Free-form DCS allows control of the timing between the light pulses from two lasers and compressive sensing factor up to 155. It provides better resolution, less background noise, or faster data collection, reducing acquisition time.
Here Comb is a special kind of laser that emits light at many equally spaced frequencies.
Traditional DCS Sampling is a method where the sampling occurs at evenly spaced time intervals. Free-form DCS provides control over the temporal offset between pulses, which allows user-selected sampling.
The Compressive Sensing method uses random, non-uniform sampling to capture the important parts of the signal, drastically reducing the number of measurements needed.
The dots indicate the Relative pulse delay compared to the time-domain response of a molecular gas (black trace, bottom)
Relative pulse delay time (T_RPD) is the difference in time between when two pulses of light (from two separate laser "combs") arrive at a detector in dual-comb spectroscopy (DCS).
When gas like Methane absorbs light, it creates a specific pattern in the signal, which repeats at regular intervals (called "recurrences").
Instead of measuring everything, recurrence sampling skips the unnecessary parts and only looks at these important repeating signals.
Ax=b
A = ΦΨ
b is Vector with k elements- sparse signal (signal where only a few frequencies are present.)Φ is matrix ; Ψ is matrix, DFT basis here., A is k x n matrix; A = ΦΨ Sensing matrix
Heterodyne signal in dual-comb spectroscopy is the result of two laser light sources (called frequency combs) interfering with each other. This creates a new signal that shifts the high-frequency information to a much lower frequency which is easier to measure and analyze.
Figure a shows an image of the methane gas plume, captured by the system using recurrence sampling. Each pixel in the image represents the methane concentration detected at that location.
The light passes through the gas plume, interacts with methane molecules, and reflects back to the camera. The methane absorption pattern creates a signal that can be detected at specific recurrence times.
The Power Spectral Density (PSD) is used to analyze the noise levels in the system. PSD measures how the power of the signal is distributed across different frequencies and helps to identify noise sources that could affect the measurement.
For each pixel, the time-domain signal is converted to the frequency domain using the Fourier transform. This allows the analysis of how the signal's power is distributed over different frequencies.
The Fourier transform of the time-domain signal gives the spectrum of the signal, which shows both the useful methane signal and any noise present.
PSD(f) is the power spectral density at frequency f.
V(f) is the Fourier transform of the time-domain signal V(t)
Δf is the bandwidth over which the PSD is calculated.
