help me retouch the following english with academic styleThe second data set is $chi_i2$ where each element represents the difference between the standard deviation of gray values of $B$ at $L^e_i$

The second data set, denoted as $\chi_{i,2}$, comprises elements that quantify the disparity between the standard deviation of gray values of the frame $B$ at $L^{e}{i}$ and the standard deviation of gray values of the input frame at $L^{i}{i}$.