Determination of the profile of atmospheric optical turbulence strength from SLODAR data

Abstract

Slope Detection and Ranging (SLODAR) is a technique for the measurement of the vertical profile of atmospheric optical turbulence strength. Its main applications are astronomical site characterization and real‐time optimization of imaging with adaptive optical correction. The turbulence profile is recovered from the cross‐covariance of the slope of the optical phase aberration for a double star source, measured at the telescope with a wavefront sensor (WFS). Here, we determine the theoretical response of a SLODAR system based on a Shack–Hartmann WFS to a thin turbulent layer at a given altitude, and also as a function of the spatial power spectral index of the optical phase aberrations. Recovery of the turbulence profile via fitting of these theoretical response functions is explored. The limiting resolution in altitude of the instrument and the statistical uncertainty of the measured profiles are discussed. We examine the measurement of the total integrated turbulence strength (the seeing) from the WFS data and, by subtraction, the fractional contribution from all turbulence above the maximum altitude for direct sensing of the instrument. We take into account the effects of noise in the measurement of wavefront slopes from centroids and the form of the spatial structure function of the atmospheric optical aberrations.

Characterisation of the Optical Turbulence at Siding Spring

“…Various methods are used for turbulence profiling, including direct sensing with microthermal sensors on towers (Pant, Stalin, & Sagar 1999) or balloons (Azouit & Vernin 2005), remote sensing with acoustic scattering (sonic detection and ranging (SODAR); Travouillon 2006), or triangulation of scintillation (SCIDAR; Vernin & Roddier 1973;Fuchs, Tallon, & Vernin 1994) or of image motion (SLODAR; Wilson 2002;Butterley et al 2006;Goodwin, Jenkins, & Lambert 2007). These techniques have reached a degree of maturity, exhibiting reasonable agreement when used together in campaigns (Tokovinin & Travouillon 2006;Cerro Tololo campaign, Sarazin et al 2005).…”

“…The parameter β avg is representative of the entire atmospheric turbulence or averaged contribution of all layer heights. The β avg was determined by the best fit of the = 0 theoretical covariance impulse response function for β ranging from 19/6 to 23/6 to the observed auto-covariance function, see Butterley et al (2006). The implications of nonKolmogorov turbulence (β ࣔ 11/3) in the measurement of atmospheric turbulence and astronomical imaging are discussed by Stribling et al (1995) and Goodwin (2009).…”

“…insensitive to the outer scale (Von Karman power spectrum) as noted by Butterley et al (2006). A fit of the outer scale would typically need an outer scale smaller than the telescope (1 m), which is not typical of other measurements at other observatories (20-40 m).…”

“…The analysis of the non-Kolmogorov model is appropriate given that the value of the power-law index, β, can be determined by the function-fitting SLODAR (slope detection and ranging) method (Butterley, Wilson, & Sarazin 2006).…”

Online estimation of the wavefront outer scale profile from adaptive optics telemetry

“…In the following section, we present a method based on the SLO-DAR technique (Butterley, Wilson & Sarazin 2006) to estimate the 'overall' L 0 from on-axis AO telemetry data. First, the goal is to highlight the limitations of SLOpe Detection And Ranging (SLODAR) when used for this purpose and, secondly, to motivate the need of a L 0 (h) profiler using multiple wavefront sensors (WFSs) available in WFAO configurations.…”