Gradient Index (GRIN) Lenses Application Note

Multiphoton Imaging with
Gradient Index (GRIN)
LensesApplication Note

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1Gradient Index (GRIN) Lenses Application Note

Table of Contents for GRIN Lens Application Note
Introduction .....................................................................................................................................3
GRIN Lens Specifications ..................................................................................................................4
Implementation ...............................................................................................................................6
On Axis GRIN Lens Imaging ....................................................................................................................... 8
GRIN Lens Tip Tilt Alignment ..................................................................................................................... 9Axial Chromatic Aberration in Objectives .................................................................................................10
Axial Chromatic Aberration in GRIN .........................................................................................................11
General Considerations ............................................................................................................................12
Magnification Changes with Focus ...........................................................................................................13
Photoactivation and GRIN Lenses .............................................................................................................14
Aberration Correction of GRIN Lenses ......................................................................................................14

Acknowledgements ........................................................................................................................15
Conclusion ......................................................................................................................................15
References .....................................................................................................................................16

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2Gradient Index (GRIN) Lenses Application Note

Introduction
Light scattering fundamentally limits
imaging depth in tissue. Since Rayleighscattering is wavelength dependent, thedevelopment of multiphoton imaging,with its use of longer wavelength light,
has permitted deeper imaging of living
tissue. Two photon imaging routinely
images through 1 mm, while threephoton imaging permits up to 50%
deeper observation. However,scattering still fundamentally limits thedepth of these techniques; imaging
deeper structures in living tissue, suchas subcortical structure, requires a novel
approach.
One possible solution is to remove thebrain above the region of interest. Thismethod is preferred - by replacing theoverlying tissue with homogeneous
saline, scattering is minimized, and deep
structure is revealed without aberration.
However, this technique requires theremoval of a significant amount ofoverlying tissue: one must remove acone of tissue above the region ofinterest equal to the numerical apertureof the objective. For experiments that
require minimal perturbation of thesurrounding brain, a more elegant
solution is required.
Gradient index (GRIN) lenses solve thisproblem nicely. GRIN lenses are so
named because of the index ofrefraction gradient orthogonal to theoptical axis (see Figure 1). This index
gradient mimics the light shaping
properties of a traditional singlet lens:light may be relayed from one focal
point to another. GRIN lenses designed

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to relay light from one end to the othermay be used to bypass scattering tissue
and acquire images at great depth,
without removing as much overlying
tissue. Different GRIN lenses that focus
light at infinity are critical to the designof miniature implantable microscopes[1]. Combining GRIN lenses withtraditional multiphoton imaging, firstpioneered independently by two groups
lead by Mark Schnitzer and Watt Webb,
has allowed unparalleled imaging ofdeep structures [2, 3].

Figure 1. GRIN Lens vs. Singlet. A
gradient lens has an index ofrefraction gradient orthogonal to its
optical axis. This gradient bends
light inside of the lens. This bendingof light can mimic the focusing
ability of traditional singlet lenses,
where light is bent by the external
shape of the lens and the refractive
index change between the lens andthe surrounding air.

3Gradient Index (GRIN) Lenses Application Note

GRIN Lens Specifications
The key design characteristic of a GRIN lens is its pitch. The pitch of a GRIN lens is the fraction ofa full sinusoidal wave period of a ray that traverses the lens and determines whether the GRIN
lens functions as an objective, or a relay lens (see Figure 2).

Figure 2. GRIN Lens Properties and Pitch. A GRIN lens’ pitch determines its imaging properties. Grin lenses
of 0.25 Pitch function like objectives, focusing an object on their front surface at infinity. GRIN lenses withslightly less than 0.25 pitch focus light at a singular working distance to infinity. Grin lenses of 0.5 pitch
relay objects from the front surface to an inverted image on the back surface. GRIN lenses of slightly lessthan 0.5 Pitch relay an object at a singular working distance to an inverted image at working distance on theother side. A GRIN lens of 1.0 pitch relays an object on one end of the GRIN lens to the other end. A GRIN
lens of slightly less than 1.0 pitch relays an image at a working distance to the other side.

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4Gradient Index (GRIN) Lenses Application Note

Figure 3. GRIN Lens and Imaging Objective. A GRIN lens aligned with an imaging objective. GRIN lens’imaging properties include working distance, field curvature, and viewing angle.

The pitch of the GRIN lens also determines other critical properties of the GRIN lens, namely its
working distance and whether the relay image is inverted. Like objectives, there is only one ideal
working distance and focusing at other depths introduces spherical aberrations. In addition, theconstruction of GRIN lenses limits their field of view (FOV), typically to a radius significantly lessthan the radius of the GRIN lens itself. Since the GRIN lens field of view changes with distance(see Figure 3), this is often described as an angle rather than a radius. Finally, GRIN lenses
typically exhibit significant field curvature. Typically, the GRIN lens is combined with an objective
in alignment (see Figure 3), with a traditional microscope objective lens focused at the GRIN lens’intermediate image plane. This arrangement relays the sample plane “seen” at the far end of the
GRIN lens to the rest of the microscope.

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5Gradient Index (GRIN) Lenses Application Note

In this orientation GRIN lenses extend achievable imaging depth well beyond multiphoton andthree photon imaging, with relatively modest perturbations of the overlying tissue due to therelatively narrow diameter of the GRIN lens. This permits the imaging of deep structures
heretofore out of range (see Figure 4). However, to fully utilize this technology it is critical tounderstand the aberrations introduced by GRIN lenses and how to mitigate them.

ImplementationIn this orientation GRIN lenses extend achievable imaging depth well beyond

multiphoton and three photon imaging, with relatively modest perturbations of the overlying
tissue due to the relatively narrow diameter of the GRIN lens. This permits the imaging of deep
structures heretofore out of range (see Figure 4). However, to fully utilize this technology it is
Figure 4. Live Imaging Through a GRIN
critical to understand the aberrations introduced by GRIN lenses and how to mitigate them.
Lens. Multiphoton imaging of GCaMP-

labeled neurons through a 4 mm long,
1 mm wide GRIN lens. Image acquiredwith Thorlabs Bergamo® microscope
equipped with a Thorlabs10X MP
objective (TL10X-2P). Image Courtesy
of Cody Siciliano, Vanderbilt
University.

Figure 4. Live Imaging Through a GRIN
Lens. Multiphoton imaging of GCaMP-

Implementation

labeled neurons through a 4mm long,
1mm wide GRIN lens. Image acquiredwith Thorlabs Bergamo® microscope

The primary consideration when imaging through a GRIN lensis alignment.
Two keyMP
elements
equippedwith a Thorlabs10X
require alignment when using a GRIN lens. The center of theobjective
GRIN lensaxis should(TL10X-2P).
Image overlay
Courtesy thetissue of interest, and the objective imaging axis should alignthat of Vanderbilt
the GRIN lens.
of withCody Siciliano,
University.

Because the optical aberrations of the GRIN lens dwarf that of the objective, it is of vital
importance to center the GRIN lens over the target of interest. In practice, this is difficult to
optimize, as the GRIN lens is often embedded in a surgically implemented canula, usually
FigureLive Imaging
Througha GRINthat
cemented in place. Post-surgery, it is impossible to reposition
the4. lens.
It is worth
notingLens. Multiphoton
imagingof GCaMP-[4].
the worst aberrations in a GRIN lens arise from off axis aberrations,primarily
astigmatism
labeledefficiency
neurons througha 4mm long,This astigmatism will decrease both resolution and multiphoton(brightness).
Moving
1mm
wide
GRIN
lens.
Image
acquiredthe objective over the region of interest may slightly improve the brightness of the ROI but willwith Thorlabs Bergamo® microscope
not recover the aberrations (see Figure 5).
equipped with a Thorlabs10X MP
objective (TL10X-2P). Image Courtesy
of Cody Siciliano, Vanderbilt
University.

6

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Figure 4. Live Imaging Through a GRIN
Lens. Multiphoton imaging of GCaMP-

Gradient Index (GRIN) Lenses Application Note

Figure 5. GRIN Lens Imaging Target On and Off Axis. Thorlabs Star Target (R1L1S1P) imaged throughfluorescein, a Thorlabs GRIN lens (G1P11), using a Bergamo® multiphoton microscope. The curvaturein the imaging field curves the imaging plane away from the target. The resolution is best in thecenter of the GRIN lens FOV and moving the microscope objective in Y or Z does not recover the
resolution lost at the edges of the GRIN FOV.

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7Gradient Index (GRIN) Lenses Application Note

On Axis GRIN Lens Imaging
Optimal imaging through a GRIN lens also
requires aligning the objective with theoptical axis of the GRIN lens (seeFigure 6). Because the imaging plane of theobjective is relayed by the GRIN lens, amisaligned objective will alter the imaging
depth across the GRIN lens FOV. This
causes multiple problems: First, as one is
not imaging into the tissue straight theimaging depth varies across the FOV. Since
the tissue is scattering, the shallow sidecloser to the GRIN lens face receives much
more effective power. Second, theeffective magnification varies across thefield of view; see Figure 6.

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Figure 6. On Axis GRIN Lens Imaging.
Thorlabs Star target imaged through a
GRIN lens with objective aligned on
axis (left) and 5° off axis (right). Off
axis imaging tilts the image plane,causing intensity gradient acrossimage in tissue due to scattering ofdeep tissue. Even small angles cause
notable gradients.

8Gradient Index (GRIN) Lenses Application Note

GRIN Lens Tip Tilt Alignment
Thorlabs recommends adjusting the alignment with widefield single photon imaging (e.g. with acamera) to locate the top surface of the GRIN lens before multiphoton imaging. This is importantas focusing the multiphoton laser inside the GRIN lens may etch the surface or interior of the
GRIN lens. To align the GRIN lens to the objective, image the top surface of the GRIN lens with acamera (Figure 7). Imperfections in the lens surface ease finding the correct focal plane. As the
GRIN lens is typically implanted in an animal, the entire animal needs to be adjusted to bring the
GRIN lens into alignment. Here it can be extremely useful for the microscope to rotate in at least
one direction, as it is easier to adjust than the animal mount. Thorlabs rotating Bergamo®
microscopes are ideal for this purpose as the whole scope and objective rotates about the pointof focus, simplifying greatly the adjustments needed to align the scope to the GRIN lens.

Figure 7. GRIN Lens Alignment. By carefully adjusting the angle of the microscope and the animal
stage, the GRIN lens can be exactly aligned with the objective. In this example (left), the GRIN lens isrotated by adjusting the animal in one axis, and the Bergamo® rotation microscope is rotated in theorthogonal axis. Alignment is checked by imaging the top surface of the GRIN lens (right), to makesure all edges are in focus.

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9Gradient Index (GRIN) Lenses Application Note

Axial Chromatic Aberration in Objectives
It is incredibly important to avoid focusing the pulsed multiphoton laser beam on the GRIN lenssurface or inside the GRIN lens as even moderate laser power is enough to etch many GRIN
lenses. We recommend that the user mark the focal depth of the GRIN lens surface (e.g., set a
zero reference), and make a note to avoid imaging at this depth. Once the GRIN lens is alignedwith the camera above, it is recommended to raise the objective by the working distance of the
GRIN lens; this will approach the GRIN lens ideal imaging plane.
Because the GRIN lens is not chromatically corrected, the working distance of the GRIN lens will
differ with wavelength with longer wavelengths elongating the GRIN working distance(WDGRIN sample, see Figure 8).
This effect is partially compensated by the objective. Most objectives are overcorrected in theinfrared, and therefore focus shallow relative to visible wavelength (shorter WDObj). Note thisshallow focus doesn’t change the sample working distance of the GRIN lens, it will still be deeper
in infrared relative to visible.

Figure 8. Axial Chromatic Aberration in Objectives and GRIN Lenses. IR uncorrected objectives are
generally over corrected in the infrared, i.e. they focus infrared light shallow relative to visible light.
Typical GRIN lenses focus longer wavelength light farther from the lens surface. When imaging through a
GRIN lens these two effects partially cancel out, and small focus shifts are needed to switch from infrared
to visible. Note the GRIN lens sample working distance is still longer in the infrared.

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10Gradient Index (GRIN) Lenses Application Note

Axial Chromatic Aberrationin GRINFor objectives that are corrected in theinfrared, the longer working distance of
the GRIN lens is more apparent, and theobjective will need to be moved
significantly further from the GRIN lens toreach the ideal working focus at therelayed image plane. (see Figure 9).

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Figure 9. Axial Chromatic Aberrationin Objectives and GRIN Lenses. IR
corrected objectives focus IR light andvisible light at the same focal plane,
this will unmask the GRIN lens
working distance change between IR
and visible, requiring an upward focal
shift of the objective when switching
between IR and visible light.

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Gradient Index (GRIN) Lenses Application Note

General Considerations
GRIN lenses generally have significant curvature of field (see Figure 10). This field curvature
varies from lens to lens, but as it is one design parameter, improving curvature of field results incompromises in other areas. Field curvature, and indeed most aberrations, are related to GRIN
pitch, the higher the pitch, the greater the aberrations.
GRIN lenses are designed to image with minimum aberrations at their working distance.
However, it is possible to image above or below the designed working distance. Imaging awayfrom the working distance will introduce aberrations into the image. On axis this will result inmoderate spherical aberrations [4]. In practice these spherical aberrations are not so apparent in
multiphoton imaging, and it is possible to image a significant-sized volume above and below theideal working distance. However, off axis aberrations increase dramatically, creating issues
towards the edge of the field. The most prominent off axis aberration is astigmatism, whichsignificantly degrades GRIN lens FOV away from the ideal working distance [4].

Figure 10. GRIN Lens Field Curvature. Thorlabs Star target imaged through fluorescein and a 1 mm
diameter, 9 mm long GRIN lens. This high pitch GRIN lens introduces significant optical aberrations,
including field curvature. Since the field curves toward the GRIN lens, one must focus deeper to image
the same focal plane off axis WD = Working distance. A flat field would have roughly equal brightness
rather than a spot or ring.

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12Gradient Index (GRIN) Lenses Application Note

Magnification Changes with
Focus
In addition to optical aberrations, imaging
away from the GRIN lens working distancewill change effective magnification. This isbecause GRIN lenses function as simple
lenses: focusing on differing depths
changes the effective magnification. Thiseffect can be quite significant, withmagnification changing with imaging depth(see Figure 11).

Figure 11. GRIN Lens Magnification
and Focus. Changing the focus of theobjective relative to the GRIN lens
shifts the relayed focus point intissue. Thorlabs Star targets imagined
through a GRIN lens at WD, WD +80 µm and WD + 160 µm. The farther
one focuses through a GRIN lens the

Since system magnification correlates withdepth, and imaging depth is uncertain due
to chromatic aberrations, care must be
taken when assigning magnification,
including scale bars. Unless one knows
they are imaging exactly at the working
distance, there is uncertainty as to the true
magnification of the system.
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lower the system magnification.

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Gradient Index (GRIN) Lenses Application Note

Aberration Correction of GRIN Lenses
Because they are simple, uncorrected lenses, GRIN lenses exhibit spherical aberrations,chromatic aberrations, and astigmatism. While these aberrations impact multiphoton imaging
less than widefield imaging, the effects are still significant, particularly off-axis and away fromthe working distance. Over the years various labs have introduced optical elements to reducethese aberrations. Initially, spherical aberrations were minimized with a compound lens design[5], which combined a singlet with a GRIN lens. A compact solution was developed by the Fellingroup, which has used aspheres and a coverglass to minimize both on axis and off axis
aberrations [6].
An alternative solution is to use adaptive optics wavefront shaping to correct for the aberrations
introduced in the GRIN lens [7]. Since multiphoton resolution is dependent upon the excitation
pathway, shaping the excitation wavefront serves to improve resolution. This technique more
extensively corrects for aberrations in the GRIN lens at the expense of introducing a wavefront
modulating device into the imaging path.

Photoactivation and GRIN Lenses
It is possible to combine photoactivation at one wavelength with GRIN lens imaging at another[8]. However, much care must be taken with calibrating the photoactivation focus vs theimaging focus: the axial chromatic aberrations in the GRIN lens, the change in working distanceand consequently magnification must be compensated. It is recommended that thephotoactivation path be calibrated with the GRIN lens of interest, relative to the imaging
pathway.
Spatial light modulators may be combined with GRIN lens imaging to photoactivate multiple
cells, in 3D, simultaneously. This multiple cell targeting is best paired with a mechanism tocorrect for GRIN lens aberrations, for instance via SLM mediated adaptive optics [9], or
combined with other optical elements that help mitigate GRIN lens’ aberrations. Either way,
careful calibration of 3D stimulation is required to correct for zoom and distortion artifacts.

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14Gradient Index (GRIN) Lenses Application Note

Conclusion
Combining GRIN lenses with multiphoton imaging greatly extends the reach of the system into
otherwise highly scattering tissue environments. GRIN lenses maintain multiphoton opticalsectioning and can facilitate highly targeted photostimulation experiments with minimal
perturbation of deep brain activity. Despite the optical aberrations and complexities arising fromthe GRIN lens and its alignment with other lens components, the benefits of including a such a
GRIN lens setup far outweigh the trouble of including and should be considered when imaging
depth is a limitation in experimental design.

Acknowledgements
Thank you to Dr. Cody Siciliano and his lab for his help in GRIN lens testing and technicalfeedback and Dr. Na Ji for her technical feedback. Thank you to Dr. Cory Dolbashian for his help
designing a GRIN lens testing apparatus.

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15Gradient Index (GRIN) Lenses Application Note

References
1. Zong W, Obenhaus HA, Skytøen ER, Eneqvist H, de Jong NL, Vale R, Jorge MR, Moser MB,
Moser EI. Large-scale two-photon calcium imaging in freely moving mice. Cell. 2022 Mar 31;
185: 1240-56.
2. Jung JC, Schnitzer MJ. Multiphoton endoscopy. Optics letters. 2003 Jun 1; 28: 902-4.
3. Levene MJ, Dombeck DA, Kasischke KA, Molloy RP, Webb WW. In vivo multiphoton
microscopy of deep brain tissue. Journal of neurophysiology. 2004 Apr; 91: 1908-12.
4. Wang C, Ji N. Pupil-segmentation-based adaptive optical correction of a high-numericalaperture gradient refractive index lens for two-photon fluorescence endoscopy. Optics
letters. 2012 Jun 1; 37: 2001-3.
5. Barretto RP, Messerschmidt B, Schnitzer MJ. In vivo fluorescence imaging with high-resolution
microlenses. Nature methods. 2009 Jul; 6: 511-2.
6. Antonini A, Sattin A, Moroni M, Bovetti S, Moretti C, Succol F, Forli A, Vecchia D,
Rajamanickam VP, Bertoncini A, Panzeri S. Extended field-of-view ultrathin microendoscopesfor high-resolution two-photon imaging with minimal invasiveness. elife. 2020 Oct 13; 9:e58882.
7. Wang C, Ji N. Characterization and improvement of three-dimensional imaging performanceof GRIN-lens-based two-photon fluorescence endomicroscopes with adaptive optics. Optics
Express. 2013 Nov 4; 21: 27142-54.
8. Jennings JH, Kim CK, Marshel JH, Raffiee M, Ye L, Quirin S, Pak S, Ramakrishnan C, Deisseroth
K. Interacting neural ensembles in orbitofrontal cortex for social and feeding behaviour.
Nature. 2019 Jan 31; 565: 645-9.
9. Accanto N, Chen IW, Ronzitti E, Molinier C, Tourain C, Papagiakoumou E, Emiliani V.
Multiplexed temporally focused light shaping through a gradient index lens for precise indepth optogenetic photostimulation. Scientific reports. 2019 May 20; 9: 7603.

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16Gradient Index (GRIN) Lenses Application Note

About Thorlabs
Thorlabs was founded in 1989 with a simple mission: make photonics lab equipment moreaccessible to graduate students and junior professors.
To this day, we have a love for science and an eye toward the future. We work hard to design andmanufacture the tools that enable the next great steps in scientific discovery.

Thorlabs was founded in 1989 with a simple mission: make photonics lab equipment moreaccessible to graduate students and junior professors.

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accessible to graduate students and junior professors.
To this day, we have a love for science and an eye toward the future. We work hard to design andmanufacture the tools that enable the next great steps in scientific discovery.

17