The spatial resolution of a conventional imaging LADAR system is constrained by the diffraction limit of the telescope aperture. The purpose of this work is to investigate Synthetic Aperture Imaging LADAR (SAIL), which employs aperture synthesis with coherent laser radar to overcome the diffraction limit and achieve fine-resolution, long range, two-dimensional imaging with modest aperture diameters. This paper details our laboratory-scale SAIL testbed, digital signal processing techniques, and image results. A number of fine-resolution, well-focused SAIL images are shown including both retro-reflecting and diffuse scattering targets. A general digital signal processing solution to the laser waveform instability problem is described and demonstrated, involving both new algorithms and hardware elements. These algorithms are primarily data-driven, without a priori knowledge of waveform and sensor position, representing a crucial step in developing a robust imaging system. These techniques perform well on waveform errors, but not on external phase errors such as turbulence or vibration. As a first step towards mitigating phase errors of this type, we have developed a balanced, quadrature phase, laser vibrometer to work in conjunction with our SAIL system to measure and compensate for relative line of sight motion between the target and transceiver. We describe this system and present a comparison of the vibrometer-measured phase error with the phase error inferred from the SAIL data.
KEYWORDS: Data modeling, Doppler effect, Vibrometry, Laser processing, Signal processing, Statistical signal processing, Stochastic processes, Spectrum analysis, Data processing, Fermium
Laser vibration sensing provides a sensitive non-contact means of measuring vibrations of objects. These measurements are used in industrial quality control and wear monitoring as well as the analysis of the vibrational characteristics of objects. In laser vibrometry, the surface motion is monitored by heterodyne laser Doppler velocimetry, and the received heterodyne signal is sampled to produce a time-series which is processed to obtain a vibrational spectrum of the object under test. Laser vibrometry data has been processed with a traditional FM discriminator approach and by spectrogram and time-frequency distribution processing techniques. The latter techniques have demonstrated improved performance over the FM discriminator method, but do not take full advantage of the prior knowledge one has about the signal of interest. We consider here a statistical signal processing approach to laser vibrometry data. In this approach the quantities of interest are the frequencies of vibration, while the phase and quadrature amplitudes are considered nuisance parameters. Because of the optimal use of prior knowledge about the laser vibrometry signal, the frequencies can be determined with much greater precision and greater noise immunity than using Fourier- or time-frequency-based approaches. Furthermore, the statistical approach is known to have superior performance when the data extends over a small number of vibrational periods. We illustrate the method with data from a fiber-optic laser Doppler velocimeter. Our results show that while the choice of processing method for determining the instantaneous velocity is relatively unimportant, the Bayesian method exhibits superior performance in determining the vibrational frequency.
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