###### Abstract  
Atmospheric turbulence is an inevitable source of wavefront distortion in all fields of long range laser propagation and sensing. However, the distorting effects of turbulence can be corrected using wavefront sensors contained in adaptive optics systems. Such systems also provide deeper insight into surface layer turbulence, which is not well understood. A unique method of profile generation by a dual source Hartmann Turbulence Sensor (HTS) technique is introduced here. Measurements of optical turbulence along a horizontal path were taken to create \(C_{n}^{2}\) profiles. Two helium-neon laser beams were directed over an inhomogeneous horizontal path and captured by the HTS. The measured differential tilt variances imposed on the laser wavefronts were used in conjunction with a set of computed weighting functions to profile the turbulence over the sensing path. The weighting function matrix is inherently ill-conditioned, therefore, Tikhonov regularization was applied to produce accurate \(C_{n}^{2}\) profiles. A distribution of sonic anemometers and a co-located boundary layer scintillator (BLS) collected independent \(C_{n}^{2}\) measurements to add confidence to the HTS profiles. The \(C_{n}^{2}\) profiles generated by this approach agree very well with the auxiliary anemometer and scintillometer measurements. This method of producing turbulence profiles may be useful in future multi-conjugate adaptive optics applications. optical turbulence; atmospheric refraction; Hartmann Turbulence Sensor; Tikhonov regularization; turbulence profiling; adaptive optics; wavefront sensors +
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atmosphere [3]. Although effective, scintillation-based techniques are prone to saturation issues over long distances that are less detrimental to phase-based techniques. Slope detection and ranging, or SLODAR, is a phase-based remote sensing method used to generate vertical \(C_{n}^{2}\) profiles by measuring wavefront Zernike tilts [4]. SLODAR is particularly useful in astronomy to generate turbulence profiles by observing the tilts from a binary star system. Previous work [5] describes a technique similar to SLODAR, but with a distinct methodology, that uses an HTS and two laser sources to profile turbulence over a path. By observing a binary star pair, SLODAR uses the auto-correlation and cross-correlations of incoming wavefront tilts to recover the normalized turbulence profile [4]. Then, by a technique called differential image motion monitoring (DIMM), the full integrated turbulence strength and \(r_{0}\) estimates can be recovered [6]. The technique introduced in Section 2 also uses local wavefront tilts to recover the turbulence profile, but by entirely different methodology. Another similar phase-based technique to turbulence profiling centers around a process called difference in differential tilt variance, first described by [PERSON] et al. [7]. This work used tilt measurements to generate \(C_{n}^{2}\) profiles under varying conditions including time of day, cloud coverage, wind velocity, and an inhomogeneous sensing path (sections of grass and concrete). This method leverages differential angle of arrival measurements between two sources to reduce the common mode noise in the wavefront tilts caused by platform vibrations or angular tracking error. Similar dual-beacon techniques for turbulence profile generation have been introduced by [PERSON] et al. [8] and [PERSON] et al. [9]. A Moore-Penrose pseudo-inversion method is used to generate the profiles from the weighting function and differential tilt variance matrices. This method minimizes the residual, but is sensitive to noise present in the data. The differential tilt variances are calculated by tracking the centroid motion of laser subimages on a sub-aperture array in a technique similar to the method described by [PERSON] et al. [10]. The weighting function matrix used to calculate the profile is ill-conditioned, and thus, Tikhonov regularization has been used to minimize the residual and the solution vectors.