3.1.

Fabrication of Depth Standards

3.2.

Refractive Index Measurement of Double Network Hydrogel

Refractive index measurements of double network hydrogels were made using a refractometer (Bellingham + Stanley, A180032). Measurements were made at room temperature (20°C) using a sodium lamp of wavelength 589 nm.

3.3.

Characterization of the Thickness of Single and Layered Phantoms

The depths of hydrogels of different thickness (spacer thickness 190, 310, 390, 490, 570, or $760\mu \mathrm{m}$) were measured using (1) digital Vernier calipers, (2) bright-field microscopy, and (3) fluorescence microscopy.

Vernier caliper measurements were taken using a Duratool. D03196. For bright-field microscopy, the individual gel layers were sectioned using a razor blade, the cross-section was viewed using a Leica microscope (DMC6200, HC PL FLUOTAR, $10\times$), and the thickness of the gels was measured [using Leica Application Suite X software (3.4.2.18368)] from the distance traversed by the microscope stage when moved from one edge of the gel to the other.

For fluorescence microscopy thickness analysis, two microscopes were used.

Single- and multi-layered phantoms were prepared with FS beads, and the thickness of the hydrogel layer ($n=6$ for each spacer thickness) was determined using the $z$-stack feature of the microscope, measuring the distance between the image plane of the beads at either side of the test gel.

3.4.

CARS, SHG, and 2PEF Characterization of the Multi-Layered Phantoms

A custom-built, multimodal laser scanning microscope was used to acquire images (using ScanImage^®,²⁵ Vidrio Technologies LLC) with coherent anti-Stokes Raman scattering (CARS), SHG, and 2PEF. For CARS imaging, the Stokes beam was the fundamental of a fiber laser (1031 nm, Emerald Engine, APE), and the pump beam was generated by an optical parametric oscillator (OPO) (650 to 950 nm, Levante Emerald, APE GmbH), which was synchronously pumped by the second harmonic (515.5 nm) of the fiber laser. The repetition rate and pulse width for both beams were 80 MHz and 2 ps, respectively. The two beams were spatiotemporally overlapped and made collinear before being coupled (through a galvanometric scanner) into an inverted microscope (Nikon Ti-E) and focused through a 20×/0.75 NA Nikon objective on the sample. All of the signals (CARS, SHG, 2PEF) were collected through the same objective in a back-scattering geometry (epi-detection), and through the appropriate dichroic and band-pass filters, and were delivered to three Hamamatsu photomultiplier tubes (PMTs). Two PMTs were used for signal acquisition (H10722-20, Hamamatsu photonics), one each for the CARS and 2PEF channels, and one PMT (H10722-210 Hamamatsu photonics) was used in the SHG channel. All of the images were acquired with a pixel dwell time of $8\mu \mathrm{s}$, with a $512\times 512\text{pixel}$ resolution, covering a field of view of $250\times 250\mu \mathrm{m}$, and they were processed with FIJI (ImageJ, Wayne Rasband and contributors, National Institute of Health, United States).²⁶

4.1.

Depth Characterization Reveals Consistent Thickness of Single-Layered and Multi-Layered Phantoms

The axial measurements of single layers of double-network gels made using Vernier calipers, bright field microscopy (cross-section measurements of the gels), and fluorescence microscopy showed repeatability in the construction of hydrogel layers of defined thicknesses (see Table 1). Thicknesses measured via digital Vernier calipers and bright-field imaging (10×, DMC6200, HC PL FLUOTAR, Leica microscope) of the cross-section of the gels were consistent and agreed with spacer thickness (see Table 1).

Table 1

Repeatability in fabrication of double network hydrogels of defined thicknesses assessed using Vernier calipers, bright-field imaging, and fluorescence microscopy. Correspondence is the thickness of the hydrogel divided by the thickness of the spacers (×100). M, measurement; C, correspondence.

Vernier caliper measurements agreed with the bright field measurements (Table 1, Fig. S1 in the Supplementary Material); however, these measurements did have an error associated with the compression of gels. However, the thicknesses were significantly different from the measurements made using fluorescence microscopy (see Table 1). The experimental setup for fluorescence microscopy is illustrated in Fig. 2 with the test gel sandwiched between two layers of FS beads, and the thickness was determined from the axial ($z$) distance traversed between the two adjacent image planes containing fluorescent beads (the beads were monodispersed and $10\mu \mathrm{m}$ in diameter). For each measurement, six samples were analyzed, and the values are presented in Table 1 along with the standard deviation. This apparent difference in axial measurements is expected due to refractive index mismatch (the refractive index of hydrogel is 1.37 and air is 1.0003²⁷). Thus, when measured through a microscope, it will result in an apparent depth/measurement depth that is smaller than the actual depth.^28,29 The bright field and fluorescence measurements differed by a factor of $1.42\pm 0.02$, and this factor here is referred to as the correction factor. This value was validated (using Zemax OpticStudio 21.3.) with raytracing to determine the relationship between the axial translation and the sample thickness. Considering the numerical aperture of the lens used (0.4) and the refractive index of the hydrogel (1.37), the correction factor calculated was 1.41 for gels ranging in size from 100 to $500\mu \mathrm{m}$ (see Table S1 in the Supplementary Material).

Fig. 2

Measurement of the thickness of a gel layer. (a) Gel sample used for thickness analysis with a lower layer of $310\mu \mathrm{m}$ (test layer) capped with a 2 mm support layer. (b) Imaging a single gel layer ($310\mu \mathrm{m}$) coated with FS beads on both surfaces and then capped with a support layer of gel (2 mm). (c) Microscopy images of the marker layers on the top and bottom of the $310\mu \mathrm{m}$ gel. The distance traversed by the microscope stage between the image planes of the beads gives the apparent thickness of the gel. The scale bar represents $50\mu \mathrm{m}$.

Following the success of these initial designs and thickness measurements, 3 new multi-layered depth standards were prepared, with overall actual depths of 950, 1550, and $1520\mu \mathrm{m}$ and with the thicknesses of the individual layers varying (190, 310, and $570\mu \mathrm{m}$) (see Figs. 3 and 4).

Fig. 3

Images of well plates containing the depth standards. (a), (b) Side views and (c) bottom view of the fabricated standards. Well plate outer dimensions ($w\times l$) $25.5\mathrm{mm}\times 75.5\mathrm{mm}$.

Fig. 4

Measurements of the thickness of the gel layers in the multi-layered phantoms showing the expected thickness from the fabrication process. (a)–(c) The design of the depth standards for the testing of optical systems. Depth standards (a) and (b) were made of 6 layers of signaling markers sandwiching 5 layers of hydrogels of defined thicknesses giving overall heights of 950 and $1550\mu \mathrm{m}$. Depth standard (c) was made of 5 layers of signaling markers sandwiching 4 layers of hydrogels of defined thicknesses giving overall heights of $1520\mu \mathrm{m}$. (d)–(f) Images of signaling markers in each sample, generated via 1PEF with the separation between each layer in $\mu \mathrm{m}$, are given in red. The scale bar represents $50\mu \mathrm{m}$.

The thickness measurements of these multi-layered phantoms were consistent using this technique (Fig. 4), showing apparent depths of 650, 1033, and $1049\mu \mathrm{m}$ for the 950, 1550, and $1520\mu \mathrm{m}$ standards, respectively. Measurements done on three different samples of the same design showed that standards were easily reproducible (see Fig. S2 in the Supplementary Material). When the measurements were made using a different fluorescence microscope (Nikon Eclipse Ti-S microscope, Nikon S-Plan Fluor ELWD, $40\times$), the apparent depth in the 3 designs was 650, 875 (up to the 5th layer of marker), and $997\mu \mathrm{m}$, demonstrating the robustness of the standards (see Fig. S3 in the Supplementary Material). The analysis of the temporal stability of standards over 60 days showed (Table 2) the stability of the gels once sealed. The robustness, stability of the standards, and compact design suggest easy handling and transport across systems and institutions that would allow for consensus and standardization in measurement.

Table 2

Depth measurements (in μm) of the multi-layered phantoms after 0, 46, and 58 days as measured via fluorescence (one-photon) microscopy.

4.2.

Depth Penetration Evaluation of Non-Linear Imaging modalities

Three sets of standards were designed for the various non-linear imaging modalities 2PEF, SHG, and CARS (see Figs. 5 and 6). Each set had 2 constructs, one with $190\mu \mathrm{m}$ hydrogel layers and the other with $310\mu \mathrm{m}$ hydrogel layers between the signaling markers. For each imaging modality, a suitable marker was selected and incorporated into the depth standard, e.g., FS beads for 2PEF, PS beads for CARS, and ${\mathrm{BaTiO}}_3$ nanocrystals for SHG imaging.

Fig. 5

Analysis of depth standard design 1 on multimodal imaging systems. (a)–(c) Illustration of depth standards incorporating “modality markers” BaTiO3 (red), FS beads (green), and PS beads (blue) and imaged via SHG, 2PEF, and coherent anti-Stokes Raman scattering, respectively. Each depth standard had 6 layers of signaling markers sandwiching 5 layers of hydrogels of defined thicknesses ($190\mu \mathrm{m}$) giving an overall height of $950\mu \mathrm{m}$. (d)–(f) SHG, 2PEF, and CARS imaging up to depths of 696, 620, and $649\mu \mathrm{m}$, respectively. The microscopy images represent the marker layers, and the distances between each layer are given in red. The scale bar represents $50\mu \mathrm{m}$.

Fig. 6

Analysis of depth standard design 2 on multimodal imaging systems. (a)–(c) Depth standards incorporating BaTiO3 (red), FS beads (green), and PS beads (blue) imaged via SHG, 2PEF, and coherent anti-Stokes Raman scattering, respectively. Each depth standard had 6 layers of signaling markers (BaTiO3/FS beads/PS beads) sandwiching 5 layers of hydrogels of defined thicknesses ($310\mu \mathrm{m}$) giving an overall height of $1550\mu \mathrm{m}$. (d)–(f) SHG, 2PEF, and CARS imaging up to depths of 835, 1046, and $814\mu \mathrm{m}$, respectively. The microscopy images represent the marker layers, and the distances between each layer are given in red. The scale bar represents $50\mu \mathrm{m}$.

The samples were imaged with a custom-built, multimodal laser scanning microscope (described in Sec. 3). In more detail, the C–H stretching mode at $2845{\mathrm{cm}}^{-1}$ was used for CARS imaging of the PS beads by tuning the OPO at 797 nm and collecting the anti-Stokes at 650 nm (Figs. 5(c) and 6(c)]. Furthermore, the ${\mathrm{BaTiO}}_3$ crystals were imaged via the means of SHG of the OPO beam collecting the corresponding signal around 400 nm [Figs. 5(a) and 6(a)]. Finally, the fluorescent beads were imaged with 2PEF using the degenerate two-photon excitation of both beams (with wavelengths of 1031 and 797 nm, respectively), as well as the non-degenerate two-photon excitation of their combination as verified by the partial delay dependence of the signal, which was collected in the spectral range between 530 and 570 nm [Figs. 5(b) and 6(b)]. It should be noted here that no focus-aiding technology was used for acquiring the images of the signaling marker; instead, images were acquired by adjusting the objective to a position at which the maximum contrast/maximum sharpness could be seen by eyes and the diameter of the beads could be determined.

Importantly, all 6 layers of “signaling markers” were detected when imaging through the samples separated by $190\mu \mathrm{m}$ hydrogel layers going up to apparent depths of 696, 620, and $649\mu \mathrm{m}$ using SHG, 2PEF, and CARS, respectively (the actual depth corrected achieved was $950\mu \mathrm{m}$) (Fig. 5). However, in samples constructed with the $310\mu \mathrm{m}$ hydrogel layers, 6 layers of signaling markers could only be imaged using 2PEF, which reached depths of $1046\mu \mathrm{m}$ (the actual corrected depth achieved was $1550\mu \mathrm{m}$). By comparison, using SHG and CARS imaging, only 5 layers were imaged, reaching depths of 835 and $814\mu \mathrm{m}$, respectively (the actual depth achieved was $1240\mu \mathrm{m}$) (Fig. 6) (here the depth evaluation was limited by the working distance of the microscope objective, which was $1000\mu \mathrm{m}$). It should be noted that, as expected, the incident laser power needed to be increased when imaging $\text{depths}>500\mu \mathrm{m}$ to generate sufficient signal (see Table S2 in the Supplementary Material).

For single and multiphoton microscopy, a good signal to background ratio was achieved. Agarose and polyacrylamide gels have been extensively characterized using ultra-violet-visible and near infra-red (UV-Vis-NIR) and Raman spectroscopy,^30–33 and polyacrylamide gels are known to exhibit minimal autofluorescence in a limited wavelength region (350 to 500 nm), which was not used in this study, whereas agarose gels are generally considered non-fluorescent.^34–37 For CARS imaging, only the symmetric methylene (CH2) stretching vibration was probed at $2845{\mathrm{cm}}^{-1}$. CARS signal depends quadratically on the number of oscillators in the focal volume, hence, the signal from the PS beads was much higher than the negligible background from the polymers in the hydrogels (which contain $\sim 80\%$ water).