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About Rainbow Refractometry
Nonintrusive laser-optical measurement techniques are suitable for the investigation of droplet characteristics. For example rainbow refractometry (RBR) was presented as an approach to determine even small variations of the refractive index. The homogeneous concentration as well as time-varying gradients of concentration inside a droplet can be resolved. Also droplet size and sphericity can be determined by a sphericity check based on RBR (for some references look here ).
In the Geometrical Optics model (GO) the first order monochromatic rainbow arises from 2nd order refracted rays.
Since the first rainbow is created by internal reflected rays which cross the droplet twice, the position of the rainbow angle j is very sensitive to the droplet 's relative refractive index . Therefore j supplies information about the concentration of a soluted substance in the droplet. The rainbow angle j also alters with the droplet size and form. j decreases by varying the shape of the droplet from oblate to prolate.
Pursuant to GO, j is only a function of the relative refractive index and is independent of the droplet diameter. If the wave character of light is considered another phenomenon takes effect: The interference of 2nd order refracted rays, that emerge out of the droplet under the same angular directon but have different impact points on the droplet surface. Furthermore, interference of internal refracted and external reflected rays gives rise to a high-frequency modulation of the rainbow signal. The fringe pattern resulting finally consists of a pronounced main maximum and several sub-maxima, found in literature as ''Supernumerary Bows'', and the superimposed high-frequency modulation called ripple structure as it is shown in this Figur.
For spherical droplets these fringes appear on concentric cones around the laser beam with the droplet as apex. However, for a spheroidal droplet the curvature of these fringes changes with increasing ratio of horizontal to vertical diameter
Interference can not be explained by GO but the Airy theory, which takes the wave character of light into account, considers the rainbow as an interference phenomenon. According to the Airy theory a cubic wave front is assumed, to calculate the far-field intensity in the Fraunhofer diffraction region. This leads to the ''rainbow integral'', that describes the intensity of light in the rainbow region scattered by a spherical droplet . Compared to the rainbow angle calculated by GO, the first maximum of the rainbow pattern according to the Airy theory is shifted by an angular interval Dj, that depends on the wavelength l of the incident light and the droplet diameter d.
If the assumption of sphericity is fulfilled, both, the rainbow angle and the angular frequency of the rainbow signal (i.e. the calculated droplet diameter) detected by two receivers taking the rainbow intensity pattern at different locations will be identical. According to the experimental setup the first rainbow receiver (CCD1) is positioned in the horizontal plane. The location of the second receiver (CCD2) is characterized by an out-of-plane-angle Y and an additional angle d, which takes the curvature of the rainbow into account. If the droplet becomes nonspherical j and angular frequency will take different values for the two receivers. This behaviour can be used for a sphericity check based on RBR
Here are some information about the experimental setup used in my study and some exaples of my results.