2.1.

Design of Thin PDMS-Based Optical Phantom Layers for Characterization of Thickness

For each thin phantom, $6.5\pm 0.1\mathrm{grams}$ of PDMS (Sylgard 184 Silicone Elastomer Kit, Dow Corning, USA) elastomer base were dispensed into an ARE-100 conditioning mixer cup (Intertronics, UK). Next, the curing agent was dispensed into a 7-mL scintillation vial (VWR, USA) based on a 10:1 ratio of base to curing agent. Titanium dioxide (Sigma-Aldrich, USA) and alcohol–soluble nigrosin (Sigma-Aldrich, USA, SKU: 211680-25G) were used to control the reduced scattering coefficient (${\mu }_s^{\prime }$) and absorption coefficient (${\mu }_a$), respectively. Titanium dioxide (${\mathrm{TiO}}_2$) was weighed and dispensed into a 7-mL scintillation vial containing the curing agent. Next, a 1% w/v solution of nigrosin in ethanol was prepared and added to the scintillation vial. The mixture in the scintillation vial was mixed for 1 min on a vortex mixer (VWR, USA) to disperse large particles of ${\mathrm{TiO}}_2$. Following this, the scintillation vial was placed in a Model 3510 sonicator (Branson Ultrasonics Corporation, USA) for 30 min to disperse small particles of ${\mathrm{TiO}}_2$ and nigrosin emulsions in the curing agent solvent. The process of vortexing for 1 min and sonicating for 30 min was repeated a total of five times to ensure uniform scattering and absorption throughout.

The mixture of curing agent, ${\mathrm{TiO}}_2$, and 1% w/v nigrosin/EtOH was then dispensed into a mixing cup containing the PDMS elastomer base. This final mixture was thoroughly mixed and degassed for three cycles in an ARE-100 conditioning mixer (Intertronics, UK) for a total of 12 min. Immediately following mixing and conditioning in the ARE-100 conditioning mixer, the uncured mixture was placed in an oven at 70°C for 3 min to initiate curing. The PDMS mixture was removed from the oven and slowly poured onto the center of a 10-cm silicon wafer (University Wafer, USA) within a G3P-8 spin coater (SCS Spin Coating Systems, USA).

The spin coater was optimized to accelerate to its peak speed in 4 s, spin at maximum speed for 20 s, and then decelerate to zero RPM in 4 s. Once the spin coater reached zero RPM, the silicon wafer, containing a thin film of partially cured PDMS mixture, was removed and placed in an oven at 70°C for 2 h to complete curing.

Thin phantoms were created at spin speeds of 100, 200, 300, 400, 500, 700, and 1000 rpm, with three trials of each. Each phantom at a particular spin coater speed was sampled six times for a total of 18 thickness measurements at each speed. Thickness was quantified by analyzing transmittance images of PDMS phantom layers. A transverse cut was made in each phantom and imaged using a wide-field microscope with a Nikon Plan Fluor 10X, 0.30 NA objective and Nikon DS-Fi2 camera. Calibration of the image scale was performed with a positive USAF 1951 resolution target. Images were analyzed using the MATLAB^® Image Analysis Toolbox (Mathworks, USA).

2.2.

Design of PDMS-Based Optical Phantoms for Characterization of Reduced Scattering and Absorption Coefficients

The ${\mu }_s^{\prime }$ and ${\mu }_a$ of phantoms containing varying amounts of ${\mathrm{TiO}}_2$ and 1% w/v nigrosin/EtOH were quantified with SFDI.^21,22 For analysis with SFDI, thicker phantoms (2.5 cm thick) were built using an ARE-100 conditioning mixer cup (Intertronics, UK) as a mold. Construction of thick phantoms followed the same procedure as the construction of thin phantoms up until the point the spin coater was introduced. Instead of using a spin coater to spin partially cured PDMS into a thin layer, completely mixed PDMS was placed in an oven at 70°C for 2 h to complete curing. Sixteen phantoms were created using this technique. Eight phantoms (#1–8 in Table 1) contained a constant amount of 1% w/v nigrosin/EtOH solution with an increasing concentration of ${\mathrm{TiO}}_2$ in a PDMS elastomer base to manipulate the ${\mu }_s^{\prime }$. Nine phantoms (#1 and 9–16 in Table 1) contained a constant amount of ${\mathrm{TiO}}_2$ with an increasing concentration of 1% w/v nigrosin/EtOH solution in a PDMS elastomer base to manipulate the ${\mu }_a$. As an example, 50 grams of PDMS elastomer base were used to create Phantom #5, 0.25 grams of ${\mathrm{TiO}}_2$ and $25\mu \mathrm{L}$ of 1% w/v nigrosin/EtOH were added. Table 1 shows the breakdown of each phantom created for the quantification of optical properties by SFDI. In addition, Fig. 1 shows an aerial view of all 16 phantoms represented in Table 1.

Table 1

Amounts of titanium dioxide (scattering agent) and nigrosin/ethanol solution (absorbing agent) per thick (2.5 cm) “semi-infinite” phantom quantified by spatial frequency domain imaging (SFDI).

Fig. 1

Aerial view of the 16 phantoms used in the spatial frequency domain imaging (SFDI) characterization of ${\mu }_s^{\prime }$ and ${\mu }_a$, corresponding to Table 1. Phantoms used in this study are #1–4 (first row), #5–8 (second row), #9–12 (third row), and #13–16 (fourth row).

2.3.

Construction of Multilayer Phantoms for Inclusion of Heterogeneities

One multilayer phantom was constructed, quantified by SFDI, and compared to a single layer, “semi-infinite” control phantom with identical concentrations of optical agents.^21,22 The primary concern during construction of multilayer phantoms was the formation of air pockets between two adjacent layers. One possible technique to avoid air pocket formation was directly spinning uncured PDMS over an existing base layer to build multilayer tissue-simulating phantoms. While this method can successfully eliminate air pocket formation, it would not be suitable for creating thin layers that are easily interchangeable.¹⁵ Instead, our method allowed for thin PDMS layers to readily be stacked and removed, creating diverse sets of multilayer phantoms for various optical imaging purposes. First, two 2.5-cm thick “semi-infinite” phantom layers were molded and cured in an ARE-100 conditioning mixer cup (Intertronics, UK), containing 0.002 g ${\mathrm{TiO}}_2$ and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per gram PDMS elastomer base. Then, using the described spin coating method, two $200\text{-}\mu \mathrm{m}$ layers were constructed, containing exactly the same concentrations of optical agents. After the two $200\text{-}\mu \mathrm{m}$ layers finished curing, they were carefully peeled off the silicon wafer. Using a scapel, the layers were cut into approximately $3{\mathrm{cm}}^2$ squares. Each thin-layer square was placed into a 70% ethanol/DI water solution and sonicated for 10 min to remove dust and other surface contaminants. Following this, two drops of ethanol were placed on one of the 2.5 cm “semi-infinite” base layers. One $200\text{-}\mu \mathrm{m}$ layer was directly placed on top of the ethanol drops so that no visible air bubbles remained. This two-layer phantom was placed in an oven at 70°C for 3 min to allow evaporation of the ethanol, creating two adjacent layers without air pockets. These steps were repeated for the second $200\text{-}\mu \mathrm{m}$ layer on the same multilayered phantom (Phantom #18 in Table 2). No thin layers were added to the second 2.5 cm “semi-infinite” base layer (Phantom #17 in Table 2). Table 2 shows the geometric specifications of the two phantoms.

Table 2

Thickness specifications for single- and multilayer control phantoms (for all layers: 0.002 g, TiO2, and 2.0  μL 1% w/v nigrosin/EtOH in PDMS elastomer base).

Both phantoms were subjected to SFDI analysis to quantify ${\mu }_s^{\prime }$ and ${\mu }_a$ at the six discrete wavelengths. This analysis served to validate the process of creating multilayer phantoms without air pocket formation. In addition, SFDI analysis on multilayered phantoms served to validate that thin ($<880\mu \mathrm{m}$) and thick (2.5 cm) phantoms layers with identical concentrations of optical agents have comparable optical properties. Because all layers contain identical concentrations of ${\mathrm{TiO}}_2$ and 1% w/v nigrosin/EtOH, ${\mu }_s^{\prime }$ and ${\mu }_a$ should be identical for both single-layer and multi-layer phantoms.

Additionally, one more three-layer multi-layer phantom was constructed and imaged using an OCT B-scan for qualitative purposes. First, one 2.5-cm thick phantom layer was molded and cured in an ARE-100 conditioning mixer cup (Intertronics, UK), containing 0.002 g titanium dioxide and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per g PDMS elastomer base. Then, using the described spin coating method, two $200\text{-}\mu \mathrm{m}$ layers were constructed. The first $200\text{-}\mu \mathrm{m}$ layer contained 0.006 g ${\mathrm{TiO}}_2$ and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per g PDMS elastomer base, tripling the scattering agent concentration while keeping the absorbing agent concentration constant. The second $200\text{-}\mu \mathrm{m}$ layer contained 0.002 g ${\mathrm{TiO}}_2$ and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per g PDMS elastomer base (identical to the base layer). The first (optically different) thin layer was placed between the base layer and the second (optically identical) thin layer to produce a heterogeneous multilayer phantom that was imaged by an OCT B-scanning technique. These phantom images are compared to various types of human epithelium (skin and oral mucosa). Table 3 shows the geometric and optical specifications of the heterogeneous multilayer phantom for this comparative study using OCT. The OCT imaging was performed on a custom-built spectral-domain OCT platform with a center wavelength of 1325 nm, axial resolution of $8.0\mu \mathrm{m}$ (in air), lateral resolution of 22.5 μm, and maximum imaging depth of 3.0 mm (in air).²³ For phantom imaging, OCT cross-sections (B-scans) contained 500 A-lines acquired over a 5 mm scan width. B-scan images were generated by standard SD-OCT processing (spectrometer wavelength calibration, interpolation to evenly spaced samples in $k$-space, and Fourier transformation).²³ The OCT system used here operates at 1325 nm, further into the near-infrared range than our SFDI system was capable of testing (591 to 851 nm). The majority of the OCT imaging of tissues (including the epithelial tissues in which our phantoms seek to mimic) is done in the 1325-nm region.²³ Therefore, OCT B-scans were used for comparative purposes and not to characterize the optical properties of the phantoms.

Table 3

Thickness and optical concentration specifications for multilayer phantom imaged by an optical coherence tomography (OCT) B-scanning technique.

3.1.

Characterization of Thickness of Thin PDMS-Based Optical Phantoms

Figure 2 shows the relationship between the primary, maximum 20-s spin speed and resulting thickness of the PDMS layers. Seven different spin speeds were used (100, 200, 300, 400, 500, 700, and 1000 rpm) to characterize the resulting thicknesses (between 115 and 880 μm) of thin PDMS-based phantoms.

Fig. 2

Relationship between thickness of thin-layer phantoms and maximum 20-s spin speed of a spin coater. Here, phantoms were constructed between approximately 115 and $880\mu \mathrm{m}$. The $R^2$ value for the curve of best fit is 0.988. Best fit lines were generated by the MATLAB curve-fitting toolbox (power fit).

3.2.

Characterization of Reduced Scattering Coefficient of PDMS-Based Optical Phantoms

Figure 3 shows the relationship between the ${\mathrm{TiO}}_2$ (scattering agent) in the PDMS elastomer base (g/g) and the resulting ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$) for six discrete wavelengths (nm) measured by SFDI (591, 621, 659, 691, 731, and 851 nm). Eight phantoms (#1–8 in Table 1) were used in this study which contained a constant amount of 1% w/v nigrosin/Et/OH (absorbing agent) and increasing concentrations of ${\mathrm{TiO}}_2$ in a PDMS elastomer base (g/g).

Fig. 3

Relationship between ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$) and ${\mathrm{TiO}}_2$ concentration in PDMS elastomer base (g/g) measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) using SFDI analysis. Here, ${\mu }_s^{\prime }$ values range between approximately 1 and $21{\mathrm{cm}}^{-1}$. $R^2$ values for best fit lines from 591 to 851 nm are 0.994, 0.994, 0.994, 0.995, 0.995, and 0.998, respectively. Best fit lines were generated by the MATLAB curve-fitting toolbox (linear fit).

In addition, ${\mu }_s^{\prime }$ was measured at increasing 1% w/v nigrosin/EtOH concentrations in the PDMS elastomer base to determine if increasing the chosen absorbing agent would affect the bulk scattering properties. Figure 4 shows the relationship between 1 w/v% of nigrosin/EtOH concentration and the resulting ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$). Results from Phantom #16 are not shown in Fig. 4. The phantoms used in this experiment (#1, 9–15 in Table 1) all contained identical concentrations of the chosen scattering agent, ${\mathrm{TiO}}_2$ ($0.001\mathrm{g}/\mathrm{g}$).

Fig. 4

Relationship between ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$) and 1% w/v nigrosin/EtOH concentrations in PDMS elastomer base ($\mu \mathrm{L}/\mathrm{g}$) measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) using SFDI analysis. Best fit lines were generated by the MATLAB curve-fitting toolbox (linear fit).

3.3.

Characterization of Absorption Coefficient of PDMS-Based Optical Phantoms

Figure 5 shows the relationship between 1 w/v% of the nigrosin/EtOH (absorbing agent) in a PDMS elastomer base ($\mu \mathrm{L}/\mathrm{g}$) and the resulting ${\mu }_a$ (${\mathrm{cm}}^{-1}$) for six discrete wavelengths measured by SFDI (591, 621, 659, 691, 731, and 851 nm). Nine phantoms (#1 and 9–16 in Table 1) were used in this study; they contained a constant amount of ${\mathrm{TiO}}_2$ (scattering agent) and increasing 1% w/v nigrosin/EtOH concentrations in a PDMS elastomer base.

In addition, ${\mu }_a$ was measured at increasing ${\mathrm{TiO}}_2$ concentrations in a PDMS elastomer base to determine if increasing the chosen scattering agent would affect the bulk absorbing properties. Figure 6 shows the relationship between ${\mathrm{TiO}}_2$ concentration and the resulting ${\mu }_a$ (${\mathrm{cm}}^{-1}$). Eight phantoms (#1-8 in Table 1) were used in this study; they contained identical concentrations of the chosen absorbing agent, 1% w/v nigrosin/EtOH ($0.5\mu \mathrm{L}/\mathrm{g}$).

Fig. 5

Relationship between ${\mu }_a$ (${\mathrm{cm}}^{-1}$) and 1% w/v nigrosin/EtOH concentration in PDMS elastomer base ($\mu \mathrm{L}/\mathrm{g}$) measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) using SFDI analysis. Here, absorption coefficients range between approximately 0 and $1.5{\mathrm{cm}}^{-1}$. Best fit curves, generated by the MATLAB curve-fitting toolbox (power fit), are shown for the 591 nm (dashed) and 851 nm (dotted) wavelengths, respectively.

Fig. 6

Relationship between ${\mu }_a$ (${\mathrm{cm}}^{-1}$) and ${\mathrm{TiO}}_2$ concentration in PDMS elastomer base (g/g) measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) using SFDI analysis.

3.4.

Validation of Multilayer PDMS-Based Optical Phantoms

For the two phantoms specified in Table 2 (Phantoms # 17 and 18), ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$) and ${\mu }_a$ (${\mathrm{cm}}^{-1}$) were quantified with SFDI.^21,22 Phantom #17 (single-layer) consisted of only one thick 2.5-cm base layer, containing 0.002 g ${\mathrm{TiO}}_2$ and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per gram PDMS elastomer base. Phantom #18 (multi-layer) consisted of one thick 2.5-cm base layer with two overlying $200\text{-}\mu \mathrm{m}$ layers, all containing 0.002 g ${\mathrm{TiO}}_2$ and $2.0\mu \mathrm{L}$ 1% w/v nigrosin/EtOH per gram PDMS elastomer base. This experiment attempted to validate the creation of multilayer phantoms by comparing the overall optical properties (${\mu }_s^{\prime }$ and ${\mu }_a$) of single- and multi-layer phantoms with all layers containing identical concentrations of scattering and absorbing agents. Figure 7 shows the relationship between the wavelength and the resulting ${\mu }_s^{\prime }$, while Fig. 8 shows the relationship between the wavelength and resulting ${\mu }_a$ for the single- (Phantom #17) and multi-layer (Phantom #18) phantoms specified in Table 2.

Fig. 7

Comparison of ${\mu }_s^{\prime }$ (${\mathrm{cm}}^{-1}$) between a single-layer and a multi-layer phantom with identical concentrations of scattering and absorbing agents measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) SFDI analysis. Average aggregate error was 7.7%.

Fig. 8

Comparison of ${\mu }_a$ (${\mathrm{cm}}^{-1}$) between a single-layer and a multi-layer phantom with identical concentrations of scattering and absorbing agents measured at six discrete wavelengths (591, 621, 659, 691, 731, and 851 nm) using SFDI analysis. Average aggregate error was 10.9%.

Figure 9 represents an OCT B-scan comparison between multilayered phantoms and several types of human epithelium from a normal volunteer (fingertip epithelium, wrist epithelium, and oral mucosa).

Fig. 9

Images of multilayered PDMS-based phantoms compared to optical coherence tomography (OCT) B-scans of various human epithelium. (a) OCT B-scan of a three-layer phantom. Thickness in layers 1 and 2 (L1 and L2) was approximately $200\mu \mathrm{m}$, respectively. ${\mathrm{TiO}}_2$ concentration in layers 1, 2, and 3 (L3) were 0.002, 0.006, and 0.002 (g/g), respectively. 1 w/v% nigrosin/EtOH concentration was $2.0\mu \mathrm{L}/\mathrm{g}$ in all layers. The comparative images show OCT B-scans from a normal volunteer of the (b) fingertip showing the epidermis (Epid) and dermis (Der), (c) wrist showing the epidermis (Epid) and dermis (Der), (d) oral mucosa showing the epithelium (Epit) and lamina propria (LP) Scale bars represents $500\mu \mathrm{m}$.

4.1.

PDMS as a Substrate Material

We have demonstrated a reproducible method for creating thin PDMS-based phantoms with tunable thicknesses and optical properties (reduced scattering and absorption coefficients).^{1,3,9–12,15} PDMS, a silicone-based polymer, was chosen as the substrate material due to its relatively long optical stability when compared to other commonly used substrates.^1,9 Bruin et al. demonstrated that the optical properties of PDMS-based phantoms using ${\mathrm{TiO}}_2$ as a scattering agent remained stable over a 6-month testing period.¹ Pogue and Patterson report that silicone-based phantoms with ${\mathrm{TiO}}_2$ and various inks should have an optical stability of at least 1 year.⁹ Furthermore, PDMS is optically clear, easily moldable, and has a comparable refractive index (1.4) to human tissue.^1,3,9

4.2.

Spin Coating to Produce Individual Thin Layers

We demonstrated an ability to create both thin phantom layers (between 115 and 880 μm) and thick phantom layers (approximately 2.5-cm thick). Thick phantoms could be made at other thicknesses as well by varying the volume dispensed into the ARE-100 conditioning mixer cup (Intertronics, UK) mold.

To create thin phantom layers, a spin coating technique was used to spin partially cured PDMS down to reproducible thicknesses as shown in Fig. 1.^15,16 Koschwanez et al. have previously outlined a spin coating technique to create multilayered PDMS phantoms by spinning uncured PDMS over an already cured layer. However, their thin phantoms ranged between 2 and $30\mu \mathrm{m}$, much thinner than our intended range (100 to $300\mu \mathrm{m}$) for mimicking epithelial tissue thickness.^13,16–18 Furthermore, our method allowed for thin layers to be used interchangeably and nonpermanently to rapidly test multiple configurations. In our studies, the relationship between the maximum 20-s spin speed of the spin coater and the resulting thicknesses of cured, individual PDMS layers containing varying amounts of ${\mathrm{TiO}}_2$ and 1% w/v nigrosin/EtOH can be seen in Fig. 1. Spin speeds of 100 rpm produced phantoms with an average thickness of 880 μm and a standard deviation of $34\mu \mathrm{m}$. Spin speeds of $1000\mu \mathrm{m}$ produced phantoms with an average thickness of $115\mu \mathrm{m}$ and standard deviation of $4\mu \mathrm{m}$. As the spin speed increased, the thickness decreased and the standard deviation tended to decrease. For researchers interested in using this technique, the following inverse equation, based on data presented here, can be used as a guideline to estimate the necessary spin speed (rpm) given a desired thickness with relative accuracy,

One consideration when using this spin coating technique is the potential nonuniformity of the absorbing and scattering agents within the PDMS material. Heterogeneities in these materials may result in increasing radial distances due to the rotational acceleration of the spin coater.³ This may also mean that thin phantoms of identical concentrations of optical agents but different thicknesses may have slightly different optical properties. Since SFDI required thick phantoms ($>2.5\mathrm{cm}$) for characterization, the optical properties of thin layers were not explicitly measured.²¹ However, from data presented in Figs. 7 and 8, we are reasonably confident that thin layers have bulk scattering and absorbing properties comparable to the thicker layers characterized by SFDI. To definitively validate the thin layer uniformity, methods capable of characterizing the optical properties of thin layers, such as integrating spheres and inverse adding-doubling methods, must be further explored.^24,25 Another limitation to this procedure was creating phantoms with a lower limit of approximately $115\mu \mathrm{m}$. While thinner layers could potentially be produced using our spin coating technique, such thin layers were increasingly difficult to work with by hand and could no longer be considered interchangeable with regard to creating multilayered phantoms. Therefore, applications in need of phantoms thinner than $115\mu \mathrm{m}$, such as retinal imaging, may benefit from other spin coating techniques such as those presented by Bae et al. or Koschwanez et al. that can produce much thinner layers.^15,16,19

4.3.

Alcohol-Soluble Nigrosin as an Absorbing Agent

The absorption coefficient (${\mu }_a$) of PDMS phantoms was manipulated by using alcohol–soluble nigrosin as the absorbing agent.^3,12 A 1% w/v solution of nigrosin/ethanol was prepared and added to phantoms at increasing concentrations as seen in Fig. 5. Figure 6 shows that ${\mu }_a$ was independent of the ${\mathrm{TiO}}_2$ concentration. However, ${\mu }_a$ was shown to be wavelength dependent when using 1% w/v nigrosin/EtOH for the absorbing agent. This can be seen in Fig. 5 in the difference between the best fit curves for the 591 nm (dashed) and 851 nm (dotted) wavelengths, respectively. As the wavelength increased, ${\mu }_a$ tended to decrease. This observation is comparable to results on similar phantoms created by Saager et al.³ In addition, ${\mu }_a$ was strongly dependent on the concentration of 1% w/v nigrosin/EtOH, as expected. Figure 5 shows that a more linear region exists between 1% w/v nigrosin/EtOH concentrations from 0 to $7\mu \mathrm{L}/\mathrm{g}$ PDMS elastomer base, corresponding to ${\mu }_a$ values between approximately 0 and $0.9-1.2{\mathrm{cm}}^{-1}$ depending on the measured wavelengths. Increases in ${\mu }_a$ began to level off for 1% w/v nigrosin/EtOH concentrations between 7 to $40\mu \mathrm{L}/\mathrm{g}$ PDMS elastomer base, corresponding to ${\mu }_a$ values between approximately 0.9–1.2 and $1.5{\mathrm{cm}}^{-1}$.

Just as in the case of the previous thickness-spin speed relationship [Eq. (1)], a useful inverse equation would be one that estimates the necessary concentration of 1% w/v nigrosin/EtOH in PDMS given a desired ${\mu }_a$. Because ${\mu }_a$ was shown to be dependent on both absorbing concentration and wavelength, a simple inverse equation was not found. Instead, the relationship between absorbing agent concentration and the desired ${\mu }_a$ was modeled by a piecewise function for each of the six studied wavelengths (591, 631, 659, 691, 731, and 851 nm). This set of equations, generated by the MATLAB curve-fitting toolbox, was used to create the lookup tables found in the Appendix. However, it should be noted that these equations and the corresponding lookup tables generated from our limited sample size of 16 PDMS-based phantoms (Table 1), should just be used as guidelines. Exact ${\mu }_a$ values cannot be accurately predicted due to our lack of extensive validation testing; therefore, optical properties should always be independently validated.

One of the major drawbacks to using alcohol–soluble nigrosin as the absorber was its hydrophilic nature. The alcohol–soluble nigrosin did not mix easily with the silicone base material used to produce the PDMS. To account for this, Bisaillon et al. and Bruin et al. suggest mixing hexane with PDMS.^1,26 However, Koschwanez et al. suggested that adding hexane swells the PDMS substrate, and instead mixed tert-butyl alcohol with PDMS.¹⁶ Using a certain percent tert-butyl alcohol within the PDMS substrate may aid in more efficient mixing of the alcohol–soluble nigrosin and should be explored in future studies. If this is to be done, however, new thickness-spin speed curves (see Fig. 1) would need to be generated between 100 and 1000 rpm for tert-butyl alcohol infused PDMS.¹⁶ However, our described procedure accounted for mixing difficulties by thoroughly mixing 1% w/v nigrosin/EtOH in PDMS with a sonicator, vortex mixer, and an ARE-100 conditioning mixer. Another limitation of the phantoms presented here was a characteristic peak in absorption in the 870 to 930 nm range when using nigrosin-silicone-based tissue phantoms.³ Because our SFDI analysis only covered a wavelength range up to 851 nm, this phenomenon was not observed. Therefore, for our purposes, the procedure presented here to manipulate ${\mu }_a$ using alcohol–soluble nigrosin is sufficient. Finally, other absorbing agents such as whole blood, inks, dyes, or fluorophores may be investigated either as a single absorber or in combination with each other in the outlined procedure for phantom construction.^3,9

4.4.

Titanium Dioxide as a Scattering Agent

The reduced scattering coefficient (${\mu }_s^{\prime }$) of PDMS phantoms was manipulated by using ${\mathrm{TiO}}_2$ as the scattering agent.³ The ${\mu }_s^{\prime }$ of PDMS phantoms was known to be dependent on the ${\mathrm{TiO}}_2$ concentration (Fig. 3), wavelength (Fig. 3), and 1% w/v nigrosin/EtOH concentration (Fig. 4). The dependence of ${\mu }_s^{\prime }$ on the scattering agent concentration and wavelength has been demonstrated in previous phantom studies.^1,3 Depending on the wavelength, Fig. 3 shows that phantoms were produced with reduced scattering coefficients between approximately 1 and $20{\mathrm{cm}}^{-1}$. However, Fig. 4 shows that as the 1% w/v nigrosin/EtOH concentration increased, ${\mu }_s^{\prime }$ decreased in phantoms with identical concentrations of ${\mathrm{TiO}}_2$ (Phantoms #1, 9–15 in Table 1). Furthermore, the decline of ${\mu }_s^{\prime }$ due to the increased concentration of 1% w/v nigrosin/EtOH was greater at lower wavelengths (591 and 621 nm) when compared to higher wavelengths (731 and 851 nm). Furthermore, in Fig. 4, once a certain concentration of 1% w/v nigrosin/EtOH was reached (around $7\mu \mathrm{L}/\mathrm{g}$), further changes in wavelength and concentration did not affect ${\mu }_s^{\prime }$.

The linear relationship between ${\mu }_s^{\prime }$ and the absorbing agent concentration over the tested wavelengths (Fig. 4) roughly implies that there may exist an empirically determined correction factor that could account for all variables (${\mathrm{TiO}}_2$ concentration, wavelength, and 1% w/v nigrosin/EtOH concentration) that affect ${\mu }_s^{\prime }$. Thus, given a desired wavelength, ${\mu }_a$, and ${\mu }_s^{\prime }$, the necessary ${\mathrm{TiO}}_2$ concentration was analytically determined. Therefore, for researchers interested in manipulating ${\mu }_s^{\prime }$ within PDMS phantoms, the provided lookup tables can predict ${\mathrm{TiO}}_2$ concentration based on data presented in this paper. Of note, however, in Fig. 4, the phenomenon that increasing 1% w/v nigrosin/EtOH concentration reduced ${\mu }_s^{\prime }$ was only observed in phantoms with minimal ${\mathrm{TiO}}_2$ concentration (0.001 g ${\mathrm{TiO}}_2/\mathrm{g}$ PDMS elastomer base). Further studies will need to be completed to validate the lookup tables presented here and determine whether this phenomenon is prevalent in phantoms with much higher ${\mathrm{TiO}}_2$ concentrations, such as 0.007 or 0.008 g ${\mathrm{TiO}}_2/\mathrm{g}$ PDMS elastomer base. It should also be noted that the lookup tables assume a linear relationship in ${\mu }_s^{\prime }$ and ${\mathrm{TiO}}_2$ concentration beyond the tested limits ($0.001\text{-}0.008\mathrm{g}/\mathrm{g}$). Further SFDI analysis will be needed to validate these values within the lookup table.

Finally, it is possible to expand this approach by using scattering agents other than ${\mathrm{TiO}}_2$. Scattering materials, such as polystyrene beads, silicon dioxide, aluminum oxide powders, or other types of microspheres, have been successfully demonstrated by other investigators and could potentially be applied using our spin coater approach.^1,9,27,28

4.5.

Multilayered Phantoms to Simulate Heterogeneities

Generally, the purpose of multilayered phantoms is to introduce geometrical and optical heterogeneities in phantoms to simulate the layered structure of epithelial tissue.^1,9 A multilayered phantom (Table 2, Phantom #18) with two thin layers (200 μm) was compared to a control phantom (Table 2, Phantom #17) with identical concentrations of optical agents. The ${\mu }_s^{\prime }$ and ${\mu }_a$ for the two phantoms were compared in Figs. 7 and 8. Only slight differences were present between the two phantoms across the six measured wavelengths. Figure 7, comparing ${\mu }_s^{\prime }$, shows an average aggregate error of 7.7%. Figure 8, comparing ${\mu }_a$, shows an average aggregate error 10.9%. We believe these differences were due to random error in dispensing the precise amounts of ${\mathrm{TiO}}_2$ and 1% w/v nigrosin/EtOH solution rather than being due to air pockets between the layers. This assumption was further validated in Fig. 9, which compares multilayered phantoms to human epithelium using an OCT B-scan technique. OCT instrumentation, operating at 1325 nm (outside the wavelength range of our SFDI equipment), was used for comparative purposes and was not meant to validate the optical properties of phantoms. The multilayered phantom (Fig. 9) shows no visible air pockets between adjacent layers. These validations give us good reason to believe that creating PDMS-based multilayered phantoms using our procedure can serve as appropriate models of various epithelia. In addition to providing evidence for the absence of air pockets, the B-scans in Fig. 9 were used for visually comparing thicknesses of the phantoms to several types of epithelium.²³

The comparative images shown in Fig. 9 as well as the data from Fig. 1 show that the thickness of individual PDMS layers accurately modeled the thickness of several types of human epithelia (skin from the finger or wrist and oral mucosa). In addition, we believe that the phantom procedure presented here could potentially model the thickness of other epithelial tissue types, such as the tongue and gingivae (100 to $200\text{-}\mu \mathrm{m}$ thick, cervical epithelium ($180\text{-}\mu \mathrm{m}$ thick), and esophageal epithelium ($250\text{-}\mu \mathrm{m}$ thick).^13,17,18

To design these phantoms, lookup tables have been provided in the Appendix to guide researchers in selecting the appropriate concentrations of scattering and absorbing agents (${\mathrm{TiO}}_2$ and 1% w/v nigrosin/EtOH). Thick or thin (between 115 and $880\mu \mathrm{m}$) phantoms can be created by either directly molding uncured PDMS or by using the described spin coating technique. Equation (1) provides guidance in selecting an appropriate spin speed based on a desired phantom layer thickness. Thick and thin layers can be combined to form multilayered phantoms to simulate the optical heterogeneities seen in tissue (Figs. 7Fig. 8–9). In addition, individual thin layers may be used interchangeably to rapidly test multiple configurations.³ These PDMS-based tissue-simulating phantoms may be used by researchers as optically stable calibration devices for various optical imaging techniques including, but not limited to, OCT, diffuse optical spectroscopic imaging, endoscopy, or microendoscopy.^1–4,9,23 Using the provided lookup tables, these phantoms have the potential to mimic the optical properties of common types of epithelia including breast, skin, colon, oral, cervical, esophagus, etc.^11,13,17,18