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Abstract
Compact and minimally invasive scanning fiber endoscopy probes with micron-level resolution have great potential in detailed tissue interrogation and early disease diagnosis, which are key applications of confocal reflectance imaging at visible wavelengths. State-of-the-art imaging probes commonly employ refractive lens triplets or gradient refractive index (GRIN) lenses as the micro-objective. However, off-axis aberration emerges as a critical factor affecting resolution, especially at the extremities of the imaging field. In response to this challenge, we propose what we believe to be a novel design integrating a metasurface with the GRIN micro-objective to address optical aberrations during beam scan. The metasurface acts as a corrector element for optical aberrations in a fiber-scanning endoscope using the same fiber for excitation and collection. Modeling such hybrid refractive-metasurface designs requires the coupling of simulation techniques across macroscale and nanoscale optics, for which we used an Ansys simulation workflow platform. Operating at a wavelength of 644 nm, this metaoptical element serves as a thin and compact aberration correction surface, ensuring uniform resolution across the entire imaging field. Experimental results from our scanning fiber endoscopy system demonstrate a notable enhancement in optical performance both on-axis and off-axis, achieving a resolution of 3 µm at the center of the imaging field. Impressively, the resolution experiences only a modest degradation by a factor of 0.13 at the edge of the field of view compared to the center.
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1. Introduction
The microendoscope [1,2] is a minimally invasive optical probe designed for imaging deeper regions within smaller body cavities (typically on the order of a few millimeters), such as the eustachian tube, fallopian tube, bile duct, etc., which are challenging to access using standard endoscopes. Gradient refractive index (GRIN) lenses are the most widely used micro-objectives in such endoscopy imaging heads [3–5] owing to their cylindrical geometry and smaller diameters (0.5-1.8 mm). However, the primary limitation of GRIN micro-objectives lies in their optical aberrations, leading to a degradation in resolution. Previous attempts to address these issues involve combining planoconvex lenses with GRIN lenses to correct on-axis spherical aberration, as reported in [6]. It should be noted that off-axis aberrations such as coma and astigmatism remain uncorrected. Researchers have used custom-fabricated GRIN lenses with a highly aspheric profile combined with refractive and diffractive optical elements [7] for reducing the off-axis aberrations. However, this works over a limited imaging field and the imaging head is to be used with expensive fiber bundle imaging systems. In addition to that, these custom-fabricated endoscopy GRIN lenses are not available commercially. Though fiber scanning endoscopy [8] probes with the same double clad fiber for both excitation and collection are reported, the imaging head consists of either a combination of custom fabricated GRIN lenses [9] or compound micro-lens triplets [10,11] and aligning them on a micron-scale is difficult. The reported prototypes to date have not achieved uniform resolution in the full field of view. Recently, researchers have investigated the use of metalenses [12,13] as micro-objectives for aberration-free imaging heads, such as the implementation described in [14] for wide field reflectance imaging at working distances of the order of 10 - 15 mm. However, the resolution achieved (140 µm) is insufficient for detecting pre-cancerous lesions. Moreover there is a notable degradation (by a factor of 2) in the resolution towards the edges of imaging field. Also, the probe requires a set of collection fibers for relaying the image of the sample area.
In this paper, we propose a novel design strategy for a fiber-scanning endoscope using the same fiber for excitation and collection to achieve high resolution (< 5 µm) at much smaller working distances of < 100 µm, which is the typical imaging depth of confocal endoscopy. The design combines a conventional GRIN lens with a phase element, implemented as a metasurface to ensure homogenous resolution across the entire imaging field. Unlike aspheric lenses for correction [15] we propose using metasurfaces to enable the correction. Metasurfaces consist of an array of subwavelength meta-atoms, which can be of the same height but varying lateral dimensions. This work presents a comprehensive design workflow for a metasurface to correct off-axis aberrations at a single wavelength for a scanning fiber endoscopy probe. The design modeling involves extracting electromagnetic fields from nanoscale structures and propagating them through macroscale optics utilizing the interoperability between the ray tracing platform Zemax OpticStudio and the Finite difference time domain (FDTD)-based electromagnetic simulation software Lumerical. To the best of our knowledge, the design of such a hybrid metasurface-GRIN lens system for endoscopy applications has not been reported so far. We have fabricated and incorporated the metasurface corrector element in an endoscopy setting and validated the overall system performance. The measured results nicely confirm the enhanced performance of our design with respect to the case without a metasurface corrector element.
2. Optical system design and modeling of endoscopy probe
In the scanning fiber confocal endoscopy system illustrated in Fig. 1, the core of a double clad fiber (DCF) guides the excitation beam onto the sample through the micro-objective (GRIN) lens, and the reflected light is coupled back to the inner clad of the same DCF. DCF couplers are reported in fiber-optic confocal endomicroscopy [16,17] for the partially coherent detection of back-coupled reflected light. The laser source operates at a wavelength of 644 nm, strategically chosen to minimize absorption and scattering, while achieving the penetration depth (50-100 µm) necessary for confocal reflectance imaging with micron-level resolution. The imaging head comprises a commercially available GRIN lens (Edmund 64524, length = 2.18 mm and diameter = 1 mm) as the micro-objective. The optical system of the imaging probe indicated in Fig. 1 is modeled in Zemax, as shown in Fig. 2(a). The scanning fiber is passed through a fiber channel along the central axis of the piezoelectric tube (PZT). The desired sample area is imaged by scanning the fiber by actuating the PZT [18].
While modeling, the fiber tip is defined as the object with object space numerical aperture set as $NA_{in}=0.11$, equal to the fiber core NA. An object-side working distance of 4 mm is maintained between the fiber tip and GRIN lens. In an endoscopy probe, the micro-objective lens is followed by a coverslip that touches the tissue. Taking this into consideration, a coverslip is introduced into the system model. The distance from coverslip to the focal point is the sample end working distance. The lateral resolution of an optical system illuminated with a Gaussian beam is related to the NA [19] at the sample end, $NA_{out}$ as
At the design wavelength of 644 nm, to get a lateral resolution of 1 µm, the $NA_{out}$ must be at least 0.4. Based on simulation results, the objective (GRIN) lens ensures tight focusing of the excitation beam onto the sample with $NA_{out}$ of 0.42 at a working distance of 220 µm from the coverslip. The magnification of the optical system can be estimated as 0.26 using the following equation.
The scan range on the sample [20] is given by,
where $D_{scan}$ is the fiber tip scan field. In our design, the field angle is set as $\pm 3^{\circ }$. The ray tracing results show that the fiber tip scan field of 420 µm gives an imaging field of 111 µm at the sample end. We examined the spot diagram which is a very effective tool for showing the effects of geometric and ray aberrations in an optical system. The black circle in the spot diagram in Fig. 2(b) represents the Airy disk of radius equal to 0.88 µm. Furthermore, the theoretical lateral resolution or full width half maximum (FWHM) of a single fiber imaging probe is also estimated as in [21] where D is the mode field diameter of the DCF, and M is the magnification from fiber-tip to sample end. For the DCF scan through GRIN lens, D = 4.6 µm and M = 0.26, the theoretical FWHM is calculated to be 0.5 µm matching the RMS spot radius on-axis. The discrepancy between the theoretical FWHM and the predicted spot size at the extreme field is due to the aberrations of the imaging optics. The calculation of the root mean square (RMS) spot radius involves squaring the distance between each ray and the reference point, averaging these across all rays, and then taking the square root. This metric provides an idea of the spread of rays, as it takes into account the contribution of each individual ray in determining the overall distribution. The spot analysis in Fig. 2(b) at the sample end for different field points indicates that the RMS spot size is minimal on-axis. However, the spot size is not maintained over the full imaging field. Owing to off-axis optical aberrations, the spot increases in size at the periphery of the imaging field, thereby reducing the resolution there.2.1 Design of phase element for aberration correction
Clearly, an element that can reduce the off-axis aberrations is required. This section presents the intricacies of designing such an element. The correction element is modeled as a Binary 2 surface in Zemax. The radial phase coefficients of the surface are set as variables to achieve a minimal RMS spot radius at the different field points (with equal weights) simultaneously. The surface phase profile of the correction element is modeled as
where $a_i$ represents the phase coefficients, N is the number of radial polynomial coefficients, $\rho$ is the radial aperture coordinate and R is the radius of the phase element. The values of N and $a_i$ are optimized to find the best excitation spot quality.Clearly, the phase element, shown in Fig. 3(a), needs a substrate. In this case, a glass substrate is used and attached to the GRIN lens without any intervening air gap. As the typical range of imaging depth in a confocal microscopy system is 50 µm to 100 µm, we set the sample working distance (from the coverslip to focal point) as 98 µm during the optimization. After the integration of the phase element, the spot analysis depicted in Fig. 3(b) reveals a notable enhancement in resolution, particularly at the extreme field points. The RMS spot spread has seen a remarkable reduction of $61.5{\% }$ at these outermost field positions. Examining the modulation transfer function (MTF) graph in Fig. 3(c), a contrast of $5{\% }$ and above is sustained at a maximum spatial frequency of approximately 960 cycles/mm, translating to a resolution of 1 µm at the extreme field points. Notably, the MTF or contrast value exhibits remarkable consistency, remaining nearly invariant across field angles up to $3^{\circ }$, as evidenced by Fig. 3(d). The optical specifications of the imaging probe, both before and after aberration correction, are tabulated in Table 1.
Fig. 3. Scanning fiber endoscope model with the phase element and simulation results for aberration correction.
Table 1. Confocal endoscope probe: Optical specifications
The impact of radial polynomial coefficients on spot quality is analyzed. In addition to RMS spot radius, GEO spot radius is another measure of the ray distribution at the sample working distance. GEO spot radius is the radius measured to the farthest ray in the ray distribution from the centroid. As illustrated in Fig. 4(a), at N = 4, the RMS spot radius and GEO spot radius reach a minimum. Specifically, when considering RMS spot radius as the only performance parameter, the phase profile incorporating only the first even-order polynomial proves adequate. Figure 4(b) shows the surface phase profile of the correction element. For larger imaging fields, the optimized spot radius values are detailed in Table 2. The phase coefficients are meticulously tuned to maintain a uniform spot across the imaging field. Notably, the GEO spot radius experiences a slight increase in the case of larger imaging fields, as observed.
Fig. 4. Optimization of the phase element. (a) Effect of radial coefficients on spot quality and (b) Surface phase of the correction element. Unit of phase is periods of $2\pi$ radians
Table 2. Optimized spot radius for different imaging fields
2.2 Collection path model and spot analysis
The design of the endoscopy probe is for reflectance imaging and aberration correction at a single wavelength. Experimentally, the collection of the reflectance signal is taken care of by the same double clad fiber (DCF) (used for excitation) with an inner clad diameter of 15 µm. To show that metacorrector works also for detection, we have modeled the excitation and collection path in a single full sequential ray tracing model as in Fig. 5. The ray distribution at the sample end of the excitation path model acts as a source for the collection path model. Light travels from there, back to the fiber tip, which now acts as the plane of interest. As illustrated in the spot diagram in Fig. 6, at the fiber tip, the RMS spot spread is within the Airy disk diameter of 7.2 µm, which is well within the diameter of the inner clad of DCF.
2.3 Realization of phase correction element as metasurface
The target phase being optimized, the next step is to design the appropriate metasurface that will provide this phase variation in a practical system. The metasurface is an array of meta-atoms that introduces a phase shift due to the scattering of subwavelength structures. To attain the desired correction element’s phase profile, we engineer an array of cylindrical nano-posts. The unit cell simulations are carried out at a wavelength of 644 nm with polysilicon as the dielectric and quartz as the substrate using Lumerical [22]. The height of the unit cell and period of the metasurface are chosen as 280 nm and 250 nm respectively with the radius of the unit cell in the range of 40-110 nm to ensure full $2\pi$ phase coverage and transmission above $90{\% }$. The unit cell’s simulated electric, magnetic fields, phase, and transmission are calculated using rigorous coupled wave analysis (RCWA).
Fig. 6. Collection spot analysis at the fiber tip: (left) on-axis and (right) extreme field for hybrid optical system. The black circle represents the Airy disk with a diameter of 7.2 µm.
To ensure the phase element works in all situations, we investigated the impact of the incident light’s angular dependence on the phase and transmittance of the meta-atoms of radii 40 nm, 70 nm, and 100 nm. In our optical system design, accounting for the extreme field point, the maximum angle of incidence on the phase element is $4.6^{\circ }$. Analyzing the findings presented in Fig. 7, we noted that, within our specified angular range of interest both the phase and transmittance remain almost constant. It was observed that this was not the case for angles above $7^{\circ }$. Simulating the field of a metasurface with dimensions on the order of 1 mm poses a computational challenge when employing conventional FDTD analysis. To address this, we utilize a near-field stitching algorithm to estimate the field generated by the entire metasurface. The algorithm takes the target phase map and field lookup table as input data files. For each sample point on the target phase mask, the algorithm identifies the closest phase value in the lookup table and then reconstructs the metasurface field by interpolating the fields of the unit cell at specific locations. The resulting simulated near field (containing amplitude and phase information) after the metasurface is exported as a Zemax beam file (ZBF).
Fig. 7. Angular dependence of incident light on the (a) phase delay and (b) transmittance imparted by meta-atoms for different radii, r of the unit cell.
3. Integrating EM simulation of the correction metasurface into physical optics propagation (POP)
The physical optics propagation (POP) option in Zemax facilitates the propagation of coherent beams through the optical system for diffraction analysis. The simulated EM field (as a ZBF) of the metasurface is imported to the POP module. The phase of the imported beam file is visualized in POP as illustrated in Fig. 8.
In POP, a pilot beam is propagated along with the actual beam to assist the algorithm in selecting the diffraction method (Fresnel/Angular spectrum method). Figure 9 shows the beam irradiance at the end surface of the coverslip (as in the design model in Fig. 3(a)) when the near field of the metasurface is propagated through the optical system. The spot diagram from ray trace analysis of the optical system with phase element, as illustrated in Fig. 10(a) at the same surface (end of coverslip), reveals an RMS spot radius of 60 µm, consistent with the radial beam width according to POP analysis. The alignment between ray tracing and POP results, tabulated in Table 3, demonstrates strong agreement, validating the nanoscale model of the metasurface.
Fig. 8. Beam file viewed in POP: Phase ($E_x$) of the metacorrector imported from EM simulation platform (X, Y coordinates are in mm).
Fig. 9. Beam file viewed in POP: Beam irradiance plot at the end surface of coverslip (in Fig. 3(a)) when the ZBF of metasurface is propagated (X, Y coordinates are in mm).
Table 3. Performance comparison: POP Vs Ray tracing
The Fresnel diffraction method models the propagation of a converging beam, i.e., for a Fresnel number, $F_n < 1$. At focus, $F_n = 0$ and the ray model is more appropriate for quantifying the imaging system’s performance. In our optical design, the pilot beam waist after the coverslip is less than the propagation wavelength, and the beam divergence is large. Therefore, scalar diffraction results may lack accuracy beyond the coverslip surface. Instead at focus (or sample working distance), the ray model is acceptable and we examined ray-based diffraction computation based on the Fraunhofer method, predicting the point spread function (PSF) cross-section as in Fig. 10(b). From the relative irradiance plot of the beam, the resolution of the scanning fiber endoscopy system is 1 µm throughout the imaging field.
4. Experimental validation of metasurface
The resolution of the scanning fiber endoscopy system is determined from the intensity distribution of the focused spot at the working distance of the micro-objective (GRIN) lens without and with metacorrector. Figure 11 shows the experimental setup for measuring the spot size. The microscope consists of an objective (Thorlabs RMS 20X, NA = 0.4, wd = 1.2 mm, f = 9 mm), a tube lens (f = 150 mm), and a camera beam profiler (Thorlabs BC106VIS). The microscope setup is positioned such that the working distance of the objective coincides with the working distance of the GRIN lens without and with metacorrector. We couldn’t include the coverslip (as in the designed model) during the measurement due to technical limitations at the moment. Initially, the focused spot of the GRIN lens alone (without the correction element) is analyzed. An object-side working distance (fiber tip to GRIN lens) is set at 4 mm and the focused spot is observed at a working distance of 350 µm after the GRIN lens. The fiber is situated along the central axis of the PZT in a dedicated fiber channel, and radial electrodes are actuated in the Y direction for scanning. The DC voltage, amplified by the PZT driver (Micromechatronics, TD250), is varied in the range of 0-250 V to actuate the PZT. Through this variation in actuation voltage, spot sizes at the minimum and maximum scan angles of the fiber are measured.
The performance of the system is then analysed by adding a metasurface-based correction element to the system. The correction element is fabricated using polysilicon for the meta-atoms and a quartz substrate with electron beam (e-beam) lithography patterning. Initially, polysilicon is deposited on a quartz substrate using low-pressure chemical vapour deposition at $640^{\circ } C$. Then the sample is coated with a negative resist, mr-EBL 6000.3, at 3000 rpm for patterning. A RAITH150 Two e-beam writer at 30 kV acceleration voltage and 15 pA beam current is used for patterning. The patterned resist is then developed using mr-Dev 600 developer. The mr-EBL resist has good dry etch resistance for etching silicon and hence the resist itself is used as a mask for etching. This reduces the process steps in contrast to conventional pattern transfer techniques utilizing positive e-beam resist, such as PMMA, which requires additional procedures like metallisation and lift-off prior to etching [23]. An inductive coupled plasma reactive ion etching tool (Oxford Plasmalab 100) with SF$_6$ and CHF$_3$ etch gases is then used to transfer the pattern on the resist to the polysilicon. Finally, the resist is removed using O$_2$ plasma to obtain the correction element.
While characterizing the system with the correction element, the metasurface is placed before the GRIN lens without any gap. The object working distance (fiber tip to phase element) is modified to 3 mm to ensure a focused spot within 300 µm after the GRIN lens. During measurement, the minimal spot is observed at a sample working distance of 220 µm from GRIN lens. The spot sizes at the on-axis and maximum field points before and after correction are consolidated in Table 4. The aberrations introduced due to the objective and tube lens in the experiment setup are not accounted for in the simulation model leading to larger measured spot sizes (in Table 4) than the predicted ones (in Table 1). In a practical endoscopy imaging probe, a coverslip is present between the last optical element and the tissue surface. However, it was very challenging to place a coverslip in our current setup for imaging the spot and hence it was not included. Nevertheless, the same metacorrector corrects the aberration in the optical system without coverslip also, but at a slightly different working distance. This experiment demonstrates the feasibility of using meta-elements in such challenging and space-compromised systems. However, there could be some errors due to the fluctuations and vibrations of the free-standing fiber cantilever and hysteresis caused by varying the actuation voltages of PZT between minimum to maximum values. We made a preliminary attempt towards the measurement of the spot sizes experimentally. There is scope for improvement in terms of the alignment and the fabrication of the metacorrector.
Table 4. Measured working distance and beamwidth without and with metacorrector (no coverslip was included in both cases).
A comparative analysis of the 2D intensity profile of the spot without and with the metaelement, captured both on-axis and at the maximum scan angle, is presented in Fig. 12. The measured beamwidth along Y direction indicates a reduction of $16{\% }$ on-axis and $21{\% }$ at the extreme field with the addition of the metaelement. Notably, in the model with the metaelement, the resolution only drops by a factor of 0.13 at the edge of the imaging field compared to the center.
Fig. 12. Measured intensity profile without and with metacorrector for incidence (a) on-axis and (b) off-axis at maximum tilt.
5. Conclusion
Our study showcases the successful integration of a metaoptical element, operating at 644 nm, as a thin and compact aberration correction surface within an endoscopic optical system. We optimize the phase correction element using Zemax, design the metasurface for the target phase using Lumerical, integrate the nearfield after metasurface into ray optics, and verify the performance of the optical system. The experimental validation of the metaelement involves a comprehensive characterization of its optical performance and the subsequent comparison with simulation results. The experimental results, particularly after incorporating the metasurface into the scanning fiber endoscopy system, reveal great potential of metasurface-enhanced endoscopic systems.
Funding
Ministry of Education, India (11/9/2019-U.3(A)); Center of Excellence on Healthcare and Assistive Technologies, IIT Madras; Methusalem and Hercules foundations; OZR of Vrije Universiteit Brussel.
Acknowledgments
S. Thomas acknowledges the Ministry of Education, India for the research grant through the Prime Ministers Research Fellowship (PMRF). ST and SB also thank Prof. Sumeet Mahajan, Univ. of Southampton for helpful discussions at the start of this work. F. Ferranti acknowledges the support from the Methusalem and Hercules foundations and the OZR of the Vrije Universiteit Brussel (VUB).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request
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