## 4 Experiment Results and Discussion  
The experiment setup is shown in Figure 5, in which the coherent plane-wave beam is generated by a He-Ne laser (\(\lambda\) = 632.8 nm), and an opaque scattering layer S is placed between the object and the Fourier lens L, the exposure level is controlled by adjusting exposure time of the camera. Figure 4: The object hidden in the scattering medium is reconstructed by adjusting the \(\beta\) value of the power-spectrum pattern with different exposure. (**a–c**) are power-spectrum patterns captured at exposure times of 5000 \(\upmu\)s, 7500 \(\upmu\)s, 15,000 \(\upmu\)s, respectively. (**b,c**) have the same scale bar as (**a**); (**e,f**) have the same scale bar as (**d**). Figure 3: The simulation results of the value of the traversing feedback coefficient \(\beta\). (**a**) Original object image ’cameraman’. (**b**) The power-spectrum pattern of the ’Cameraman’ provided by fast Fourier transform (FFT). (**c**) The reconstructed object image with \(\beta\) = 0.1, (**d**) \(\beta\) = 0.7, (**e**) \(\beta\) = 1.5, and (**f**) \(\beta\) = 2. With character '5' on a USAF 1951 resolution test chart as the object, we collected 200 pieces of coherent power-spectrum patterns with exposure time ranged from 100 us to 20,000 us to cover underexposure, moderate exposure, and overexposure. We used NRMS to evaluate the termination condition and reconstructed effect of the iterative algorithm. For each power-spectrum pattern, the suitable \(\beta\) value for successful reconstruction is selected by going through 0-2 with interval 0.01 to get the minimum NRMS value. The suitable \(\beta\) values for the 200 power-spectrum patterns are shown in Figure 6.  
It can be seen from Figure 6, that the optimal \(\beta\) values for various exposure level input patterns are different, with an increasing trend in 0.2-1.3 for underexposure, moderate exposure, and overexposure cases. According to the statistics, the optimal \(\beta\) values for underexposure, moderate exposure, and overexposure cases lay in the range of 0.3-0.8, 0.8-1.1, and 1.0-1.25 respectively, which could be expressed by a fitting expression, as shown in Equation (5). \[\beta=b+0.01\times\sum_{i=1}^{i=4}R(a_{i})\times M(a_{i}) \tag{5}\]  
Figure 5: Single-shot coherent power-spectrum scattering imaging experimental light path diagram. O represents object; S represents a scattering layer (Thorlabs DG10-600-MD); L represents Fourier transform lens. Figure 6: The optimum \(\beta\) value for the 200 reconstructions. where, \(R(a_{i})\) represents the pixel number proportion of interval \(a_{i}\), \(M(a_{i})\) represents the median of interval \(a_{i}\), and \(b\) represents the bias set [\(-1\):\(0\)] by the exposure state, \(b\) = 0 for underexposure or moderate exposure, otherwise, \(b\) set [\(-1\):\(-0.7\)]. According to Equation (5), three power-spectrum patterns, in underexposure, moderate exposure, and overexposure states, respectively, are input for the reconstructions, and the corresponding results are shown in Figure 7. Obviously, for different exposure level cases, the reconstructions with corresponding different \(\beta\) values are clear. Furthermore, the time consumption for every reconstruction is no more than 9 s.  
The other objects are also used for the experiments, as shown in Figure 8. For the practical power-spectrum patterns with different exposure levels, by choosing carefully the \(\beta\) value according to the given optimal \(\beta\) interval according to Equation (5), the images of the objects hidden by the scattering medium can be reconstructed well, which confirms the feasibility of the adaptive selection method of \(\beta\) value for the algorithm. Figure 8: Reconstruction results for other objects. (**a**–**c**) and (**d**–**f**) are the power-spectrum patterns of the underexposure, moderate exposure, and overexposure, respectively; (**g**–**i**) are the results for (**a**–**c**) reconstruction; (**j**–**l**) are the results for (**d**–**f**).