Fig. 1. Decomposition and reconstruction of the rotationally symmetric amplitude objects. (a1) and (b1) are the spiral spectra of the objects. (a2) and (b2) are the original amplitude objects. (a3) and (b3) are the LG amplitude spectra of the objects. (a4), (b4) and (a5), (b5) are the reconstructed objects using SOC and TVAL3 CS algorithms, respectively. The pixel number of reconstructed images is 512 × 512.

Fig. 2. Decomposition and reconstruction of the complex amplitude Chinese character “hang” by zero-frequency detection and bucket detection. (a1) and (a2) are the LG amplitude spectrum of the Chinese character. (b1) and (b2) are the LG phase spectrum. (c1)–(c4) and (d1)–(d4) are the results of the object reconstruction using two algorithms under zero-frequency detection and bucket detection, respectively. The pixel number of reconstructed images is 512 × 512.

Fig. 3. Schematic diagram of experimental setup. P, polarizer; Ob, objective lens; Ph, pinhole; L1–L4, lenses; SLM1 and SLM2, spatial light modulators; PD, photodetector.

Fig. 4. Analysis of LG mode correlations before and after normalization. (a1) and (b1) illustrate the correlation matrices for the LG modes along the radial and azimuthal dimensions before normalization. (a2) and (b2) display the corresponding correlation matrices after normalization.

Fig. 5. Experimental results for the symmetric objects. (a1) and (a2) depict the respective LG amplitude spectrum corresponding to the cloverleaf and pentagram objects. Column b and Column c, respectively, show the reconstructed images using the entire LG spectrum before the LG mode correction and with only the LG modes whose azimuthal indices are multiples of the object’s symmetry order. Columns d and e correspondingly display the reconstructed images after the correction has been applied.

Fig. 6. Experimental results for complex amplitude objects. (a1)–(d1) The original amplitude and phase of the object to be imaged. (a2)–(d2) Images reconstructed by the SOC algorithm under zero-frequency detection. (a3)–(d3) Images reconstructed by the CS algorithm under zero-frequency detection. (a4)–(d4) Images reconstructed by the SOC algorithm under bucket detection. (a5)–(d5) Images reconstructed by the CS algorithm under bucket detection.

Fig. 7. Imaging results of the USAF1951 resolution test target. (a) and (b) represent the image reconstructed by the CS and SOC algorithms, respectively. The pixel number of reconstructed images is 512 × 512. The smallest units that can be distinguished are both element 6 in group 2, as shown in the red box. (c) and (d) are the reconstructed results of the SOC algorithm, and the reconstructed pixels are 1024 × 1024 and 2028 × 2048, respectively. The hot dots in the upper right corner of (b)–(d) are magnifications of the yellow dashed box area in (b).

Fig. 8. Reconstruction results after LG mode preprocessing. (a)–(c) Reconstruction results of the USAF1951 resolution test target when the beam waist radius is 0.3, 0.5, and 0.6 mm, respectively. (d)–(f) Reconstructed edges of the cloverleaf, pentagram, and Chinese character “hang,” respectively.