Particle and speckle imaging velocimetry applied to a monostatic lidar
Trailing vortices are an unavoidable byproduct of the differing air flow on the upper and lower sides of the wings of an aircraft: they persist for many miles and can be hazardous for small aircraft following larger ones (see Figure 1). The structure and behavior of the phenomenon during takeoff and landing has been extensively studied using ground-based aerosol Doppler lidar (light detection and ranging). This technique involves scanning the turbulence field at a slanted angle to the vortex tubes and then measuring the axial Doppler shift of movements of their encapsulated aerosols.1 Because future airports will require shorter landing distances to accommodate a general increase in air traffic, there is a need for a compact airborne forward-looking sensor to monitor clear air turbulence ahead of smaller aircraft.
The main hazard associated with a trailing wake vortex occurs when the aircraft behind happens to fly along the stream's axis of rotation. A disadvantage of airborne Doppler sensors is that resolution is low in the angular scanning range near the flight axis. Moreover, the axial Doppler shift due to air turbulence must be extracted from the much stronger shift owing to the aircraft movement itself. Finally, the time needed to scan a full image frame over the vortices typically lasts several seconds, which leads to severe distortion in the geometry of the resulting image.
To address these drawbacks, we have investigated2 applying the fluid mechanics techniques of particle imaging velocimetry (PIV)3 and speckle imaging velocimetry (SIV)4 to a lidar setup for this task. In both methods, two subsequent short camera exposures of particles or speckle arising by particle diffraction or nonuniformity of the index of refraction in air are used to monitor the air flow velocity transverse to the camera axis by the displacements between the two pulses. This enables almost instantaneous measurement in a slice through the air flow and insensitivity to movement in the camera's axial direction.
Currently, PIV and SIV are limited to short-distance measurements by seeding the airflow in wind tunnels with aerosols of definite sizes and concentrations. Here the test volume is defined by a light sheet of a double-pulse laser beam formed by a cylinder lens and a camera facing perpendicular to it. Applying these techniques to an aircraft required choosing a single-axis, monostatic (coaxial) lidar setup. It consists of a forward-looking sensor with a range of several hundreds or thousands of meters and an expanded laser beam for covering the vortices. A telescope receiver lens images the illuminated area on a camera sensor array. The target particles for an airborne sensor are the natural aerosols at ground level and from the engine exhaust. Also included is the speckle produced by refractive-index variations of the air, mainly caused by the hot air of engine exhaust trapped in the vortices and the viscous heat dissipation of the turbulence eddies. Instead of the light sheet in PIV, a gated viewing-in-time domain must be applied to define a fixed measurement volume in a certain distance by adequately synchronizing the pulses of the laser and the exposure time of the camera. A schematic of our proof-of-principle setup is depicted in Figure 2.
A double-pulse second-harmonic Nd:YAG (neodymium-doped yttrium aluminum garnet) laser and a multichannel plate (MCP) image–intensified CCD camera, both developed for the PIV technique, were used. The distance between the scattering atmospheric layer and the transmitter-receiving optical system was 45m, and the thickness of the atmospheric layer adjusted by gated viewing of the camera was 3m. A fan was used to generate artificial wind in the area of the scattering layer. Measurements were performed for three different scattering conditions: during snowfall, under artificial CO2 fog, and in clear air. Particle and speckle images of the scattering layer obtained in 2ms intervals at 3Hz were cross-correlated with two different algorithms written in MATLAB, a standard PIV algorithm based on fast Fourier transform and a phase-based optical flow algorithm. The result is a 2D visualization of the velocity field in the scattering plane. Figures 3 – 5 show snapshots of velocity distributions transverse to the laser beam axis.
To study the feasibility of the concept and to optimize various system parameters, we carried out a computer simulation of the measurement setup. It is known5,6 that high resolution of the receiving telescope generates an exact copy of the coherent image of the laser-illuminated flat object. Thus, for the telescope spatial resolution area of the illuminated atmospheric layer , where ρs = (0.55 Cn2k2L)−3/5 is the spatial coherence radius of a spherical wave in a turbulent atmosphere with atmospheric structure constant Cn2, k is the wave number k = 2π/λ, L is the distance of telescope aperture to the scattering layer (see Figure 2), ae is the radius of the illuminating beam at that layer (radius of a spot), and at is the radius of a telescope objective. The coherent instantaneous image of a spot in the image plane of the camera, in distance l from the telescope aperture, contains turbulent speckles of size. Temporal variations of these speckles due to wind and (or) vortex movement of turbulent inhomogeneities of the refractive index enable assessment of the velocity of wind and (or) visualization of the vortices. For Cn2 in the range 10−14 – 10−15m−2/3, path lengths 1–3km, and visible range of wavelengths, the mean size of the turbulent speckles exceeds a few tens of micrometers, and the turbulent structure of the image can be resolved by the CCD camera.
We use the technique of random phase screens for calculating wave propagation through the turbulent atmosphere.8 The reciprocity theorem allows us to replace backward propagation by a direct one7 for computing the correlation 〈 I(l, ρ, L, t) I(l, ρ, L, t + Δ t)〉 of the intensity in the image plane in consecutive temporally separated recordings by Δt. Modeling different magnitudes of Cn2 and changing the setup parameter showed that for air atmospheric movements and path lengths of a few kilometers, an optimal time delay exists (here Δt= 0.03s) during which the speckles in the images are not randomly destroyed and their displacements indicate the transverse wind velocity (see Figure 6).
Our experimental results and computer simulation show that visualization of large-scale atmospheric 2D velocity fields based on the PIV method is feasible both for particle imaging (snowfall) and for speckle imaging (CO2 fog and clear air conditions) in a backscatter lidar setup. Moreover, the approach could be an interesting alternative to Doppler lidar for airborne monitoring of wake vortices. An objective of further experiments will be to improve the range of the lidar. We will also include a second camera to spatially differentiate speckle contribution from layers at different distances. Finally, we will theoretically optimize the technique.