Fig. 1.

The effect of scattering and sample-induced aberrations in the reflectance imaging. a Description of sample-induced aberrations in the illumination and imaging paths. The phase of the unscattered component of an incident wave with transverse wavevector ${\overrightarrow{\mathbf{k}}}^{\mathrm{i}}$ is retarded by ${\varphi }_{\mathrm{i}}\left({\overrightarrow{\mathbf{k}}}^{\mathrm{i}}\right)$, and that of the reflected wave from the target object is retarded by ${\varphi }_{\mathrm{o}}\left({\overrightarrow{\mathbf{k}}}^{\mathrm{o}}\right)$. ${\mathcal{E}}_{\mathrm{o}}^{\mathrm{S}}\left({\overrightarrow{\mathbf{k}}}^{\mathrm{o}}\right)$ and ${\mathcal{E}}_{\mathrm{o}}^{\mathrm{M}}\left({\overrightarrow{\mathbf{k}}}^{\mathrm{o}}\right)$ stand for single- and multiple-scattered waves. O(x,y): amplitude reflectance of a target object. b Layout of the phantom sample. An asymmetric aberrating layer made of a clean PDMS block with a cylindrical groove was placed on the top of a 7l _s-thick scattering layer. A resolution target was placed underneath the scattering layer. The gray scale image is the topography of the target measured by atomic force microscopy. Scale bar, 4 μm. Color map, height in nanometers. c Incoherent image of the target without the scattering and aberrating layers. The image was recorded in the reflection geometry, and light emitting diode (λ = 780nm) was used as a light source. Scale bar, 4 µm. d, e Same as (c), but with an aberrating layer and with both the scattering and aberrating layers, respectively. Color bars in (c–e), intensity in arbitrary unit