# Imaging Flow Velocimetry with Laser Mie Scattering
## 1 Introduction  
Understanding, designing and optimizing flows is crucial, e.g., for improving fuel injections [1], combustons [2; 3], fuel cells [4], wind turbines [5], turbomachines [6], human air and blood flows in medicine [7; 8], as well as for the fundamental task of modeling flow turbulence [9]. For this purpose, optical measurement methods are essential tools that promise fast and precise field measurements of complex flows. The advances of optoelectronic components and systems, in particular concerning powerful pulsed lasers (up to 1 J/pulse) with up to megahertz repetition rate and high-speed cameras with megapixel image resolution, allow qualitative flow imaging with ultra-high speed, up to 1 MHz [10]. The combination of powerful lasers and high-speed cameras enables the fast imaging of two or three flow dimensions. Note, however, that at the maximum megahertz acquisition rate, the available number of successive laser pulses is limited to about 100 pulses. Besides a qualitative understanding of complex flow phenomena, the flow field needs to be quantified. An essential physical quantity for understanding the flow behavior is the flow velocity, which is the sole measurand that is considered in the subsequent article. In order to optically measure the flow velocity, the flow of interest is illuminated. For this purpose, a laser light source is usually applied, because laser light sources provide a high light power and a narrow linewidth. Both are beneficial for reducing the cross-talk between the optical measurement and the ambient light. The incident light is scattered on the fluid molecules or atoms, and the scattered light is detected and analyzed. As the size of the fluid atoms or molecules in the order of 0.1 nm is significantly smaller than the wavelength of visible light (0.4 \(\upmu\)m-0.8 \(\upmu\)m), the light scattering is so-called Rayleigh scattering. Optical flow velocity measurements based on Rayleigh scattering are described for instance in [11; 12; 13; 14; 15; 16; 17]. An overview article exists from [PERSON], 2001 [18]. The flow velocitymeasurements are based on the optical Doppler effect, which causes a shift in the observed scattered light frequency due to the scattering at the moving fluid particles. The evaluated Doppler frequency is proportional to the flow velocity in the inertial frame of the measurement system. Rayleigh scattering has a comparatively low scattering efficiency, which means that the ratio between the scattered light intensity and the incident is low. For this reason, a temporal averaging in the order of 16 min is required to achieve an acceptable measurement uncertainty of 2% for the flow velocity images of a tube flow with a maximum velocity of 120 m/s [19; 20]. Faster flow velocity measurements are possible for single point measurements. A single point measurement system with 32 kHz [21] was reported, as well as a 10 kHz measurement system with a minimal accuracy of 1.23 m/s [22]. Hence, the fast measurement of flow velocity images with kilohertz rates and a low uncertainty is only achievable by increasing the scattering efficiency of the scattering particles. Increasing the scattering efficiency can be achieved by inserting scattering particles (if not naturally present), which follow the flow with negligible slip and do not disturb the flow. The insertion of particles is called seeding, and the particles are seeding particles. In the Rayleigh scattering regime, the scattering efficiency is proportional to the particle diameter to the power of four. Hence, doubling the particle diameter results in a 16-times higher scattering efficiency. This condition changes in the Mie scattering regime [23; 24; 25], i.e., when the particle size is near the wavelength of the light. As a compromise between a high scattering efficiency and a negligible slip, typical seeding particles have a size between 100 nm and several micrometer [26]. Hence, the use of seeding particles leads to optical flow measurements based on Mie scattering.