# Measurement of turbulence profile from single-star scintillations: how it works?

Intensity of light falling into each of the ring apertures A, B, C, and D (see below) is measured by photon counters. Scintillation index in each aperture is computed as the variance (dispersion) of intensity normalized by the average intensity squared (or, equivalently, variance of the natural logarithm). In this way the scintillation index does not depend on the brightness of the star and reflects only the strength of atmospheric scintillation. Contribution of photon noise is carefully subtracted in the calculation.

Similarly, differential scintillation index for a pair of apertures (e.g. A and B) is defined as the variance of the ratio of intensities in A and B normalized by the square of the average intensity ratio A/B (or, equivalently, the variance of the natural logarithm of the intensity ratio).

Both normal and differential scintillation indices produced by a given turbulent layer are computed as product of the turbulence intensity in this layer (integral of Cn2 measured in m^1/3) by some weighting function which depends on the distance to the layer as well as on the shape and size of the apertures.

 The weighting functions for normal (bottom left) and differential (bottom right) scintillation indices (in monochromatic light) for the case of four MASS ring apertures. By measuring normal and differential scintillation indices, we sense turbulent layers at different altitudes with different weights. Intensities of individual layers can then be retrieved by solving the "inverse problem". Practically, it is possible to obtain about 6 independent points on the vertical turbulence profile. As can be noted in the Figure, all weighting functions go to zero at telescope pupil. To sense the turbulent layers near the ground, the 2 smallest MASS apertures can be conjugated to a negative altitude of -0.5 or -1 km This permits full measurement of the profile and seeing, and also the measurement of the atmospheric time constant (by analyzing the temporal behavior of scintillations).