$$\begin{array}{cc}\hfill & \text{for}\mathrm{i}=1:\text{imNum}\hfill \\ \hfill & \text{Hs}=\text{exp}(\text{-}1\mathrm{j}\ast 2\ast \text{pi}.\ast (\text{FX0}.\ast \text{locX}(\mathrm{i})∕\text{imSize0}+\text{FY0}.\ast \text{locY}(\mathrm{i})∕\text{imSize}0));\%\text{generate the phase factor}\hfill \\ \hfill & \text{imRefRefineSum}=\text{imRefRefineSum}+\text{ifft2}(\text{fft2}(\text{imRawCrop}(:,:,\mathrm{i}).\ast \text{Hs});\%\text{sup-pixel level shift}\hfill \\ \hfill & \text{end}\hfill \\ \hfill & \text{imRefRefine}=\text{imRefRefineSum}∕\text{imNum};\%\text{imRefRefine: the refined reference image}\hfill \end{array}$$