Fig. 1. Schematic diagram of the integral for PTF along the left–right axis in the polar coordinate system. (a) The radius ρ of the point Q is in the range of NAobj≤ρ≤2NAobj. (b) The radius ρ of the point Q is in the range of 0≤ρ<NAobj.

Fig. 2. PTF and C(ρ,θ) with four illumination patterns. (a1)–(a4) Four illumination patterns. (b1)–(b4) PTFs along the left–right axis. (c1)–(c4) C(ρ,θ) with two-axis illumination. (d) Quantitative curves of C(ρ,θ) along the black straight line under the four illumination patterns. (e1)–(e3) Quantitative curves of C(ρ,θ) under the four illumination patterns on three radii.

Fig. 3. Simulation results with different regularization parameters under four illumination patterns. (a) Original phase image. (b) Diffraction limit phase image of DPC (2NAobj). (c1)–(c4), (d1)–(d4) Phase results with regularization parameters of 0 and 0.2. (e) Phase values along three small circles corresponding to different spatial frequencies evenly distributed from 0 to 2NAobj. (f) Phase values along a small circle of the same radius in (d1)–(d4) under four illumination patterns.

Fig. 4. Phase reconstruction results of a phase resolution target QPTTM. (a) A bright-field image. (b) A zoom-in of the interest region of the bright-field image. (c) Phase reconstruction result under the half-circular uniform illumination pattern. (d) Phase reconstruction result under the optimal illumination scheme. (d) Phase values along three small circles evenly distributed from 0 to 2NAobj under the optimal illumination pattern. (e) Phase values along a small circle of the same radius in (c), (d) under the half-circular uniform illumination pattern and optimal illumination pattern.

Fig. 5. Phase reconstruction results of HeLa cells under the optimal illumination scheme. (a) Full-field-of-view phase distribution. (b), (c) Phase maps of two selected zooms. (d) Phase results at different time points.

Fig. 6. Schematic diagram of the integral for PTF along the left–right axis illumination in the polar coordinate system. (a) The radius ρ of the point Q is in the range of NAobj≤ρ≤2NAobj. (b) The radius ρ of the point Q is in the range of 0≤ρ<NAobj.

Fig. 7. PTF and C(ρ,θ) with a different L(ρ) function. (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C(ρ,θ) with two-axis illumination. (d) Quantitative curves of C(ρ,θ) along the black line.

Fig. 8. PTF and C(ρ,θ) with different thickness of the annulus (three σ). (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C(ρ,θ) with two-axis illumination. (d) Quantitative curves of C(ρ,θ) along the black line.

Fig. 9. PTF and C(ρ,θ) with a different n. (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C(ρ,θ) with two-axis illumination. (d) Quantitative curves of C(ρ,θ) along the black line.

Fig. 10. Simulation results of the optimal illumination scheme with different aberration levels. (a1)–(f1) Pupil with different aberration levels. (a2)–(f2) Reconstruction phase. (g) Quantitative curves of the reconstruction phase.