# Second-harmonic imaging microscopy

Second-harmonic imaging microscopy (SHIM) is based on a nonlinear optical effect known as second-harmonic generation (SHG). SHIM has been established as a viable microscope imaging contrast mechanism for visualization of cell and tissue structure and function.[1] A second-harmonic microscope obtains contrasts from variations in a specimen’s ability to generate second-harmonic light from the incident light while a conventional optical microscope obtains its contrast by detecting variations in optical density, path length, or refractive index of the specimen. SHG requires intense laser light passing through a material with a noncentrosymmetric molecular structure. Second-harmonic light emerging from an SHG material is exactly half the wavelength (frequency doubled) of the light entering the material. While two-photon-excited fluorescence (TPEF) is also a two photon process, TPEF loses some energy during the relaxation of the excited state, while SHG is energy conserving. Typically, an inorganic crystal is used to produce SHG light such as lithium niobate (LiNbO3), potassium titanyl phosphate (KTP = KTiOPO4), and lithium triborate (LBO = LiB3O5). Though SHG requires a material to have specific molecular orientation in order for the incident light to be frequency doubled, some biological materials can be highly polarizable, and assemble into fairly ordered, large noncentrosymmetric structures. Biological materials such as collagen, microtubules, and muscle myosin[2] can produce SHG signals. The SHG pattern is mainly determined by the phase matching condition. A common setup for an SHG imaging system will have a laser scanning microscope with a titanium sapphire mode-locked laser as the excitation source. The SHG signal is propagated in the forward direction. However, some experiments have shown that objects on the order of about a tenth of the wavelength of the SHG produced signal will produce nearly equal forward and backward signals.

SHIM offers several advantages for live cell and tissue imaging. SHG does not involve the excitation of molecules like other techniques such as fluorescence microscopy therefore, the molecules shouldn’t suffer the effects of phototoxicity or photobleaching. Also, since many biological structures produce strong SHG signals, the labeling of molecules with exogenous probes is not required which can also alter the way a biological system functions. By using near infrared wavelengths for the incident light, SHIM has the ability to construct three-dimensional images of specimens by imaging deeper into thick tissues.

## History

Before SHG was used for imaging, the first demonstration of SHG was performed in 1961 by P. A. Franken, G. Weinreich, C. W. Peters, and A. E. Hill at the University of Michigan, Ann Arbor using a quartz sample.[3] In 1968, SHG from interfaces was discovered by Bloembergen [4] and has since been used as a tool for characterizing surfaces and probing interface dynamics. In 1971, Fine and Hansen reported the first observation of SHG from biological tissue samples.[5] In 1974, Hellwarth and Christensen first reported the integration of SHG and microscopy by imaging SHG signals from polycrystalline ZnSe.[6] In 1977, Colin Sheppard imaged various SHG crystals with a scanning optical microscope. The first biological imaging experiments were done by Freund and Deutsch in 1986 to study the orientation of collagen fibers in rat tail tendon.[7]. In 1993, Lewis examined the second-harmonic response of styryl dyes in electric fields. He also showed work on imaging live cells. In 2006, Goro Mizutani group developed a non-scanning SHG microscope that significantly shortens the time required for observation of large samples, even if the two-photons wide-field miscroscope was published in 1996 [8] and could have been used to detect SHG. The non-scanning SHG microscope was used for observation of plant starch,[9][10] megamolecule,[11] spider silk[12][13] and so on. In 2010 SHG was extended to whole-animal in vivo imaging.[14][15]. In 2019, SHG applications widened when it was applied to the use of selectively imaging agrochemicals directly on leaf surfaces to provide a way to evaluate the effectiveness of pesticides. [16]

## Applications

SHG microscopy and its expansions can be used to study various tissues: some example images are reported in the figure below: collagen inside the extraccellular matrix remains the main application. It can be found in tendon, skin, bone, cornea, aorta, fascia, cartilage, meniscus, intervertebral disks...

Myosin can also be imaged in skeletal muscle or cardiac muscle.

Table 1: Materials visible by or that efficiently generate SHG.
TypeMaterialFound inSHG signalSpecificity
CarbohydrateCelluloseWood, green plant, algae.Quite weak in normal cellulose [16], but substantial in crystalline or nanocrystalline cellulose.-
StarchStaple foods, green plantQuite intense signal [17]chirality is at micro and macro level, and the SHG is different under right or left-handed circular polarization
Megamolecular polysaccharide sacranCyanobacteryFrom sacran cotton-like lump, fibers, and cast filmssignal from films is weaker [11]
ProteinFibroin and sericinSpider silkQuite weak[12]
Collagen [7]tendon, skin, bone, cornea, aorta, fascia, cartilage, meniscus, intervertebral disks ; connective tissuesQuite strong, depends on the type of the collagen (does it form fibrils, fibers ?)nonlinear susceptibility tensor components are ${\displaystyle d_{33}}$, ${\displaystyle d_{31}}$, ${\displaystyle d_{15}}$, with ${\displaystyle d_{31}}$ ~ ${\displaystyle d_{15}}$ and ${\displaystyle d_{33}}$/${\displaystyle d_{15}}$ ~ 1.4 in most cases
MyosinSkeletal or cardiac muscle [2]Quite strongnonlinear susceptibility tensor components are ${\displaystyle d_{33}}$, ${\displaystyle d_{31}}$, ${\displaystyle d_{15}}$ with ${\displaystyle d_{31}}$ ~ ${\displaystyle d_{15}}$ but ${\displaystyle d_{33}}$/${\displaystyle d_{15}}$ ~ 0.6 < 1 contrary to collagen
TubulinMicrotubules in mitosis or meiosis[18], or in dendrites [19]Quite weakThe microtubules have to be aligned to efficiently generate
MineralsPiezoelectric crystalsAlso called nonlinear crystalsStrong if phase-matchedDifferent types of phase-matching, critical of non-critical

## Quantitative measurements

### Orientational anisotropy

SHG polarization anisotropy can be used to determine the orientation and degree of organization of proteins in tissues since SHG signals have well-defined polarizations. By using the anisotropy equation[20]:

${\displaystyle {\frac {I_{par}-I_{perp}}{I_{par}+2I_{perp}}}=r}$

and acquiring the intensities of the polarizations in the parallel and perpendicular directions. A high ${\displaystyle r}$ value indicates an anisotropic orientation whereas a low ${\displaystyle r}$ value indicates an isotropic structure. In work done by Campagnola and Loew[20], it was found that collagen fibers formed well-aligned structures with an ${\displaystyle r=0.7}$ value.

### Forward over backward SHG

SHG being a coherent process (spatially and temporally), it keeps information on the direction of the excitation and is not emitted isotropically. It is mainly emitted in forward direction (same as excitation), but can also be emitted in backward direction depending on the phase-matching condition. Indeed, the coherence length beyond which the conversion of the signal decreases is:

${\displaystyle l_{c}=2/\Delta k}$

with ${\displaystyle \Delta k\propto 1/(n_{2\omega }-n_{\omega })}$ for forward, but ${\displaystyle \Delta k_{bwd}\propto 1/(n_{2\omega }+n_{\omega })}$ for backward such that ${\displaystyle l_{c}}$ >> ${\displaystyle l_{c,bwd}}$. Therefore, thicker structures will appear preferentially in forward, and thinner ones in backward: since the SHG conversion depends at first approximation on the square of the number of nonlinear converters, the signal will be higher if emitted by thick structures, thus the signal in forward direction will be higher than in backward. However, the tissue can scatter the generated light, and a part of the SHG in forward can be retro-reflected in the backward direction [21]. Then, the forward-over-backward ratio F/B can be calculated [21], and is a metric of the global size and arrangement of the SHG converters (usually collagen fibrils). It can also be shown that the higher the out-of-plane angle of the scaterrer, the higher its F/B ratio (see fig. 2.14 of [22]).

### Polarization-resolved SHG

The advantages of polarimetry were coupled to SHG in 2002 by Stoller et al. [23]. Polarimetry can measure the orientation and order at molecular level, and coupled to SHG it can do so with the specificity to certain structures like collagen: polarization-resolved SHG microscopy (p-SHG) is thus an expansion of SHG microscopy. [24] p-SHG defines another anisotropy parameter, as:

${\displaystyle \rho ={\sqrt {\frac {I_{par}}{I_{perp}}}}}$

which is, like r, a measure of the principal orientation and disorder of the structure being imaged. Since it is often performed in long cylindrical filaments (like collagen), this anisotropy is often equal to ${\displaystyle \rho ={\frac {\chi _{XXX}^{(2)}}{\chi _{XYY}^{(2)}}}}$ [25], where ${\displaystyle \chi ^{(2)}}$ is the nonlinear susceptibility tensor and X the direction of the filament (or main direction of the structure), Y orthogonal to X and Z the propagation of the excitation light. The orientation ϕ of the filaments in the plane XY of the image can also be extracted from p-SHG by FFT analysis, and put in a map [25].

### Fibrosis quantization

Collagen (particular case, but widely studied in SHG microscopy), can exist in various forms : 28 different types, of which 5 are fibrillar. One of the challenge is to determine and quantify the amount of fibrillar collagen in a tissue, to be able to see its evolution and relationship with other non-collagenous materials [26].

To that end, a SHG microscopy image has to be corrected to remove the small amount of residual fluorescence or noise that exist at the SHG wavelength. After that, a mask can be applied to quantify the collagen inside the image [26]. Among other quantization techniques, it is probably the one with the highest specificity, reproductibility and applicability despite being quite complex [26].

### Others

It has also been used to prove that backpropagating action potentials invade dendritic spines without voltage attenuation, establishing a sound basis for future work on Long-term potentiation. Its use here was that it provided a way to accurately measure the voltage in the tiny dendritic spines with an accuracy unattainable with standard two-photon microscopy.[27] Meanwhile, SHG can efficiently convert near-infrared light to visible light to enable imaging-guided photodynamic therapy, overcoming the penetration depth limitations [28].

## Sources

• Schmitt, Michael; Mayerhöfer, Thomas; Popp, Jürgen; Kleppe, Ingo; Weisshartannée, Klaus (2013). Handbook of Biophotonics, Chap.3 Light–Matter Interaction. Wiley. doi:10.1002/9783527643981.bphot003. ISBN 9783527643981.
• Pavone, Francesco S.; Campagnola, Paul J. (2016). Second Harmonic Generation Imaging, 2nd edition. CRC Taylor&Francis. ISBN 978-1-4398-4914-9.
• Campagnola, Paul J.; Clark, Heather A.; Mohler, William A.; Lewis, Aaron; Loew, Leslie M. (2001). "Second harmonic imaging microscopy of living cells" (PDF). Journal of Biomedical Optics. 6 (3): 277–286. Bibcode:2001JBO.....6..277C. doi:10.1117/1.1383294. hdl:2047/d20000323. PMID 11516317.
• Campagnola, Paul J.; Loew, Leslie M (2003). "Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms" (PDF). Nature Biotechnology. 21 (11): 1356–1360. doi:10.1038/nbt894. PMID 14595363.
• Stoller, P.; Reiser, K.M.; Celliers, P.M.; Rubenchik, A.M. (2002). "Polarization-modulated second harmonic generation in collagen". Biophys. J. 82 (6): 3330–3342. Bibcode:2002BpJ....82.3330S. doi:10.1016/s0006-3495(02)75673-7. PMC 1302120. PMID 12023255.
• Han, M.; Giese, G.; Bille, J. F. (2005). "Second harmonic generation imaging of collagen fibrils in cornea and sclera". Opt. Express. 13 (15): 5791–5797. Bibcode:2005OExpr..13.5791H. doi:10.1364/opex.13.005791. PMID 19498583.

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