Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

Chunhao Liang; Yashar E. Monfared; Xin Liu; Baoxin Qi; Fei Wang; Olga Korotkova; Yangjian Cai

doi:doi:10.3788/COL202119.052601

Chinese Optics Letters, 2021, 19 (5): 052601, Published Online: Feb. 25, 2021

Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

Chunhao Liang ¹Yashar E. Monfared ²Xin Liu ¹Baoxin Qi ¹Fei Wang ^3,*Olga Korotkova ^4,**Yangjian Cai ^1,3,***

Author Affiliations

¹ Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250014, China

² Department of Chemistry, Dalhousie University, Halifax, NS B3H 4R2, Canada

³ School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China

⁴ Department of Physics, University of Miami, Coral Gables, Florida 33146, USA

Figures & Tables

Fig. 1. Schematic diagram for a telecentric imaging system with lenses $L_{1} {, L}_{2}$ and a pupil.

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Fig. 2. Variation of CDC with $Δ$ x/b for different values of a/b.

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Fig. 3. Images of two pinholes under (a)–(c) partially coherent illumination (normalized S_im) for three values of ratio a/b; (d) incoherent illumination; (e) the cross lines (ρ_y = 0) of S_im in (a)–(d).

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Fig. 4. (a)–(c) Images (S_im) of two pinholes with three values of d under partially coherent illumination with a/b = 15; (d) cross lines (ρ_y = 0) of S_im in (a)–(d); (e) dependence of resolution on ratio a/b.

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Fig. 5. (a) Density plot of the CDC’s real part; (b) cross line (ρ_y = 0) at Δy/b = 0.

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Fig. 6. (a)–(c) Images (S_im) of three pinholes with different separations under the illumination of partially coherent beams with the CDC in Eq. (18). (d)–(f) The corresponding images of three pinholes with incoherent illumination.

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Chunhao Liang, Yashar E. Monfared, Xin Liu, Baoxin Qi, Fei Wang, Olga Korotkova, Yangjian Cai. Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit[J]. Chinese Optics Letters, 2021, 19(5): 052601.

Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

Fig. 1. Schematic diagram for a telecentric imaging system with lenses $L_{1} {, L}_{2}$ and a pupil.

Fig. 2. Variation of CDC with $Δ$ x/b for different values of a/b.

Fig. 3. Images of two pinholes under (a)–(c) partially coherent illumination (normalized S_im) for three values of ratio a/b; (d) incoherent illumination; (e) the cross lines (ρ_y = 0) of S_im in (a)–(d).

Fig. 4. (a)–(c) Images (S_im) of two pinholes with three values of d under partially coherent illumination with a/b = 15; (d) cross lines (ρ_y = 0) of S_im in (a)–(d); (e) dependence of resolution on ratio a/b.

Fig. 5. (a) Density plot of the CDC’s real part; (b) cross line (ρ_y = 0) at Δy/b = 0.

Fig. 6. (a)–(c) Images (S_im) of three pinholes with different separations under the illumination of partially coherent beams with the CDC in Eq. (18). (d)–(f) The corresponding images of three pinholes with incoherent illumination.

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Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit

Fig. 1. Schematic diagram for a telecentric imaging system with lenses L1, L2 and a pupil.

Fig. 2. Variation of CDC with Δx/b for different values of a/b.

Fig. 3. Images of two pinholes under (a)–(c) partially coherent illumination (normalized Sim) for three values of ratio a/b; (d) incoherent illumination; (e) the cross lines (ρy = 0) of Sim in (a)–(d).

Fig. 4. (a)–(c) Images (Sim) of two pinholes with three values of d under partially coherent illumination with a/b = 15; (d) cross lines (ρy = 0) of Sim in (a)–(d); (e) dependence of resolution on ratio a/b.

Fig. 5. (a) Density plot of the CDC’s real part; (b) cross line (ρy = 0) at Δy/b = 0.

Fig. 6. (a)–(c) Images (Sim) of three pinholes with different separations under the illumination of partially coherent beams with the CDC in Eq. (18). (d)–(f) The corresponding images of three pinholes with incoherent illumination.

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Fig. 1. Schematic diagram for a telecentric imaging system with lenses $L_{1} {, L}_{2}$ and a pupil.

Fig. 2. Variation of CDC with $Δ$ x/b for different values of a/b.

Fig. 3. Images of two pinholes under (a)–(c) partially coherent illumination (normalized S_im) for three values of ratio a/b; (d) incoherent illumination; (e) the cross lines (ρ_y = 0) of S_im in (a)–(d).

Fig. 4. (a)–(c) Images (S_im) of two pinholes with three values of d under partially coherent illumination with a/b = 15; (d) cross lines (ρ_y = 0) of S_im in (a)–(d); (e) dependence of resolution on ratio a/b.

Fig. 5. (a) Density plot of the CDC’s real part; (b) cross line (ρ_y = 0) at Δy/b = 0.

Fig. 6. (a)–(c) Images (S_im) of three pinholes with different separations under the illumination of partially coherent beams with the CDC in Eq. (18). (d)–(f) The corresponding images of three pinholes with incoherent illumination.