Fig. 1. Principle and schematic of RPD-CTMR. (a) Schematic of RPD-CTMR. (b) Illustration of phase constraint. ∠BAC=∠B′AC′=∠B′′AC′′. (c) Numerical simulations of CTM measurement via the RPD-CTMR and C-CTMR with α equal to four. The top, middle, and bottom rows are the amplitude and phase distribution of ground truth (GT), and CTMs measured by RPD-CTMR and C-CTMR, respectively. The red pixels correspond to the CTM entries whose value deviates from the true value by more than 10%.

Fig. 2. Numerical simulation for comparison between the RPD-CTMR and C-CTMR. (a), (b) NMSE distribution of 1024 rows of X with α equal to (a) 4 and (b) 12. The NMSEs were calculated with respect to the amplitude, denoted by “||”, and phase, denoted by “∠”. The subscripts R and C correspond to RPD-CTMR and C-CTMR, respectively. (c) Relation between the coefficient α and TM measurement accuracy. The vertical coordinate of data points corresponds to the median of 1024 NMSEs. (d)–(f) Influence of the number of phase masks K (d), phase shift between two consecutive masks ϕ0=ϕk+1−ϕk (e), and the ratio between the areas of phase-shifted region and phase-preserved region in a phase mask (f) on the NMSE.

Fig. 3. Schematic and characterization of the RPD-CTMR system. (a) System setup. HWP, half-wave plate; AS, aperture stop; CAS, customized aperture stop; PBS, polarized beam splitter; BS, non-polarizing beam splitter; OL, objective lens. (b) Comparison between the recorded speckle pattern (denoted as GT) and estimated speckle patterns via RPD-CTMR and C-CTMR at α equal to six. Scale bar: 150 µm. (c) Relative error distributions in the speckle patterns.

Fig. 4. Anti-scattering focusing. (a) Single-spot anti-scattering focusing using XR and XC. Scale bar: 100 µm. (b) Normalized cross-section profiles of focal spots along the white dashed lines in (a). (c) Multi-spot anti-scattering focusing using XR and XC. (d) Normalized cross-section profiles of focal spots along the white dashed lines in (c).

Fig. 5. Anti-scattering image transmission. The first column shows the binary images to be transmitted through the SM. The second column shows the speckle patterns recorded by the camera. The two RPD-CTMR columns show the retrieved (left) and later binarized (right) images restored by XR. The two C-CTMR columns show the retrieved (left) and later binarized (right) images retrieved by XC. The values on the right side of the binary images represent their BERs.