Open Access
Add to BibSonomy
Abstract
Fiber-optical microendoscopy has made significant improvements to in vivo neural imaging, minimally invasive diagnostics, and microsurgery. However, high resolution, miniaturization, and low complexity cannot be simultaneously achieved together in the lens system for fiber-optical microendoscopy because current lens systems are in shape and dimensions restricted by limitations of manufacturing. Recently, two-photon direct laser writing (DLW) has been implemented in the fabrication of low-resolution micro-optics structures. Here, we demonstrate a high-resolution miniaturized singlet aspherical microlens fabricated on the fiber facet using DLW. The microlens has a high numerical aperture (NA), of 0.9, in air with only one aspherical surface, and is 10–20 times smaller in diameter than a typical gradient refractive index (GRIN) microlens. The designs of aspherical microlenses with NAs of 0.3, 0.6, and 0.9 in air are aberration-free at three wavelengths (561, 590, and 630 nm). The full width at half maximum of the effective intensity point spread function of a 0.9 NA aspherical microlens is 0.85 μm. We demonstrate fiber-optical microendoscopy imaging with a 0.6 NA aspherical microlens. The proposed aspherical microlens can potentially be applied to the development of a high-resolution, extremely miniaturized fiber-optical microendoscope.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber-optical microendoscopy has become more significant in the applications of in vivo neural imaging, minimally invasive diagnostics, and microsurgery, owing to its high performance, compact size and flexibility [1–3]. However, obtaining high resolution and miniaturization for fiber-optical microendoscopy remains a challenge. The lens system in the fiber-optical microendoscope is essential in the improvement of the imaging resolution and miniaturization of the microendoscopy probe [4,5]. High resolution in all fiber-optical imaging modalities [1] requires a lens system with a high numerical aperture (NA). Except for micro-electro-mechanical system (MEMS) mirrors [4–7] and micro-scanners [8], the size of the microendoscopy probe depends on the dimensions of the lens system. However, there is a tradeoff between resolution, dimensions and complexity in the lens system for fiber-optical microendoscopy. High resolution, miniaturization and low complexity cannot be simultaneously achieved because the current lens systems are restricted in shape and dimensions, owing to the limitations in fabricating complex surfaces with sub-millimeter dimensions.
Custom-made objective lenses with NAs from 0.35–1 [4,7–12] exhibit high performance and low aberration in applications of non-fluorescence, one-photon and two-photon fluorescence fiber-optical microendoscopy. It is noted that a 1.0 NA objective lens can be implemented in water [10] (effectively 0.75 NA in air). A lateral resolution of 0.64 μm can be achieved in two-photon fluorescence fiber-optical microendoscopy with a 0.8 NA objective lens [4], and high resolution can be achieved with a high NA objective lens. However, the outer diameters of the objective lenses are as large as 3–7 mm [4,7–12]. Moreover, the objective lenses are typically assembled by a group of lenses, which results in high system complexity.
Because custom-made objective lenses are difficult to further miniaturize and reduce the complexity of, gradient refractive index (GRIN) microlenses with a diameter of 350–1000 μm are applied to fiber-optical micro-endoscopy [5,6,13–17]. They typically have NAs of 0.4–0.6, and the sizes are smaller than those of objective lenses. However, the aberrations of GRIN microlenses limit the resolution to approximately twice the diffraction limit. A resolution of 0.74 μm can be achieved in one-photon fluorescence microendoscopy with a 0.7 NA GRIN microlens [5]. A 0.8 NA GRIN microlens system with a larger diameter (1400 μm) was developed by combining a GRIN microlens with an objective lens; however, the resolution was approximately 1.5 times that of the aberration-free resolution, and the optical complexity increases [18].
Besides, tapered or lensed fibers, which improve coupling to and from waveguides, laser diodes and photodiodes or be integrated with scanning probe microscopes, are produced by glass pulling technology, IR laser shaping or precise polishing [19,20]. In addition, some lensed fibers can be fabricated by applying electric arc discharges on the fibers using the conventional fusion splicer [21] and have been already applied in optical coherence tomography [22,23] and nonlinear optical imaging [24]. However, these lensed fibers are restricted in the shape due to the fabrication principle, as a result of which they typically have a low NA.
Recently, two-photon direct laser writing (DLW) has been used to fabricate complex optical opponents with sub-millimeter dimensions [25–28]. The photoresist polymerized by two-photon DLW acts as an optical material (e.g., lens materials); thus, the structures fabricated by DLW can be used as optical opponents. A triplet objective lens system with a diameter of 120 μm, was designed and fabricated on the fiber facet using two-photon DLW [25]. However, this lens system for endoscopic application is a telescope system with a large field of view of 80°, which is not suitable for fiber-optical microendoscopy.
In this study, we propose a high-resolution miniaturized singlet aspherical microlens fabricated on the fiber facet using two-photon DLW. Our result indicates that two-photon DLW of aspherical microlenses can overcome the tradeoff between resolution, miniaturization, and complexity in the fiber-optical microendoscopy lens system, simultaneously providing high resolution and compact size. Three aspherical microlenses with NAs of 0.3, 0.6, and 0.9 were designed, fabricated, and characterized.
2. Optical design of aspherical microlenses on the fiber facet
2.1 Optical properties of photoresist
The IP-S photoresist (Nanoscribe GmbH, Germany) was used for the DLW of the microlenses, because it is suitable for dip-in mode writing and is also optimized for a smooth surface.
A commercial optical design software (Zemax) computed the refractive index from its relationship with the dispersion of glass using the index of d-light, Nd (at 587.5618 nm), the Abbe number (Vd), and the deviation of the partial dispersion ($\mathrm{\Delta }{\textrm{P}_{\textrm{g,\; F}}}$).The partial dispersion ($\mathrm{\Delta }{\textrm{P}_{\textrm{g,\; F}}}$) can be calculated by:
Table 1. Optical parameters of photoresist IP-S
2.2 Design requirements
The aspherical microlens for fiber-optical microendoscopy delivers illumination from the core of a double-cladding fiber (Fibercore SMM900), focuses light on the sample, and then collects the reflected light in the inner cladding of the fiber. The aspherical microlens can be implemented in air (n = 1). Generally, an objective lens for fiber-optical microendoscopy is designed in two halves [10–12]; each half is designed separately and forms a telecentric lens system. In the initial design, there were two aspherical microlenses, used for collimating and focusing, respectively. The NA of the collimating aspherical microlens in fiber space is NAfiber = 0.2, which aligns with the NA of the fiber that obtains the highest efficiency. At the working wavelength of 561 nm, the diameter of the Airy disk of a 0.2 NA microlens is 3.42 μm, which approximates to the diameter of the fiber core (3.6 μm). For the NA of the focusing aspherical microlens in tissue space, a series of lenses with NAtissue of 0.3, 0.6, and 0.9 were designed for different resolution demands. In the final design, one aspherical microlens combined the collimating and focusing microlenses and enabled simultaneous collimating and focusing.
To achieve high spatial resolution, the aspherical microlenses for fiber-optical microendoscopy are designed to be aberration-free. The modulation transfer function (MTF), Rayleigh’s quarter wavelength [30], and Maréchal criterion [31] are applied to assess the performance of the microlenses.
To be considered for application in fluorescent imaging, aspherical microlenses for fiber-optical microendoscopy are required to be tolerant of wavelengths between 561–630 nm. Therefore, the design and assessment of aspherical microlenses for wavelengths of 561, 590, and 630 nm needs to be considered.
2.3 Design results
Because the collimating and focusing aspherical microlenses can be integrated into one aspherical microlens, we designed one singlet microlens to reduce the optical complexity, which thereby reduces the difficulty of fabrication.
In the design of the aspherical microlenses on the fiber facet, the applied surface is an even aspherical surface, which can be expressed as
The optical design of the aspherical microlenses with NAs of 0.3, 0.6, and 0.9 is optimized using Zemax to achieve the lowest aberrations at a wavelength of 590 nm, and the design results are presented in Table 2 and Fig. 1. With the increase in NA, higher order coefficients are required in the design because more aberrations need to be compensated. The MTFs of the designed aspherical microlenses approximately coincide with the corresponding diffraction-limit MTF.
Fig. 1. Optical designs of aspherical microlenses on the fiber facet for (a) 0.3 NA, (b) 0.6 NA, and (c) 0.9 NA. The polychromatic diffraction MTF for (d) 0.3 NA, (e) 0.6 NA, and (f) 0.9 NA aspherical microlenses.
Table 2. Optical design of the aspherical microlenses
The maximum optical path difference (OPD), the maximum root mean square (RMS) wavefront error and Strehl ratio of the aspherical microlenses at three working wavelengths were calculated and the results are presented in Table 3. From the Rayleigh’s quarter wavelength criterion, if the maximum OPD < λ/4, the lens can be considered as aberration-free. From the Maréchal criterion, the lens is considered aberration-free if the Strehl ratio > 0.82 and the maximum RMS wavefront error < λ/14. According to the Rayleigh’s quarter wavelength and Maréchal criteria, the aspherical microlenses with NAs of 0.3, 0.6, and 0.9 are considered aberration-free at the three working wavelengths in the design.
Table 3. Aberration assessments of aspherical microlenses
3. Aspherical microlens fabrication
The designs of the aspherical microlenses were exported to a computer-aided design file format and subsequently transformed into a stereolithographic (STL) file format. Additional holders, with small holes for supporting and the developing process, have been added to the design of the microlenses using the 3ds Max software, creating a new STL file for fabrication. The STL file was then transformed into the tracing data documents in three-dimensional (3D) coordinates for DLW with our home-built fabrication system.
The experimental setup of the system is illustrated in Fig. 2(a). A femtosecond laser beam operating at a wavelength of 535 nm (Fidelity), with a pulse width of 270 fs and a repetition rate of 50 MHz, was transmitted through a combination of a 4f imaging system, 2D galvo mirrors (Thorlabs) and a 1.4 NA 100× oil-immersion objective (Olympus) and focused into the photoresist. The beam power was controlled by an acoustic optical modulator (AOM). A fiber was inserted into the photoresist and fixed vertically towards the oil-immersion objective lens. The structures were fabricated by scanning with the piezoelectric nano-translation (PZT) stage (Physik Instrumente) in the axis direction and the 2D galvo mirrors in the lateral plane.
Fig. 2. Fabrication of the aspherical microlens on the fiber facet. (a) Setup of two-photon DLW system to fabricate the aspherical microlens on the fiber facet. (b) A 0.6 NA aspherical microlens fabricated on the fiber facet; scale bar is 20 μm. (c) SEM image of 0.6 NA aspherical microlens fabricated on glass.
After the DLW process, the sample was immersed in a bath of SU8 developer (1- Methoxy-2-propyl acetate) for 1 min, and then in isopropanol for 30 s, for the development process. No further baking, polishing, or other operations were required.
A 0.6 NA aspherical microlens fabricated on the fiber facet is shown in Fig. 2(b). The scanning electron microscope (SEM) image of the 0.6 NA aspherical microlens fabricated on glass is also presented in Fig. 2(c).
The outer diameter of the micro-optics structure is 40 μm and the length is 82, 84, and 89 μm for NAs of 0.3, 0.6, and 0.9, respectively. The diameter of the micro-optics structure is approximately one third of the diameter of the fiber (125 μm) and 10–20 times smaller than that of a typical GRIN microlens. The size of the lens system has been significantly reduced, and the size of the fiber is now the limitation of miniaturization.
4. Characterization and analysis of focus spot of aspherical microlens
To test the performance of the aspherical microlenses fabricated on the fiber, the focus spot of each microlens was imaged by a microscope system with a 40× 0.65 NA objective (Olympus) and a continuous wave (CW) laser at a wavelength of 561 nm to characterize the point spread function (PSF). The characterization of the focus spot distribution is shown in Figs. 4(a)–4(f). There are side lobes in the focus spot of the 0.9 NA aspherical microlens (visible in Fig. 4(c)) because the Fresnel number is 70, which is >>1.
By fitting the detected focus spot with a Gaussian function, its full width at half maximum (FWHM) could be obtained. The FWHMs of detected focus spot of the aspherical microlenses with NAs of 0.3, 0.6, and 0.9 are 2.00, 1.23, and 0.96 μm respectively. The FWHM resolution of the microscope system with a 40× 0.65 NA objective is 0.44 μm. By deconvolution, the FWHMs of the effective intensity PSFs of the aspherical microlenses are 1.95, 1.15, and 0.85 μm for NAs of 0.3, 0.6, and 0.9, respectively. The predicted resolution in confocal fiber-optical microendoscopy using each aspherical microlens is approximately 1.38, 0.81, and 0.60 μm for NAs of 0.3, 0.6, and 0.9, respectively.
Because the size of the fabricated microlens is significantly smaller than that in conventional microendoscopy, the fiber core cannot be considered as a point light source. If only the fundamental mode is delivered from the fiber, the intensity distribution of the Gaussian beam at the fiber core, which is considered as an extended light source can be expressed as
where ${I_0}$ is the peak irradiance at the center of the beam, r is the radial distance from the axis, and ${w_0}\; $is the waist of the Gaussian beam.The effective intensity PSF of the microlens is the square of the convolution of the Gaussian beam amplitude intensity distribution and its amplitude PSF [32]. Therefore, the extended light source widens the effective PSF of the microlens, thereby reducing the resolution. The intensity distribution of the extended light source from the fiber core is shown in Fig. 3(g), which was imaged using a microscope system with a 40× 0.65 NA objective. The waist of the Gaussian beam is 2 μm.
Fig. 3. Characterization of the effective intensity PSFs of the aspherical microlenses on the fiber. Intensity distribution of the focus spots of (a) 0.3 NA, (b) 0.6 NA, and (c) 0.9 NA aspherical microlenses in the focus plane. Intensity cross-section of (d) 0.3 NA, (e) 0.6 NA, and (f) 0.9 NA aspherical microlenses along the x direction. Intensity distribution of the extended light source from the fiber core in (g) the focus plane and (h) the cross-section along the x direction. (i) FWHM of effective intensity PSF versus NA. All the scale bars in (a), (b), (c), and (g) are 5 μm.
If the microlenses are aberration-free, the FWHMs of the intensity PSFs of the aspherical microlenses with NAs of 0.3, 0.6, and 0.9 are 0.96, 0.48, and 0.32 μm, respectively, owing to the diffraction limit. The theoretical FWHMs of the effective intensity PSFs were calculated with convolution, which are 1.76, 0.88, and 0.58 μm, for NAs of 0.3, 0.6, and 0.9, respectively.
Figure 4 shows the error contributed by each error source and the corresponding FWHM percentage change compared with the diffraction-limit PSF, based on the calculation.
Fig. 4. Error analysis of the aspherical microlenses on the fiber facet. FWHM change versus (a) axis shift from the core center, (b) holder length reduction, (c) diameter reduction, (d) thickness reduction, (e) aspheric coefficients reduction, and (f) refractive index error.
Although the aspherical microlenses on the fiber facet are designed to be aberration-free, aberrations still exist, owing to errors from fabrication and the photoresist. Thermal drift during the fabrication process may lead to shifts in the axis direction. The photoresist exhibits shrinkage after the development process, which causes a mismatch between the design and fabrication for the shape of the structure. The shrinkage of the photoresist contributes to the reduction of the parameters of the microlens, including the holder length, diameter, thickness, and aspheric coefficients of the microlens. In addition, the optical properties of the photoresist may also include errors because the refractive is strongly dependent on the exposure time and intensity [29].
The FWHM change of the 0.6 NA aspherical microlens is larger than that of the 0.3 NA microlens, for the error sources of axis shift and holder length reduction, as shown in Figs. 4(a) and 4(b), because the 0.3 NA aspherical microlens has no aspheric coefficients to compensate or the spherical aberrations. Figure 4(c) shows that with a diameter reduction, a smaller NA microlens generates a larger FWHM change. The reduction in the diameter decreases the effective NA. However, the aspheric coefficients prevent the reduction of the effective NA, which results in a small FWHM change. In the other cases, the higher NA microlens is more sensitive to the error sources, demonstrated in Figs. 4(d), 4(e), and 4(f). Generally, the 0.9 NA microlens exhibits the largest FWHM change, except in Fig. 4(c). This result indicates that a higher NA microlens requires more precision in fabrication and lower shrinkage in the photoresist.
5. Fiber-optical microendoscopy imaging with aspherical microlens
Figure 5(a) shows the schematic setup for fluorescence fiber-optical microendoscopy imaging with an aspherical microlens on the fiber facet.
Fig. 5. Fiber-optical microendoscopy imaging with the 0.6 NA aspherical microlens on the fiber facet. (a) Schematic setup for fluorescence fiber-optical microendoscopy imaging. (b) Image of a fluorescent sample normalized by the maximum intensity; scale bar: 20 μm. (c) Cross-section along the dotted line in (b).
The excitation laser beam, with a wavelength of 561 nm, was focused on the sample using the 0.6 NA aspherical microlens. The fluorescence signal from the sample was collected by the microlens and fiber, separated from the excitation beam by a dichroic mirror (Semrock, FF580-FDi02-t3-25 × 36) and filtered using a thick glass filter (Semrock, FF01-600/52-25) before being transmitted to a photomultiplier (PMT).
Currently, the images are obtained by scanning the sample with a PZT stage, as shown in Figs. 5(b) and 5(c). If a micro-scanner was applied to the microendoscope probe, the images would be obtained by scanning the micro-probe [33]. The fluorescent sample was fabricated on glass with Rhodamine 6G and IP-S using two-photon DLW.
6. Conclusion
We have demonstrated a high-resolution miniaturized singlet aspherical microlens, fabricated on the fiber facet using two-photon DLW. A series of aspherical microlenses with NAs of 0.3, 0.6, and 0.9 on the fiber facet was designed for fiber-optical microendoscopy with only one aspheric surface. These aspherical microlenses are aberration-free at working wavelengths of 561, 590, and 630 nm. We have also demonstrated two-photon DLW of the aspherical microlens on the fiber facet. The diameter of each aspherical microlens is only 30 μm. The micro-optics structure, including a microlens and a holder, has an outer diameter of 40 μm and a length between 80–90 μm. The diameter is 10–20 times smaller than that of a GRIN microlens. The miniaturization of the lens system has neared the limit for optical-fiber microendoscopy. The 0.9 NA aspherical microlens provides a resolution of 0.85 μm at a wavelength of 561 nm. If it is applied in the confocal imaging modality of fiber-optical microendoscopy, a resolution of approximately 0.60 μm is expected. The degraded resolution is caused by an extended light source and aberrations. The aberrations result from the fabrication precision, shrinkage in the photoresist, and the optical properties of the photoresist. In the error analysis, the 0.9 NA aspherical microlens exhibits strict requirements for the fabrication accuracy and material properties. The size of the lens system is no longer the primary limitation for the miniaturization of the fiber-optical microendoscope if an aspherical microlens is applied. This ultra-compact microendoscope system may be advantageous for future in vivo microendoscopy imaging.
Funding
Zhangjiang National Innovation Demonstration Zone (ZJ2019-ZD-005).
Acknowledgments
Baokai Wang acknowledges the technical support of laser fabrication from Dr. Benjamin Cumming.
Disclosures
The authors declare no conflicts of interest.
References
1. B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005). [CrossRef]
2. J. M. Jabbour, M. A. Saldua, J. N. Bixler, and K. C. Maitland, “Confocal endomicroscopy: instrumentation and medical applications,” Ann. Biomed. Eng. 40(2), 378–397 (2012). [CrossRef]
3. M. Gu, H. Bao, and H. Kang, “Fibre-optical microendoscopy,” J. Microsc. 254(1), 13–18 (2014). [CrossRef]
4. W. Zong, R. Wu, M. Li, Y. Hu, Y. Li, J. Li, H. Rong, H. Wu, Y. Xu, Y. Lu, and H. Jia, “Fast high-resolution miniature two-photon microscopy for brain imaging in freely behaving mice,” Nat. Methods 14(7), 713–719 (2017). [CrossRef]
5. G. Matz, B. Messerschmidt, W. Göbel, S. Filser, C. S. Betz, M. Kirsch, O. Uckermann, M. Kunze, S. Flämig, A. Ehrhardt, and K. M. Irion, “Chip-on-the-tip compact flexible endoscopic epifluorescence video-microscope for in-vivo imaging in medicine and biomedical research,” Biomed. Opt. Express 8(7), 3329–3342 (2017). [CrossRef]
6. L. Fu, A. Jain, H. Xie, C. Cranfield, and M. Gu, “Nonlinear optical endoscopy based on a double-clad photonic crystal fiber and a MEMS mirror,” Opt. Express 14(3), 1027–1032 (2006). [CrossRef]
7. L. Liu, E. Wang, X. Zhang, W. Liang, X. Li, and H. Xie, “MEMS-based 3D confocal scanning microendoscope using MEMS scanners for both lateral and axial scan,” Sens. Actuators, A 215, 89–95 (2014). [CrossRef]
8. H. Bao, J. Allen, R. Pattie, R. Vance, and M. Gu, “Fast handheld two-photon fluorescence microendoscope with a 475 μm× 475 μm field of view for in vivo imaging,” Opt. Lett. 33(12), 1333–1335 (2008). [CrossRef]
9. K. Carlson, M. Chidley, K. Sung, M. Descour, A. Gillenwater, M. Follen, and R. Richards-Kortum, “In vivo fiber-optic confocal reflectance microscope with an injection-molded plastic miniature objective lens,” Appl. Opt. 44(10), 1792–1797 (2005). [CrossRef]
10. C. Liang, K. B. Sung, R. R. Richards-Kortum, and M. R. Descour, “Design of a high-numerical-aperture miniature microscope objective for an endoscopic fiber confocal reflectance microscope,” Appl. Opt. 41(22), 4603–4610 (2002). [CrossRef]
11. A. R. Rouse, A. Kano, J. A. Udovich, S. M. Kroto, and A. F. Gmitro, “Design and demonstration of a miniature catheter for a confocal microendoscope,” Appl. Opt. 43(31), 5763–5769 (2004). [CrossRef]
12. L. Yang, J. Wang, G. Tian, J. Yuan, Q. Liu, and L. Fu, “Five-lens, easy-to-implement miniature objective for a fluorescence confocal microendoscope,” Opt. Express 24(1), 473–484 (2016). [CrossRef]
13. J. C. Jung, A. D. Mehta, E. Aksay, R. Stepnoski, and M. J. Schnitzer, “In vivo mammalian brain Imaging using one- and two-photon fluorescence microendoscopy,” J. Neurophysiol. 92(5), 3121–3133 (2004). [CrossRef]
14. B. A. Flusberg, J. C. Lung, E. D. Cocker, E. P. Anderson, and M. J. Schnitzer, “In vivo brain imaging using a portable 3.9 gram two-photon fluorescence microendoscope,” Opt. Lett. 30(17), 2272–2274 (2005). [CrossRef]
15. W. Göbel, J. N. D. Kerr, A. Nimmerjahn, and F. Helmchen, “Miniaturized two-photon microscope based on a flexible coherent fiber bundle and a gradient-index lens objective,” Opt. Lett. 29(21), 2521–2523 (2004). [CrossRef]
16. D. Bird and M. Gu, “Two-photon fluorescence endoscopy with a micro-optic scanning head,” Opt. Lett. 28(17), 1552–1554 (2003). [CrossRef]
17. W. Piyawattanametha, E. D. Cocker, L. D. Burns, R. P. Barretto, J. C. Jung, H. Ra, O. Solgaard, and M. J. Schnitzer, “In vivo brain imaging using a portable 2.9 g two-photon microscope based on a microelectromechanical systems scanning mirror,” Opt. Lett. 34(15), 2309–2311 (2009). [CrossRef]
18. G. Matz, B. Messerschmidt, and H. Gross, “Design and evaluation of new color-corrected rigid endomicroscopic high NA GRIN-objectives with a sub-micron resolution and large field of view,” Opt. Express 24(10), 10987–11001 (2016). [CrossRef]
19. Nanonics Imaging, “Lensed Fiber,” https://www.nanonics.co.il/products/lensed-fiber.
20. OZ Optics, “Tapered and lensed fibers,” http://www.ozoptics.com/ALLNEW_PDF/DTS0080.pdf.
21. G. J. Kong, J. Kim, H. Y. Choi, J. E. Im, B. H. Park, U. C. Paek, and B. H. Lee, “Lensed photonic crystal fiber obtained by use of an arc discharge,” Opt. Lett. 31(7), 894–896 (2006). [CrossRef]
22. S. Y. Ryu, H. Y. Choi, J. Na, W. J. Choi, and B. H. Lee, “Lensed fiber probes designed as an alternative to bulk probes in optical coherence tomography,” Appl. Opt. 47(10), 1510–1516 (2008). [CrossRef]
23. Y. Qiu, Y. Wang, K. D. Belfield, and X. Liu, “Ultrathin lensed fiber-optic probe for optical coherence tomography,” Biomed. Opt. Express 7(6), 2154–2162 (2016). [CrossRef]
24. H. Bao and M. Gu, “A 0.4-mm-diameter probe for nonlinear optical imaging,” Opt. Express 17(12), 10098–10104 (2009). [CrossRef]
25. T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016). [CrossRef]
26. T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7(1), 11763 (2016). [CrossRef]
27. R. Guo, S. Xiao, X. Zhai, J. Li, A. Xia, and W. Huang, “Micro lens fabrication by means of femtosecond two photon photopolymerization,” Opt. Express 14(2), 810–816 (2006). [CrossRef]
28. M. Malinauskas, A. Zukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukeviciute, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010). [CrossRef]
29. T. Gissibl, S. Wagner, J. Sykora, M. Schmid, and H. Giessen, “Refractive index measurements of photo-resists for three-dimensional direct laser writing,” Opt. Mater. Express 7(7), 2293 (2017). [CrossRef]
30. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
31. A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–277 (1947).
32. M. Gu, Principles of Three-dimensional Imaging in Confocal Microscopes (World Scientific, 1996).
33. N. Mihajlovic, B.H.W. Hendriks, W.C.J. Bierhoff, C.A. Hezemans, R. Harbers, A.L. Braun, J.J.L. Horikx, and A.E. Desjardins, “Electromagnetically-Controlled Fiber-Scanning Confocal Microscope,” OSA Optics & Photonics Congress, NWC5, (2009).
