Fig. 1. Principle of axial beam coding. (a) Transverse beam coding versus axial beam coding. (b) Hadamard basis patterns for beam coding both in the x-y plane and along the z-axis. (c) Axial beam coding based on a phase-only SLM. (d) Distribution of phase masks on the SLM screen for achieving multiple axial foci. (e) Reallocation of the laser power from “0” to “1” intensities. (f) Arbitrary distributions of the laser power among “1” intensities.

Fig. 2. Simulation of the axial-coded beam. (a) Axial-coded beams for 5 and 10 planes with evenly distributed intensities among the foci. Axial-coded beams for 10 planes with exponentially increasing (1.3n) and decreasing (1.3−n) intensity distributions. n is the focus position. (b) Corresponding axial intensity distributions for panel (a). (c) Fluorescence intensity distributions of the axial-coded beam in the x-z plane under the 1-, 2-, and 3-photon (1P, 2P, and 3P) excitations. (d) and (e) Intensity comparison of the focus and gap positions [indicated by the dashed lines in panel (c)] among 1P, 2P, and 3P excitations.

Fig. 3. Working principle of AIMED. (a) Schematic representation of the experimental setup for the AIMED technique. (b) Technique comparison between the conventional 2PM based on G-PSF and the AIMED based on the AC-PSF.

Fig. 4. AC-PSF of AIMED. (a) Complete set of AC-PSFs for imaging five planes in a laser scanning 2PM, including the coding matrix and coded beam. Scale bar: 5 μm. (b) Axial intensity distribution of the AC-PSF coded with “11111.” (c) Spatial intensity distributions of the Gaussian PSFs coded with “10000,” “01000,” “00100,” “00010,” and “00001.” (d) Lateral and axial resolutions provided by the AC-PSF in 2PM. Scale bar: 1μm. (Video 2, AVI, 1.10 MB [URL: https://doi.org/10.1117/1.AP.7.4.046010.s2]).

Fig. 5. AIMED imaging in mouse brain neurons. (a) and (b) Comparison of the imaging results of the mouse brain neurons between the CS-reconstructed image and the Gaussian-scanned image. “CS (1/3∼1/2)” denotes that the laser power used for AIMED in each plane is either Ptotal/3 or Ptotal/2. “Gaussian (1/2)” denotes that the laser power used for Gaussian scan is Ptotal/2. (c) Comparison of the CS and Gaussian images at different planes for panel (a). (d) Corresponding PSNR and SSIM at different planes for panel (c). (e) and (f) Comparisons of the CS-reconstructed and Gaussian-scanned images in the x-y plane (e1, e2, f1, and f2) and x-z plane (e3 and f3) based on the different coding matrices. “Gaussian (1/1)” denotes the laser power used for Gaussian scan is Ptotal. (Video 3, AVI, 1.57 MB [URL: https://doi.org/10.1117/1.AP.7.4.046010.s3].)

Fig. 6. Compression ratio in AIMED. Comparison of CS-reconstructed neuron images with different CRs and the Gaussian-scanned images for eight depths. (a)–(c) CS-reconstructed 3D neuron images with different coding matrices. (d) and (e) Gaussian-scanned results with different illumination powers. “1/4,” “1/3,” and “1/2” denote that the laser power used at each imaging plane is Ptotal/4, Ptotal/3, and Ptotal/2, respectively. (Video 4, AVI, 3.09 MB [URL: https://doi.org/10.1117/1.AP.7.4.046010.s4].)