Single-star optical turbulence profiling techniques for the SHIMM and other Shack-Hartmann instruments

Abstract

Atmospheric optical turbulence (OT) monitoring is crucial for site characterisation at astronomical observatories and optical communications ground stations. The Shack-Hartmann Image Motion Monitor (SHIMM) instrument implements a fast, infrared Shack-Hartmann sensor to measure a low-resolution OT profile continuously throughout the day and night. This work presents advances made in Shack-Hartman optical turbulence profiling techniques implemented on the SHIMM, including the derivation and validation of Z-tilt weighting functions, implementation of methods for correcting for non-zero exposure times, and for estimating the coherence time of optical turbulence using the profile coupled with the Fast Defocus method. These techniques were tested via end-to-end Monte Carlo simulations of the SHIMM instrument. All measurements of integrated OT parameters were found to be in strong agreement with the simulation inputs evidenced by correlation coefficients close to one, small RMS error and bias. The accuracy of a four-layer model was also investigated, which showed high correlation with simulation inputs for all layers even in daytime OT conditions. This study suggests a Cn^2 sensitivity limit in the region of 2x10^-15 m^(1/3) and displays evidence of a cross-talk effect between the strong ground layer and first atmospheric layer.

Figures (10)

• Figure 1: Theoretical response functions for the using a four layer model. The graph contrasts the response functions calculated using the original profiling method laid out in Griffiths2023 (top) with the method detailed in this work (bottom) which combines the slopes and intensities in the inversion.
• Figure 2: Left: A comparison of a cut-through of the $x$-slope weighting functions calculated through the G-tilt (red), Z-tilt (black) and original SHIMM/SLODAR methods (blue). Right: residuals of the comparison plot, for G-tilt and SHIMM/SLODAR weighting functions subtracted from the Z-tilt.
• Figure 3: Weighting functions used by the profiling technique. The top row shows the weighting functions for a layer at 1 km in covariance matrix format for the (from left to right) x-slopes, y-slopes and intensity fluctuations. The middle row shows the same weighting functions in the auto-covariance format. The bottom row shows a cut through of the centre of the auto-covariance maps in the $\delta j$ direction. These cut-throughs have been plotted for four layers at 0, 4 12 and 20 km.
• Figure 4: Condition number of the weighting function matrix $\mathbf{W}$ plotted against number of layers in the model. Results are presented for several layer placement regimes for heights between 0 km and 20 km. The nominal and configurations are indicated by the red and blue crosses respectively.
• Figure 5: Effect of changing exposure time on three terms in the $x$ slopes autocovariance matrix. The theoretical prediction derived from Eq. (\ref{['eq:wind filter']}) is plotted in red, and simulation results for a single moving layer with wind speed 10 m/s at the ground are plotted with uncertainties in black. The moving layer simulations extend the phase screen by adding rows, simulating wind speed aligned in the $y$ direction.