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Research Paper

Curr. Opt. Photon. 2021; 5(1): 40-44

Published online February 25, 2021 https://doi.org/10.3807/COPP.2021.5.1.040

Copyright © Optical Society of Korea.

Reflective Fourier Ptychographic Microscopy Using Segmented Mirrors and a Mask

Hee Kyung Ahn , Byong Hyuk Chon

Optical Imaging and Metrology Team, Korea Research Institute of Standards and Science, Daejeon 34113, Korea

Corresponding author: *hk.ahn@kriss.re.kr, ORCID 0000-0002-1685-0814

Received: October 16, 2020; Revised: December 11, 2020; Accepted: December 18, 2020

In this paper, LED arrays with segmented mirrors and a mask are presented as a new dark-field illuminator for reflective Fourier ptychographic microscopy (FPM). The illuminator can overcome the limitations of the size and the position of samples that the dark-field illuminator using a parabolic mirror has had. The new concept was demonstrated by measuring a USAF 1951 target, and it resolved a pattern in group 10 element 6 (274 nm) in the USAF target. The new design of the dark-field illuminator can enhance competitiveness of the reflective FPM as a versatile measurement method in industry.

Keywords: Phase retrieval, Three-dimensional imaging, 3D shape measurement

OCIS codes: (110.0180) Microscopy; (110.1758) Computational imaging; (110.2945) Illumination design

Fourier ptychographic microscopy (FPM) is a promising technique which can simultaneously achieve high resolution and wide field of view (FOV) [1]. In the field of FPM, transmission type FPM has been used to measure transparent samples such as cells and biological tissues [215]. However, it cannot be used to measure reflective materials such as metal and semiconductors, which are typically employed in industry, and recently reflective FPM has gained interest as an alternative to transmission type FPM. Investigations of reflective FPM have been performed since 2015 [1619], and by 2019 its resolution was down to 250 nm, by using a parabolic reflector to improve its signal to noise ratio (SNR) [19]. Nevertheless, it still has limited applications in industry, because of a geometrical difficulty with the setup when using a parabolic reflector. Figure 1 shows the setup of the reflective FPM with a parabolic reflector. BI and DI represent bright-field illuminator, and dark-field illuminator, respectively.

Figure 1.Experimental setup of reflective Fourier ptychographic microscopy using a parabolic reflector.

As shown in Fig. 1, the DI is located in the same plane as the plane where the sample S is located. This is because the focal point of the parabolic reflector needs to be in the sample plane so that all dark-field beams are collimated and directed to the sample. As a consequence, the size of the sample is limited by the diameter of the smallest LED ring of the DI, which makes this system difficult to use in industry.

In this paper, the parabolic reflector is replaced with segmented mirrors and a mask. By locating them far from the sample plane, there is far less restriction on the size and shape of the sample. This arrangement allows reflective FPM to be more suitable for use in industry.

Figures 2(a) and (b) show the difference between a dark-field illuminator using a parabolic reflector, and one using segmented mirrors. As mentioned in the previous section, when a parabolic reflector is used, the size of the sample is limited (Fig. 2(a), blue dashed box). On the other hand, when using segmented mirrors located in the dark-field LED array, there is no sample size restriction (Fig. 2(b), blue dashed box).

Figure 2.Comparison between two types of dark-field illuminator: (a) dark-field illuminator using a parabolic reflector, (b) dark-field illuminator using segmented mirrors. The blue dashed boxes in (a), (b) indicate the space available for a sample.

However, segmented mirrors cannot be independently used as an illuminator. Unlike a laser, an LED has a large divergence angle. Therefore, two beam components are created: one is a beam reflected from a segmented mirror (red line), and the other is a direct beam (orange line), as illustrated in Fig. 3(a).

Figure 3.Two beam components created by a segmented mirror. (a) Layout of beams from the LED. Red rays represent a beam component reflected from a segmented mirror, Orange rays represent a beam component directly incident on a sample. A green region indicates where the two beam components overlap. (b) When a pinhole was placed in the overlapping region, the two beam components were projected onto the bottom. (c) A mask (gray lines) can block the direct beam component which acts like noise in the FPM reconstruction.

To show that two beam components are generated and illuminated on the sample, we put a pinhole in the sample plane and the two beam components were detected, as shown in Fig. 3(b). Since the direct beam behaves like noise, we used a mask to eliminate it, as in Fig. 3(c). We made two measurements to prove the effect of the mask: one was without a mask, and the other was with a mask. The results are described in the next section.

We conducted experiments to demonstrate the feasibility of the segmented mirrors and a mask as a dark-field illuminator for reflective FPM. The experimental setup and the picture of it are depicted in Fig. 4. In practice, we made a compact prototype of the experimental setup using folding mirrors.

Figure 4.Experimental setup (left) and picture (right) of the reflective Fourier ptychographic microscope with segmented mirrors and a mask.

16 LED beams from a bright-field illuminator (BI) are image relayed to the back-focal plane of the objective lens (OL, Mitutoyo 10x, 0.28 NA) by using 4-f imaging with L1 (f = 150 mm) and L2 (f = 300 mm). They are then collimated by OL and illuminated on the sample. A dark-field illuminator (DI) consists of an LED array with 72 LEDs and 72 segmented mirrors and a mask. As a result, 88 LED beams give an increase in NA more than 1.0. Figure 5 shows the k-space diagram (left) and the resulting signals in Fourier domain (right).

Figure 5.Comparison of signals obtained from on-axis illumination and oblique illumination. The signals when an on-axis beam is illuminated (up) and the ones when 88 LEDs in bright-field illuminator and dark-field illuminator are illuminated (down). The pictures on the left represent k-space diagram and the ones on the right represent the signals in Fourier domain.

When the 72 beams from the LED array are sequentially on and off, each beam is reflected by its segmented mirror and illuminated on the sample. The reflected beams from the sample are detected by a camera (CMOS, Basler acA 4112-20 μm), after passing through OL, beamsplitter (BS), and a tube lens (f = 180 mm). The LED arrays in BI and DI have a ring shape which enables effective FPM reconstruction [20]. As shown in Fig 4, there are no obstructions which can restrict the position and size of the sample.

After setting up, we measured a USAF 1951 target (Newport, HIGHRES-1) to prove the feasibility of the new dark-field illuminator. Figures 6(a), (b) show the results obtained by FPM reconstruction without a mask and with a mask, respectively.

Figure 6.The resulting high-resolution images after FPM reconstruction using the dark-field illuminator including (a) segmented mirrors-only, and (b) segmented mirrors and a mask. In (a), a pattern in group 10 and element 2 (G10E2, 435 nm) are resolved, while a pattern in group 10 and element 6 (G10E1, 274 nm) are resolved in (b). In the graphs of the contrast ratio, ‘L’ and ‘R’ represent left and right, respectively.

In Fig. 6(a), we can see that most of the patterns on the sample have point-like noises (red circles) and low contrast. It is because the direct beam component creates another wave vector, causing noise during FPM reconstruction. Since the noise from the direct beam component and the signal from the reflected beam component are coherent, they could make unwanted interference patterns during FPM reconstruction, seeming like bright and dark spots. In this case, the patterns in group 10 element 2 on the USAF 1951 sample were resolved. Alternatively, when using a mask, the noise was greatly reduced and the contrast was improved. As a result, the patterns in group 10 element 6 (about 274 nm) on the USAF 1951 sample were resolved.

The resolution of the system with the new dark-field illuminator recorded a resolution of 274 nm, which is a little degraded compared to a system using a parabolic reflector [19]. One of the reasons is that the mask could not totally eliminate the unwanted beam component. It could be overcome by designing a mask using a ray tracing to effectively eliminate the noise. Moreover, the segmented mirrors and the masks are placed separately as shown in Fig. 4, so it is hard to align them. If they are made as an all-in-one illuminator, the direction of the beam component reflected from each segmented mirror is much more easily controlled, resulting in a more clear reconstruction image.

In addition, if the reflected beam components illuminating the sample are not perfectly collimated, it could affect FPM reconstruction. Fortunately, its effect is small because the distance between the LED array in DI and the sample is more than 67 mm, which is far enough to make uniform intensity on the sample plane.

Segmented mirrors and a mask are proposed as an alternative to a parabolic mirror for reflective FPM. The new illuminator has the advantage of providing more freedom in terms of sample size and position. The feasibility of the new illuminator was demonstrated by measuring a USAF 1951 target, first with the segmented mirrors alone, and then with the segmented mirrors and a mask. Compared with the segmented mirrors alone, the new illuminator with the added mask had better performance, resolving a group 10 element 6 (274 nm) of the USAF target. We expect that the new dark-field illuminator consisting of segmented mirrors and a mask will make reflective FPM more applicable for sample measurement in industry.

This study was supported by a grant from Korea Research Institute of Standards and Science (KRISS) (GP2020-0009-04).

  1. G. Zheng, R. Horstmeyer and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739-745 (2013).
    Pubmed KoreaMed CrossRef
  2. Z. Bian, S. Dong and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21, 32400-32410 (2013).
    Pubmed CrossRef
  3. L. Tian, X. Li, K. Ramchandran and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376-2389 (2014).
    Pubmed KoreaMed CrossRef
  4. X. Ou, G. Zheng and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960-4972 (2014).
    Pubmed KoreaMed CrossRef
  5. Y. Zhang, W. Jiang and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23, 33822-33835 (2015).
    Pubmed CrossRef
  6. X. Ou, R. Horstmeyer. G. Zheng and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472-3491 (2015).
    Pubmed KoreaMed CrossRef
  7. C. Zuo, J. Sun and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24, 20724-20744 (2016).
    Pubmed CrossRef
  8. J. Sun, Q. Chen, Y. Zhang and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336-1350 (2016).
    Pubmed KoreaMed CrossRef
  9. J. Sun, C. Zuo, L. Zhang and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
    Pubmed KoreaMed CrossRef
  10. A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
    Pubmed CrossRef
  11. A. Pan, Y. Zhang, K. When, M. Zhou, J. Min, M. Lei and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26, 23119-23131 (2018).
    Pubmed CrossRef
  12. B. Lee, J.-Y. Hong, D. Yoo, J. Cho, Y. Jeong, S. Moon and B. Lee, “Single-shot phase retrieval via Fourier ptychographic microscopy,” Optica 5, 976-983 (2018).
    CrossRef
  13. J. Sun, C. Zuo, J. Zhang, Y. Fan and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8, 7669 (2018).
    Pubmed KoreaMed CrossRef
  14. A. Zhou, W. Wang, N. Chen, E. Y. Lam, B. Lee and G. Situ, “Fast and robust misalignment correction of Fourier ptychographic microscopy for full field of view reconstruction,” Opt. Express 26, 23661-23674 (2018).
    Pubmed CrossRef
  15. X. Chen, Y. Zhu, M. Sun, D. Li, Q. Mu and L. Xuan, “Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy,” Opt. Express 27, 14099-14111 (2019).
    Pubmed CrossRef
  16. S. Pacheco, B. Salahieh, T. Milster, J. J. Rodriguez and R. Liang, “Transfer function analysis in epi-illumination Fourier ptychography,” Opt. Lett. 40, 5343-5346 (2015).
    Pubmed KoreaMed CrossRef
  17. S. Pacheco, G. Zheng and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
    Pubmed CrossRef
  18. K. Guo, S. Dong and G. Zheng, “Fourier ptychography for brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging,” IEEE J. Sel. Top. Quantum Electron. 22, 77-88 (2016).
    CrossRef
  19. H. Lee, B. H. Chon and H. K. Ahn, “Reflective Fourier ptychographic microscopy using a parabolic mirror,” Opt. Express 27, 34382-34391 (2019).
    Pubmed CrossRef
  20. K. Guo, S. Dong, P. Nanda and G. Zheng, “Optimization of sampling pattern and the design of Fourier ptychographic illuminator,” Opt. Express 23, 6171-6180 (2015).
    Pubmed CrossRef

Article

Research Paper

Curr. Opt. Photon. 2021; 5(1): 40-44

Published online February 25, 2021 https://doi.org/10.3807/COPP.2021.5.1.040

Copyright © Optical Society of Korea.

Reflective Fourier Ptychographic Microscopy Using Segmented Mirrors and a Mask

Hee Kyung Ahn , Byong Hyuk Chon

Optical Imaging and Metrology Team, Korea Research Institute of Standards and Science, Daejeon 34113, Korea

Correspondence to:*hk.ahn@kriss.re.kr, ORCID 0000-0002-1685-0814

Received: October 16, 2020; Revised: December 11, 2020; Accepted: December 18, 2020

Abstract

In this paper, LED arrays with segmented mirrors and a mask are presented as a new dark-field illuminator for reflective Fourier ptychographic microscopy (FPM). The illuminator can overcome the limitations of the size and the position of samples that the dark-field illuminator using a parabolic mirror has had. The new concept was demonstrated by measuring a USAF 1951 target, and it resolved a pattern in group 10 element 6 (274 nm) in the USAF target. The new design of the dark-field illuminator can enhance competitiveness of the reflective FPM as a versatile measurement method in industry.

Keywords: Phase retrieval, Three-dimensional imaging, 3D shape measurement

I. INTRODUCTION

Fourier ptychographic microscopy (FPM) is a promising technique which can simultaneously achieve high resolution and wide field of view (FOV) [1]. In the field of FPM, transmission type FPM has been used to measure transparent samples such as cells and biological tissues [215]. However, it cannot be used to measure reflective materials such as metal and semiconductors, which are typically employed in industry, and recently reflective FPM has gained interest as an alternative to transmission type FPM. Investigations of reflective FPM have been performed since 2015 [1619], and by 2019 its resolution was down to 250 nm, by using a parabolic reflector to improve its signal to noise ratio (SNR) [19]. Nevertheless, it still has limited applications in industry, because of a geometrical difficulty with the setup when using a parabolic reflector. Figure 1 shows the setup of the reflective FPM with a parabolic reflector. BI and DI represent bright-field illuminator, and dark-field illuminator, respectively.

Figure 1. Experimental setup of reflective Fourier ptychographic microscopy using a parabolic reflector.

As shown in Fig. 1, the DI is located in the same plane as the plane where the sample S is located. This is because the focal point of the parabolic reflector needs to be in the sample plane so that all dark-field beams are collimated and directed to the sample. As a consequence, the size of the sample is limited by the diameter of the smallest LED ring of the DI, which makes this system difficult to use in industry.

In this paper, the parabolic reflector is replaced with segmented mirrors and a mask. By locating them far from the sample plane, there is far less restriction on the size and shape of the sample. This arrangement allows reflective FPM to be more suitable for use in industry.

II. METHODS

Figures 2(a) and (b) show the difference between a dark-field illuminator using a parabolic reflector, and one using segmented mirrors. As mentioned in the previous section, when a parabolic reflector is used, the size of the sample is limited (Fig. 2(a), blue dashed box). On the other hand, when using segmented mirrors located in the dark-field LED array, there is no sample size restriction (Fig. 2(b), blue dashed box).

Figure 2. Comparison between two types of dark-field illuminator: (a) dark-field illuminator using a parabolic reflector, (b) dark-field illuminator using segmented mirrors. The blue dashed boxes in (a), (b) indicate the space available for a sample.

However, segmented mirrors cannot be independently used as an illuminator. Unlike a laser, an LED has a large divergence angle. Therefore, two beam components are created: one is a beam reflected from a segmented mirror (red line), and the other is a direct beam (orange line), as illustrated in Fig. 3(a).

Figure 3. Two beam components created by a segmented mirror. (a) Layout of beams from the LED. Red rays represent a beam component reflected from a segmented mirror, Orange rays represent a beam component directly incident on a sample. A green region indicates where the two beam components overlap. (b) When a pinhole was placed in the overlapping region, the two beam components were projected onto the bottom. (c) A mask (gray lines) can block the direct beam component which acts like noise in the FPM reconstruction.

To show that two beam components are generated and illuminated on the sample, we put a pinhole in the sample plane and the two beam components were detected, as shown in Fig. 3(b). Since the direct beam behaves like noise, we used a mask to eliminate it, as in Fig. 3(c). We made two measurements to prove the effect of the mask: one was without a mask, and the other was with a mask. The results are described in the next section.

III. RESULTS

We conducted experiments to demonstrate the feasibility of the segmented mirrors and a mask as a dark-field illuminator for reflective FPM. The experimental setup and the picture of it are depicted in Fig. 4. In practice, we made a compact prototype of the experimental setup using folding mirrors.

Figure 4. Experimental setup (left) and picture (right) of the reflective Fourier ptychographic microscope with segmented mirrors and a mask.

16 LED beams from a bright-field illuminator (BI) are image relayed to the back-focal plane of the objective lens (OL, Mitutoyo 10x, 0.28 NA) by using 4-f imaging with L1 (f = 150 mm) and L2 (f = 300 mm). They are then collimated by OL and illuminated on the sample. A dark-field illuminator (DI) consists of an LED array with 72 LEDs and 72 segmented mirrors and a mask. As a result, 88 LED beams give an increase in NA more than 1.0. Figure 5 shows the k-space diagram (left) and the resulting signals in Fourier domain (right).

Figure 5. Comparison of signals obtained from on-axis illumination and oblique illumination. The signals when an on-axis beam is illuminated (up) and the ones when 88 LEDs in bright-field illuminator and dark-field illuminator are illuminated (down). The pictures on the left represent k-space diagram and the ones on the right represent the signals in Fourier domain.

When the 72 beams from the LED array are sequentially on and off, each beam is reflected by its segmented mirror and illuminated on the sample. The reflected beams from the sample are detected by a camera (CMOS, Basler acA 4112-20 μm), after passing through OL, beamsplitter (BS), and a tube lens (f = 180 mm). The LED arrays in BI and DI have a ring shape which enables effective FPM reconstruction [20]. As shown in Fig 4, there are no obstructions which can restrict the position and size of the sample.

After setting up, we measured a USAF 1951 target (Newport, HIGHRES-1) to prove the feasibility of the new dark-field illuminator. Figures 6(a), (b) show the results obtained by FPM reconstruction without a mask and with a mask, respectively.

Figure 6. The resulting high-resolution images after FPM reconstruction using the dark-field illuminator including (a) segmented mirrors-only, and (b) segmented mirrors and a mask. In (a), a pattern in group 10 and element 2 (G10E2, 435 nm) are resolved, while a pattern in group 10 and element 6 (G10E1, 274 nm) are resolved in (b). In the graphs of the contrast ratio, ‘L’ and ‘R’ represent left and right, respectively.

In Fig. 6(a), we can see that most of the patterns on the sample have point-like noises (red circles) and low contrast. It is because the direct beam component creates another wave vector, causing noise during FPM reconstruction. Since the noise from the direct beam component and the signal from the reflected beam component are coherent, they could make unwanted interference patterns during FPM reconstruction, seeming like bright and dark spots. In this case, the patterns in group 10 element 2 on the USAF 1951 sample were resolved. Alternatively, when using a mask, the noise was greatly reduced and the contrast was improved. As a result, the patterns in group 10 element 6 (about 274 nm) on the USAF 1951 sample were resolved.

IV. DISCUSSION

The resolution of the system with the new dark-field illuminator recorded a resolution of 274 nm, which is a little degraded compared to a system using a parabolic reflector [19]. One of the reasons is that the mask could not totally eliminate the unwanted beam component. It could be overcome by designing a mask using a ray tracing to effectively eliminate the noise. Moreover, the segmented mirrors and the masks are placed separately as shown in Fig. 4, so it is hard to align them. If they are made as an all-in-one illuminator, the direction of the beam component reflected from each segmented mirror is much more easily controlled, resulting in a more clear reconstruction image.

In addition, if the reflected beam components illuminating the sample are not perfectly collimated, it could affect FPM reconstruction. Fortunately, its effect is small because the distance between the LED array in DI and the sample is more than 67 mm, which is far enough to make uniform intensity on the sample plane.

V. CONCLUSION

Segmented mirrors and a mask are proposed as an alternative to a parabolic mirror for reflective FPM. The new illuminator has the advantage of providing more freedom in terms of sample size and position. The feasibility of the new illuminator was demonstrated by measuring a USAF 1951 target, first with the segmented mirrors alone, and then with the segmented mirrors and a mask. Compared with the segmented mirrors alone, the new illuminator with the added mask had better performance, resolving a group 10 element 6 (274 nm) of the USAF target. We expect that the new dark-field illuminator consisting of segmented mirrors and a mask will make reflective FPM more applicable for sample measurement in industry.

ACKNOWLEDGMENT

This study was supported by a grant from Korea Research Institute of Standards and Science (KRISS) (GP2020-0009-04).

Fig 1.

Figure 1.Experimental setup of reflective Fourier ptychographic microscopy using a parabolic reflector.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

Fig 2.

Figure 2.Comparison between two types of dark-field illuminator: (a) dark-field illuminator using a parabolic reflector, (b) dark-field illuminator using segmented mirrors. The blue dashed boxes in (a), (b) indicate the space available for a sample.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

Fig 3.

Figure 3.Two beam components created by a segmented mirror. (a) Layout of beams from the LED. Red rays represent a beam component reflected from a segmented mirror, Orange rays represent a beam component directly incident on a sample. A green region indicates where the two beam components overlap. (b) When a pinhole was placed in the overlapping region, the two beam components were projected onto the bottom. (c) A mask (gray lines) can block the direct beam component which acts like noise in the FPM reconstruction.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

Fig 4.

Figure 4.Experimental setup (left) and picture (right) of the reflective Fourier ptychographic microscope with segmented mirrors and a mask.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

Fig 5.

Figure 5.Comparison of signals obtained from on-axis illumination and oblique illumination. The signals when an on-axis beam is illuminated (up) and the ones when 88 LEDs in bright-field illuminator and dark-field illuminator are illuminated (down). The pictures on the left represent k-space diagram and the ones on the right represent the signals in Fourier domain.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

Fig 6.

Figure 6.The resulting high-resolution images after FPM reconstruction using the dark-field illuminator including (a) segmented mirrors-only, and (b) segmented mirrors and a mask. In (a), a pattern in group 10 and element 2 (G10E2, 435 nm) are resolved, while a pattern in group 10 and element 6 (G10E1, 274 nm) are resolved in (b). In the graphs of the contrast ratio, ‘L’ and ‘R’ represent left and right, respectively.
Current Optics and Photonics 2021; 5: 40-44https://doi.org/10.3807/COPP.2021.5.1.040

References

  1. G. Zheng, R. Horstmeyer and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739-745 (2013).
    Pubmed KoreaMed CrossRef
  2. Z. Bian, S. Dong and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21, 32400-32410 (2013).
    Pubmed CrossRef
  3. L. Tian, X. Li, K. Ramchandran and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376-2389 (2014).
    Pubmed KoreaMed CrossRef
  4. X. Ou, G. Zheng and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960-4972 (2014).
    Pubmed KoreaMed CrossRef
  5. Y. Zhang, W. Jiang and Q. Dai, “Nonlinear optimization approach for Fourier ptychographic microscopy,” Opt. Express 23, 33822-33835 (2015).
    Pubmed CrossRef
  6. X. Ou, R. Horstmeyer. G. Zheng and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472-3491 (2015).
    Pubmed KoreaMed CrossRef
  7. C. Zuo, J. Sun and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24, 20724-20744 (2016).
    Pubmed CrossRef
  8. J. Sun, Q. Chen, Y. Zhang and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336-1350 (2016).
    Pubmed KoreaMed CrossRef
  9. J. Sun, C. Zuo, L. Zhang and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
    Pubmed KoreaMed CrossRef
  10. A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22, 096005 (2017).
    Pubmed CrossRef
  11. A. Pan, Y. Zhang, K. When, M. Zhou, J. Min, M. Lei and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26, 23119-23131 (2018).
    Pubmed CrossRef
  12. B. Lee, J.-Y. Hong, D. Yoo, J. Cho, Y. Jeong, S. Moon and B. Lee, “Single-shot phase retrieval via Fourier ptychographic microscopy,” Optica 5, 976-983 (2018).
    CrossRef
  13. J. Sun, C. Zuo, J. Zhang, Y. Fan and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8, 7669 (2018).
    Pubmed KoreaMed CrossRef
  14. A. Zhou, W. Wang, N. Chen, E. Y. Lam, B. Lee and G. Situ, “Fast and robust misalignment correction of Fourier ptychographic microscopy for full field of view reconstruction,” Opt. Express 26, 23661-23674 (2018).
    Pubmed CrossRef
  15. X. Chen, Y. Zhu, M. Sun, D. Li, Q. Mu and L. Xuan, “Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy,” Opt. Express 27, 14099-14111 (2019).
    Pubmed CrossRef
  16. S. Pacheco, B. Salahieh, T. Milster, J. J. Rodriguez and R. Liang, “Transfer function analysis in epi-illumination Fourier ptychography,” Opt. Lett. 40, 5343-5346 (2015).
    Pubmed KoreaMed CrossRef
  17. S. Pacheco, G. Zheng and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21, 026010 (2016).
    Pubmed CrossRef
  18. K. Guo, S. Dong and G. Zheng, “Fourier ptychography for brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging,” IEEE J. Sel. Top. Quantum Electron. 22, 77-88 (2016).
    CrossRef
  19. H. Lee, B. H. Chon and H. K. Ahn, “Reflective Fourier ptychographic microscopy using a parabolic mirror,” Opt. Express 27, 34382-34391 (2019).
    Pubmed CrossRef
  20. K. Guo, S. Dong, P. Nanda and G. Zheng, “Optimization of sampling pattern and the design of Fourier ptychographic illuminator,” Opt. Express 23, 6171-6180 (2015).
    Pubmed CrossRef