Fig. 1. Schematic diagram of the experimental setup, where “L1” and “L2” represent lenses, “Rotating Diffuser” denotes the rotating Frosted glass specified with a diffusion grain size of 220, “Iris” stands for the adjustable aperture, “Object” denotes the object under test, “U” is the distance from the object plane to the scattering medium, and “V” represents the image distance.

Fig. 2. Flowchart for obtaining the speckle dual-spectrum phase and image reconstruction. (a) is the speckle pattern. The estimated (b) Fourier amplitude and (c) Fourier phase are shown. (d) is the result of single inverse Fourier transformation (IFT) imaging with bispectrum, and (e) is the imaging result obtained through our method.

Fig. 3. Comparative experimental results of different algorithms. (a) is the actual object images collected by a Nikon microscope, (b) is the speckle intensity patterns, (c) represents the results of single inverse Fourier imaging, (d) depicts the imaging results of the HIO-ER iterative recovery algorithm, and (e) shows the image recovery results of the hybrid input-output (HIO) algorithm combined with the dual-spectrum phase.

Fig. 4. (a) The corresponding reconstruction images using different sizes of target autocorrelation under identical initial conditions. (b) The normalized curves of image clarity functions. An assessment of image quality is conducted on the image restoration outcomes derived from nine distinct autocorrelation dimensions spanning from 200 pixel × 200 pixel to 280 pixel × 280 pixel, utilizing the image clarity metric. Scale bar: 10 camera pixels, corresponding to 90 µm at the object plane.

Fig. 5. Experimental flowchart of dual-spectrum phase recursive image recovery program based on adaptive image clarity. The red dashed box outlines the process of acquiring the bispectrum phase and the phase iteration component of the image recovery program. The blue dashed box indicates the acquisition of autocorrelation sizes, while the green dashed box encompasses the integration of the previously estimated Fourier phase size with the HIO-ER algorithm for iterative image restoration. “A” denotes the Fourier assignment, which is the speckle autocorrelation, “g” denotes the phase, and “k” represents the number of iterations. The iterative algorithm is employed to progressively refine the phase estimate, ultimately converging toward the true phase of the object. The symbol “β” represents the feedback parameter that governs the convergence of the HIO-ER algorithm, typically ranging between 0.5 and 1. The symbol “γ” denotes the set of all points on “g” that violate the object constraint conditions.