Gradient-index Rod Lenses Research Articles

GRIN-lens-based in-line digital holographic microscopy.

In-line digital holographic microscopy (DHM) provides three-dimensional images with large fields of view and depths of field and micrometer-scale resolution, using a compact, cost-effective, and stable setup. Here, we develop the theoretical background and experimentally demonstrate an in-line DHM based on a gradient-index (GRIN) rod lens. In addition, we develop a conventional pinhole-based in-line DHM with different configurations to compare the resolution and image quality of both GRIN-based and pinhole-based systems. We show that in a high-magnification regime, where the sample is positioned near a source that produces spherical waves, our optimized GRIN-based setup provides better resolution (∼1.38µm). Furthermore, we employed this microscope to holographically image dilute polystyrene micro-particles with diameters of 3.0 and 2.0µm. We investigated the effect of light source-detector and sample-detector distances on the resolution, by both theory and experiment. Our theoretical and experimental results are in good agreement.

A novel needle probe for deeper photoacoustic viscoelasticity measurement

We present for the first time, to the best of our knowledge, a needle probe for photoacoustic viscoelasticity (PAVE) measurements at a depth of 1 cm below the sample surface. The probe uses a gradient index rod lens, encased within a side-facing needle (0.7 mm outer diameter), to direct excitation light (532 nm) and detection light (1325 nm) focused on the sample, collecting and directing the returned detection light in a spectral domain low coherence interferometry system, which allows for obtaining optical phase differences due to photoacoustic oscillations. The feasibility of needle probe for PAVE depth characterization was investigated on gelatin phantoms and in vitro biological tissues. The experimental results in an in vivo animal model predict the great potential of this technique for in vivo tumor boundary detection.

Objective-lens-free confocal endomicroscope using Lissajous scanning lensed-fiber

We report an objective-lens-free endomicroscopic catheter for compact Lissajous scanned confocal endomicroscopic system using a scanning lensed-fiber. The fiber scanner comprises a single-mode fiber (SMF) spliced with a coreless silica fiber segment and quadrupole piezoelectric tube. An objective lens was directly formed at the distal end of an SMF using a fusion splicer. The lensed fiber eliminates the need for conventional beam focusing elements such as a gradient index rod lens and precise optical alignment, allowing low cost and facile fabrication of an exceptionally short endomicroscopic catheter. The endomicroscopic scanner was fully packaged within a stainless tube of 2.6 mm in outer diameter and 20 mm in length, which can be easily inserted through the working channel of conventional laparoscope or colonoscope. The microscopic images of a stained kidney section and ear of a mouse were successfully obtained with the Lissajous scanning confocal endomicroscope. The compact Lissajous scanning lensed fiber can provide a new route for diverse in vivo endomicroscopic applications.

Optical tomography of residual stresses in GRIN rod lenses with transverse and longitudinal translucence

The residual stresses (RS) in gradient-index (GRIN) rod lens are formed due to the material characteristics gradient. RS can lead to the birefringence effect. If a GRIN lens is birefringent, its applications may be limited, because the anisotropy can cause the image quality degradation. According to this, the urgent task is to develop a non-destructive diagnostic method of RS in the gradient optical structures. This paper presents the relations of the generalized method of integral photoelasticity for reconstructions of RS (optical tomography of the stress field) for the case of the bending probing rays in GRIN optical rods with a radial distribution of the refractive index. The problem is solved with plane strain approximations. RS Distributions are given reconstructed from tomographic data obtained with transverse and longitudinal (coaxial) translucence of GRIN rod lens.

PiezoGRIN: A High-Pressure Chamber Incorporating GRIN Lenses for High-Resolution 3D-Microscopy of living Cells and Tissues.

A high‐pressure optical chamber, PiezoGRIN, that facilitates label‐free 3D high‐resolution live‐cell multiphoton microscopy in thick tissue samples is presented. A set of two Gradient Index (GRIN) rod lenses is integrated into the chamber as an optical guide and allows for the adjustment of the focal plane through the sample providing a field of view volume of 450 × 450 × 500 µm (x, y, z). An optical lateral resolution of 0.8 µm is achieved by using two‐photon excitation with 150 fs pulses of a 810 nm titanium–sapphire laser at hydrostatic pressures up to 200 MPa. With the PiezoGRIN setup, it is possible to follow pressure‐induced changes in subcellular structure of unstained vital mouse skeletal muscle tissue up to 200 µm below the tissue surface.

Dynamic compensation of gradient index rod lens aberrations by using liquid crystals.

An electrically variable liquid crystal lens is used to compensate the aberrations of commercial gradient index rod lenses used for deep brain endoscopy. This is achieved by the use of a weakly conductive layer in the so-called "modal control" lens approach with a segmented peripheral electrode. The root mean square aberrations of the system are reduced by a factor of 4.3. The proposed solution can be used in many photonic applications using fixed optical components with high aberrations that have significant sample-to-sample variability.

Robustness of Light-Transport Processes to Bending Deformations in Graded-Index Multimode Waveguides.

Light transport through a multimode optical waveguide undergoes changes when subjected to bending deformations. We show that optical waveguides with a perfectly parabolic refractive index profile are almost immune to bending, conserving the structure of propagation-invariant modes. Moreover, we show that changes to the transmission matrix of parabolic-index fibers due to bending can be expressed with only two free parameters, regardless of how complex a particular deformation is. We provide detailed analysis of experimentally measured transmission matrices of a commercially available graded-index fiber as well as a gradient-index rod lens featuring a very faithful parabolic refractive index profile. Although parabolic-index fibers with a sufficiently precise refractive index profile are not within our reach, we show that imaging performance with standard commercially available graded-index fibers is significantly less influenced by bending deformations than step-index types under the same conditions. Our work thus predicts that the availability of ultraprecise parabolic-index fibers will make endoscopic applications with flexible probes feasible and free from extremely elaborate computational challenges.

Development of an Image Sensor for Dentistry - Fiber Connecting Technique with the Gradient Index (GRIN) Rod Lens

In dentistry, endodontic treatment becomes necessary when dental caries progresses deep into the tooth and reaches the dental pulp or the periapical tissue. A large part of this treatment is performed without direct observation of the root canals. Previously, we reported a prototype of a dental endoscope. In this study, we attempted to develop a novel image sensor for dental endodontic diagnosis and treatment that allows capturing an image of the fine constructions inside the root canals. Our fabricated probe contains an image fiber, a GRIN lens, and optical fibers as light sources. These materials are encased inside a stainless steel tube to ensure the durability. In previous experiments, we attempted to connect all materials in one step. However, the captured images had deviations along the center axis between the image fiber and GRIN lens. To solve this problem, we considered a new, two-step method for connecting the two materials. In this method, an image fiber and a GRIN lens with the same diameter were placed on stages capable of three-dimensional fine positional adjustments at a resolution of 0.01 mm. The surfaces of the materials were connected under observation through a microscope. An evaluation of the captured images showed that the deviations in the previous images were 22.4 μm along the X-axis and 45.7 μm along the Y-axis. In contrast, the deviations with the new method were 16.7 μm and 8.9 μm along the X-axis and Y-axis, respectively. Therefore, the new method greatly improved precision along each axis. With this method, our fabricated probe could capture and evaluate images more efficiently. We are now trying to fabricate and evaluate a new image sensor.

Compact, lensless digital holographic microscope for remote microbiology.

In situ investigation of microbial life in extreme environments can be carried out with microscopes capable of imaging 3-dimensional volumes and tracking particle motion. Here we present a lensless digital holographic microscope approach that provides roughly 1.5 micron resolution in a compact, robust package suitable for remote deployment. High resolution is achieved by generating high numerical-aperture input beams with radial gradient-index rod lenses. The ability to detect and track prokaryotes was explored using bacterial strains of two different sizes. In the larger strain, a variety of motions were seen, while the smaller strain was used to demonstrate a detection capability down to micron scales.

Development of a hybrid Raman spectroscopy and optical coherence tomography technique for real-time in vivo tissue measurements.

We report on the development of a unique sideview handheld hybrid Raman spectroscopy (RS) and optical coherence tomography (OCT) technique for real-time in vivo tissue measurements. A sideview handheld RS-OCT optical probe is designed to coalign the optical paths of RS and OCT sampling arms, whereby a compact long-pass dichroic mirror (LPDM) is utilized to transmit the OCT signal through a gradient index rod lens and a reflection mirror, whereas the LPDM deflects the tissue Raman signal by 90°, leading to coaligned RS/OCT optical samplings on the tissue. Further study shows that the hybrid RS and OCT technique developed is capable of simultaneously acquiring both morphological and biochemical information about the oral tissue in vivo, facilitating real-time, in vivo tissue diagnoses and characterizations in the oral cavity.

In Vivo Voltage-Sensitive Dye Imaging of Subcortical Brain Function.

The whisker system of rodents is an excellent model to study peripherally evoked neural activity in the brain. Discrete neural modules represent each whisker in the somatosensory cortex (“barrels”), thalamus (“barreloids”), and brain stem (“barrelettes”). Stimulation of a single whisker evokes neural activity sequentially in its corresponding barrelette, barreloid, and barrel. Conventional optical imaging of functional activation in the brain is limited to surface structures such as the cerebral cortex. To access subcortical structures and image sensory-evoked neural activity, we designed a needle-based optical system using gradient-index (GRIN) rod lens. We performed voltage-sensitive dye imaging (VSDi) with GRIN rod lens to visualize neural activity evoked in the thalamic barreloids by deflection of whiskers in vivo. We stimulated several whiskers together to determine the sensitivity of our approach in differentiating between different barreloid responses. We also carried out stimulation of different whiskers at different times. Finally, we used muscimol in the barrel cortex to silence the corticothalamic inputs while imaging in the thalamus. Our results show that it is possible to obtain functional maps of the sensory periphery in deep brain structures such as the thalamic barreloids. Our approach can be broadly applicable to functional imaging of other core brain structures.

Numerical ray tracing method for an eccentric radial gradient-index rod lens.

We propose a ray tracing method for a radial gradient-index (GRIN) rod lens with an eccentric refractive index distribution. Radial GRIN rod lenses are typically treated as being rotationally symmetric around the optical axis. However, there are several eccentricities of the refractive index distribution in the transverse section, and an eccentricity point is the position of the highest refractive index with respect to the rod axis. Some manufacturing techniques can introduce these eccentricities in the refractive index distribution, and the effect of eccentricity on the lens performance cannot be neglected in some cases. Ray tracing in an eccentric refractive index distribution is possible by extending the conventional method. This allows analysis of the imaging performance of a radial GRIN rod lens with an eccentric refractive index distribution. Since the proposed method builds on the conventional formalism for a rotationally symmetric refractive index distribution, it is simple and easy to implement.

Focusing, collimation and beam shaping by active GRIN rod lenses: Theory and simulation

This work presents a theoretical analysis as well as the simulation of different optical functions that can be obtained from Gaussian beam transformations by active GRIN (GRadient-INdex) rod lenses having quadratic gain or loss. Profiles of the real and imaginary parts of the complex refractive index have been studied in order to show guidance behaviour and gain or loss effects of active rod lenses on the Gaussian beam propagation. General conditions for obtaining focusing, collimation and beam shaping by active rod lenses as circle diagrams plotted in the complex plane of the real and imaginary parts of the input complex curvature are discussed. MATLAB simulations of on-axis gain and loss selfoc GRIN rod lenses, acting as uniform beam shapers, focusers and collimators are presented. In particular, it is shown that an on-axis gain GRIN lens of semiaperture 1mm and length 8. 252mm transforms an input Gaussian beam into a uniform beam. On the other hand, an on-axis loss GRIN lens with the same semiaperture can carry out the same transformation for a propagation length of 4.936mm. Besides, an input Gaussian beam is focused by an active GRIN lens of semiaperture 1mm at a propagation length of 9.99mm, for both on-axis gain and loss material, being turned into a uniform collimated beam when the propagation length is 19.99mm.

A forward-imaging needle-type OCT probe for image guided stereotactic procedures

A forward-imaging needle-type optical coherence tomography (OCT) probe with Doppler OCT (DOCT) capability has the potential to solve critical challenges in interventional procedures. A case in point is stereotactic neurosurgery where probes are advanced into the brain based on predetermined coordinates. Laceration of blood vessels in front of the advancing probe is an unavoidable complication with current methods. Moreover, cerebrospinal fluid (CSF) leakage during surgery can shift the brain rendering the predetermined coordinates unreliable. In order to address these challenges, we developed a forward-imaging OCT probe (740 μm O.D.) using a gradient-index (GRIN) rod lens that can provide real-time imaging feedback for avoiding at-risk vessels (8 frames/s with 1024 A-scans per frame for OCT/DOCT dual imaging) and guiding the instrument to specific targets with 12 μm axial resolution (100 frames/s with 160 A-scans per frame for OCT imaging only). The high signal-to-background characteristic of DOCT provides exceptional sensitivity in detecting and quantifying the blood flow within the sheep brain parenchyma in real time. The OCT/DOCT dual imaging also demonstrated its capability to differentiate the vessel type (artery/vein) on rat’s femoral vessels. We also demonstrated in ex vivo human brain that the location of the tip of the OCT probe can be inferred from micro-anatomical landmarks in OCT images. These findings demonstrate the suitability of OCT guidance during stereotactic procedures in the brain and its potential for reducing the risk of cerebral hemorrhage.

The Optical Design of Miniaturized Microscope Objective for CARS Imaging Catheter with Fiber Bundle

In coherent anti-Stokes Raman scattering (CARS) microscopy reported until now, conventional microscope objectives are used, so that they are limited for introduction into a living body. Gradient-index (GRIN) rod lenses might be a solution for miniaturized microscope objectives for in-vivo CARS microscopy. However, due to the inherent large amount of chromatic aberration, GRIN rod lenses cannot be utilized for this purpose. CARS imaging catheter, composed of miniaturized microscope objective and fiber bundle, can be introduced into a living body for minimally invasive diagnosis. In order to design the catheter, we have to first investigate design requirements. And then, the optical design is processed with design strategies and intensive computing power to achieve the design requirements. We report the miniaturized objective lens system with diffraction-limited performance and completely corrected chromatic aberrations for an in-vivo CARS imaging catheter.

The Optical Design of Probe-type Microscope Objective for Intravital Laser Scanning CARS Microendoscopy

A stack of gradient-index (GRIN) rod lenses cannot be used for coherent anti-Stokes Raman scattering (CARS) microendoscopy for insertion to internal organs through a surgical keyhole with minimal invasiveness. That's because GRIN lens has large amount of inherent chromatic aberrations in spite of absolutely requiring a common focus for pump and Stokes beam with each frequency of <TEX>${\omega}_p$</TEX> and <TEX>${\omega}_S$</TEX>. For this endoscopic purpose, we need to develop a long slender probe-type objective, namely probe-type microscope objective (PMO). In this paper, we introduce the structure, the working principle, and the design techniques of PMO which is composed of a probe-type lens module (PLM) and an adaptor lens module (ALM). PLM is first designed for a long slender type and ALM is successively designed by using several design parameters from PLM for eliminating optical discords between scanning unit and PLM. A combined module is optimized again to eliminate some coupling disparities between PLM and ALM for the best PMO. As a result, we can obtain a long slender PMO with perfectly diffraction-limited performance for pump beam of 817 nm and Stokes beam of 1064 nm.

Design of optical coupling systems between two-dimensional quasi-stadium laser diodes and single-mode optical fibers

Optical coupling systems between a two-dimensional quasi-stadium laser diode and single-mode optical fibers using gradient-index rod lenses are designed for both stable and unstable laser resonators for the first time. A novel numerical approach using a combination of the extended Fox-Li calculation method and Gaussian beam transformations is proposed. In the case of a stable laser resonator, two kinds of beam propagation modes appear, namely the axis mode, in which an optical beam propagates along the cavity axis, and the ring mode, in which optical beams propagate along the diamond-shaped trajectory. The coupling efficiencies are found to be 54% for the axis mode and 52% for the ring mode. In contrast, an unstable laser resonator exhibits complicated modes, in which several highly directional beams are emitted from the end mirrors. The total coupling efficiency for these output beams is calculated to be 9.6%. The 3-dB tolerances for the lens pitch and alignment angles of the gradient-index rod lenses are also discussed.

Flexible miniature compound lens design for high-resolution optical coherence tomography balloon imaging catheter

We report on a new optics design for an optical coherence tomography (OCT) balloon imaging catheter. The design involves a miniature compound gradient-index (GRIN) rod lens, which consists of a fiber optic mode-field reducer and relay rod lenses to achieve predictable high lateral resolution at a desired large working distance. The compound lens design significantly simplifies the engineering process for an OCT catheter and enables 3-D full circumferential cross sectional imaging of large luminal organs such as human esophagus. An as-designed OCT catheter is developed and demonstrated for real-time in vivo swine esophagus imaging in a 3-D spiral fashion.

Characterization of gradient-index lens-fiber spacing toward applications in two-photon fluorescence endoscopy

We report on the experimental investigation into the characterization of two-photon fluorescence microscopy based on the separation distance of a single-mode optical fiber coupler and a gradient-index (GRIN) rod lens. The collected two-photon fluorescence signal exhibits a maximum intensity at a defined separation distance (gap length) where the increasing effective excitation numerical aperture is balanced by the decreasing confocal emission collection. A maximum signal is found at gap lengths of approximately 2, 1.25, and 1.75 mm for GRIN lenses with pitches of 0.23, 0.25, and 0.29 wavelength at 830 nm. The maximum two-photon fluorescence signal collected corresponds to a threefold reduction of axial resolution (38.5 microm at 1.25 mm), compared with the maximum resolution (11.6 microm at 5.5 mm), as shown by the three-dimensional imaging of 10 microm beads. These results demonstrate an intrinsic trade-off between signal collection and axial resolution.

Two-photon fluorescence endoscopy with a micro-optic scanning head.

A major obstacle in the race to develop two-photon fluorescence endoscopy is the use of complicated bulk optics to transmit an ultrashort-pulsed laser beam and return the emitted fluorescence signal. We describe an all-fiber two-photon fluorescence microendoscope based on a single-mode optical fiber coupler, a microprism, and a gradient-index rod lens. It is found that the new endoscope exhibits an axial resolution of 3.2 microm and is capable of imaging transverse cross sections of internal cylindrical structures as small as approximately 3.0 mm in diameter. This device demonstrates the potential for developing a real-time diagnostic tool for biomedical research without the need for surgical biopsy and may find applications in photodynamic therapy, microsurgery, and early cancer detection.