Table 1.

Statistics of diffraction-enhanced imaging (DEI) attenuation and refraction images under symmetric-acquisition (SA) condition.

Image	Mean	Variance	Signal-to-noise ratio
Attenuation ${\widehat{I}}_r$	$I_r(\text{unbiased})$	$\mathrm{var}({\widehat{I}}_r)=\frac{I_r}{2R({\theta }_L)}$	$\sqrt{2I_{r}R({\theta }_L)}$
Refraction $\mathrm{\Delta }\widehat{\theta }$	$\mathrm{\Delta }\theta (\text{unbiased})$	$\frac{1}{2I_r}[\frac{R({\theta }_L)}{{[\frac{\mathrm{d}R}{\mathrm{d}\theta }({\theta }_L)]}^2}-\frac{{(\mathrm{\Delta }\theta )}^2}{R({\theta }_L)}]$	$\frac{|\mathrm{\Delta }\theta |\frac{\mathrm{d}R}{\mathrm{d}\theta }({\theta }_L)\sqrt{[2I_{r}R({\theta }_L)]}}{\sqrt{\{R^2({\theta }_L)-\mathrm{\Delta }{\theta }^2{[\frac{\mathrm{d}R}{\mathrm{d}\theta }({\theta }_L)]}^2\}}}$