Fig. 1. MEIF network framework based on CNNs. During each processing step, images with different exposure times under the same illumination angle are input for fusion. The iteration iterates through all illumination angles to process all original images. The input accepts three or more grayscale images ($n\times n$) with multiple exposures. CONV 1 and CONV 2, each with 64 convolutional kernels, handle feature extraction and adjustment. Element-wise fusion follows, and after that, CONV 3 (64 kernels) and CONV 4 (1 kernel) contribute to image reconstruction, resulting in a single-channel grayscale output. CONV 1 is pretrained and fixed during training. Utilizing public datasets, the training avoids redundancy for the MEIF task in computational microscopy systems.

Fig. 2. MEIF-FPM full pipeline. (a) Overview of the entire pipeline, illustrating the process of capturing multi-exposure images, grouping them based on illumination angles, performing MEIF on sets of multi-exposure images with the same illumination angle, and finally obtaining the MEIF results for FPM reconstruction. (b) Model of raw data acquisition, where samples are illuminated at different angles by an LED array, and the imaging system collects multiple intensity images. For MEIF-FPM, multi-exposure image acquisition is crucial for MEIF. (c) Traditional FPM reconstruction approach incorporates modulus constraints and support constraints, and conducts Fourier space updates iteratively. (d) The reconstruction strategy of FD-FPM involves iteratively recovering information extracted after feature extraction, resembling the principles outlined in panel (c), for intensity and phase recovery during the iteration process. This iterative process comprises six steps, indicated as (i) to (vi) along the way.

Fig. 3. Comparison between raw data from normal exposure and MEIF results. (a) Stitched image of raw data from normal exposure based on illumination angles. (b) Stitched image of MEIF results based on illumination angles. (c1)–(c3) Comparison of representative illumination angles between normal exposure (left) and MEIF images (right), with relative positions marked by colored rectangles in panels (a) and (b).

Fig. 4. Reconstruction results of the USAF target. (a1) Whole slide imaging (WSI) reconstruction with MEIF; (a2) zoomed-in view of the MEIF reconstruction; (a3) zoomed-in view with HDR; (a4) quantitative distribution corresponding to the lines in (a2) and (a3). (b1)–(b4) Phase reconstruction results with MEIF algorithm, magnified views, and the quantitative distribution along the indicated lines. (c1)–(c4) Phase reconstruction results with HDR algorithm, magnified views, and the quantitative distribution along the indicated lines.

Fig. 5. Reconstruction results of the onion epidermis. (a) WSI intensity reconstruction; (b) WSI phase reconstruction; (c1, d1, e1) Ground truth for ROIs 1 to 3; (c2 to c7, d2 to d7, e2 to e7) Amplitude and phase reconstruction results for ROIs 1 to 3; (e8 to e14) Quantitative distribution for the line-scan regions in ROI 3 (e1 to e7), where the horizontal coordinate is 0 to $25\mu \text{m}$.

Fig. 6. FD-FPM reconstruction results of animal connective tissue: (a1)–(a4) Stitching-free reconstruction results after MEIF processing, where (a1) and (a2) represent the whole block recovery of intensity and phase results, respectively. (a3), (a4) Zoomed-in results of the ROIs, which are circled in the images. Similarly, (b1), (b2), (b3), and (b4) are the stitching-free recovery results for intensity and phase, along with zoomed-in ROI results. (c) The results directly captured by a higher-resolution objective (20×/0.75 NA). The reconstruction data are acquired using a lower-resolution (4×/0.1 NA, Nikon) objective.