Algorithm 1 Frequency-Filtered Angular Measurement Algorithm

Input:  Reference image ${\mathbf{I}}_{\mathbf{ref}}$, displaced image ${\mathbf{I}}_{\mathbf{disp}}$, Talbot distance ${\mathbf{D}}_{\mathbf{Talbot}}$, number of pixels N. Output:  Angular offset in the x-direction ${\theta }_x$; Angular offset in the y-direction ${\theta }_y$. 1:Acquire the reference image ${\mathbf{I}}_{\mathbf{ref}}$ and the displaced image ${\mathbf{I}}_{\mathbf{disp}}$. 2:Compute the horizontal and vertical sums of ${\mathbf{I}}_{\mathbf{ref}}$ to obtain ${\mathbf{S}}_{\mathbf{row},\mathbf{ref}}$ and ${\mathbf{S}}_{\mathbf{col},\mathbf{ref}}$, respectively. Similarly, compute the horizontal and vertical sums of ${\mathbf{I}}_{\mathbf{disp}}$ to obtain ${\mathbf{S}}_{\mathbf{row},\mathbf{disp}}$ and ${\mathbf{S}}_{\mathbf{col},\mathbf{disp}}$. 3:Perform Fourier transform on ${\mathbf{S}}_{\mathbf{row},\mathbf{ref}}$, ${\mathbf{S}}_{\mathbf{col},\mathbf{ref}}$, ${\mathbf{S}}_{\mathbf{row},\mathbf{disp}}$, and ${\mathbf{S}}_{\mathbf{col},\mathbf{disp}}$ to obtain their respective frequency domain representations ${\mathbf{FT}}_{\mathbf{row},\mathbf{ref}}$, ${\mathbf{FT}}_{\mathbf{col},\mathbf{ref}}$, ${\mathbf{FT}}_{\mathbf{row},\mathbf{disp}}$, and ${\mathbf{FT}}_{\mathbf{col},\mathbf{disp}}$. 4:Calculate the frequency domain phase information by computing ${\varphi }_x=\mathrm{angle}({\mathbf{FT}}_{\mathbf{row},\mathbf{disp}}/{\mathbf{FT}}_{\mathbf{row},\mathbf{ref}})$ for the horizontal direction and ${\varphi }_y=\mathrm{angle}({\mathbf{FT}}_{\mathbf{col},\mathbf{disp}}/{\mathbf{FT}}_{\mathbf{col},\mathbf{ref}})$ for the vertical direction. 5:Compute the frequency domain phase slopes $k_x={\varphi }_x·{\mathbf{FT}}_{\mathbf{row},\mathbf{ref}}$ in the x-direction and $k_y={\varphi }_y·{\mathbf{FT}}_{\mathbf{col},\mathbf{ref}}$ in the y-direction. 6: Calculate the angular offsets ${\theta }_x$ and ${\theta }_y$ in the x-direction and y-direction, respectively, using the following formulas: $${\theta }_x={tan}^{-1}\left({\displaystyle \frac{k_x·N}{2\pi D_{Talbot}}}\right),{\theta }_y={tan}^{-1}\left({\displaystyle \frac{k_y·N}{2\pi D_{Talbot}}}\right)$$