Photonic Doppler Velocimetry Measurements of Materials Under Dynamic Compression

摘要

Photonic Doppler velocimetry (PDV), also known as heterodyne velocimetry [1], is a compact displacement interferometer system that is rapidly becoming a standard diagnostic in dynamic compression research. A PDV system is essentially a fiber-based Michelson interferometer, utilizing recent advances in near-infrared (λ_0 = 1550 nm) detector technology and fast digitizers to record beat frequencies in the gigahertz range. Compared to the traditional shock wave diagnostic VISAR [2], some advantages of PDV include simple assembly and operation, readily available components, and the lack of an intrinsic delay time. In PDV measurements, Doppler shifted light from a moving target is combined with unshifted light, creating a beat frequency that is proportional to the target velocity (f = 2v/λ_0). For a target moving at 1 km/s, a measured PDV signal would have a beat frequency of 1.29 GHz. The frequency content of the PDV signal is typically calculated using a sliding short-time Fourier transform (STFT). Within each signal segment of time duration τ, the beat frequency is extracted from the peak of the power spectrum where the velocity resolution is defined by how well the frequency peak can be resolved. In a typical (standard) PDV configuration, a single laser light source is used to illuminate a target and provide an unshifted reference light for interference with the target light (see Fig. 1a). When the target is stationary, no beating within the PDV signal occurs since the reflected light from the target also remains unshifted. The relationship between the time duration τ and characteristic peak width Δf follows the uncertainly product: (Δf) τ > (4π)~(-1). For example, to achieve a velocity precision Δv = 10 m/s, the minimum time duration needed in the STFT analysis is τ = 6 ns. For measured velocities that are reasonably large (> 1 km/s), the relative velocity precision (Δv/v < 1%) is sufficient to investigate many dynamic material properties. However, low velocity (< 100 m/s) transients can be difficult to resolve with standard PDV since the beat period of the feature of interest may be longer than the time duration of the analysis. Also, in order to improve the poor relative velocity precision (Δv/v ～10%), τ must be increased thus sacrificing time precision.