WIND PROFILING BY PASSIVE OPTICAL METHOD

There are several optical approaches to the remote measurements of crosswind speed [1-6]. An evident advantage of passive techniques is that they do not need in proper radiation sources. This allows measurement instruments to be simplified and their cost to be reduced, as well as the domain of applicability of contactless wind speed meters to be expanded to the situations where it is impossible to mount a radiation transmitter/receiver at one of the ends of an atmospheric path under study, e.g., in problems of line-of-sight correction.


INTRODUCTION
There are several optical approaches to the remote measurements of crosswind speed [1][2][3][4][5][6]. An evident advantage of passive techniques is that they do not need in proper radiation sources. This allows measurement instruments to be simplified and their cost to be reduced, as well as the domain of applicability of contactless wind speed meters to be expanded to the situations where it is impossible to mount a radiation transmitter/receiver at one of the ends of an atmospheric path under study, e.g., in problems of line-of-sight correction.
We suggest an approach which is based on the analysis of the dynamics of anisoplanar (inhomogeneous) turbulent distortions in object images formed by wide-field cameras [7][8][9][10]. In this case, the shift of distortions in an object image, which characterizes the speed of displacement of turbulent inhomogeneities, can be determined from the analysis of two neighbor frames of a video sequence of images. The advantages of this approach are a high speed due to the lack of a need in accumulation of a series of observations to construct temporal correlation functions and a capability of determining the instantaneous wind speed.
Two key problems are to be solved for the development of the method for wind profiling: first, it is necessary to derive a relationship between turbulent inhomogeneities and image distortions caused by them, and, second, it is required to identify (visualize) turbulent distortions in images of distant objects.

INFLUENCE OF LOCATION OF TURBULENT INHOMOGENEITIES ON THE CHARACTER OF DISTORTIONS CAUSED BY THEM
To determine the relation between the character of distortions in the image of an object and the location of atmospheric inhomogeneities in the region between the object and an observer, the process of imaging in the presence of some bounded region (thin layer) of turbulent inhomogeneities along the observation path was numerically simulated. To suppress the effect of the structure of complex objects, we choose a test object with the rough (Lambertian) surface and periodic variations in the reflection coefficient like Figure 1 shows the scheme of formation of the incoherent image of an object in the presence of a thin layer of turbulent inhomogeneities (one phase screen) located at a different distance from the observer zts. In this case, the displacement of the phase screen along the optical axis allows us to separate the effect of air inhomogeneities located at different distances from the receiving system along the observation path. The numerical simulation results allowed us to ascertain that the characteristic size of anisoplanar distortions produced by the layer of a turbulent medium (phase screen) located at the distance zts from the observer inversely relates to the distance: where A is the dimensional parameter and is a function of the atmospheric conditions and receiving system.

TURBULENT INHOMOGENEITIES VISUALISATION
During the processing of images analyzed, the information about the object structure is to be filtered, i.e., the so-called quality map of an image should be constructed, which includes only data on atmospheric distortions. Based on the sharpness functional, the image quality map can be defined in the form: is the image sharpness functional; ak is the smoothing coefficient; K(r, ak) is the certain smoothing function defined as Gaussian:

WIND PROFILING METHOD
To profile the wind speed in an arbitrary section of the atmosphere, the observation path between the object and receiving optical system is divided into N segments; the contribution of every segment is considered similar to the contribution of an infinitely thin screen. The algorithm for wind speed profiling at the object observation path is the following: -the number N of layers of turbulent inhomogeneities, for which the drift velocity is to be calculated, is determined; -the smoothing parameters is calculated to filter the small-scale distortions introduced by turbulent inhomogeneities located farther than the second layer; -the drift velocity of the second layer V2 is calculated; -the difference (2) (1) ' r r r is calculated; -the last steps are repeated until VN is calculated.
This algorithm allows serial filtration of distortions introduces by each layer of turbulent inhomogeneities (phase screen), beginning from the layer the closest to the observer toward the object. It should be noted that there are inhomogeneities on different scales in each turbulent layer. It is evident that imaging through a real atmosphere can be subjected to distortions on a certain scale induced by air inhomogeneities located at different distances from the observer. In this case, when using the method suggested, distortions introduced by different turbulent layers are filtered only partially.
For more rigorous filtration of the distortions of near turbulent layers, an additional parameter can be used, i.e., the angular size of the image region to be analyzed. We suggest reducing this region to sizes of about the characteristic size of the distortions which are to be filtered. This reduction also allows the spatial averaging of the measured drift velocity of distortions over the whole area of the object observed and, thus, a decrease in the random error of wind speed calculated along the observation path.

COMPARISON OF THE RESULTS OF PROCESSING OF VIDEO SEQUENCE WITH CONTACT MEASUREMENTS OF WIND VELOCITY
The efficiency of the method suggested was estimated during processing of a video image of a real object. Shooting was conducted with a frequency of 100 Hz. The accuracy of wind speed retrieval by a passive optical method is determined from the comparison with measurements of ten acoustic anemometers, equispaced along a 500-m atmospheric path. Figure 3 shows the object image and its sharpness functional. The upper part of the image (a fragment of deciduous forest) was used during the processing.
The wind velocity strongly changed along the observation path during imaging. Therefore, to weakens the effect of the random measurement error, the path was divided into three segments, within which the wind velocity value averaged over three (or four) anemometers was found. a b c d Fig. 3. Object image (a), its sharpness functional (b) and quality maps (c-d). The horizontal size of the region observed is 5 m; at=5 cm, the distance zobj =500 m, and Δt = 10 ms. Figure 4 shows that the wind speed retrieved in the nearby layers of turbulent inhomogeneities is in a good agreement with the wind speed contact measurements averaged over three acoustic anemometers.

CONCLUSIONS
The comparison of the results of the algorithm developed by us showed a good agreement with contact measurements. The wind velocity is retrieved with the minimal error near the receiving optical system. Retrieval of wind speed in the atmospheric region near the object is problematic due to the small scale of the distortions introduced by it. To increase the range of crosswind determination by the method suggested, it is necessary to increase the camera resolution.