In order to eliminate the influence of laser frequency nonlinearity, the frequency-scanning interferometry (FSI) often uses the beat signal of an auxiliary interferometer as the external clock. The time points at every amplitude peaks and bottoms of the auxiliary beat signal are selected as the sampling time points for the main interferometer signal. To satisfy the Nyquist sampling requirement, the optical path difference (OPD) of the delay fiber in auxiliary interferometer should be at least twice longer than the measurement distance. In this paper, we proposed a method to shorten the length of delay fiber. The Hilbert transform was used to extract the phase of the auxiliary interference signal and calculate the time points corresponding to subdivided phase intervals. Then, the main interference signal was resampled at these moments, and the fast Fourier transform was performed on the resampled signal. The experimental results showed that the target at the distance of about 5 m was measured when the OPD of the auxiliary interferometer was about 4.5 m. The standard deviation of the distance measurement results could reach 4.64 μm.

Photon-counting LIDAR has effective ability to detect significantly weak echo. However, for imaging application, it typically needs a long acquisition time to obtain sufficient counts to reconstruct clear depth image, which obviously limits imaging efficiency and prevents its wide deployment. In this paper, we proposed a low acquisition time photon-counting imaging method based on two single element SPADs and pixel scanning structure. Compared to fast imaging with SPAD array, the method has low requirement on laser energy and can obtain depth image with arbitrary pixel resolution. Experiment result demonstrates its feasibility and a dynamic target can be clearly captured by the system with our specifically designed reconstruction algorithm. We also detailly investigated the working conditions for the method. It reveals more than 2 echo photons per pulse would be enough to reconstruct clear depth image even when noise is intensive. Restricted to our 10 KHz laser source, the result only exhibited 1 frame per second(fps) imaging with pixel resolution of 100*100. If a common 10 MHz laser is adopted, 512*512 pixels resolution images can be captured at the rate of nearly 40 fps.

The high image sparsity is very important to improve the accuracy of compressed sensing reconstruction image, and the wavelet transform can make the image sparse obviously. This paper is the optimization method based on wavelet sparse transform in image reconstruction based on compressed sensing, and we have designed a restraining matrix to optimize the wavelet sparse transform. Firstly, the wavelet coefficients are obtained by wavelet transform of the original signal data, and the wavelet coefficients have a tendency of decreasing gradually. The restraining matrix is used to restrain the small coefficients and is a part of image sparse transform, so as to make the wavelet coefficients more sparse. When the sampling rate is between 0. 15 and 0. 45, the simulation results show that the quality promotion of the reconstructed image is the best, and the peak signal to noise ratio (PSNR) is increased by about 0.5dB to 1dB. At the same time, it is more obvious to improve the reconstruction accuracy of the fingerprint texture image, which to some extent makes up for the shortcomings that reconstruction of texture image by compressed sensing based on the wavelet transform has the low accuracy.