters would be useful. This would have transmit and receive aperture sizes, filter width, carrier\nwavelength, laser energy per pulse, rep rate and pulse width and jitter, frame rate, el and az FOV,and any other relevant\nparameters. Multiple modes can also be highlighted in the table.\nA table with fused passive visible camera parameters would be useful as well, including camera bandwith and wavelengths.\n474 – Maybe I missed where BRG is defined.\n“following which BGR is induced” BRG?"}, "author_response": "Dear Reviewers,\nWe sincerely appreciate your thorough review of our manuscript and your invaluable\ncomments and constructive suggestions. We have carefully addressed each of your\ncomments and provided point-by-point responses. The manuscript has been revised\naccordingly. Please find attached our detailed response letter and the revised version of\nthe manuscript for your kind consideration. Below, we provide our point-by-point\nresponses to the reviewers’ comments. Thank you very much for your time and effort.\nRevision Notes\n1. Regarding the RX aperture size, the previously reported value did not account for the\n30° incident angle of the beam onto the MEMS mirror, resulting in an incorrect value.\nWe have corrected it from 15.85 mm² to 13.17 mm².\n2. As all reviewers pointed out that the content was scattered and difficult to follow, we\nhave substantially reorganized the manuscript. In the revised manuscript, we have\nhighlighted major revisions made in response to the reviewers’ comments in yellow, and\nall other changes in blue for clarity. Please note that our main claims remain unchanged.\n3. As the additional content could not be accommodated within the main article, we\nhave provided Supplementary Notes 1–4.\n4. During the revision process, we have incorporated the following references to further\nsubstantiate our work. References: 6, 7, 12, 16, 20, 22, 24, 25, 26, 31, 32, 38, 39, 42, 43,\n44, 46, 48, 49, 52, 53, 54, 55, and 56.\nRevision for Reviewer #1:\n(We will present your questions in red, our responses in black, and excerpts from the\nrevised manuscript in blue.)\n1. What are the potential application scenarios for the author's ultra-light single photon\nLiDAR? What are the existing solutions in these scenarios, and what problems do they\nsuffer from? Which practical problems does the proposed device solve?\nThe following statements have been added to the Introduction on pages 5 and 6.\n“The purpose of this study is to resolve the trade-offs among dense point clouds,\ndistance precision, ultra-miniaturization, and low cost in LiDAR systems. Therefore, we\nintroduce an ultralight solid-state SPL (SS-SPL) system comprising the following\ndevices, each addressing specific conventional issues: A pulsed semiconductor laser\nenhanced by bandgap renormalization (BGR) provides low beam quality factors (M²),\nwhich was difficult to achieve with conventional high-intensity pulsed semiconductor\nlasers20-23, and contributes to improved angular resolution of point clouds. A large-\naperture two-dimensional (2D) micro-electro-mechanical system (MEMS) mirror\nachieves more than twice the figure of merit (FoM) compared to conventional devices24-\n26. As a result, it provides the field of view (FoV) required for 3D modeling, while being\nmore compact than traditional mechanical optical systems. A proposed feedforward\nfrequency control using an up-down direct digital synthesizer (DDS) eliminates the\nbeam trajectory instability caused by changes in the resonant frequency in conventional\nfeedback methods27-29, thereby improving the positional accuracy and spatial filling rate\nof point clouds. A high-precision time-to-digital converter (TDC) reflects a state-of-the-\nart architecture with picosecond-level accuracy30, 31, unlike the conventional TDCs with\naround 100 ps resolution typically used in LiDAR systems32. This contributes to\nimproved distance precision, and also shows that such advanced architecture exhibits\nsufficient electrical noise tolerance.\nTherefore the SS-SPL, reflecting the features of the introduced devices and maintaining\na high optical efficiency carried by the principle of SPL, solves the critical issues\ndiscussed above such as insufficient point cloud density for 3D modeling and payload\nlimitations in drone applications. To demonstrate the capabilities of SS-SPL, we\ncompare the ground truth target with the corresponding point clouds and present colored\n3D models obtained by fusing the super-dense point clouds generated by SS-SPL with\ncamera data. The demonstration suggests new possibilities for introducing LiDAR into a\nwide range of fields, such as 3D modeling and compact drones that represent rapidly\ngrowing and large-scale markets, with applications spanning industries including\nentertainment, sports, construction, logistics, and other sectors.”\nWe hope this revision addresses your concerns.\n2. The manuscript lacks a detailed collection of systematic parameters, and comparisons\nwith existing LiDAR systems. Indices such as imaging frame rate, lateral resolution,\nand ranging error beyond 10m are not provided. The system's main capabilities and\nparameters are scattered throughout the text, making direct comparison with other\nLiDARs difficult. Also, explicit comparisons (like size and weight) with other LiDARs\n(e.g., the one in Ref.[1] and those cited in Ref.[2]) would better demonstrate the value of\nthe author's achievement.\nWe have addressed your concerns by newly adding the LiDAR subheading on page 24.\nA comprehensive summary of the main SS-SPL system parameters is now provided in\nTable 1 on page 30. As you suggested, Table 1 also includes a comparison with the\nstate-of-the-art FMCW-LiDAR, which is discussed in detail on pages 28 and 29.\nAdditionally, Table 2 on page 31 presents a comparison with conventional UAV-\nLiDAR systems, with a particular focus on LiDAR size and weight.\nRegarding the measurement of distance accuracy in Fig. 4e on page 23, we used an\nautomatic rail system. However, due to equipment limitations, we were unable to\nmeasure the maximum distance of 25 m. To address this, we conducted additional\nquantitative evaluations using a dedicated target, and verified the distance accuracy at\n25 m, as shown in Fig. 5 on page 26.\nThe following discussion has been added to page 25:\n“The standard deviations of the distances at 3 m and 10 m were nearly the same as the\nresults shown in Fig. 4e. At 25 m, they were 47.7 mm (x) and 45.8 mm (y), which lie on\nthe extended trend line of the SP-mode results for m = 1, from 5 to 10 m shown in Fig.\n4e.”\nThank you for your valuable feedback.\n3. The paper describes the author's work on the laser, 2D MEMS, and TDC. What\nimprovements do these components offer compared to existing corresponding\ncomponents? Can these developments be generalized and applied to other LiDARs?\nWe have carefully addressed your concerns by adding Supplementary Notes 3, which\nprovides detailed comparisons with existing devices.\nFor the laser, we have included the following statement at the end of the relevant\nsubheading on page 16:\n“Although some other semiconductor laser emits a higher-power laser pulse, none of the\nconventional semiconductor lasers satisfy all four characteristics required for SS-SPL\nsuch as the pulse width on the order of several tens of picoseconds, the nJ-class pulse\nenergy, the tail-free pulse, and the low two-axis M² values.”\nFor the 2D MEMS mirror, we have included the following statement at the end of the\nrelevant subheading on page 20:\n“An FoM44, 45 of the MEMS mirror is more than twice as high as that of conventional\nones24-26 operating at atmospheric pressure, and is more than half that of those operating\nin a vacuum46.”\nFor the TDC, we have included the following statement at the end of the relevant\nsubheading on page 24:\n“The obtained results based on 40 nm technology fell between those of the introduced\n180 nm and 28 nm technologies in terms of both precision and FoM. The commonly\nused FoM did not include precision, but in LiDAR applications, designing both with a\ngood balance is crucial.”\nIn addition, we have discussed the versatility of our approach and its applicability to\nother LiDAR systems in the Discussion section (pages 36 and 37). The following\nstatements have been added to the Discussion section:\n“To increase laser pulse energy of the Q-switching semiconductor laser while\naddressing nonlinear gain saturation, an approach involves expanding the beam cross-\nsectional area by adding a tapered amplifier section23. However, exceeding the pulse\nenergy of broad-stripe EELs or PCSELs is difficult, making the approach unsuitable for\nconventional LiDAR applications. The method of current-induced bandgap\nrenormalization is not limited to narrow-stripe EELs and can be applied to any\nsemiconductor laser to increase pulse energy and reduce pulse tail.\nDespite the MEMS mirror operating at atmospheric pressure, a high FoM and strong\nshock robustness suggest that applications are not limited to SS-SPL and may extend to\na wide range of fields. Although the large 2D MEMS mirror was designed to achieve\nboth TX and RX apertures using the perforated freeform mirror, it enables a large TX\naperture in biaxial optical systems and wide FoV, while maintaining small laser\ndivergence angles for long-range applications.\nThe experimental demonstration of the PSGBR architecture of the TDC operating\nreliably under noisy conditions and achieving the single-shot timing jitter of 3 ps\nalleviates concerns regarding the limitations associated with the use of fine-TDCs. Even\nif drifts arise from longer measurement times, they can be reduced either directly or\nthrough calibration by using a temperature-compensated crystal oscillator (TCXO)68.”\nThank you for raising this important issue.\n4. The experimental scene presented in the manuscript is overly complex, making it\ndifficult for readers to intuitively understand the LiDAR's performance. It is suggested\nto use 3D resolution test targets or construct a simple scene where dimensions can be\nquantified. Comparing the results with ground truth would more effectively show the\nsystem's capabilities. Some quantitative analyses for reconstruction performance are\nneeded.\nWe have newly conducted quantitative analyses using a 3D resolution test target, and\npresented the results as colorless point cloud data in Fig. 5 on page 26. Experiments\nwere performed at target distances of 3 m, 10 m, and 25 m. The reconstruction method\nusing anisotropic voxels is described in the caption of Fig. 5. We hope this quantitative\nanalysis meets your expectations.\nAdditionally, for the colored point clouds acquired by our fusion system introduced in\nthe 3D modeling subheading, we have added relevant parameters to Table 3 on page 32\nand provided an overview in Fig. 6 on page 33.\n5. There are some writing errors in the paper. In Fig. 4, the x-axis labels for the last two\nplots should be \"Wavelength\" instead of \"Time\". The multiplication symbol should be\n\"×\" instead of the letter \"x\".\nThank you for your suggestion. We have corrected the x-axis labels in the last two plots\nof Fig. 1 in Supplementary Notes 1, which was converted from Fig. 4 in the previous\nversion, from “Time” to “Wavelength”. Additionally, we have revised the multiplication\nsymbol to “×” throughout the manuscript, including “ (5.5 mm × 4.0 mm × 1.5 mm)”\non page 11 and “(25 mm × 26 mm × 18 mm)” on page 11, and “42° × 26°” on page 19.\n6. What are the perspectives for the proposed LiDAR to work or contribute to longer\nranges? Like the one used in self-driving cars, or the one for ultralong ranges [3].\nWe have addressed your question regarding longer-range capabilities by adding a\ndetailed discussion in the Discussion section on pages 37 and 38.\n“We discuss further long-range measurement from two perspectives: indoor and\noutdoor. In the proposed coaxial optical system, further improvement of the RX\naperture is challenging; therefore, increasing the laser pulse energy serves as a dominant\nfactor for indoor use. Approximately five times greater measurement range can be\nachieved owing to the existence of high-power light sources such as PCSELs. In\nSupplementary Notes 4, we theoretically analyzed the influence of sunlight and\ndemonstrated good agreement with the experimental results52-54. The 10 nm bandwidth\noptical filter was used in the experiment, taking into account the spectral width of 2.56\nnm for the present laser. However, by narrowing the filter bandwidth to, for example,\n0.2 nm, outdoor ranging beyond 100 m becomes feasible. Notably, a report that DFB-\ntype semiconductor lasers23 can achieve a sufficiently narrower spectral width is shown\nin Supplementary Notes 3. The maximum pulse energy achievable with state-of-the-art\nchip-scale high-peak-power semiconductor/solid-state vertically integrated lasers55 may\ndetermine the ultimate measurement range limit of SS-SPL. Conversely, applying SS-\nSPL to ultra-long-range measurements is not feasible56, both due to limitations in\nachievable laser power and the influence of sunlight.”\n[1] Rogers, C., Piggott, A.Y., Thomson, D.J. et al. A universal 3D imaging sensor on a\nsilicon photonics platform. Nature 590, 256–261 (2021).\n[2] N. Li, C. P. Ho, J. Xue, L. W. Lim, G. Chen, Y. H. Fu, L. Y. T. Lee, A Progress\nReview on Solid-State LiDAR and Nanophotonics-Based LiDAR Sensors. Laser\nPhotonics Rev 2022, 16, 2100511.\n[3] Li, Z. P., Ye, J. T., Huang, X., Jiang, P. Y., Cao, Y., Hong, Y., ... & Pan, J. W. (2021).\nSingle-photon imaging over 200 km. Optica, 8(3), 344-349.\nThe suggested references [1], [2], and [3] are included in the main article as references\n48, 39, and 56, respectively.\nRevision for Reviewer #2:\n(We will present your questions in red, our responses in black, and excerpts from the\nrevised manuscript in blue.)\nWhile I think this is a good paper, I find it confusing. It should be clearer.\nWe have revised the overall structure without changing the main content. In particular,\nwe have carefully adjusted the subheadings in the Methods section to ensure they\naccurately reflect the content. To provide an overview before discussing the details of\neach device, we have also added an explanation of the principle of SS-SPL in Fig. 1a on\npage 10.\nIf this paper highlights fusion between a high density single photon lidar and a passive\nsensor each sensor should be described in a clear manner. One or two tables with\nsensor parameters could be used to assist this description.\nTable 1 on page 30 summarizes the LiDAR and its specifications. In the 3D modeling\nsubheading on page 31, we have described the fusion method. On page 32, we have\nadded Table 3 comparing the specifications of the LiDAR, camera, and fusion system.\nAdditionally, Fig. 6 on page 33 provides an overview for reconstruction and fusion,\nillustrating the concept of spatial resolution for both the reconstructed point cloud and\nthe photograph. We hope this revision addresses your concern.\nThis paper does provide a description of a light weight, small, high density lidar, but the\ndescription of the Lidar is not clear.\nThe range resolution of this lidar is very good. 50 psec pulse width can result in a range\nresolution of 7.5 mm.\nIt is possible to develop range information from stereo images, but wide angles and\nexcellent angle resolution are required.\nThis is applicable to short range systems. The lidar only has a 25 m range.\nThis study introduces an ultralight solid-state SPL (SS-SPL) system comprising a newly\ndesigned semiconductor laser, a time-to-digital converter (TDC), and a MEMS mirror.\nThe characteristics of the LiDAR are summarized in Table 1 on page 30. Weight, size,\nand other specifications are compared with conventional UAV LiDAR systems in Table\n2 on page 31. Thank you for your helpful suggestion.\nLine 93 – “detected by the silicon photomultiplier (SiPM) via a coaxial optical path. As\nthe SiPM comprised thousands of single-photon avalanche diode (SPAD) elements, its\noutput corresponded to the number of simultaneously incident photons16, 17.”. I’d be\ninterested in knowing more about the detector. Is this a photo multiplier tube? Is it an\narray of solid state SPAD detectors? It was not clear to me. The lack of a good\ndescription is characteristic of this paper.\nWe have added a description of the SiPM at the beginning of the Concept subheading\non pages 6 and 7.\n“The ranging principle of SS-SPL is illustrated in Fig. 1a. A single short-pulse laser\nbeam is directed at an object, and weak light scattered by the object is detected by a\nsilicon photomultiplier (SiPM). The detected light corresponds to photons ranging from\na single to several tens, which can be converted into quantized weak electrical pulses.\nThis occurs because the SiPM consists of thousands of single-photon avalanche diode\n(SPAD) elements connected to a common cathode and a common anode, resulting in a\nlinear output for weak signals33, 34. If the temporal resolution of both the pulsed laser\nand the SiPM is sufficiently high, a single electrical pulse can exhibit quantized levels,\nas illustrated in the figure.”\nWe hope this additional explanation clarifies the detector configuration.\nIn the newly added SiPM subheading in the Methods section on page 43, we have\nprovided detailed information on the production of the SiPM.\n“MPPC® S15369-1325PS, manufactured by Hamamatsu Photonics, was used. It\nconsisted of 2,120 SPAD elements. We designed a dedicated CMOS driver that was\ncontrolled by the FPGA.”\nMain point is this lidar is very small, and has high 3D point density.\nLine 219 – “precisely using Lissajous trajectories”. Why Lissajous trajectories? With\nRisley prisms I am aware scanning usually uses Lissajous patterns, but I was not aware\nMEMs scanning uses Lissajous trajectories. Can this paper include an explanation why\nthis lidar uses Lissajous scanning?\nWe have provided an explanation for the selection of the 2D MEMS mirror in this study\nin the 2D laser beam scanner subheading on pages 16 and 17.\n“In beam steering for the SS-SPL, priority is given to capturing more photons, while\nalso ensuring a wider field of view (FoV), uniform scanning across the entire FoV, and a\ncompact size. Beam steering methods can be categorized into mechanically driven\nmotor systems, MEMS mirrors, and fully solid-state nanophotonics with no moving\nparts38, 39. In this study, we designed a low-Q resonant 2D MEMS mirror that operates in\nair due to three fundamental advantages. It consists of a single gold-coated mirror,\nresulting in minimal optical loss. It scans the entire FoV within a short period by\nemploying a relatively higher slow-axis frequency. It possesses superior robustness\nagainst electrical noise due to its mechanical inertia, in comparison with other linear\nscanners. From these advantages, the risk of missing the target in dynamic 3D modeling\napplications can be reduced, and uniform non-repetitive scanning of the entire field of\nview can be achieved with only stable frequency control due to the inertia when the\nexposure time is increased. The trajectory generated by the two-axis resonant MEMS\nmirror forms a Lissajous pattern (Fig. 1b), as described in the Methods section.”\nWe have added an explanation of the beam trajectory in the Lissajous trajectory of\nresonant 2D MEMS mirror subheading in the Methods section on pages 43 and 44.\n“The optical scanning angle of the 2D MEMS mirror, featuring a fast beam on the inner\ncircumference and a slow beam on the outer circumference as shown in Fig. 1b, can be\nexpressed as:\ncos𝜑 0 (cid:3398)sin𝜑 1 0 0\n𝑅 (cid:4666)𝜑(cid:4667)(cid:3404)(cid:3437) 0 1 0 (cid:3441), 𝑅 (cid:4666)𝜃(cid:4667)(cid:3404)(cid:3437)0 cos𝜃 (cid:3398)sin𝜃(cid:3441)\n(cid:3052) (cid:3051)\nsin𝜑 0 cos𝜙 0 sin𝜃 cos𝜃\n𝑛(cid:4652)⃗ (cid:3404)𝑅 (cid:4666)𝜃(cid:4667)𝑅 (cid:4666)𝜑(cid:4667)𝑛(cid:4652)(cid:4652)(cid:4652)(cid:4652)⃗\n(cid:3051) (cid:3052) (cid:2868)\n𝑟⃗ (cid:3404)𝑠⃗(cid:3398)2(cid:4666)𝑠⃗∙𝑛(cid:4652)⃗(cid:4667)𝑛(cid:4652)⃗\nwhere 𝑅 (cid:4666)𝜑(cid:4667) and 𝑅 (cid:4666)𝜃(cid:4667) are the rotation matrices, 𝑛(cid:4652)(cid:4652)(cid:4652)(cid:4652)⃗ represents the normal of the\n(cid:3052) (cid:3051) (cid:2868)\nfixed MEMS mirror, 𝑛(cid:4652)⃗represents the normal during rotation, 𝑠⃗ denotes the direction of\nlaser incidence, and 𝑟⃗ denotes the direction of laser reflection. The trajectory is referred\nto as a Lissajous curve.”\nThank you for pointing out the need for this explanation.\nFor dynamic situations, can you comment if there are any issues with the MEMs\nscanning? For an auto lidar using MEMs when a stone hits the vehicle there could be a\nresonance. In this case that may not apply.\nThis is a highly interesting and important concern when utilizing MEMS technology.\nTherefore, we conducted new experiments and summarized the details of the Hertz\ntheory and our experimental results in Supplementary Notes 2. In the main article, we\nhave included the following description under the 2D laser beam scanner subheading on\npage 18.\n“The shock robustness42,43 of the MEMS fixed to the resin frame exceeded 2771 G\nduring operation, as discussed in Supplementary Notes 2 and demonstrated in\nSupplementary Video 1. Since no hysteresis was observed in the resonant spectrum as\nshown in Figs. 2a and 2b, the Lissajous trajectories remained after the impact.”\nWe hope this addresses your concern.\n320 – “distance to the target of white paper for SP-mode (black), DP-“ should have or\ninstead of “of” before white paper.\nWe apologize for the confusing expression. We have corrected it as follows in the High\nFunctional Time-to-Digital Converter subheading on page 21 and in the caption of Fig.\n4 on page 24.\n“depending on the distance to the target for SP-mode (circular), DP-mode (triangle), and\nTP-mode (rhombus), is illustrated in Fig. 4c.”\n“depending on the distance to the target for SP-mode (black), DP-mode (red), and TP-\nmode (blue).”\nI missed how narrow the filter is. In the discussion on sky brightness how narrow the\nfilter is, is important. It is probably there, but should be highlighted when sky\nbackground is decisioned. Also the wavelength of operation should be discussed.\nWe sincerely apologize for not sufficiently emphasizing this important aspect of our\nLiDAR system in the original manuscript. In Supplementary Notes 4, we have\nprovided a detailed analytical evaluation of the impact of sunlight. Under the conditions\nof the laser center wavelength of 825 nm and the optical filter bandwidth of 10 nm, the\ninfluence of wrong signals induced by sunlight becomes significant. At an illuminance\nof 30,000 lx, the wrong signal rate is estimated to be approximately 3.5 Mcps. When\ncombined with the SiPM dark count rate of 0.7 Mcps, the total wrong signal rate\nreaches 4.2 Mcps, which constitutes the major factor limiting the measurement range in\noutdoor environments. Conversely, reducing the wrong signal rate is expected to extend\nthe measurement range, and we have highlighted this point in the Discussion section on\npages 37 and 38.\n“In Supplementary Notes 4, we theoretically analyzed the influence of sunlight and\ndemonstrated good agreement with the experimental results52-54. The 10 nm bandwidth\noptical filter was used in the experiment, taking into account the spectral width of 2.56\nnm for the present laser. However, by narrowing the filter bandwidth to, for example,\n0.2 nm, outdoor ranging beyond 100 m becomes feasible. Notably, a report that DFB-\ntype semiconductor lasers23 can achieve a sufficiently narrower spectral width is shown\nin Supplementary Notes 3. The maximum pulse energy achievable with state-of-the-art\nchip-scale high-peak-power semiconductor/solid-state vertically integrated lasers55 may\ndetermine the ultimate measurement range limit of SS-SPL.”\nThis discusses the fusion of lidar and visible imagery. Sometimes it could be clearer\nwhich sensor is being discussed.\nWe have added a definition of the fusion system used in this study on page 31\n“We propose a fusion system based on super-dense point clouds with high geometric\nfidelity and a single-view full-color photograph instead of performing advanced fusion\nusing multiple photographs in post-processing, and visualize the expressive power of\nthe resulting colored point clouds. Table 3 summarizes conversion parameters used for\nthe fusion system in this study.”\nWe have added the sensor information for each 3D modeling case on page 33.\n“A meticulously stitched 3D model of a restaurant floor (Figs. 7a-c) obtained by the\nfusion system demonstrated geometric accuracy in global coordinates, including scenes\nwith less texture information and sufficient density to project fine textures.”\n“Cherry blossom trees captured by the fusion system from a single viewpoint for several\nconditions are shown in Figs. 7d and 7e and Supplementary Video 2.”\n“A dynamic view of basketball shot acquired by the SS-SPL without the fusion is shown\nin Fig. 7f and Supplementary Video 3 to illustrate another interest: how the dense point\nclouds model dynamic scenes.”\nThank you for your suggestion.\nA table with the Lidar parameters would be useful. This would have transmit and\nreceive aperture sizes, filter width, carrier wavelength, laser energy per pulse, rep rate\nand pulse width and jitter, frame rate, el and az FOV,and any other relevant\nparameters. Multiple modes can also be highlighted in the table.\nAll of the LiDAR parameters discussed in the manuscript have been consolidated in\nTable 1 on page 30, including the distance precisions of the SP-mode, the DP-mode,\nand the TP-mode.\nA table with fused passive visible camera parameters would be useful as well, including\ncamera bandwidth and wavelengths.\nThe camera parameters are listed in Table 3 on page 32. As the commercial camera was\nused, only its sensitivity to the visible spectrum is known; other specifications are not\navailable. We appreciate your understanding.\n474 – Maybe I missed where BRG is defined.\n“following which BGR is induced” BRG?\nThank you for pointing this out. We apologize for any inconvenience caused by\nexplaining specialized technical abbreviations only once at the beginning. We have\nrevised the manuscript to include these explanations at appropriate intervals. The term\n“bandgap renormalization (BGR)” is now defined on pages 5, 13, 41, and 43.\nSincerely,\nTomoki Ohno\nResearch Division 3, Sony Semiconductor Solutions Corporation, 4-14-1, Asahi-cho,\nAtsugi, Kanagawa, 243-0014, Japan.\nEmail Address: Tomoki.ono@sony.com"}, {"round": 2, "reviewer_comments": {"reviewer_2": "I think theydid a good job of addressing my concerns. I recommend publications"}, "author_response": "Dear Reviewers,\nWe sincerely appreciate the reviewer’s thorough evaluation of our revised manuscript\nand thank them for their time and effort.\nResponse to Reviewer #1:\n(We will present your questions in red and our responses in black.)\nThe authors have addressed all my comments. I am happy to recommend its publication.\nWe thank the reviewer for the positive assessment and recommendation.\nResponse to Reviewer #2:\n(We will present your questions in red and our responses in black.)\nI think they did a good job of addressing my concerns. I recommend publication.\nWe thank the reviewer for the positive assessment and recommendation.\nSincerely,\nTomoki Ohno\nResearch Division 3, Sony Semiconductor Solutions Corporation, 4-14-1, Asahi-cho,\nAtsugi, Kanagawa, 243-0014, Japan.\nEmail Address: Tomoki.ono@sony.com"}]

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