Abstract

The trade-off between spot size and depth of focus (DOF) often limits the performance of optical systems, such as optical coherence tomography and optical tweezers. Although researchers have proposed various methods to extend the DOF in free-space optics, many are difficult to implement in miniaturized optical probes due to space limitations. In this study, we present an optical probe with an extended DOF using a binary phase spatial filter (BPSF). The BPSF pattern was fabricated on the distal tip of an optical probe with a diameter of 1 mm by replica molding soft lithography, which can be easily implemented in a miniaturized optical probe due to its simple configuration. We optimized the BPSF pattern to enhance DOF, spot diameter, and light efficiency. To evaluate the fabricated endoscopic optical probe, we measured the three-dimensional point spread function of the BPSF probe and compared it with a probe without BPSF. The BPSF probe has a spot diameter of 3.56 μm and a DOF of 199.7 μm, while the probe without BPSF has a spot diameter of 3.69 μm and a DOF of 73.9 μm, representing a DOF gain of 2.7. We anticipate that this optical probe can be used in biomedical applications, including optical imaging and optical trapping techniques.

© 2016 Optical Society of America

1. Introduction

Endoscopic optical probes are widely used in various applications, such as optical imaging [1, 2] and optical tweezers [3]. Although many applications require a small spot size and long depth of focus (DOF), there is a tradeoff between the spot diameter (D) and the DOF. The diameter of the beam spot and the depth of focus of a Gaussian beam are defined as:

D=4λπNA,
DOF=8λπNA2,
where λ is the wavelength of the light and NA is the numerical aperture of the focusing lens [4]. The spot size can be decreased by using a lens with a higher NA; however, the DOF decreases rapidly at the same time [4]. To overcome this limitation, various methods have been proposed to maintain a small spot size over a long range.

Existing DOF extension methods can be categorized into three groups [5]: digital refocusing methods [5–10], Bessel-like beam generation [11–14], and amplitude or phase modulation methods [15–20]. Phase modulation methods are attractive for biomedical applications because of their simple configuration and high light efficiency [17]. L. Liu et al. developed a four-zone binary phase spatial filter and applied it in optical coherence microscopy [17]. Y. Xu et al. described a multi-zone rotationally symmetrical complex pupil filter that modulates both amplitude and phase to generate an ultra-long high resolution beam [18]. However, these multi-zone filters have not yet been implemented in endoscopic systems due to the difficulty of miniaturizing the multi-zone filters. In fact, there are few reports of miniaturized endoscopic probes with extended DOF [3, 20]. In this paper, we propose a practical method to design and fabricate a miniaturized multi-zone phase modulation filter for endoscopic optical systems.

First, we optimally designed a binary phase spatial filter (BPSF) to enhance the DOF, minimize the spot size, and maintain the light efficiency. Then, we fabricated the BPSF at the distal tip of a miniaturized optical probe with a diameter of 1mm by replica molding soft lithography. Replica molding soft lithography has been widely used in micro- and nanostructure fabrication because it can easily produce multiple copies without damaging the master [21]. Recently, using replica molding soft lithography, D. Kang et al. successfully fabricated a miniature grating at the distal tip of the optical fiber for an ultra-small endoscopic imaging probe [22]. Finally, we observed the three-dimensional (3-D) point spread function (PSF) of the BPSF probe to evaluate the performance and compared it with that of a probe without BPSF.

2. Methods

2.1 BPSF probe design

A schematic of the BPSF probe with an outer diameter of 1.0 mm is shown in Fig. 1(a). Light from a single mode fiber (SMF) passes through a glass spacer and is focused by a gradient index (GRIN) lens (GoFoton, Somerset, NJ). We set the length of the glass spacer and the GRIN lens to 2.5 mm and 1.88 mm, respectively, to achieve a working distance of 1.5 mm and a spot diameter of 3.0 μm. At the distal tip of the GRIN lens, the BPSF modulates the spatial phase distribution to extend the DOF. The schematic of the BPSF pattern is shown in Fig. 1(b), following the work of L. Liu et al. [17]. It has four circular phase delay zones with a shifting phase of 0 (white zones) or π (gray zones). The phase delay, induced by the optical path difference, can be written as:

φ=π2(n1)dλ,
where d is the height of the BPSF, n is the refractive index of the BPSF, and λ is the light wavelength. Thus, the required height of the BPSF to obtain the binary phase at each zone is given as:
d=λ2(n1).
We used a UV curing epoxy (OG603, Epoxy Technology Inc., Billerica, MA) to make the BPSF. The refractive index of the UV curing epoxy (n = 1.50) and the wavelength of the light source (λ = 800 nm) determined that the height of the BPSF should be 0.8 μm.

 figure: Fig. 1

Fig. 1 (a) Schematic of the probe without (top) and with (bottom) BPSF. (b) Structure of the BPSF and its cross-section. The height d was set to 0.8 μm to achieve the phase delay of π (gray zones).

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2.2 Simulation and optimization

The performance of the BPSF depends on the radius of each zone. To search for the optimal radii (ra, rb, rc), we simulated the 3-D PSF of all combinations of ra, rb, and rc within the range of 5 μm to 300 μm. We calculated the following parameters for this simulation: (1) DOF, which we defined as two times the Rayleigh range; (2) full-width at half maximum (FWHM) of the spot at the focal plane; and (3) light efficiency (LE), which we defined as the ratio between the peak intensity of the BPSF probe and that of the probe without BPSF. We excluded simulation results that met the following conditions: (1) The peak intensity of the center lobe on the focal plane was smaller than 50% of the maximum intensity of the 3-D PSF, and (2) the peak intensity of the first side lobe on the focal plane was more than 50% of the peak intensity of the central lobe. Figures 2(a)-2(c) show exemplary maps of DOF, FWHM, and LE, respectively, with changes of rb and rc when ra = 40 μm. To find the optimal result, we built a merit function:

f=w1DOF+w2×FWHM+w3LE,
where w1, w2, and w3 are the weighting values, and DOF, FWHM, and LE were normalized by their maximum value to generate the merit function. Because our main purpose was to extend the DOF while maintaining proper spot size and light efficiency, we put more weighting on DOF, then empirically determined the weighting values, w1, w2, and w3, as 10, 5 and 5, respectively. Figure 2(d) shows the values of the merit function f. The red and green boxes indicate the locations of the optimal results, where the merit function has the minimum value. Because the result in the red box is more sensitive to the change of radius than that in the green box, we selected an optimal result from the green box. The selected optimal radii were: ra = 40 μm, rb = 185 μm, and rc = 210 μm.

 figure: Fig. 2

Fig. 2 The maps of the (a) DOF, (b) FWHM diameter, (c) LE, and (d) merit function f, with the change of rb and rc when ra = 40 μm. The red and green boxes in (d) indicate the candidates of optimal design.

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Figures 3(a) and 3(b) shows the simulated XZ PSF (left) and the X-intensity profiles at different defocus distances (right panels) of the probe without BPSF and the optimized BPSF probe, respectively. Figures 3(c) and 3(d) shows the FWHM diameter and the normalized on-axis intensity profile, respectively, for the probe without (blue line) and with the BPSF (red line). The dashed line in Fig. 3 (c) indicates the range of DOF. The probe without BPSF has a minimum FWHM diameter and DOF of 3.11 μm and 72.7 μm, respectively. As shown in Fig. 3, the BPSF probe maintains a small spot size over a long range. The DOF of the BPSF probe is 192.2 μm, representing a DOF gain of 2.6 over the probe without BPSF. Also, the axial intensity distribution of the BPSF probe is maintained in a longer range than it is for the probe without BPSF.

 figure: Fig. 3

Fig. 3 (a, b) Simulated XZ PSF (left) and X intensity profiles at different defocus distances (right panels) of (a) the probe without BPSF and (b) the BPSF probe. (c) Simulated FWHM diameter as a function of defocus without (blue) and with (red) BPSF. The dashed line indicates the range of DOF. (d) Simulated normalized on-axis intensity distribution without (blue) and with (red) BPSF.

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2.3 Fabrication method of the BPSF probe

In a previous research by L. Liu et al, programmable phase modulator (PPM) was used to generate the BPSF for extending DOF of optical coherence microscopy in a free-space setup [17]. However, due to the space limitation, bulky optical components, such as the PPM, cannot be used in an optical probe. To implement the BPSF for miniaturized endoscopic systems in a practical way, we used replica molding soft lithography to pattern the optimal BPSF at the distal tip of an optical probe. A silicon elastomer, PDMS (Sylgard 184, Dow Corning, Auburn, MI), was used as a stamp to copy the BPSF pattern from the master onto the probe. Figure 4 shows the flowchart of the fabrication process. First, we made the optimal BPSF pattern on a silicon wafer by anisotropic etching (NanoFab Center, KAIST, Korea). The patterned silicon wafer was used as a master pattern [Fig. 4(a)]. Then, we coated the silicon wafer with the PDMS, which we used as a stamp to produce multiple copies, and baked it at 60°C for 2 hours [Fig. 4(b)]. The PDMS layer was carefully peeled from the surface while it was still warm [Fig. 4(c)]. To stamp the pattern on the distal tip of the probe, we applied a thin layer (~20 μm) of UV curing epoxy (OG603, Epoxy Technology Inc., Billerica, MA) on the distal surface of the GRIN lens and aligned it with the PDMS stamp [Fig. 4(d)]. The epoxy was cured with UV light (Blue Wave 75, Dymax Corp., Torrington, CT) for 60 seconds [Fig. 4(e)]. Once the epoxy was cured, the PDMS stamp was separated from the cured epoxy, leaving the BPSF pattern in the UV epoxy on the surface of the GRIN lens [Fig. 4(f)]. Last, we aligned the SMF fiber, the glass spacer, and the GRIN lens with the BPSF pattern [Fig. 4(g)]. To ensure that the center of the BPSF was on the optical axis, the alignment process was monitored by observing the light distribution of the BPSF surface using a beam profiler (WinCamD-UCD12, DataRay Inc., Redding, CA).

 figure: Fig. 4

Fig. 4 Schematic diagram of fabrication processes.

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3. Results

3.1 Fabrication results

The fabricated BPSF probe is shown in Fig. 5(a). Figure 5(b), a picture of the distal tip of the probe, clearly shows the BPSF pattern under a stereo microscope. To assess whether the height of the BPSF pattern was accurately replicated, we measured its surface profile using a confocal three-dimensional microscope (Nanoscope System Inc., Daejeon, Korea), as shown in Figs. 5(c) and 5(d). The height of the pattern was 0.766 μm, which corresponds well to the design value of 0.8 μm.

 figure: Fig. 5

Fig. 5 Results of the fabricated BPSF probe. A photograph of (a) the probe and (b) the BPSF pattern on the distal tip of the probe. (c) The 3D surface profile of the BPSF and (d) its height profile measured by a confocal three-dimensional microscope.

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3.2 Performance test

To evaluate the BPSF probe, we measured the 3-D PSF using the experimental setup shown in Fig. 6. To magnify and record the 3-D PSF, we aligned the probe, a 20x objective lens with an effective focal length of 8.55 mm (#38-339, Edmund Optics, Barrington, NJ), and the beam profiler. An SLD light source (BLMS-mini-341-HP1-SM-PD-FC/APC, SUPERLUM Inc., Ireland) was used, which has a center wavelength of 809.9 nm and a bandwidth of 25.3 nm. We recorded the magnified XY PSFs while we moved the probe back and forth from its focal plane along the optical axis in 10 μm steps with a defocus range from −150 to 150 μm.

 figure: Fig. 6

Fig. 6 Experimental setup for measuring the 3-D PSF of the probe.

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Figure 7(a) and 7(b) shows the measured XZ PSF of the probe without and with BPSF, respectively. Compared with the probe without BPSF, the BPSF probe maintained the spot size over a longer range. Figure 7(c) shows the FWHM diameter of the probe without (blue line) and with BPSF (red line). The minimum FWHM diameter of the probe with and without BPSF was 3.56 μm and 3.69 μm, respectively. On the other hand, the DOF was extended by a factor of 2.7 from 73.9 to 199.7 μm. The on-axis intensity distribution is shown in Fig. 7(d). It confirms that the BPSF probe maintains its intensity over a longer range than the probe without BPSF. As shown in Figs. 3 and 7, The experimental results showed a close agreement between the simulated results. Slight discrepancy between the experiment and the simulation might be caused by the center wavelength and the bandwidth of the light source, unexpected aberration in the probe, and measurement errors.

 figure: Fig. 7

Fig. 7 Measured 3-D PSF of (a) the probe without BPSF and (b) the BPSF probe. Intensity profiles are shown in the right panels through the defocus distances. (c) Measured FWHM diameter without (blue) and with (red) BPSF. The dashed line indicates the range of DOF. (d) Measured normalized on-axis intensity distribution without (blue) and with (red) BPSF.

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4. Conclusion

We have developed a 1-mm-diameter optical probe with an extended depth of focus using a BPSF. We obtained DOF gains of 2.6 and 2.7 in our simulation and experiment, respectively, while maintaining the spot diameter. Also, the axial intensity distribution of the BPSF probe was more uniform than that of the probe without BPSF.

Replica molding soft lithography is a cost-effective way to fabricate the BPSF probe, not only because the BPSF pattern can be easily generated by a simple stamping process, but also because multiple copies of the BPSF pattern can be fabricated using the PDMS mold. Another advantage of this method is that a failed pattern can be easily removed using an acetone solution, and then a new pattern can be fabricated on the same probe. This cost-effectiveness is especially attractive in biomedical applications in which probes need to be disposable for safety reasons.

One limitation of the presented BPSF probe is the decreased peak intensity, which was 40% of the peak intensity of the probe without BPSF in this study. In fact, the decrease of the peak intensity in BPSF probe is inevitable due to the compromise between the peak intensity and the DOF. In imaging applications, such as optical coherence tomography (OCT), the decrease of the peak intensity will lead to a drop of signal-to-noise ratio (SNR). Since current state-of-the-art OCT systems have very high sensitivity [23], increasing DOF at the expense of the slightly reduced SNR is reasonable in majority of applications for OCT [17, 20]. Depending on the applications, of course, the design of the BPSF pattern could be re-optimized to strike a different compromise among the spot size, axial range, and light efficiency. Also, this problem could be addressed by increasing the optical power of the source.

We anticipate that this miniaturized optical probe with an extended DOF will be used in biomedical studies, including optical imaging and optical tweezers. Specifically, the BPSF probe can be used directly as a high-resolution endoscopic imaging probe for optical coherence tomography to visualize tomographic images of biological tissues. With improved imaging properties such as high-resolution with an extended imaging range, the BPSF probe can be applied in clinical and pre-clinical studies in various medical fields, including cardiology and gastroenterology.

Acknowledgments

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2015R1A1A1A05027209).

References and links

1. G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997). [CrossRef]   [PubMed]  

2. S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007). [CrossRef]   [PubMed]  

3. J. Kim, Y. Jeong, S. Lee, W. Ha, J. S. Shin, and K. Oh, “Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping,” Opt. Lett. 37(4), 623–625 (2012). [CrossRef]   [PubMed]  

4. B. Bouma, Handbook of Optical Coherence Tomography (Informa Health Care, 2001).

5. J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013). [CrossRef]   [PubMed]  

6. Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express 14(3), 1006–1020 (2006). [CrossRef]   [PubMed]  

7. L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express 15(12), 7634–7641 (2007). [CrossRef]   [PubMed]  

8. B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008). [CrossRef]   [PubMed]  

9. I. Grulkowski, K. Szulzycki, and M. Wojtkowski, “Microscopic OCT imaging with focus extension by ultrahigh-speed acousto-optic tunable lens and stroboscopic illumination,” Opt. Express 22(26), 31746–31760 (2014). [CrossRef]   [PubMed]  

10. Y. Z. Liu, N. D. Shemonski, S. G. Adie, A. Ahmad, A. J. Bower, P. S. Carney, and S. A. Boppart, “Computed optical interferometric tomography for high-speed volumetric cellular imaging,” Biomed. Opt. Express 5(9), 2988–3000 (2014). [CrossRef]   [PubMed]  

11. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, “High-resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27(4), 243–245 (2002). [CrossRef]   [PubMed]  

12. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef]   [PubMed]  

13. C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express 19(13), 12141–12155 (2011). [CrossRef]   [PubMed]  

14. D. Lorenser, C. Christian Singe, A. Curatolo, and D. D. Sampson, “Energy-efficient low-Fresnel-number Bessel beams and their application in optical coherence tomography,” Opt. Lett. 39(3), 548–551 (2014). [CrossRef]   [PubMed]  

15. H. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40(31), 5658–5662 (2001). [CrossRef]   [PubMed]  

16. M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22(2), 272–277 (2005). [CrossRef]   [PubMed]  

17. L. Liu, C. Liu, W. C. Howe, C. J. Sheppard, and N. Chen, “Binary-phase spatial filter for real-time swept-source optical coherence microscopy,” Opt. Lett. 32(16), 2375–2377 (2007). [CrossRef]   [PubMed]  

18. Y. Xu, J. Singh, C. J. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007). [CrossRef]   [PubMed]  

19. L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011). [CrossRef]   [PubMed]  

20. D. Lorenser, X. Yang, and D. D. Sampson, “Ultrathin fiber probes with extended depth of focus for optical coherence tomography,” Opt. Lett. 37(10), 1616–1618 (2012). [CrossRef]   [PubMed]  

21. D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010). [CrossRef]   [PubMed]  

22. D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013). [CrossRef]   [PubMed]  

23. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003). [CrossRef]   [PubMed]  

References

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  1. G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
    [Crossref] [PubMed]
  2. S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
    [Crossref] [PubMed]
  3. J. Kim, Y. Jeong, S. Lee, W. Ha, J. S. Shin, and K. Oh, “Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping,” Opt. Lett. 37(4), 623–625 (2012).
    [Crossref] [PubMed]
  4. B. Bouma, Handbook of Optical Coherence Tomography (Informa Health Care, 2001).
  5. J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013).
    [Crossref] [PubMed]
  6. Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express 14(3), 1006–1020 (2006).
    [Crossref] [PubMed]
  7. L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express 15(12), 7634–7641 (2007).
    [Crossref] [PubMed]
  8. B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
    [Crossref] [PubMed]
  9. I. Grulkowski, K. Szulzycki, and M. Wojtkowski, “Microscopic OCT imaging with focus extension by ultrahigh-speed acousto-optic tunable lens and stroboscopic illumination,” Opt. Express 22(26), 31746–31760 (2014).
    [Crossref] [PubMed]
  10. Y. Z. Liu, N. D. Shemonski, S. G. Adie, A. Ahmad, A. J. Bower, P. S. Carney, and S. A. Boppart, “Computed optical interferometric tomography for high-speed volumetric cellular imaging,” Biomed. Opt. Express 5(9), 2988–3000 (2014).
    [Crossref] [PubMed]
  11. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, “High-resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27(4), 243–245 (2002).
    [Crossref] [PubMed]
  12. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008).
    [Crossref] [PubMed]
  13. C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express 19(13), 12141–12155 (2011).
    [Crossref] [PubMed]
  14. D. Lorenser, C. Christian Singe, A. Curatolo, and D. D. Sampson, “Energy-efficient low-Fresnel-number Bessel beams and their application in optical coherence tomography,” Opt. Lett. 39(3), 548–551 (2014).
    [Crossref] [PubMed]
  15. H. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40(31), 5658–5662 (2001).
    [Crossref] [PubMed]
  16. M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22(2), 272–277 (2005).
    [Crossref] [PubMed]
  17. L. Liu, C. Liu, W. C. Howe, C. J. Sheppard, and N. Chen, “Binary-phase spatial filter for real-time swept-source optical coherence microscopy,” Opt. Lett. 32(16), 2375–2377 (2007).
    [Crossref] [PubMed]
  18. Y. Xu, J. Singh, C. J. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007).
    [Crossref] [PubMed]
  19. L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
    [Crossref] [PubMed]
  20. D. Lorenser, X. Yang, and D. D. Sampson, “Ultrathin fiber probes with extended depth of focus for optical coherence tomography,” Opt. Lett. 37(10), 1616–1618 (2012).
    [Crossref] [PubMed]
  21. D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
    [Crossref] [PubMed]
  22. D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
    [Crossref] [PubMed]
  23. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
    [Crossref] [PubMed]

2014 (3)

2013 (2)

J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013).
[Crossref] [PubMed]

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (2)

C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express 19(13), 12141–12155 (2011).
[Crossref] [PubMed]

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

2010 (1)

D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
[Crossref] [PubMed]

2008 (2)

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008).
[Crossref] [PubMed]

2007 (4)

2006 (1)

2005 (1)

2003 (1)

2002 (1)

2001 (1)

1997 (1)

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Adie, S. G.

Ahmad, A.

Biedermann, B. R.

Blatter, C.

Boppart, S. A.

Y. Z. Liu, N. D. Shemonski, S. G. Adie, A. Ahmad, A. J. Bower, P. S. Carney, and S. A. Boppart, “Computed optical interferometric tomography for high-speed volumetric cellular imaging,” Biomed. Opt. Express 5(9), 2988–3000 (2014).
[Crossref] [PubMed]

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Bouma, B. E.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Bower, A. J.

Brezinski, M. E.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Carney, P. S.

Y. Z. Liu, N. D. Shemonski, S. G. Adie, A. Ahmad, A. J. Bower, P. S. Carney, and S. A. Boppart, “Computed optical interferometric tomography for high-speed volumetric cellular imaging,” Biomed. Opt. Express 5(9), 2988–3000 (2014).
[Crossref] [PubMed]

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

Chan, R. C.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Chen, N.

Chen, Z.

Choma, M.

Christian Singe, C.

Curatolo, A.

Davis, B. J.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

de Boer, J. F.

J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

de Groot, M.

Desjardins, A. E.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Ding, Z.

Eigenwillig, C. M.

Evans, J. A.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Fujimoto, J. G.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Gan, F.

Gardecki, J. A.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

Grajciar, B.

Grulkowski, I.

Guo, S.

Ha, W.

Howe, W. C.

Huber, R.

Itoh, M.

Izatt, J.

Jang, I. K.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Jeong, Y.

Kang, D.

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

Kim, J.

Lee, K. S.

Lee, S.

Leitgeb, R. A.

Liu, C.

Liu, D.

Liu, L.

Liu, Y. Z.

Lorenser, D.

Makita, S.

Marks, D. L.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

Martinez, R. V.

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

Mo, J.

Nadkarni, S. K.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

Nakamura, Y.

Nelson, J. S.

Nishioka, N. S.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Oh, K.

Oh, W. Y.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Pitris, C.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Qin, D.

D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
[Crossref] [PubMed]

Ralston, T. S.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

Rao, B.

Ren, H.

Rolland, J. P.

Sampson, D. D.

Sando, Y.

Sarunic, M.

Shemonski, N. D.

Sheppard, C. J.

Shin, J. S.

Shishkov, M.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Singh, J.

Southern, J. F.

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Su, J.

Sugisaka, J.

Sun, J.

Suter, M. J.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Szulzycki, K.

Tearney, G. J.

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Toussaint, J. D.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

Vakoc, B. J.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Wang, H.

Wang, Q.

Whitesides, G. M.

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
[Crossref] [PubMed]

Wieser, W.

Wojtkowski, M.

Xia, Y.

D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
[Crossref] [PubMed]

Xu, Y.

Yagi, Y.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

Yang, C.

Yang, X.

Yasuno, Y.

Yatagai, T.

Yu, L.

Yun, M.

Yun, S. H.

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Zhang, J.

Zhao, Y.

Appl. Opt. (1)

Biomed. Opt. Express (1)

J. Opt. Soc. Am. A (1)

Lab Chip (1)

D. Kang, R. V. Martinez, G. M. Whitesides, and G. J. Tearney, “Miniature grating for spectrally-encoded endoscopy,” Lab Chip 13(9), 1810–1816 (2013).
[Crossref] [PubMed]

Nat. Med. (2)

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011).
[Crossref] [PubMed]

S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. 12(12), 1429–1433 (2007).
[Crossref] [PubMed]

Nat. Protoc. (1)

D. Qin, Y. Xia, and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nat. Protoc. 5(3), 491–502 (2010).
[Crossref] [PubMed]

Opt. Express (7)

Y. Xu, J. Singh, C. J. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15(10), 6409–6413 (2007).
[Crossref] [PubMed]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[Crossref] [PubMed]

I. Grulkowski, K. Szulzycki, and M. Wojtkowski, “Microscopic OCT imaging with focus extension by ultrahigh-speed acousto-optic tunable lens and stroboscopic illumination,” Opt. Express 22(26), 31746–31760 (2014).
[Crossref] [PubMed]

J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013).
[Crossref] [PubMed]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express 14(3), 1006–1020 (2006).
[Crossref] [PubMed]

L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express 15(12), 7634–7641 (2007).
[Crossref] [PubMed]

C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express 19(13), 12141–12155 (2011).
[Crossref] [PubMed]

Opt. Lett. (6)

Science (1)

G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997).
[Crossref] [PubMed]

Sensors (Basel) (1)

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors (Basel) 8(6), 3903–3931 (2008).
[Crossref] [PubMed]

Other (1)

B. Bouma, Handbook of Optical Coherence Tomography (Informa Health Care, 2001).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the probe without (top) and with (bottom) BPSF. (b) Structure of the BPSF and its cross-section. The height d was set to 0.8 μm to achieve the phase delay of π (gray zones).
Fig. 2
Fig. 2 The maps of the (a) DOF, (b) FWHM diameter, (c) LE, and (d) merit function f, with the change of rb and rc when ra = 40 μm. The red and green boxes in (d) indicate the candidates of optimal design.
Fig. 3
Fig. 3 (a, b) Simulated XZ PSF (left) and X intensity profiles at different defocus distances (right panels) of (a) the probe without BPSF and (b) the BPSF probe. (c) Simulated FWHM diameter as a function of defocus without (blue) and with (red) BPSF. The dashed line indicates the range of DOF. (d) Simulated normalized on-axis intensity distribution without (blue) and with (red) BPSF.
Fig. 4
Fig. 4 Schematic diagram of fabrication processes.
Fig. 5
Fig. 5 Results of the fabricated BPSF probe. A photograph of (a) the probe and (b) the BPSF pattern on the distal tip of the probe. (c) The 3D surface profile of the BPSF and (d) its height profile measured by a confocal three-dimensional microscope.
Fig. 6
Fig. 6 Experimental setup for measuring the 3-D PSF of the probe.
Fig. 7
Fig. 7 Measured 3-D PSF of (a) the probe without BPSF and (b) the BPSF probe. Intensity profiles are shown in the right panels through the defocus distances. (c) Measured FWHM diameter without (blue) and with (red) BPSF. The dashed line indicates the range of DOF. (d) Measured normalized on-axis intensity distribution without (blue) and with (red) BPSF.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

D= 4λ πNA ,
DOF= 8λ πN A 2 ,
φ=π 2(n1)d λ ,
d= λ 2(n1) .
f= w 1 DOF + w 2 ×FWHM+ w 3 LE ,

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