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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27142–27154
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Characterization and improvement of three-dimensional imaging performance of GRIN-lens-based two-photon fluorescence endomicroscopes with adaptive optics

Chen Wang and Na Ji  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 27142-27154 (2013)
http://dx.doi.org/10.1364/OE.21.027142


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Abstract

Inherent aberrations of gradient index (GRIN) lenses used in fluorescence endomicroscopes deteriorate imaging performance. Using adaptive optics, we characterized and corrected the on-axis and off-axis aberrations of a GRIN lens with NA 0.8 at multiple focal planes. We demonstrated a rotational-transformation-based correction procedure, which enlarged the imaging area with diffraction-limited resolution with only two aberration measurements. 204.8 × 204.8 µm2 images of fluorescent beads and brain slices before and after AO corrections were obtained, with evident improvements in both image sharpness and brightness after AO correction. These results show great promises of applying adaptive optical two-photon fluorescence endomicroscope to three-dimensional (3D) imaging.

© 2013 Optical Society of America

1. Introduction

With the development of optical sectioning microscopy, such as confocal microscopy and multiphoton microscopy, three-dimensional (3D) optical imaging can be performed in highly scattering biological samples [1

1. J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).

, 2

2. D. B. Murphy and M. W. Davidson, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2012).

]. However, with increasing imaging depth, scattering of both the excitation light and the emitted light causes the imaging signal and quality to degrade, and ultimately limits imaging depth to several hundred micrometers for typical tissue samples such as mouse brains or skins [3

3. P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 microm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 28(12), 1022–1024 (2003). [CrossRef] [PubMed]

]. Using longer excitation wavelength and red-shifted dyes allows deeper structures to be reached [4

4. M. Balu, T. Baldacchini, J. Carter, T. B. Krasieva, R. Zadoyan, and B. J. Tromberg, “Effect of excitation wavelength on penetration depth in nonlinear optical microscopy of turbid media,” J. Biomed. Opt. 14(1), 010508 (2009). [CrossRef] [PubMed]

7

7. N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013). [CrossRef]

], but even there, light scattering ultimately confines the optical penetration depth to a few millimeters. As many interesting biological questions lie beyond this depth range, minimally invasive techniques that can image several millimeters or deeper are highly desired for in vivo biological research and clinical applications. Endomicroscope techniques employing gradient-index (GRIN) lenses [8

8. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer-Verlag, 2002).

] have been developed to address this issue. GRIN lenses are miniature rod-like lenses with diameters of around 1 mm or less. Their refractive power comes from a radial refractive index profile of nearly parabolic shape, rather than from surface curvature as in conventional lenses made of optically homogeneous materials. Their miniature size allows them to be embedded in biological tissues and relay the excitation and emitted light between a conventional microscope objective and the structure of interest. Recent work incorporating GRIN lenses into confocal or multiphoton microscopes showed various promising applications in vivo where microscopic images were taken from depths of several millimeters to centimeters below sample surface [9

9. J. C. Jung and M. J. Schnitzer, “Multiphoton endoscopy,” Opt. Lett. 28(11), 902–904 (2003). [CrossRef] [PubMed]

16

16. C. M. Brown, D. R. Rivera, I. Pavlova, D. G. Ouzounov, W. O. Williams, S. Mohanan, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using a compact and flexible multiphoton microendoscope,” J. Biomed. Opt. 17(4), 040505 (2012). [CrossRef] [PubMed]

].

However, one problem with the application of GRIN lenses in microscopy is their intrinsic aberration [17

17. W. M. Lee and S. H. Yun, “Adaptive aberration correction of GRIN lenses for confocal endomicroscopy,” Opt. Lett. 36(23), 4608–4610 (2011). [CrossRef] [PubMed]

, 18

18. F. Bortoletto, C. Bonoli, P. Panizzolo, C. D. Ciubotaru, and F. Mammano, “Multiphoton fluorescence microscopy with GRIN objective aberration correction by low order adaptive optics,” PLoS ONE 6(7), e22321 (2011). [CrossRef] [PubMed]

], which is especially severe for those of high numerical aperture (NA) (e.g., NA 0.8) [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

]. Unlike conventional microscope objectives or the ‘stick objectives’ (e.g., Microprobe objectives from Olympus) [20

20. H. Alencar, U. Mahmood, Y. Kawano, T. Hirata, and R. Weissleder, “Novel multiwavelength microscopic scanner for mouse imaging,” Neoplasia 7(11), 977–983 (2005). [CrossRef] [PubMed]

], which contain many optical elements for light path correction and aberration minimization over a large image field, high-NA GRIN lenses only have their on-axis aberration corrected [21

21. R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods 6(7), 511–512 (2009). [CrossRef] [PubMed]

, 22]. For a 0.8-NA GRIN lens, the off-axis aberrations at 100 μm from center were found to be so drastic that they degraded signal more than ten folds. By measuring and correcting these off-axis aberrations using a pupil-segmentation-based adaptive optical (AO) method [23

23. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010). [CrossRef] [PubMed]

, 24

24. N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A. 109(1), 22–27 (2012). [CrossRef] [PubMed]

], we recovered diffraction-limited performance across a 200 × 200 μm2 imaging field at the design working distance, by applying the wavefront correction patterns obtained at 9 field positions [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

].

For 3D volume imaging, a conventional microscope moves its objective axially relative to the sample, with the distance between the objective and the focus stay constant. With a GRIN lens serving as the relay between the conventional microscope objective and the sample, however, to have a fixed distance between the GRIN lens and the final focus inside the sample, one has to move both the objective and the GRIN lens axially relative to the sample, which can be difficult because the miniature size of the GRIN lens makes it hard to manipulate. For GRIN lenses that are directly embedded in biological samples, such movement may also cause additional sample damage and motion. An alternative mode of operation is to have the GRIN lens stationary with respect to the sample, but change the distance between the microscope objective and the GRIN lens. This causes changes in the “image working distance (image WD)” of the GRIN lens, defined as the distance between the objective focus and the top surface of the GRIN lens, which are relayed by the GRIN lens into axial movement of final focus inside the sample (Fig. 1
Fig. 1 Schematics and characterization of on-axis aberrations. (a) Schematic diagrams of a GRIN-lens-based endomicroscope, where the GRIN lens serves as a relay lens between the microscope objective and the sample, illustrating image working distance (WD), Δd, and image field position (FP). (b-d) Focal series images of a 2 μm diameter fluorescence bead at FP(0,0) before and after AO correction for (b) Δd = −100 µm, (c) Δd = 0 µm, (d) Δd = 100 µm, respectively. The corrective wavefronts in units of waves (λ = 900 nm) are (c) for the on-axis system aberration and (b, d) the additional corrective wavefronts (residue wavefronts) to the system aberration measured in (c). Images taken without AO are digitally enhanced so that the brightest pixel in the focal series has the same value as that after AO correction. (e) Zernike decomposition of the residue wavefronts shown in (b) and (d). Z1 piston, Z2 and Z3, tip and tilt; Z4 and Z6, astigmatism; Z5, defocus; Z7 and Z10, trefoil aberration; Z8 and Z9, coma; Z13, spherical aberration. Scale bars: 5 µm.
). Because the GRIN lenses are often designed to work at a particular image WD where the intrinsic on-axis aberration is minimized, varying image WD away from the design value would introduce additional aberrations. In this paper, using an adaptive optical two-photon fluorescence endomicroscope, we characterized and corrected the aberrations encountered by varying the image WD for a two-photon fluorescence endomicroscope incorporating a GRIN lens with NA = 0.8. We measured both the on-axis (i.e., center of image field) and off-axis aberrations at different image WDs. Larger-than-designed image WD, which corresponds to more superficial focus depth, was found to exacerbate off-axis aberrations; while smaller-than-designed image WD, which corresponds to deeper image depth, was found to alleviate off-axis aberrations. Moreover, to make aberration correction less laborious, we made use of the near-cylindrical symmetry of the GRIN lens and demonstrated a rotation-based correction procedure, in which aberration correction pattern measured at one field position (FP) was used for other FPs at the same distance away from field center after rotational transformations. With this procedure, only two instead of nine aberration corrections (as demonstrated previously in [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

]) were needed to achieve diffraction-limited images over a large field of view (FOV), which should facilitate the 3D imaging applications of GRIN-lens-based endomicroscopes.

2. Adaptive optical two-photon fluorescence endomicroscope

Both the home-built adaptive optical two-photon fluorescence endomicroscope and pupil-segmentation based AO method have been previously described [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

, 22]. A phase-only liquid crystal spatial light modulator (SLM) (Boulder Nonlinear Systems, Inc.) conjugated to the back pupil of a microscope objective was used for aberration measurement and correction. We mounted the objective (Nikon, CFI Plan Apochromat Lambda, 10 × , NA = 0.45) to a single-axis piezo stage (P-733.ZCL, Physik Instrumente GmbH) to adjust its vertical position. A GRIN lens (GRINTECH GmbH, GT-MO-080-0415-810, 1.92 × , object NA = 0.8, image NA = 0.415) was placed below the objective. To control its position, we built a custom assembly composed of an XY manual translation stage, a Z piezo translational stage (8301NF, Newport) with a closed-loop controller (8751-C, Newport), and a 2” kinetic tilt/tip adjustment platform mount (KM100B, Thorlabs). Precise alignment was carried out so that the GRIN lens shared the optical axis of the objective. A 2D motorized stage (XYRB-1010, Dover motion) was used for XY sample positioning, and a long-travel piezo stage (M-501, Physik Instrumente GmbH) was used for precise control of the distance between the GRIN lens and the specimen. A Ti: Sapphire femtosecond oscillator (Coherent Inc., Ultra II) tuned to 900nm was used as the excitation light source for all experiments.

The designed image WD of this GRIN lens is 100 µm. We use Δd to describe the GRIN lens position relative to the objective focus: for Δd = 0, the designed image WD was used; for Δd = 100 µm, the image WD was 200 μm; for Δd = −100 µm, the image WD was 0 μm, with the objective focus on the top surface of the GRIN lens, as shown in Fig. 1(a). Each 100 µm change in image WD caused ~40 µm focal shift on the sample side. The image FP is denoted by its X and Y coordinates (X, Y), with FP (0,0) describing the center of the image field where on-axis aberration was measured.

3. Characterization and correction of GRIN lens aberrations in 3D

First, using the pupil-segmentation-based approach described before [22], we measured the on-axis aberrations for three different image WDs with Δd = −100 µm, 0 µm, and 100 µm, respectively, by putting 2 µm diameter fluorescence beads at FP(0,0). For each Δd, Z image stacks (or “focal series images”) of the bead before and after AO correction were acquired by moving the sample axially in 0.5 µm steps while keeping the positions of objective and GRIN lens fixed [Figs. 1(b)1(d)]. At Δd = 0 µm, i.e., the design image WD, the corrective wavefront (Fig. 1(c), right panel) corresponds to the system aberration of the GRIN lens, caused by errors in the manufacture and assembly of the GRIN lens. Correcting this system aberration led to a 50% increase of maximal signal of the bead, similar to what we observed before on another GRIN lens with the same NA [15

15. D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express 3(5), 1077–1085 (2012). [CrossRef] [PubMed]

]. For Δd = −100 µm [Fig. 1(b)] and Δd = 100 µm [Fig. 1(d)], the corrective wavefronts shown are the residual wavefronts after subtracting the system aberration correction obtained at Δd = 0 µm from their respective full correction patterns, thus represent the aberration caused by image WD shift alone. The fact that these patterns are not circularly symmetric suggests that our imaging system was not truly cylindrically symmetric, due to component defects and alignment errors. Upon visual inspection, these wavefront distortions are toward opposite directions, which is hardly surprising, for the defocus at Δd = −100 µm and Δd = 100 µm are on the opposite sides of the design focal plane. Zernike decomposition of these two aberrations confirmed that most of their Zernike coefficients are opposite in sign, with spherical aberration as the dominant factor [Fig. 1(e)]. These additional aberrations caused by image WD changes, small in their magnitudes, did not impact the on-axis image quality significantly. Correcting them increased signal by only an additional 10-20%.

The changes in image WD did impact the severity of the off-axis aberrations drastically, however. Figure 2
Fig. 2 Characterization of off-axis aberrations. (a-c) Focal series images of a 2 µm fluorescence bead at FP(100 µm,0) for three different image WDs (a) Δd = −100µm, (b) Δd = 0 µm, (c) Δd = 100 µm before and after AO correction. Right panel of (c) shows the axial projections of the focal series at Δd = 100 µm before and after AO correction. Images taken without AO have their brightness digitally enhanced so that both focal series images for the same FP have the same maximal signal before and after AO correction. (d) Corrective wavefronts after system aberration subtraction at the three different image WDs in units of waves (λ = 900 nm). (e) Zernike decomposition of the three corrective patterns in (d). Z1 piston, Z2 and Z3, tip and tilt; Z4 and Z6, astigmatism; Z5, defocus; Z7 and Z10, trefoil aberration; Z8 and Z9, coma; Z13, spherical aberration. (f) Fluorescence beads imaged over a large FOV at all three Δd’s before AO correction. Scale bars: (a-d) 5 µm; (f) 20 µm.
showed aberration measurements at FP(100 µm,0) at Δd = −100 µm, 0 µm, and 100 µm, respectively. At the design image WD, the off-axis aberration caused a 5.7 × decrease in the maximal signal in the focal series images of a 2 μm diameter fluorescence bead [Fig. 2(b)]. At larger image WD (i.e., Δd = 100 µm, Fig. 2(c)) that would move the final focus closer to sample surface, the off-axis aberration at FP(100 µm, 0) was even larger, resulting in a 11 × reduction in maximal signal. At smaller image WD (i.e., Δd = −100 µm, Fig. 2(a)) that would move the final focus deeper into sample, the off-axis aberration at FP(100µm, 0) was much reduced, resulting in only a 1.6 × signal reduction. The deterioration in image resolution with the increase of Δd can be clearly seen in the Z stacks taken without AO correction (top panels, Figs. 2(a)2(c)), with Δd = 100 µm gave rise to the largest image distortion characteristic of astigmatism [Fig. 2(c)]. If we compare the maximal signal in the image plane with the least blur (“circle of least confusion”), the signal improvement was even higher (14.7 × at Δd = 100 µm). Figure 2(d) showed the corrective wavefront patterns after system aberration subtraction. Clearly, astigmatism became more prominent with the increase of Δd, which is by far the most dominant aberration mode as shown in their Zernike mode decomposition [Fig. 2(e)]. As a result, the effective image FOV decreases when the final focus is more superficial (larger Δd), and increases when the final focus is away from the GRIN lens and deeper inside the sample (smaller Δd), as shown in Fig. 2(f).

Figure 3
Fig. 3 Summary of the aberration correction results at FP(0,0), FP(75 μm,0), and FP(100 μm,0) for all three Δd’s. (a) Signal enhancement after AO correction at the focal plane with least blur. (b-d) Integrated signal of focal series images of a 2µm fluorescence bead plotted against their axial positions before and after AO correction at all three Δd’s for each FP.
summarizes the aberration correction results at FP(0,0), FP(75 μm,0), and FP(100 μm,0) for all three Δd’s. Figure 3(a) shows the signal enhancement after AO correction at the focal plane with least blur. Figures 3(b)3(d) show the integrated signal of focal series images plotted against their focal positions before and after AO correction for each FP. In principle, for the same image WD, the more off-axis the FP, the larger the aberration should be. It is the case for Δd = 0 and Δd = 100 µm, but not for Δd = −100 µm, where aberration measured at FP(75 µm,0) reduced signal less than that measured at FP(0,0). This is because the off-axis aberration at FP(75µm,0) was partly canceled out by the asymmetric system aberration. More importantly, as discussed above, for the same off-axis FP, the larger the image WD, the more severe the off-axis aberration, and the larger the signal improvement after AO correction. At all FPs and image WDs, AO correction recovered diffraction-limited imaging performance, with the post-correction image stacks having similar axial full-wide-half-maximum (FWHM) values between 3.8 and 4.1µm (solid lines, Figs. 3(b)3(d)). Therefore, even with the severe off-axis aberrations at larger image WD, if we take multiple images of the sample with aberration corrections measured at distinct FPs, we could achieve diffraction-limited image performance over a large area.

4. A rotational-transformation-based correction procedure for enlargement of FOV

Previously, we showed that by correcting the off-axis aberrations at eight FPs 100 μm away from the center of the field, we could significantly enlarge the FOV [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

]. However, together with the on-axis aberration correction, nine AO corrections were needed for this procedure. We proposed that the cylindrical symmetry of the GRIN lens should allow us to reduce the number of AO measurements. In reality, however, factors such as fabrication imperfections and alignment errors make the system less than perfectly cylindrically symmetric (e.g., none of the on-axis aberration patterns in Fig. 1 are circularly symmetric). Here we evaluated the experimental validity of this proposal in our two-photon endomicroscope setup and developed a correction procedure based on rotational transformation that can greatly reduce the number of corrections needed.

Firstly, we measure the aberration at the center of FOV, FP(0,0), and consider it as the system aberration (SA) at this image WD. Secondly, we measure aberration at an off-axis field position; Thirdly, we subtract SA correction from the off-axis corrective pattern, thus obtain the part of aberration that is caused by off-axis light propagation, rather than by the optical imperfections. Fourthly, we rotate the corrective pattern from the third step by seven different angles: 45°, 90°, 135°, 180°, 225°, 270°, and 315° and obtain the aberrations due to off-axis light propagation for seven other FPs located at the same distance from the center of FOV; Lastly, we combine these patterns with SA correction, and get the final composite correction patterns for these different FPs. As we show below, this procedure only requires two aberration measurements to cover a large FOV, rather than nine as demonstrated previously [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

].

To validate this approach, we compared the focal series images of a 2 μm diameter fluorescence bead without AO, with SA correction only, with aberration correction obtained from the above procedure, and with full AO correction patterns experimentally measured at seven different off-axis FPs with Δd = 100 μm. We chose this particular image WD because it had the largest off-axis aberration among those three image WDs characterized above. The original two correction patterns were obtained at the FP(0,0) (i.e., SA) and FP(75 µm, 0) (i.e., off-axis aberration). Figures 4(a)
Fig. 4 Comparison of focal series images of a 2µm fluorescence bead without AO, with system aberration (SA) correction only, with correction obtained via the rotational-transformation-based procedure (R45°, R90°, and R180° denotes the rotation angle used for calculation), and with experimentally measured correction for (a) FP(53 µm, 53 µm), (b) FP(0, 75 µm), (c) FP(−75 µm, 0) with Δd = 100 µm. (d) Integrated signal of the focal series images in (a-c) plotted against their axial positions, respectively. Green dash line in the leftmost panel is the normalized axial profile from R45° correction. (e) Top panel: the off-axis corrective pattern (R0°) and its rotational-transformations (R45°, R90°, and R180°). Bottom panel: Final composite correction patterns obtained by adding the SA correction to the patterns in the top panel. Dashed black circle represents the back pupil of the objective, and the red square represents the border of the SLM. Scale bar: 5 µm.
4(c) show the focal series images for three example FPs: FP(53 µm, 53 µm), FP(0,75 µm), and FP(−75µm,0). Without any AO correction (top row, Figs. 4(a)4(c)), aberrations at these three FPs reduce the signal strength by ratios varyingfrom 2.2 × to 6.0 × ; With SA correction (second row, Figs. 4(a)4(c)), signal reduction at these three FPs become more comparable, varying between 3.3 × and 4.5 × , due to the removal of the asymmetric SA (a perfectly manufactured, assembled, and aligned GRIN lens would have identical signal reductions at all FPs equidistant from field center). These focal series images after SA correction show the characteristics of astigmatism. Following the procedure described above, we generated correction patterns for these three FPs (R45°, R90°, and R180°) by rotating the correction pattern at FP(75 µm, 0) counterclockwise by 45°, 90°, and 180°, respectively, then adding to them the SA correction. For FP(0,75 µm) and FP(−75 µm, 0), the calculated patterns almost fully recovered signal and resolution to those obtained with full, experimentally measured AO corrections at these FPs, as indicated by the integrated intensity profile in axial direction (middle and right panels of Fig. 4(d)). For FP(53 µm, 53 µm), the calculated pattern improved the integrated signal to 70% of that obtained with full AO correction, with the resolution not fully recovered (left panel of Fig. 4(d)). The absence of full signal and resolution recovery is not due to the failure of our procedure. Instead, because our SLM was square and, through conjugation, inscribed in the back pupil of the objective, rotating the pattern 45° reduces the usable SLM area by 17%, and leads to both the reduction in effective NA and two photon fluorescence signal (Fig. 4(e), second panel from left). A different experimental configuration where the SLM pattern is larger than the back pupil would avoid this problem and presumably fully recover image performance at the oblique rotation angles.

To evaluate how well these correction patterns help to enlarge FOV, we imaged a dense bead sample over a 204.8 µm × 204.8 µm area. Because the focal plane of this GRIN lens is curved but the bead sample is 2D, we took a 204.8 µm × 204.8 µm Z stack of these beads at 0.5 μm step size with each of the nine aberration correction patterns (2 measured, 7 calculated) separately applied and presented the maximal intensity projection of each stack in Fig. 5(a)
Fig. 5 (a) Maximal intensity projections from focal series images of 2 µm diameter fluorescence beads obtained with two measured corrective wavefronts (SA and AO R0°, yellow labels) and seven calculated corrective patterns (AO R45°, AO R90°, AO R135°, AO R180°, AO R225°, AO R270°, and AO R315°, white labels). (b) The calculated corrective patterns significantly improve image quality, as shown in the enlarged views of two sample areas (blue and green squares in (a)) imaged without AO, with calculated corrective patterns, and with corrective patterns experimentally measured at the center of each area. Intensity profiles shown in the top and bottom line figures were measured along the blue and green lines in the images, respectively. (c) Corrective pattern at FP(X,Y) improves image quality at the opposing FP(-X,-Y), as shown in two examples where images at FP(53 µm,-53 µm) and FP(−75 µm,0) were measured using the correction patterns calculated for its their opposite FPs (FP(−53 µm,53 µm) and FP(75 µm,0), R135° and R90°), as well as with the corrective patterns experimentally measured at FP(53 µm,-53 µm) and FP(−75 µm,0). Intensity profiles were measured along the orange lines in the images. (d) Maximal intensity projections of images over an area 204.8µm × 204.8 µm taken, from top to bottom, without AO, with five correction patterns (two measured, SA and AO R0°, and three calculated, AO R45°, AO R90°, and AO R135°), and with the nine correction patterns used in (a). Scale bar: 20 µm.
. Obviously, each FP-specific correction pattern improved the image quality in its neighboring field area, as well as in the opposing area across the field center, because the opposing FPs have identical astigmatism [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

]. Figure 5(b) provides the enlarged views of two areas (blue and green squares in Fig. 5(a)). Comparing these images to those obtained without AO correction and with full, experimentally measured AO correction, we can see that these calculated correction patterns recover signal at off-axis locations either as well as the experimentally measured ones (when the rotation angle modulo 90° is zero) or to about 75% level of full correction (due to the reduced NA when the rotation angle modulo 90° is 45°), in either case leading to image quality far superior to the uncorrected case. Additional, as we discovered before [19

19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

], the correction pattern at one off-axis FP also improves the image quality at the opposing FP relative to the field center. Figure 5(c) compares images taken around FP(53 µm,-53 µm) and FP(−75 µm,0), respectively, using the correction pattern calculated for their opposite FPs (FP(−53 µm,53 µm) and FP(75 µm,0), R135° and R90°) with those obtained with full, experimentally measured AO correction at FP(53 µm,-53 µm) and FP(−75 µm,0) (data shown were from another experimental session with different bead sample). The line intensity profiles show that corrections at the opposite FP recovered signal intensity up to 85% of the full correction level. This may help us reduce the number of images needed to cover the full FOV: instead of applying all nine correction patterns, we only need five correction patterns. As shown in Fig. 5(d), the composite image (maximal intensity projection of the images in Fig. 5(a)) from five correction patterns (including two original measured and three calculated) exhibited very similar image qualities to the one obtained after measurements with all nine correction patterns (including two original and seven composite patterns calculated).

With the same correction patterns, similar improvement was observed on a fixed brain slice from a YFP line 16 transgenic mouse (Fig. 6
Fig. 6 (a) Maximal intensity projections of 10-μm-thick focal series images of a brain slice of Thy-1 line 16 mouse taken with two measured (SA and AO R0°, yellow labels) and seven calculated corrective patterns (AO R45°, AO R90°, AO R135°, AO R180°, AO R225°, AO R270°, and AO R315°, white labels). (b-c) Enlarged views centering at two off-axis locations, FP(53 µm,-53 µm) and FP(0,75 µm) (orange and purple squares in (a)) without AO and with the calculated patterns, AO R315° and AO R90°, respectively. (d) Maximal intensity projections of images over an area 204.8µm × 204.8 µm taken, from top to bottom, without AO, with five correction patterns (two measured, SA and AO R0°, and three calculated, AO R45°, AO R90°, and AO R135°), and with the nine correction patterns used in (a), respectively. Scale bar: 20 µm.
). Figures 6(b) and 6(c) show enlarge images at two off-axis locations, FP(53 µm,-53 µm) and FP(0,75 µm) with corrected patterns calculated via rotation of 315° and 90°, respectively. Comparing them with images taken without AO correction, we can see evident improvements in image sharpness and contrast, with more cell bodies distinguished and the resolution sufficient to clearly resolve axons and dendrites. In Fig. 6(d), we showed the composite images over 204.8 µm × 204.8 µm. Before AO, the fluorescence intensity faded at the edges of the FOV because of off-axis aberrations. After AO corrections using either five or nine composite patterns, the effective FOV was extended remarkably, with many more fine neuronal processes resolvable at off-axis locations.

In these examples, for the same FOV, samples were imaged multiple times with different correction patterns applied. In principle, if the wavefront modulator has a response time similar to that of scanning galvos and thus can adopt different correction patterns during different portions of the same image scan, only one image scan is needed without any sacrifice of speed. With the low refresh rate of our liquid crystal SLM (60Hz), 1 Hz frame rate (i.e., 5 images taken at 5 Hz) is still easily achievable even in microscopes with conventional, nonresonant galvos, which is more than enough for applications such as calcium imaging experiments in the brains [26

26. C. Grienberger and A. Konnerth, “Imaging calcium in neurons,” Neuron 73(5), 862–885 (2012). [CrossRef] [PubMed]

].

5. Discussions and conclusions

For in vivo imaging conditions that require GRIN lens to be stationary relative to the sample, 3D imaging is achieved by moving the objective relative to the GRIN lens and the sample. By measuring and correcting the optical aberrations at different locations inside a 3D image volume, we found that off-axis aberrations get more severe with the increase of image WD (i.e., the distance between the objective focus and the top of GRIN lens), or equivalently, at the more superficial planes in the volume. Even though the GRIN lens characterized above has a high NA of 0.8 and is a two-element system made of a GRIN lens and a spherical lens [20

20. H. Alencar, U. Mahmood, Y. Kawano, T. Hirata, and R. Weissleder, “Novel multiwavelength microscopic scanner for mouse imaging,” Neoplasia 7(11), 977–983 (2005). [CrossRef] [PubMed]

], we found similar trend on a lower-NA singlet GRIN lens (1mm diameter, 3.74 mm length, NA 0.45). Table 1

Table 1. Signal enhancement and axial resolution at different image WD’s before and after AO correction for a singlet GRIN lens with NA 0.45 and 3.74mm length.

table-icon
View This Table
shows the signal improvements and axial FWHMs of focal series image stacks of 2-μm diameter beads before and after AO correction at FP(0,0) and FP(250 μm,0) for image WDs ranging from 0 to 500μm. Even at NA 0.45, where aberrations are less severe, AO improved both signal and resolution at all locations. Similar to the NA 0.8 GRIN lens, at off-axis FP(250 μm,0), larger aberrations and higher signal recovery after AO were observed at larger image WDs. Even at on-axis FP(0,0), significant aberrations were observed, because singlet GRIN lenses have uncorrected intrinsic on-axis spherical aberration [15

15. D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express 3(5), 1077–1085 (2012). [CrossRef] [PubMed]

, 17

17. W. M. Lee and S. H. Yun, “Adaptive aberration correction of GRIN lenses for confocal endomicroscopy,” Opt. Lett. 36(23), 4608–4610 (2011). [CrossRef] [PubMed]

, 25

25. T. Sakamoto, “Estimation of the fourth-order index coefficient of GRIN-rod lenses,” Appl. Opt. 25(15), 2613–2619 (1986). [CrossRef] [PubMed]

], with the on-axis aberration also increasing with larger image WD.

These observations can be explained by a simple physical picture: When image WD increases and the objective focus moves away from the GRIN lens, the marginal rays move towards the edge of GRIN lens entrance pupil, leading to larger aberrations, because the rays hitting the lens at greater distances from the optical axis experience larger refractive error. As a result, both on-axis and off-axis aberrations increase with increasing image WD.

For the 0.45-NA GRIN lens, the effective NA, as reflected by the axial FWHM after AO correction, also increases with image WD. Optically, a singlet radial GRIN rod lens behaves similarly to a conventional spherical lense. When image WD increases and the objective focus moves away from the GRIN lens, the focus on the sample side moves towards the GRIN lens, with the angle between the marginal rays and the optical axis getting larger, corresponding to an increase of NA and smaller axial FWHMs, although our ray-tracing results suggested that the strength of this effect strongly depends on the length of the GRIN lens.

One way to achieve 3D imaging with both the microscope objective and the GRIN lens stationary is by adding defocus to the wavefront directly [27

27. P. Kner, J. W. Sedat, D. A. Agard, and Z. Kam, “High-resolution wide-field microscopy with adaptive opticsfor spherical aberration correction and motionless focusing,” J. Microsc-Oxford 237(2), 136–147 (2010). [CrossRef]

]. Same as the GRIN lenses, microscope objectives are designed for particular beam convergence (e.g., infinity-corrected objectives vs. those requiring specific tube length), simply introducing defocus to the excitation wavefront would lead to additional aberrations in the imaging system. The severity of these aberrations depends on the specifics of the image system (i.e., microscope objective – GRIN lens combination). Adaptive optics methods could again be used for system characterization and to achieve aberration-free focusing via wavefront shaping.

The chromatically corrected microprobe objectives with millimeter tip diameters are interesting alternatives to GRIN-lens-based systems [28]. However, at comparable NA, these microprobes are not as small as the GRIN lenses. For example, the 0.8 NA GRIN lens characterized here has an outer diameter of 1.4 mm, while a 0.7 NA microprobe has an outer diameter of 3.5mm. 0.5 mm diameter GRIN lenses can achieve 0.5 NA, but a microprobe at 0.5 NA has an outer diameter of 1.3mm. This dimension difference may not be significant for many applications, but for small samples such as mouse brain (~10 × 10 × 10 mm3), an aberration-corrected GRIN lens system provides a more compact footprint. For both the 0.7 NA microprobe of 3.5mm diameter and the 0.5 NA microprobe of 1.3 mm diameter, the practical FOV is limited to 200 µm. If their FOV is limited by off-axis aberrations, the same AO correction procedure as described in our manuscript may be applied to increase their field of view as well.

In conclusion, by characterizing and correcting the intrinsic aberrations of GRIN lens at different fields of position and multiple image WDs, we demonstrated that diffraction-limit imaging performance could be obtained in 3D by using an adaptive optics two-photon fluorescence endomicroscope. Making use of the near-cylindrical symmetry of the GRIN lens itself, we designed and validated an experimental procedure that requires only two AO measurements and five images with AO corrective patterns to cover a large imaging FOV. The same procedure may also be used to evaluate the off-axis aberrations in the stick objectives and possibly enlarge the imaging FOV of these microprobes as well. This would make AO-enabled two-photon endomicroscope a powerful tool for in vivo application.

Acknowledgments

We thank Dr. Jayaram Chandrashekar and Dr. Robert Barretto for helpful discussion. This research is supported by the Howard Hughes Medical Institute.

References and links

1.

J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).

2.

D. B. Murphy and M. W. Davidson, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2012).

3.

P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 microm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 28(12), 1022–1024 (2003). [CrossRef] [PubMed]

4.

M. Balu, T. Baldacchini, J. Carter, T. B. Krasieva, R. Zadoyan, and B. J. Tromberg, “Effect of excitation wavelength on penetration depth in nonlinear optical microscopy of turbid media,” J. Biomed. Opt. 14(1), 010508 (2009). [CrossRef] [PubMed]

5.

D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17(16), 13354–13364 (2009). [CrossRef] [PubMed]

6.

C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc. 243(2), 179–183 (2011). [CrossRef] [PubMed]

7.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013). [CrossRef]

8.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer-Verlag, 2002).

9.

J. C. Jung and M. J. Schnitzer, “Multiphoton endoscopy,” Opt. Lett. 28(11), 902–904 (2003). [CrossRef] [PubMed]

10.

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol. 91(4), 1908–1912 (2004). [CrossRef] [PubMed]

11.

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] [PubMed]

12.

P. Kim, M. Puoris’haag, D. Côté, C. P. Lin, and S. H. Yun, “In vivo confocal and multiphoton microendoscopy,” J. Biomed. Opt. 13(1), 010501 (2008). [CrossRef] [PubMed]

13.

R. P. J. Barretto, T. H. Ko, J. C. Jung, T. J. Wang, G. Capps, A. C. Waters, Y. Ziv, A. Attardo, L. Recht, and M. J. Schnitzer, “Time-lapse imaging of disease progression in deep brain areas using fluorescence microendoscopy,” Nat. Med. 17(2), 223–228 (2011). [CrossRef] [PubMed]

14.

T. A. Murray and M. J. Levene, “Singlet gradient index lens for deep in vivo multiphoton microscopy,” J. Biomed. Opt. 17(2), 021106 (2012). [CrossRef] [PubMed]

15.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express 3(5), 1077–1085 (2012). [CrossRef] [PubMed]

16.

C. M. Brown, D. R. Rivera, I. Pavlova, D. G. Ouzounov, W. O. Williams, S. Mohanan, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using a compact and flexible multiphoton microendoscope,” J. Biomed. Opt. 17(4), 040505 (2012). [CrossRef] [PubMed]

17.

W. M. Lee and S. H. Yun, “Adaptive aberration correction of GRIN lenses for confocal endomicroscopy,” Opt. Lett. 36(23), 4608–4610 (2011). [CrossRef] [PubMed]

18.

F. Bortoletto, C. Bonoli, P. Panizzolo, C. D. Ciubotaru, and F. Mammano, “Multiphoton fluorescence microscopy with GRIN objective aberration correction by low order adaptive optics,” PLoS ONE 6(7), e22321 (2011). [CrossRef] [PubMed]

19.

C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett. 37(11), 2001–2003 (2012). [CrossRef] [PubMed]

20.

H. Alencar, U. Mahmood, Y. Kawano, T. Hirata, and R. Weissleder, “Novel multiwavelength microscopic scanner for mouse imaging,” Neoplasia 7(11), 977–983 (2005). [CrossRef] [PubMed]

21.

R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods 6(7), 511–512 (2009). [CrossRef] [PubMed]

22.

GRINTECH, GmbH, “High NA for 2-photon microscopy,” http://www.grintech.de/grin-lens-systems-for-medical-applications.html?file=tl_files/content/downloads/GRIN_High-NA_Objective-2_Photon_Microscopy. pdf.

23.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7(2), 141–147 (2010). [CrossRef] [PubMed]

24.

N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A. 109(1), 22–27 (2012). [CrossRef] [PubMed]

25.

T. Sakamoto, “Estimation of the fourth-order index coefficient of GRIN-rod lenses,” Appl. Opt. 25(15), 2613–2619 (1986). [CrossRef] [PubMed]

26.

C. Grienberger and A. Konnerth, “Imaging calcium in neurons,” Neuron 73(5), 862–885 (2012). [CrossRef] [PubMed]

27.

P. Kner, J. W. Sedat, D. A. Agard, and Z. Kam, “High-resolution wide-field microscopy with adaptive opticsfor spherical aberration correction and motionless focusing,” J. Microsc-Oxford 237(2), 136–147 (2010). [CrossRef]

28.

Olympus, “Microprobe objectives,” http://www.olympusamerica.com/seg_section/seg_microprobe_objectives.asp.

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(110.2760) Imaging systems : Gradient-index lenses
(170.2150) Medical optics and biotechnology : Endoscopic imaging
(180.0180) Microscopy : Microscopy
(180.2520) Microscopy : Fluorescence microscopy
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Imaging Systems

History
Original Manuscript: July 29, 2013
Revised Manuscript: September 26, 2013
Manuscript Accepted: October 13, 2013
Published: November 1, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Chen Wang and Na Ji, "Characterization and improvement of three-dimensional imaging performance of GRIN-lens-based two-photon fluorescence endomicroscopes with adaptive optics," Opt. Express 21, 27142-27154 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-27142


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References

  1. J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).
  2. D. B. Murphy and M. W. Davidson, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2012).
  3. P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 microm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett.28(12), 1022–1024 (2003). [CrossRef] [PubMed]
  4. M. Balu, T. Baldacchini, J. Carter, T. B. Krasieva, R. Zadoyan, and B. J. Tromberg, “Effect of excitation wavelength on penetration depth in nonlinear optical microscopy of turbid media,” J. Biomed. Opt.14(1), 010508 (2009). [CrossRef] [PubMed]
  5. D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express17(16), 13354–13364 (2009). [CrossRef] [PubMed]
  6. C. Wang, L. Qiao, F. He, Y. Cheng, and Z. Xu, “Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source,” J. Microsc.243(2), 179–183 (2011). [CrossRef] [PubMed]
  7. N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics7(3), 205–209 (2013). [CrossRef]
  8. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer-Verlag, 2002).
  9. J. C. Jung and M. J. Schnitzer, “Multiphoton endoscopy,” Opt. Lett.28(11), 902–904 (2003). [CrossRef] [PubMed]
  10. M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004). [CrossRef] [PubMed]
  11. 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] [PubMed]
  12. P. Kim, M. Puoris’haag, D. Côté, C. P. Lin, and S. H. Yun, “In vivo confocal and multiphoton microendoscopy,” J. Biomed. Opt.13(1), 010501 (2008). [CrossRef] [PubMed]
  13. R. P. J. Barretto, T. H. Ko, J. C. Jung, T. J. Wang, G. Capps, A. C. Waters, Y. Ziv, A. Attardo, L. Recht, and M. J. Schnitzer, “Time-lapse imaging of disease progression in deep brain areas using fluorescence microendoscopy,” Nat. Med.17(2), 223–228 (2011). [CrossRef] [PubMed]
  14. T. A. Murray and M. J. Levene, “Singlet gradient index lens for deep in vivo multiphoton microscopy,” J. Biomed. Opt.17(2), 021106 (2012). [CrossRef] [PubMed]
  15. D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012). [CrossRef] [PubMed]
  16. C. M. Brown, D. R. Rivera, I. Pavlova, D. G. Ouzounov, W. O. Williams, S. Mohanan, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using a compact and flexible multiphoton microendoscope,” J. Biomed. Opt.17(4), 040505 (2012). [CrossRef] [PubMed]
  17. W. M. Lee and S. H. Yun, “Adaptive aberration correction of GRIN lenses for confocal endomicroscopy,” Opt. Lett.36(23), 4608–4610 (2011). [CrossRef] [PubMed]
  18. F. Bortoletto, C. Bonoli, P. Panizzolo, C. D. Ciubotaru, and F. Mammano, “Multiphoton fluorescence microscopy with GRIN objective aberration correction by low order adaptive optics,” PLoS ONE6(7), e22321 (2011). [CrossRef] [PubMed]
  19. C. Wang and N. Ji, “Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy,” Opt. Lett.37(11), 2001–2003 (2012). [CrossRef] [PubMed]
  20. H. Alencar, U. Mahmood, Y. Kawano, T. Hirata, and R. Weissleder, “Novel multiwavelength microscopic scanner for mouse imaging,” Neoplasia7(11), 977–983 (2005). [CrossRef] [PubMed]
  21. R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods6(7), 511–512 (2009). [CrossRef] [PubMed]
  22. GRINTECH, GmbH, “High NA for 2-photon microscopy,” http://www.grintech.de/grin-lens-systems-for-medical-applications.html?file=tl_files/content/downloads/GRIN_High-NA_Objective-2_Photon_Microscopy . pdf.
  23. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010). [CrossRef] [PubMed]
  24. N. Ji, T. R. Sato, and E. Betzig, “Characterization and adaptive optical correction of aberrations during in vivo imaging in the mouse cortex,” Proc. Natl. Acad. Sci. U.S.A.109(1), 22–27 (2012). [CrossRef] [PubMed]
  25. T. Sakamoto, “Estimation of the fourth-order index coefficient of GRIN-rod lenses,” Appl. Opt.25(15), 2613–2619 (1986). [CrossRef] [PubMed]
  26. C. Grienberger and A. Konnerth, “Imaging calcium in neurons,” Neuron73(5), 862–885 (2012). [CrossRef] [PubMed]
  27. P. Kner, J. W. Sedat, D. A. Agard, and Z. Kam, “High-resolution wide-field microscopy with adaptive opticsfor spherical aberration correction and motionless focusing,” J. Microsc-Oxford237(2), 136–147 (2010). [CrossRef]
  28. Olympus, “Microprobe objectives,” http://www.olympusamerica.com/seg_section/seg_microprobe_objectives.asp .

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