Frequency-modulated continuous-wave LiDAR compressive depth-mapping.
TL;DR: An inexpensive architecture for converting a frequency-modulated continuous-wave LiDAR system into a compressive-sensing based depth-mapping camera that can obtain higher signal-to-noise ratios over detector-array based schemes while scanning a scene faster than is possible through raster-scanning is presented.
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Abstract: We present an inexpensive architecture for converting a frequency-modulated continuous-wave LiDAR system into a compressive-sensing based depth-mapping camera. Instead of raster scanning to obtain depth-maps, compressive sensing is used to significantly reduce the number of measurements. Ideally, our approach requires two difference detectors. Due to the large flux entering the detectors, the signal amplification from heterodyne detection, and the effects of background subtraction from compressive sensing, the system can obtain higher signal-to-noise ratios over detector-array based schemes while scanning a scene faster than is possible through raster-scanning. Moreover, by efficiently storing only 2m data points from m < n measurements of an n pixel scene, we can easily extract depths by solving only two linear equations with efficient convex-optimization methods.
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Figures
Fig. 4. Image (a) shows the 2 MHz Lorentzian linewidth on the beat notes expected from a laser’s 1 MHz Lorentzian linewidth as seen by an oscilloscope sampling at 33.3 MHz. Image (b) shows the noiseless, positive-frequency components from a single noiseless projection from Fig. 3 when using a zero-linewidth laser. When accounting for a 2 MHz beat-note linewidth, image (c) shows the broadened expected frequency components. When including a peak SNR = 5 (based on the SNR of the brightest object or pixel), image (d) presents a realistic noisy signal one would measure in an experiment. Image (e) presents the result of denoising the signal in (d) with a Bayes-shrink denoising filter using a symlet-20 wavelet decomposition. Image (f) presents the result of deconvolving the 2 MHz Lorentzian linewidth with the denoised signal in (e) using a Weiner filter. Image (f) is the cleaned signal from the (1,0) projection. A similarly cleaned result from the (0,1) signal will then be subtracted from (f) and then used to form yI and yIν . 
Fig. 1. (Proposed Experiment) HWP: half-wave plate, PBS: polarizing beam-splitter, DMD: digital micro-mirror device, BS: beam-splitter. A linearly chirped laser is split into two beams, designated as a local-oscillator and a signal, via a HWP and a PBS. The signal illuminates a target scene and the reflected radiation is used to image the scene onto a DMD. The DMD takes pseudo-random spatial projections, consisting of ±1 pixel values, and directs the projections to balanced-heterodyne detectors using the local-oscillator. 
Fig. 6. (a) Reconstruction Mean-Squared Error: Each data point corresponds to the average mean squared error from 10 different reconstructions of different data sets for varying sample ratios (m/n) and peak-SNR cases. The standard error for each mean is given by the shaded regions. (b) Depth Uncertainty to Toroid: Each data point represents the average uncertainty in depth to the toroid within Fig. 2. Points were calculated by first considering the standard deviation of each pixel over 10 different reconstructions. Standard deviations associated with only the toroid pixels were then averaged. Different peak-SNR scenarios, FWHM Lorentzian linewidths for the beat-note frequency uncertainties, and sample ratios were considered and compared to the results obtained by simulating raster scans. Raster scans were not affected by linewidth uncertainty. 
Fig. 5. When using a PSNR = 5, image (a) shows a typical total-variation minimization reconstruction from a 25% sample-ratio intensity-measurement vector yI . Shapes are identified, but the pixel values are incorrect. Image (b) is a binary mask generated by hardthresholding image (a). After representing image (b) in a sparse basis, such as a Haar-wavelet decomposition, least-squares can be performed on the m/3 largest signal components to construct xI and xIν . After applying Eq. (11), a depth map is presented in image (c). Images (d), (e), and (f) demonstrate the same process for a 5% sample ratio, again with PSNR = 5. Image (g) is the true depth-map presented for easy comparison. Images (h) and (i) are smoothed depth-maps after applying a 4×4 pixel averaging kernel to depth-maps (f) and (c), respectively. 
Fig. 2. Image (a) presents a 3-dimensional scene composed of Lambertian-scattering targets. Image (b) presents the depth map we wish to compressively recover. 
Fig. 3. Image (a) presents an illumination profile that consists of 1 Watt in total power. The scene is discretized into a 128 × 128 pixel resolution scene with a maximum power per pixel of 119 µW. When using a 2 inch collection optic and modeling each object as a Lambertian scatter, image (b) presents a single projection taken by the DMD of the reflected radiation as seen by one detector. The maximum power per pixel is of order nanowatts.
Citations
SPADs and SiPMs Arrays for Long-Range High-Speed Light Detection and Ranging (LiDAR).
TL;DR: In this article, the authors provide an extensive review of silicon-single photon avalanche diode (SPAD)-based LiDAR detectors (both commercial products and research prototypes) analyzing how each architecture faces the main challenges of LIDAR (i.e., long ranges, centimeter resolution, large field-of-view and high angular resolution, high operation speed, background immunity, eye-safety and multi-camera operation).
121
Application of contact laser interferometry in precise displacement measurement
TL;DR: In this article, an innovative contact type long-range displacement sensor based on frequency modulated continuous wave (FMCW) is proposed, which has the characteristics of less than traditional interferometer devices, high precision, large range and antielectromagnetic interference.
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Multi-point spectroscopic gas sensing based on coherent FMCW interferometry.
TL;DR: An innovative spectroscopic method based on coherent optical frequency-modulated continuous-wave (FMCW) interferometry that can realize multi-point gas detection with high spatial resolution, high sensitivity, and high selectivity is presented.
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Dynamic cascade-model-based frequency-scanning interferometry for real-time and rapid absolute optical ranging.
TL;DR: The proposed FSI scheme eliminates nonlinear optical-frequency scanning effects in dynamic measurements and realizes real-time measurement only current observed data are used, and experimental results verify high tracking performance for a vibrating target with approximately 10 μm amplitude and 50-500 Hz frequency.
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Realization of Multitone Continuous Wave Lidar
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