Recently, a novel class of optical imaging markers have been introduced [8–12], which emit light through the second-harmonic generation (SHG) mechanism rather than the widely used fluorescence. SHG is a nonlinear quadratic process only present in a non-centrosymmetric environment. For example materials with non-centrosymmetric crystal structure generally produce SHG. We refer to this class of biomarkers as Second Harmonic Radiation IMaging Probes (SHRIMPs). SHRIMPs possess several key features, including long-term observation without photobleaching, flexibility in the choice of the excitation wavelength, coherent signals for scanningless 3D imaging [11,13], narrow signal bandwidth for greater noise rejection, ultrafast response time, and excellent biocompatibility [14,15]. These properties offer new modalities that are of interest in cell tracking experiments over long period of time, such as embryo development, or in 3D localization using interferometric detection. Moreover the recent demonstration of enhancement of the SHG signal with core-shell SHRIMPs provides high brightness for optimal contrast [16].

The SHG properties of several kinds of nanocrystals have been recently reported: KTP [8], Fe(IO₃)₃ [9], ZnO [10], BaTiO₃ [11] and organic/inorganic hybrid nanocrystals [12]. Specific labeling of SHG nanocrystals to biological target molecules has been developed with ZnO and BaTiO₃ nanoparticles [10,17]. Later on, more specific properties of the SHRIMPs were used such as the coherence of the emitted radiation by imaging through turbid media via digital phase conjugation [3]. SHRIMPs have been demonstrated as efficient biomarkers under 20 μm of in vitro liver tissue [18], and used in vivo in optically transparent zebra fish [19].

We choose BaTiO₃ nanoparticles because of the high second-order susceptibility tensor, which makes them a good marker for second-harmonic imaging. Moreover, this material is easily available, and its excellent biocompatibility was recently demonstrated [14,15]. The 100 nm particles have been characterized by dynamic light scattering [13]. The 300 nm BaTiO₃ nanoparticles were measured by a scanning electron microscope giving an average diameter measurements over 1000 nanoparticles of 280 nm [21]. For the in-vitro experiments, the particles in powder form were suspended in methanol and dispersed on a microscope glass slide. Prior each use, the solution was ultrasonicated to obtain a uniform suspension. For the in vivo experiments, the particles were suspended in deionized water and ultrasonicated before taking a small amount for the injection. No surface coating was used in the present study as compared with previous works in cells [13,17].

The in vitro sample preparation consists of depositing a droplet of the BaTiO₃ SHRIMPs (concentration 6 mg/4 ml) diluted in methanol on a glass slide and adding a controlled thickness of mouse tail (20 to 200 μm thick) tissue on top via conventional histology preparation (Fig. 1 (a)). The samples are conserved in phosphate buffered saline (PBS) solution with a cover glass. The laser light is focused through a water immersion lens on the nanoparticles under the mouse tail tissue and the cover glass. The peak intensity at the sample position is 13.2 GW/cm² nearly 10 times smaller than the cell damage threshold of 100 GW/cm² [22]. Figure 1 (b) shows the cross section image of the sample where the 300 nm SHRIMPs are readily detectable under 120 μm of mouse tail tissue in the presence of a strong endogenous SHG from the top layer of the sample. The endogenous SHG mainly comes from the dermal collagen present at the upper part of the tissue close to the air interface, which is followed by tissues without endogenous SHG and the SHRIMPs layer on the glass slide [23]. In Fig. 1 (b), the SHRIMPs are shown as elongated bright spots due to the scattering of the turbid medium, the lower axial resolution of the microscope and the aberration caused by the interface between the tissue and the immersion water. Moreover, some SHRIMPs were displaced from the glass slide and did not lie on a single plane as they were before the histology procedure. This is because during the sample preparation some of the SHRIMPs did not stick to the glass due to the pressure applied while positioning the layer of the tissue.

Figure 2 (a-c) show section (x-y plane) images of 300 nm SHRIMPs with no tissue, 20 μm and 120 μm of mouse tail tissue on top of the SHRIMPs. By showing the SHG signal of isolated SHRIMPs, we can better see the effect of the different tissue thicknesses. On these images (Fig. 2 (a-c)), we observe the increase of the background noise with increasing tissue thicknesses. It is worth mentioning that the incident 812 nm light and the measured 406 nm light are scattered differently. This wavelength dependent effect can explain the not so strong alteration of the point spread function at 406 nm on Fig. 2 (a-c).

To quantify the results of the contrast of the SHRIMPs for different thicknesses of the in vitro tissue, we calculated an averaged signal-to-noise ratio (SNR) of several SHRIMPs in the corresponding section (x-y plane) images. The signal of a SHRIMP is calculated as the average intensity within the bright spot. This averaging of the intensity is needed because the signal of each nanoparticle will vary with the incident laser polarization according to its orientation. Indeed, the SHG signal is polarization and orientation sensitive since SHG is a coherent process [24].The noise is defined as the standard deviation of the fluctuating background. We expect two main sources of noise: the endogenous SHG and the detector noise. For SHG scanning microscopes, the signal mostly takes place at the focal point of the objective due to the optical nonlinearity and therefore, optical sectioning can be achieved [20]. However, when imaging with a sample with significant endogenous SHG at the surface, we noticed that the out-of-focus endogenous SHG sources contribute as additional noise in the image which is considerable compared to the detector noise.

The average SNR for different thicknesses of the tissue are plotted in Fig. 3 . We observe the decay of the averaged SNR that is spanning from 366 for SHRIMPs with no tissue to 9 for SHRIMPs below 120 μm of mouse tail tissue (Fig. 3). The error bars are the standard deviation from up to 60 isolated SHRIMPs SNR measurements. The decrease in SNR is mostly due to the decrease of SHG signal; when the SHRIMP is deep in the scattering tissue, the excitation is scattered before reaching the SHRIMP, and the SHG signal generated from the SHRIMP is also being scattered before being collected by the microscope objective. We will discuss the single exponential decay in SHG signal as a function of tissue thickness later in the text where we use a Monte Carlo simulation to estimate the effect.

Similarly, we prepared in vitro sample with BaTiO₃ SHRIMPs of 100 nm in diameter under 50, 80, 100 μm of mouse tail tissue. We detected few SHRIMPs under 50 μm of tissue as shown on Fig. 4 (a) , and not under thicker tissue. We calculated a SNR of 8 for this limited numbers of SHRIMP. For comparison in Fig. 4 (b), we display the 300 nm SHRIMPs under 120 um of tissue, which has a SNR of 9.

For the in vivo experiments, we first anesthetize the mouse by an intraperitoneal injection of xylasine/ketamine. We then used a syringe with a 350 μm needle to inject the 300 nm nanoparticles (2·10¹⁰ particles/ml) in distilled water (5 to 10 μl) around the middle of the tail of the living mouse. We bent the needle to inject the particles just under the skin and not in the blood flow. The injection site was marked with a pen for the convenience of relocation under the microscope. The mouse is then placed under the microscope objective with the tail immersed in water for matching the objective requirement (Fig. 5 (a) ). After two hours of imaging experiments and before the animal woke up, the animal was sacrificed by cervical dislocation.

We can observe second harmonic signals from nanoparticles as deep as 100 μm below the surface of the tail with a SNR of 9 (Fig. 5 (b)). As with the in vitro experiment, a z-scan allows for imaging a superposition of section x-y planes of the mouse tail. The (x-z) section view of Fig. 5 (b) shows the elongated point spread function (PSF) of the SHRIMP due, again, to the scattering of the turbid medium the axial resolution of the microscope, and some aberration. Note that we look at the particles from the injections sites and track their positions under the skin tail. Few millimeters away from the injection site, no particles-like SHG signal was observed. This reasonably confirms that the signal we obtained was from SHRIMP rather than collagen aggregates.

The method simulates the behavior of a very large number of photon (3·10⁶ photons), having a certain probability to be absorbed or scattered by the media cut in many successive layers from the input to the output surface. In our case, we divide the layer in 500 x 500 array of elements with a depth dz = 2·10⁻⁶ cm and width dr = 2·10⁻⁶ cm. The tissue parameters for the excitation and SHG wavelengths are listed in Table 1 . The macroscopic values of scattering efficiency (μ_scat), the absorption efficiency (μ_abs) and the anisotropy (g) for mouse skin tissue are taken from [26], and adapted for the two different wavelengths of the incident light and the SH emission.

In the model, we assume a narrow and highly directional beam reaching the tissue and we consider only the photons arriving within the area limited by the SHRIMP SHG cross-section. Moreover, we limit the angle of the photons reaching the SHRIMP (θ_in < 10°) in order to take into account only photons that have undergone few scattering events, sometimes called snake photons [27]. After the first run of the Monte Carlo simulation, we obtain the local excitation intensity of a SHRIMP. We then calculate the SHG emission power from the SHRIMP according to the cross-section calculation (σ) of a 300 nm BaTiO₃ adapted from [16] for a 4π solid angle. A second Monte-Carlo simulation is then used for the SHG emission taking into account the numerical aperture of the objective. Thus we obtain the number of photons reaching the detector. We ran the simulation for different thicknesses of tissue as well as two different particle sizes (100 and 300 nm BaTiO₃).

Figure 6 displays the results of the simulations. The SHG signal decreases exponentially as a function of the tissue thickness, which is consistent with the previous reported studies [18]. The physical origin of this exponential decay is explained by the fact that the transmission coefficient in a medium with extinction (absorption or scattering) is an exponential function of the length of the medium. We calculate an extinction coefficient of 0.113 and 0.112 cm⁻¹ for 100 and 300 nm SHRIMPs, respectively. In Fig. 6, we also show the approximate tissue thicknesses at which the 100 and 300 nm were still detectable at 50 and 120 μm, respectively. It is tempting to conclude from Fig. 6 that the minimum detectable signal level is several picowatts. Since the specification of the PMT sensitivity is only a few femtowatts, the noise floor is primarily determined by the background of endogenous SHG signal. It should be noticed that the simulation only considers the decrease in the signal strength due to the scattering by the tissue. It does not consider the endogenous SHG nor the detector noise which also contribute to the reduction in SNR with tissue thickness.