Fig. 1. Comparison between the optical field modulation in the spatial domain^［40］ and the spatial frequency domain^［41］

Fig. 2. The diagram of the GS algorithm^［39］

Fig. 3. The diagram of the AA algorithm^［63］

Fig. 4. Comparison of the intensity distribution of the axial plane optical points array generated by using the S algorithm and the APGS algorithm^［64］

Fig. 5. The diagram of the TPGS algorithm^［66］

Fig. 6. Intensity distribution of the axial plane optical points array generated by using the multi-plane 3D GS algorithm and the TPGS algorithm，respectively^［66］. The scale bar is 5 μm

Fig. 7. Concept of complex amplitude modulation by using two SLM^［71］

Fig. 8. Function f（A）versus A for three different complex amplitude encoding algorithms^［40］

Fig. 9. Theoretical resconstruction of the spheroidal accelerating beam^［75］

Fig. 10. Hologram calculated by using the Davis Algorithm，the Arrizón1 Algorithm and the Arrizón2 Algorithm，and corresponding theoretical reconstructed intensity distribution，respectively^［75］

Fig. 11. The spatial intensity distribution and phase distribution of the incident complex optical field and the reconstructed complex optical field ^［88］

Fig. 12. Experimental measured intensity distributions of focused complex optical fields designed along 3D curves and application in optical tweezers^［82］

Fig. 13. Schematic of Tao Algothrim. The blank regions stand for the constraint on the amplitude or the phase distribution，while the shadow region stand for the constraint free. a and p represent domains of amplitude and phase in the input plane，respectively. A and P represent domains of amplitude and phase in the output plane，respectively. α and β are two complementary plane which can consist to the output plane^［86］

Fig. 14. Schematic of the common path interferometer for the generation of arbitrary VVB^［92］

Fig. 15. Schematic of the optical field modulater based on the TCPI^［7］

Fig. 16. Schematic of the optical field modulater based on the cascade SLM method^［103］. SF：Spatial Filters

Fig. 17. Schematic of the compact optical field modulater for the generation of arbitrary vector vortex beam^［93］

Fig. 18. Experiment setup for the generation and measurement of the complex degree of coherence of the partially coherent beams^［112］

Fig. 19. Schematic for the calculation of the incident field based on the antenna pattern synthesis method^［128］

Fig. 20. Schematic diagram of parameters involved in the focal field shaping problem^［131］

Fig. 21. Flow chart for iteratively searching for the optimal amplitude，phase，and polarization distribution of incident beam^［134］

Fig. 22. Optical transport of multiple particles along the trefoil knot circuit^［143］

Fig. 23. Observe the motion of the thermophila by using the lattices light-sheet microscopy^［146］

Fig. 24. Scheme for multi-dimension parallel optical storage^［147］