Fig. 1. (a) Setup used to observe the SHEL of pseudothermal light via weak measurement. The diffuser is kept still when taking the inset picture. The incident angle is set to be 48.3°. (b) The setup to test the effect of overlapping density. A cylindrical lens is added to vary the overlapping density of the speckles. When the cylindrical lens is set horizontal (vertical), the overlapping density is relatively large (small), thus the dark strip of pseudothermal light is expected to be narrow (broad). The results captured by CCD are given in Fig. 2. The polarizer is deviated by 0.3° from being crossed with the incident beam’s polarization, which decides the amplification factor of the weak measurement.

Fig. 2. SHEL of pseudothermal light in different cases. The first row shows the SHEL observed using a normal lens to focus the pseudothermal light, the second is using a vertical cylindrical lens, while the third is using a horizontal cylindrical lens. The autocorrelations are listed in the second column. It can be seen that pairs of peaks emerge in each picture, but the positions are the same. This can be interpreted as the SHEL of the PCB being a superposition of the coherent speckles’ SHELs. Autocorrelation reveals the SHEL of unit speckles. The outermost pair of peaks can be seen as higher-order autocorrelation peaks. (The frosted glass is rotating with an angular velocity of 0.027 rad/s in this experiment. Autocorrelations are obtained by averaging 20,000 results. Each picture’s exposure time is 10 ms. The gain is set to be 500. The size of the CCD pixel used is 6.45 μm by 6.45 μm.)

Fig. 3. SHEL of PCBs at different incident angles. It is confirmed that the SHEL of coherent light decreases if the incident angle is approaching the Brewster angle (56.55° for a BK7 prism)^[29]. This experiment proves that PCBs follow the same trend.

Fig. 4. Rotation of the strip of PCBs at different polarizations agrees with the rotation of coherent beams. We can determine that our theory applies to both the Imbert–Fedorov (IF) shift and the GH shift.

Fig. 5. Sketch of the intensity and polarization distribution of coherent individual speckles with an SHEL. The right/left circular polarization part of the incident beam is shifted due to the IF effect. The separation of two polarization components is on the order of a wavelength. Because the intensity follows a Gaussian-like distribution, the overall polarization is illustrated with the black arrows. The pseudothermal beam, as a whole, also follows this distribution.