Fig. 1. Schematic of frequency domain weak measurement system^[35]. Polarized light is split by a polarization beam splitter (PBS) into two arms of the interferometer. Polarization states of the two arms are |H> and |V>, respectively. Propagation time between different arms is different, and the light of the two arms on the latter polarizing beam splitter is combined, and it passes through the latter polarizer at the same time for post-selection

Fig. 2. Variation of center wavelength shift with phase difference in weak frequency domain measurement^[35]

Fig. 3. Experimental setup diagram for realizing weak value enlargement by interferometer^[17]. Beam with a wavelength of 780 nm is collimated by the objective lens. Beam enters the Sagnac interferometer composed of three mirrors and a 50∶50 beam splitter arranged in a square after passing through the polarizer. Output port consists of a quadrant detector and a CCD surveillance camera. SBC and half-wave plate in the interferometer allow adjustment of the output intensity of the interferometer. Piezoelectric mirror achieves minimal deviation of the beam

Fig. 4. Experimental setup diagram for near-balanced weak measurement of extremely small angular velocity^[36]. Interferometer is composed of a beam splitter (BS) and two mirrors (M1 and M2). Beams propagating in opposite directions at the angular velocity of 156×10^-9 rad/s of M1 are spatially separated, which introduces a phase shift caused by the tilt of the rotating mirror. Both ports measure the interference signal of the combined beams of the two paths. Experiment can use weak value amplification (WVA) or almost-balanced weak values (ABWV) to measure the deflection angular velocity simultaneously

Fig. 5. Spin Hall effect^[8]. Light is refracted when it enters the glass, where |+> and |-> spin components have opposite transverse displacements in y direction. Magnitude of the displacement is related to the angle of incidence and the refractive index of the glass

Fig. 6. Schematic of weak measurement phase demodulation system^[49]. Illustration in the upper left corner: schematic of total reflection. In figure: 1, collimating lens; 2, Gaussian filter; 3, polarizer, front selection state; 4, prism; 5 and 6, quarter wave plates; 7, polarizer, post-selection state; 8, coupling lens

Fig. 7. Detection experiment of different concentration gradients sodium chloride solution via total internal reflection sensor system based on weak measurement (left) and refractive index fitting line (right)^[51]

Fig. 8. Sensor system schematic^[54]. SLD: light source; GF: Gaussian filter; P1 and P2: polarizers; SC: sample cell; QWP: quarter wave plate

Fig. 9. Use weak measurement method to measure the concentration response curve of L-Alanine and D-Alanine, L-Tryptophan and D-Tryptophan, and L-Proline and D-Proline^[52]

Fig. 10. Weak measurement system based on Mach-Zehnder interferometer (upper)^[28] and Michelson interferometer (below) ^[55]. SLD: light source; GF: Gaussian filter; PBS: polarization beam splitter; H: horizontally polarized light; V: vertically polarized light; WM: weak measurement; QWP: quarter wave plate

Fig. 11. Structural design of MIP sensor based on weak measurement (left) and specific screening process of serum proteins (right)^[56]

Fig. 12. Schematic of detection of cancer marker molecules by a total internal reflection sensor system based on weak measurement (left) and real-time shift of system’s spectral center wavelength during the detection process (right)^[50]

Fig. 13. Real-time detection of the process of DNA melting and re-stranding by linear rotation optical weak measurement system^[60]