We report a study of gradient index (GRIN) lenses as a miniaturized micro-objective for in vivo imaging in the context of the development of a nonlinear endomicroscope. A numerical study of the parameters influencing the lateral resolution, excitation, and collection efficiency, when GRIN lens is coupled with a double clad fiber (DCF), is exposed. Four commercial DCFs, previously identified from the literature as potential endoscopic fibers, are simulated. Then, an experimental study characterizes two GRIN lenses (one commercial, one homemade) by their dispersion and nonlinear effects, potential intrinsic fluorescence, and use for fluorescence lifetime measurements. Images of neural cells from brain tissues of mice through a GRIN lens are presented.
© 2015 Optical Society of America
Two-photon microscopy (TPM) has become an important tool for live tissue imaging, and many advances have been reported in the last decade [1,2]. In contrast to confocal microscopy, TPM offers an increased penetration depth—up to a few hundred microns with a subcellular resolution, reduced photo-bleaching and an ability of intrinsic sectioning, allowing three dimensional imaging. The use of optical fibers would allow in vivo implementation of TPM in hollow organs or tissues, similar to the commercial confocal endomicroscopy .
The building of an endomicroscope requires several constituents: a femtosecond near infrared (NIR) laser source, an endoscopic fiber combined to a distortion compensation unit, a miniaturized scanning device, and a distal lens for focusing the excitation beam on the target and collecting the nonlinear signal. Each part of the system is crucial and requires an optimization. The choice of the distal lens should take five factors into consideration: (1) its miniaturization, (2) background fluorescence from glass composition, (3) the temporal and spatial confinement of the NIR pulses indispensable for multi-photon excitation, (4) large field of view (FOV), and (5) high collection efficiency. In the context of in vivo imaging of brain tissues, TPM is limited by the tissue accessibility and the degree of invasiveness. Thanks to their very small diameter (less than 1 mm), GRIN lenses allow imaging of much deeper structures like brain tissues with much higher accessibility and less invasiveness requiring only a small trepanation. GRIN lenses have a radial refractive index profile of parabolic shape that is maximum at the cylinder axis. This causes light to bend and focus inside the long tube-shaped lens, thereby reaching the imaging site. GRIN lenses can be designed to have a high numerical aperture (NA) ranging from 0.4 to 0.6, flat surface, small diameter (0.35–1 mm), big length (up to several centimeters), and are biocompatible and already validated for clinical use . These characteristics make it an ideal choice for deep TPM in humans .
There have been many works with two-photon endomicroscopic design with GRIN lenses [4,5] or achromatic doublet with a double clad fiber, in which a grating pair was used to compensate for dispersion, introduced by the fiber . In this Letter, we present a study to optimize a nonlinear endomicroscope. We have characterized and optimized numerically and experimentally a GRIN lens that was adapted for nonlinear imaging and combined with a commercial DCF. The study focused on resolution, two-photon fluorescence (TPF) collection, as well as the management of nonlinear effects and dispersion that was introduced by the lenses.
The first lens is custom made with a diameter adapted for minimal invasiveness in small animal imaging and a NA compatible with a standard optical fiber. The second lens is designed for high-resolution two-photon imaging and is commercially available. The custom designed GRIN lens (GRIN #1) is a lens doublet (GT-IRLS-050-11-50-NC) with a diameter of 500 μm and length of 24.25 mm. It is made of an objective lens (, ), which is glued to a relay lens (, ). Its image space NA is 0.081. This lens combination produced a high magnification capable of focusing the laser beam into a tight spot at the tissue site. The second lens (GRIN #2) is a commercial high numerical aperture objective system lens (GT-MO-080-018-810) with 1.4-mm diameter. It is a complex optical system with a spherical lens and two GRIN lenses fabricated with a special gradient profile in order to decrease wave-front aberrations; its object space NA is 0.8, thus providing high spatial resolution and signal collection, while the image space NA is 0.18 for optimal coupling with a fiber. The total length of this assembly is 7.53 mm. Both GRIN systems are mounted in stainless steel tubing. Note that the details of the design of the commercial GRIN #2 with high NA is an intellectual property of GRINTECH and has not been made public yet.
Consequently, only the GRIN #1 combined with a DCF that delivers the excitation beam was characterized numerically using Zemax. Both geometric ray tracing and Gaussian beam approach were considered with a Gaussian–Lorentzian spatial profile at the focus, while the diffraction effect by the finite aperture of the GRIN lens is neglected.
First, the axial and lateral resolutions at FWHM and the collection efficiency of the combination of GRIN #1 with a commercial DCF were calculated. We have previously selected and characterized four commercial DCFs  used in the literature in a context of nonlinear endomicroscopy. Their parameters are summarized in Table 1, highlighting the lateral resolution at full width half-maximum (FWHM), calculated from the excitation spot size at the focal plane of GRIN #1 by considering the Gaussian beam approximation. The core size of the fiber and its NA define the focal volume and thus the optical resolution—the smaller the focal volume, the higher the resolution. The best resolution was obtained with the Fibercore. The excitation coupling efficiency between each of the four DCFs and the GRIN #1 was calculated by using geometrical ray tracing at 800 nm. At a separation distance of 1.64 mm (corresponding to an object WD of 50 μm), the best coupling efficiency was obtained with the Crystal Fiber. This DCF was the ideal commercial DCF, identified in our previous work . These results highlight that the better resolution was obtained with the DCF having the smallest core diameter, and the best excitation efficiency was obtained with the smallest core NA.
The distance between DCF output and GRIN lens defines the image space working distance (WD). As shown by the calculation depicted in Fig. 1, image WD varies linearly with the object WD. The object WD can be set between 0 and 100 μm, which hugely limits the penetration depth of the excitation beam inside the target. This parameter is also correlated with the fluorescence collection efficiency, depending on the DCF NA and inner cladding diameter.
GRIN lens suffers from severe chromatic aberrations, as shown in Fig. 2, causing an important shift of the focal point between the excitation signal and the TPF focal points [Fig. 2(a)], consequently reducing the TPF collection [Fig. 2(b)]. For example, with an excitation at 800 nm, emission at 530 nm, and a distance between the DCF and the GRIN #1 of 0.61 mm, the back focal plane of TPF will be around 1.4 mm in front of the fiber tip, due to chromatic aberration.
We have quantified the effect of chromatic aberration on TPF collection efficiency in the case of each of the four DCFs coupled with the GRIN #1, varying the image WD [Fig. 2(b)]. This simulation was done for a range of nonlinear emitted signal wavelength between 400 and 600 nm. The optimal DCF should give a high collection efficiency on the largest wavelength range with better resolution. We have computed this enhancement with the geometric ray tracing and summarized it in Fig. 3 for three-image WD: 3.28 mm [Fig. 3(a), object WD: 0 μm], 1.64 mm [Fig. 3(b), object WD: 50 μm] and 3.28 mm [Fig. 3(c), object WD: 0 μm]. For each image WD and wavelength, the best coupling efficiency was obtained with the Crystal Fiber and the worst with the Fibercore; corroborating the results shown in Table 1.
Assuming the ideal situation where the full diameter of the GRIN #1 is used to scan the laser beam, the maximum FOV would be , without reference to the other parameters (NAs, distance between the DCF tip and the GRIN lens, DCF core diameter, etc.). This parameter is very restrictive, considering the need of surgeon of a large FOV, at minimum 100 times bigger than the shown here, to be able to understand the images obtained with an endomicroscope with this GRIN lens.
Both GRIN lenses were then characterized experimentally to quantify pulse distortions due to linear and nonlinear effects, tunability, an eventual background fluorescence, spatial resolution, and FOV.
First, the effects of GRIN lenses on pulse delivery, including dispersion and nonlinear effects, were assessed by autocorrelation and spectral measures. In the setup exposed in Fig. 4(a), detailed in previous publications [8,9], pulses were first broadened spectrally and temporally into a standard single-mode fiber (SMF) up to 40 nm at the full width half-maximum (FWHM) and 4 ps due to nonlinear effects and positive dispersion. Then, a grisms line compensates for the second and the third orders of dispersion, thanks to its adjustment of the distance between the two grisms and the incident angle of the beam on the first grism. At the grisms line output, the minimum of pulse duration was 30 fs, considering a secant hyperbolic square shape (), with 75 mW of average power. The dispersion inside each GRIN lens was experimentally characterized in two steps. First, the pulse duration was measured after a lens doublet system without the presence of the GRIN lens. In the second step, each GRIN lens was sandwiched inside the doublet. After a step of beam collimation of the doublet, the pulse duration at the GRIN lens output was measured as a function of the pulse duration at the GRIN lens input, varied by the distance between the grisms. For both GRIN lenses, the minimum pulse duration achieved was 30 fs (), identical to the duration without the GRIN lens, at for GRIN #1 [Fig. 4(b)] and for GRIN #2 [Fig. 4(c)]. With and without GRIN #2, the duration was slightly modified for the pulses in the range of 200 fs resulting from the small quantity of glass traversed. However, higher divergence in the GRIN #1 was observed starting for the pulse duration around 60 fs and beyond [Fig. 4(b)]. This is characterizing the presence of a non-negligible dispersion introduced by the 24.25 mm of material. In our configuration, these effects are easily compensated by a simple adjustment of the grisms line.
In a second set of measures, the GRIN lens tunability was tested for central wavelengths ranging between 750 and 810 nm with steps of 10 nm. No significant change of pulse duration were highlighted [Fig. 4(d)], characterizing a good tunability on this spectral range. At the same time, spectral measures were done. No significant spectral difference in shape and bandwidth was observed with and without the GRIN lenses, as illustrated in Fig. 4(e) for the GRIN #1 at 780 nm. This indicates that no significant, nonlinear effect occurs inside the GRIN lenses.
Then, the auto-fluorescence from each lens was characterized with a confocal microscope using 488-nm excitation wavelength. Auto-fluorescence from the glue, located in the region between the lens and the tubing around both GRIN lenses, is shown in Figs. 5(a) and 5(b). No fluorescence was observed inside the effective FOV. Consequently, the peripheral auto-fluorescence is not affecting the fluorescence collected from the target. No fluorescent element inside the GRIN lens glass was characterized. Figure 5 presents an image of fluorescent beads, showing the circular homogeneous FOV that can be obtained with this kind of lens. As an illustration, fixed neural cells of mice olfactory bulb inside a microscope slide were imaged through GRIN #1 and #2 with the confocal microscope and shown in Figs. 5(d) and 5(e), respectively. The point spread function (PSF) measurement, using the sub-resolution fluorescent beads, revealed a lateral resolution of , as presented in Fig. 5.
For the discrimination of cancerous and healthy cells in microscopy, the fluorescence lifetime measurement is one of the essential parameters . In that context, we tested the effect of GRIN #1 and #2 on the instrument response function for lifetime measurement. We measured lifetimes of Rhodamine B in water with both GRIN lenses. The lifetime via GRIN #1 was and for the GRIN #2. These results are in agreement with the literature . Consequently, the effect of the GRIN #1 and #2 on the instrument response function for lifetime measurement was negligible.
In conclusion, the global effect of GRIN lens on the excitation beam was presented and considered when coupled with a commercial DCF. First, the optimization of the distance between the GRIN lens and the DCF must be set precisely because of chromatic aberrations, which reduce the nonlinear signal collection efficiency by the inner cladding of the DCF. Second, no nonlinear effect inside the GRIN lens was characterized, and a non-negligible part of dispersion was highlighted; however, the grisms line compensated for it. Third, the presence of auto-fluorescence of the glue around the GRIN lens did not create problematic background fluorescence on the image FOV, and no perturbation of the fluorescence lifetime measurements had been detected. A real limitation of the FOV size had been highlighted. Finally, a compromise between enhancing the resolution and optimizing the nonlinear signal collection efficiency must be taken into consideration when choosing the commercial DCF as an endoscopic fiber. After defining the design goals (resolution and signal detection level), the choice can easily be made. According to these points, DCFs from Crystal Fiber and Fibercore are both good candidates for a nonlinear endomicroscope design. The DCF from Fibercore achieved a good lateral resolution and acceptable collection efficiency, while the Crystal Fiber achieved the poorest lateral resolution and the highest collection efficiency over the entire wavelength range, despite the effect of chromatic aberrations of the GRIN lens. Moreover, we have previously shown  that, even if its core diameter is restrictive for the resolution, the DCF from Crystal Fiber achieved the best pulse duration among the four selected DCFs. Consequently, the ideal DCF for an endomicroscopic architecture is not commercially available and requires a specific architecture, depending on the kind of distal lens.
“Plan Cancer” with the Physicancer program grant (for MEVO project) has supported this work and a “Défi instrumental” program grant from CNRS.
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