Real time characterization of atmospheric turbulence using speckle texture

Abstract A new method is proposed for the characterization of the atmospheric turbulence strength parameter ( <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ) based on the principal component analysis (PCA) of the texture of the speckle intensity pattern obtained on long-range propagation of a focused charge +1 vortex beam. Employing the split-step propagation method, datasets containing instantaneous intensity images of the focused vortex beam are generated for three distinct <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values, specifically <?CDATA $1\times10^{-14}\,\textrm{m}^{-2/3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> , <?CDATA $5\times10^{-14}\,\textrm{m}^{-2/3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>5</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> , and <?CDATA $1\times10^{-13}\,\textrm{m}^{-2/3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mtext>m</mml:mtext> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> , representing medium to high turbulence levels for a 2 km propagation distance. The gray level co-occurrence matrix (GLCM) methodology is employed to extract key texture attributes, like contrast, correlation, homogeneity, and energy from the intensity images. These extracted texture parameters serve as inputs for training a PCA model, enabling the identification of associated <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values. The PCA analysis exhibits distinct clustering of the first three principal components for each of the three <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values, forming individual clusters on the PCA plot. Standard deviational ellipses are drawn to clearly demarcate these clusters on the PCA plot. The texture-based PCA classification of atmospheric turbulence was also performed for a focused Gaussian beam. The comparison of PCA plots between vortex and Gaussian beams showed that a pronounced clear separation of <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values is obtained for the vortex beam. This indicates that the non-zero orbital angular momentum of the vortex beam also plays an important role in achieving the distinct separation of <?CDATA $C_n^2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values on the PCA plot. The proposed method can provide efficient real-time turbulence estimation solely on the basis of texture of the instantaneous intensity speckle with prior training and therefore may simplify the estimation of turbulence strength parameter.