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1 Complex Jones matrix calculated for a birefringent digital phantom with an illumination angle of $\theta = 25^ \circ$  θ  =      25    ∘   and $\phi = 0^ \circ$  ϕ  =      0    ∘  . The synthetic measurements were generated using the V-BPM. In order to visualize the complex values, brightness shows the amplitude, and the color-code shows the phase of each Jones matrix component.
2 Residual maps from polishing the lattice backed mirror. The								locations of each map: (a) 12 o’clock, (b) 3 o’clock,								(c) 6 o’clock, and (d) center. The								peripheral samples (a)–(c) are at the same radial								distance, which is equal to the mounting radial								distance.
3 Preprocessed DLHM holograms after normalizing (a) with $I_0^2({\vec r})$      I    0    2    (                    r        →              ) and (b) with $I_0^3({\vec r})$      I    0    3    (                    r        →              ). Intensity reconstructions for (c) the $I_0^2({\vec r})$      I    0    2    (                    r        →              ) normalization and (d) the $I_0^3({\vec r})$      I    0    3    (                    r        →              ) normalization. A loss in the diffraction efficiency of the resulting DLHM holograms is found.
4 CCD arrangement in numerical simulation.
5 Fluence profiles of the 		  $s\!$		      s		      		    		-polarized beam after passage through (a) one Si plate, (b) two Si plates (beam-displacement compensating arrangement), and (c) three Si plates consisting of two plates in the beam-displacement compensating arrangement and one additional parallel plate.
6 POM images at different focal planes: (a) 11.91, (b) 12.13, (c) 12.34, (d) 12.55, (e) 12.78, and (f) 12.99 mm.
7 TG-SSSI measurements of fundamental and SHG STOVs. (a) Top: Intensity profile 	      ${I_S}({x,\tau})$            I      S        (      x    ,    τ    )	     of fundamental 	      $l = + 1$  l  =  +  1	     STOV; bottom: spatiotemporal phase 	      ${\Delta}{{\Phi}}({x,\tau})$      Δ              Φ        (      x    ,    τ    )	     showing one 	      ${{2}}\pi$            2        π	     winding. (b) Top: SHG output pulse 	      $I_S^{2\omega}({x,\tau})$      I    S          2      ω        (      x    ,    τ    )	     showing two donut holes embedded in pulse; bottom: spatiotemporal phase profile 	      ${\Delta}{{{\Phi}}^{2\omega}}({x,\tau})$      Δ                                Φ                            2        ω              (      x    ,    τ    )	     showing two 	      ${{2}}\pi$            2        π	     windings. Phase traces are blanked in regions of negligible intensity, where phase extraction fails. These images represent 500 shot averages: the extracted phase shift from each spectral interferogram is extracted, then the fringes of each frame (shot) are aligned and averaged, and then the phase map is extracted [23].
8 Illustration on overlapping region selection. (a) One of the adjacent images. The red arrow indicates the direction for searching overlapping region. (b) The other of the adjacent images. (c-d) The adjacent images after overlapping region selection. Here the green dash box represents the pre-determined region used for searching the overlapping region, the green solid box represents the overlapping region, and the yellow dashed box represents the sliding candidate region.
9 Results of optimization constraints. (a) The result of 		  ${f_{1{\rm st}}}$		      						  f			  			    1			    			      s			      t			    			  					      		    		 with a value of 1.15 nm. (b) The result of 		  ${\gamma _g}$		      						  γ			  g					      		    		 with a value of 1.56 nm.
10 (a) Channel structure of the full Stokes parameters in the							Fourier domain. Fourier transformation of inputs for various							bandwidth scenarios: (b) low spatial, high temporal;							(c) medium spatial, medium temporal; (d) high spatial, low							temporal.
11 Velocity and flow direction maps estimated by tracking flowing microdroplets in consecutive frames with DOLI. (a) Reconstructed velocity maps with color-encoded velocity in the range of 0–12 mm/s. (b) Reconstructed direction map with color-encoded angle indicated by the color-wheel.
12 Amplitude and phase of the transmission matrix components connecting the different incident modes to a single output mode (amplitude maps are average of ${n} = 10$  0.17            l      ∗       experiments). (a) For diffusive media, the amplitude of each transmission matrix element is nearly uniform regardless of the illumination NA. (b), (c) For thin anisotropic scattering media, transmission matrix elements show higher amplitude bias for lower spatial frequency input modes. (d) As the thickness is increased, the amplitude distribution of each transmission matrix component becomes more similar with the diffusive medium and evenly distributed showing that more input modes have similar contribution to the corrected focus. The corrected phase maps shown in the insets for all samples are random showing that multiple scattering is induced for all samples considered.