# Imaging Flow Velocimetry with Laser Mie Scattering
## 3 Developed Measurement Techniques and Their Imaging Evolution  
### Fundamentals for the Evaluation of the Measurement Techniques  
The quantity of interest is the fluid velocity (or flow velocity):  
\[\vec{v}(\vec{x},t), \tag{3}\]  
which is in general a time-dependent vector field in the three-dimensional space with \(\vec{x}\) as the space vector and \(t\) as the time variable. Hence, the flow measurements can be characterized and evaluated based on the following properties:  
* The flow velocity is a vector quantity. Therefore, the number of measured velocity components is an important property. The abbreviated form 1c, 2c or 3c means that one, two or three components are measured, respectively.
* In order to characterize the spatial behavior of the flow velocity, the number of resolved space dimensions is an important property. Measurements are for instance pointwise, along a line, planar or volumetric, which is indicated by the abbreviated forms 0d, 1d, 2d or 3d, respectively. Characterizing the measurement along each space dimension is possible with the following parameters (cf. Figure 5a):  
Figure 4: Categorization of flow velocity measurement approaches based on Mie scattering.  
spatial resolution, * spatial distance between the adjacent measurements, * number of measurements along the respective space dimension or size of the measurement volume in the respective space dimension.
* In addition, the temporal behavior of the measured flow velocity is characterized with the parameters
* temporal resolution,
* temporal distance between the sequent measurements or measurement rate,
* number of measurements along the time dimension or measurement duration. The term measurement rate requires temporally-equidistant measurements. Otherwise, a mean measurement rate can be specified. The introduced terms are explained in Figure 5b. Note that the temporal resolution does not necessarily equal (or is smaller than) the reciprocal value of the measurement rate. Both quantities are independent.
* Each velocity value over space and time can finally be characterized with a measurement uncertainty by applying the international guide to the expression of uncertainty in measurements (GUM) [38; 39]. According to the GUM, the measurement uncertainty is a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand.
* Due to possible cross-sensitivities (for instance with respect to the temperature, vibrations or electromagnetic fields) or other impairments of the measurements (for instance limited optical access), it is important if the measurements concern non-reactive or reactive flows (flames), if the measurements are performed in a laboratory or in an industrial environment, if the measurement object is a simplified model or the real measurement object. For this reason, the surrounding and boundary conditions have to be described.  
In the following subsection, the development of each measurement approach from Section 2 to an imaging flow velocimetry system is summarized. Note that the summary is not meant to be exhaustive, but to give an overview of the state-of-the-art of current flow measurement systems. Since it is focused on the development of the respective measurement systems for achieving at least 2d1c measurements with high speeds, application examples, as well as the discussion of the measurement uncertainty are outsourced to Section 5.  
Figure 5: Illustration of the terms (**a**) spatial resolution, spatial distance of the measurements and size of the measurement volume along one space dimension and (**b**) temporal resolution, measurement rate and measurement duration.