Fig. 2: Aberration correction by the time-resolved reflection matrix.

a Sample geometry; a custom-made Siemens star target was placed under a 600-µm-thick, rough-surfaced plastic layer exhibiting strong aberrations. b Set of E-field images of reflected waves E_lab(r_o; r_i) in the laboratory coordinates r_o = (x_o, y_o). Four representative amplitude images are shown. The white “ × ” marks indicate illumination points r_i. The FOD defined by the image size was set to 40 × 40 µm². Scale bar, 10 µm. c Time-resolved reflection matrix R(r_o; r_i) in the position space constructed from the set of E-field images in b. Each image was converted to a column vector and assigned to its corresponding column in R. d OCM intensity image constructed from the main diagonal of R in c before aberration correction. Scale bar, 10 µm. e Reflection matrix \({\tilde{\boldsymbol{R}}}\) in spatial frequency space. f Aberration-corrected reflection matrix R_c converted from \({\tilde{\boldsymbol{R}}}\) after application of CLASS algorithm. g, h Phase maps ϕ_i(k_i) and ϕ_o(k_o) for aberrations in illumination and detection pupils retrieved by the CLASS algorithm, respectively. The radii of the maps correspond to a numerical aperture of 1.0. The number of modes N_c used for aberration correction in the pupil was about 6200. i Aberration-corrected CLASS intensity image obtained from the main diagonal of R_c in f. j Schematic of hardware wavefront correction. Conjugate of the illumination pupil phase map in g displayed on the SLM in Fig. 1a to physically compensate for the aberrations. k OCM intensity image after hardware correction (HC) of aberrations. l Intensity image of reflected PSF measured at the camera after physical aberration correction by SLM (HC PSF). Scale bar, 10 µm. m Line profiles of the PSFs obtained without wavefront correction (black), after computational wavefront correction by the CLASS algorithm (blue), and after hardware wavefront correction by SLM (red).