Continuous-streaming high-speed two-photon dual-comb LiDAR with free-running lasers

This paper demonstrates continuous-streaming high-speed two-photon dual-comb LiDAR using free-running femtosecond lasers to achieve sub-micrometer precision at 11.5 kHz, enabling low-data-burden applications such as capturing audio from mirror displacement without the need for sophisticated stabilization or gigasample-rate digitization.

The Gist

Imagine you are trying to measure the distance to a moving object with extreme precision—so precise that you could detect if the object moved the width of a single human hair. Now, imagine doing this thousands of times every second, without needing a supercomputer to process the data, and using lasers that aren't even perfectly tuned to a specific frequency.

That is exactly what this research team from Heriot-Watt University has achieved. They built a "super-fast ruler" using a clever trick called Two-Photon Dual-Comb LiDAR.

Here is a breakdown of how it works, using simple analogies:

1. The Problem: The "Data Traffic Jam"

Traditional high-speed laser rulers (LiDAR) work like a strobe light flashing at a target. To get super-fast measurements, you need to flash the light incredibly fast. However, this creates a massive amount of data—like trying to download a movie every second. Usually, you need expensive, complex computers to process this flood of information instantly, or the system has to stop and start, missing the action.

2. The Solution: The "Two-Beat Drummer" Analogy

The team used two lasers that act like two drummers playing slightly different rhythms.

• Drummer A plays at a very fast beat (540 million beats per second).
• Drummer B plays at almost the same speed, but just a tiny bit slower.

When you listen to two drummers with slightly different tempos, you hear a "wah-wah-wah" sound that gets louder and softer in a slow, rhythmic pattern. This is called a beat frequency.

In their system, the "loudness" of this beat happens exactly when the pulses from the two lasers line up. By measuring when these beats happen, they can calculate the distance to an object.

3. The Magic Trick: "Time-Stamping" instead of "Video Recording"

Most systems try to record the entire wave of the laser (like recording a high-definition video of the beat). This creates huge files.

The team's innovation is like this: Instead of recording the whole song, they just write down the time on a stopwatch every time the beat hits a specific point.

• Old way: Recording a 4K video of a runner (huge file size).
• New way: Just writing down "Runner passed the 10m mark at 1.2 seconds, 1.3 seconds, 1.4 seconds..." (tiny file size).

Because they only record the "time stamps," the data burden is tiny. This allows them to stream measurements continuously without choking their computer.

4. The "Free-Running" Lasers

Usually, to get perfect measurements, lasers need to be locked into a stable, atomic-clock-like state. This is like tuning a guitar perfectly before every song. It's slow and requires complex equipment.

These researchers used "free-running" lasers. Think of these as two drummers who aren't perfectly tuned to a metronome; their speed drifts slightly. However, because their system measures the relationship between the two lasers, it doesn't matter if they drift. The system automatically corrects for the drift, like a smart camera that stabilizes a shaky video in real-time.

5. What Did They Actually Do?

To prove their system works, they did two amazing things:

• The Microscopic Ruler: They measured a distance with a precision of 1 micrometer (about 1/80th the width of a human hair) in just 10 milliseconds. That's faster than you can blink.
• The "Audio" Ruler: They attached a mirror to a loudspeaker and played a song (Hozier's "Too Sweet"). As the speaker cone moved back and forth to the music, the laser measured its position thousands of times a second. They successfully recorded the entire 4-minute song as a stream of distance data.

Why Does This Matter?

This technology is a game-changer for industry. Imagine a robotic arm in a factory that needs to assemble a car engine. Currently, it might rely on sensors that aren't perfectly accurate, leading to tiny errors that add up.

With this new system:

• It's Fast: It can update the robot's position 10,000+ times a second.
• It's Cheap: It uses simpler, cheaper lasers that don't need complex stabilization.
• It's Light: It doesn't clog up the computer's memory, allowing for real-time adjustments.

In a nutshell: They turned a complex, data-heavy laser measurement problem into a simple, fast, and continuous "time-stamping" game, allowing machines to "see" and measure movement with incredible speed and precision, even using lasers that are a little bit "wobbly."

Technical Summary

Here is a detailed technical summary of the paper "Continuous-streaming high-speed two-photon dual-comb LiDAR with free-running lasers."

1. Problem Statement

Dual-comb distance metrology offers sub-micrometer precision over meter-scale non-ambiguity ranges, making it ideal for high-precision industrial applications. However, traditional interferometric implementations face significant hurdles for continuous, real-time streaming:

• Data Burden: They require digitization at near-gigasample/second rates, generating massive data volumes that are difficult to process in real-time.
• Complexity: Achieving continuous streaming often necessitates sophisticated hardware (FPGAs, GPUs) and complex algorithms to handle coherent averaging or peak detection.
• Stability Requirements: Many systems require stabilized lasers (carrier-envelope offset frequency control) to maintain accuracy, increasing system complexity and cost.

The authors aim to overcome these limitations by leveraging two-photon dual-comb LiDAR, which naturally produces low-data-burden signals, to achieve continuous, high-speed distance streaming using free-running (unstabilized) lasers.

2. Methodology

A. Laser Sources

The system utilizes two nearly identical, free-running Er,Yb:glass femtosecond lasers operating at a repetition rate ($f_{rep}$) of approximately 540 MHz.

• Configuration: Both lasers use a 540 MHz cavity geometry with a 2 mm thick Brewster-angled Er,Yb:glass gain medium pumped by a 980 nm diode.
• Wavelength Separation: To avoid interference artifacts and improve cross-correlation quality, the lasers are tuned to different wavelengths using distinct Semiconductor Saturable Absorber Mirrors (SESAMs):
  • Probe Laser: 1557 nm (60 mW output).
  • Local Oscillator (LO) Laser: 1530 nm (13 mW output).
• Pulse Characteristics: The lasers produce transform-limited pulses with durations of ~534 fs.

B. Optical and Detection Scheme

The system employs a two-photon absorption (TPA) detection scheme:

1. Multiplexing: The 1557 nm probe pulses are split between a target and a reference reflector. They are then polarization-multiplexed with the 1530 nm LO pulses.
2. Detection: A fiber-pigtailed laser diode (Luminent MRLDFC010) acts as the TPA detector. It generates a sequence of cross-correlation signals (envelope-like signals) rather than requiring high-speed analog digitization of the full waveform.
3. Signal Conditioning: The weak cross-correlation signals (~2 mV) are amplified to 150 mV and passed through a Constant Fraction Discriminator (CFD) to generate CMOS-compatible 3.3 V pulses. The rising edges of these pulses are insensitive to amplitude variations.

C. Timing and Data Acquisition

Instead of time-stamping with a microcontroller (limited to ~1.67 ns precision), the authors implemented a high-precision timing architecture:

• Hardware: Two TDC7200 Time-to-Digital Converters (TDCs) synchronized to a common 16 MHz clock.
• Demultiplexing: A D-type flip-flop and AND gates separate the LO-Reference (R) and LO-Target (T) cross-correlations into two channels.
  • TDC1 measures the short gap (Reference $\to$ Target).
  • TDC2 measures the long gap (Target $\to$ Reference).
• Data Stream: Timing data is streamed via SPI to a Teensy 4.0 microcontroller and transmitted to a host PC via USB.
• Data Efficiency: Each sample requires only 64 bits (two unsigned integers), drastically reducing the data burden compared to analog digitization.

D. Distance Calculation

The distance ($d_i$) is calculated using a ratio of the measured time intervals ($t_{TR}$ and $t_{RT}$) between consecutive cross-correlations:
$$d_i = \frac{v_g}{2 f_{rep}} \cdot \frac{t_{TR}}{t_{TR} + t_{RT}}$$
This method provides strong common-mode rejection against fluctuations in the repetition rate difference ($\Delta f_{rep}$), allowing the use of free-running lasers without active stabilization.

3. Key Contributions

1. Continuous Streaming at High Rates: Demonstrated sustained continuous streaming of absolute distance measurements at 11.5 kHz (up to 20 kHz for short durations), a significant achievement for dual-comb systems without FPGA/GPU acceleration.
2. Free-Running Laser Operation: Proved that high-precision metrology is possible using unstabilized Er,Yb:glass lasers, relying on the self-calibrating nature of the two-photon ratio method rather than laser locking.
3. Low Data Burden Architecture: Replaced high-speed analog digitization with time-stamping of cross-correlations, reducing the data rate to a level manageable by standard USB interfaces and microcontrollers.
4. High Precision: Achieved a distance precision of ~1 µm with an averaging time of only 10 ms.

4. Results

• Precision and Stability:
  • At a sampling rate of 11.5 kHz, the system achieved a standard deviation of 11.7 µm in raw distance measurements.
  • Through averaging, the precision improved to 1 µm within 10 ms.
  • Allan deviation analysis confirmed the expected $1/\sqrt{\tau}$ behavior, validating the noise characteristics.
• Dynamic Target Demonstration:
  • The system successfully recorded a four-minute audio track ("Too Sweet" by Hozier) by mounting a mirror on a loudspeaker.
  • The audio was encoded in the mirror's displacement and captured at a sampling rate of 9.3 kHz.
  • The reconstructed waveform matched the original audio, demonstrating the system's ability to track dynamic, high-frequency mechanical displacements in real-time.
• Limitations:
  • The maximum theoretical sampling rate is limited by the SPI bus and TDC data transfer (theoretical limit ~31.25 kS/s) and the USB 2.0 transfer speed for continuous streaming.
  • The fundamental optical limit for $\Delta f_{rep}$ is ~133 kHz, but the current system is bottlenecked by data transfer speeds.

5. Significance

This work represents a paradigm shift in dual-comb LiDAR implementation by removing the need for complex, expensive stabilization and high-speed digitization hardware.

• Industrial Application: The ability to perform high-speed, low-data-burden metrology with simple, free-running lasers makes this technology highly viable for real-time calibration and control of robotic arms and machine tools, where encoder-based position tracking often introduces uncertainty.
• Scalability: The use of standard microcontrollers and TDCs suggests a path toward compact, cost-effective, and portable high-precision sensing systems.
• Future Potential: The authors note that the system could be extended to atomic-referenced measurements using GPS clocks, further enhancing its utility for long-term, high-accuracy applications.