2.1.

Experimental Setup

The DR experimental setup consists of two multimode fibers. One fiber was used as a source fiber with a diameter of $1500\mu \mathrm{m}$ and NA of 0.5 (M107L02, Thorlabs, denoted by S in Fig. 1). Another fiber with a 0.5 NA was used to collect the re-emitted signal from the sample (fiber denoted by D in Fig. 1). The light source was a tungsten-halogen lamp (HL-2000-HP-FHSA, Ocean Insight, with 20 W output power). A spectrometer collects the optical measurement (FLAME-T-VIS-NIR-Spectrometer, Ocean Insight). The detector fiber was moved with a precise step size using a stepper motor controller (KST101, Thorlabs).

Fig. 1

The DR setup using fibers with different core diameters. The source fiber (S) had a $1500\mu \mathrm{m}$ core diameter, and the detection fiber (D) core was 400, 600, or $1500\mu \mathrm{m}$. The motor moves the detector fiber (white arrow indicates the direction of movement) with a precise step size according to the fiber cladding. The increase in core diameter will reduce the number of sampling points, illustrated on the left panel. Phantom mimicking the optical properties of tissue, were measured by the different collection fibers.

Before choosing a specific fiber core diameter as a detector fiber, we optimize the DR experimental setup using different fiber core diameters. We used 400, 600, $1500\mu \mathrm{m}$ (QP400-1-UV-VIS ocean Insight, M53L02, and M107L02 Thorlabs) fiber cores with the same NA (0.5) for DR measurement to extract the optical properties. The intensity was collected in a step size that matches the fiber clad diameter. Hence, one step from the $1500\mu \mathrm{m}$ fiber diameter is equivalent to three steps, from the fiber having a diameter of $600\mu \mathrm{m}$ (fiber illustrated in the left panel in Fig. 1). Due to ferrule connectors present in the optical fiber (different manufacturers), the initial distance $r$ between illumination fiber and the detection fiber was $\sim 9$ to 11 mm. At first, the light source and dark spectra were calibrated against a DR standard Spectralon (Newport). After the calibration, the reflected light intensity was measured by moving the detector fiber using a motor controller with a step size of 500, 700, or $1600\mu \mathrm{m}$ according to the fiber clad diameters (corresponding to a core of 400, 600, and $1500\mu \mathrm{m}$). The spectra were recorded in the wavelength range from 350 to 1000 nm in each step size. The experiment was repeated with four sequential measurements for a different position on the sample.

2.2.

Tissue Mimicking Optical Phantom Preparation

We prepared three types of tissue-mimicking solid phantoms with different optical properties: 1L phantoms, 2L phantoms, and 2L phantoms with different ink concentrations between the layers.

In the first type, 1L phantoms were prepared by varying Intralipid (IL) concentrations (0.75%, 1%, 1.25%, 1.5%, and 1.75%). Here, IL (Intralipid 20% emulsion, Sigma-Aldrich, Israel) was used as a scattering component, and 1% agarose powder (agarose, low gelling temperature, Sigma-Aldrich, Israel) converted the solution into gel (agarose will allow solidification of the sample). Double distilled water (DDW) was heated to the temperature of $\sim 65°\mathrm{C}$ while the 2% agarose was slowly added to distilled water. Once the agarose melted completely, IL and additional DDW were added to the solution and mixed for 1 min with a continuous stir and a mixing temperature of $\sim 40°\mathrm{C}$ to make a homogeneous solution. Note that the 2% agarose was first melted into half of the amount of the final volume, and then it was diluted to 1% following the additional IL and DDW. The homogeneous solution was poured into tissue culture plates (with a diameter of 60 mm and a height of 10 mm) and cooled under vacuum conditions (to avoid air bubbles).¹⁵

The 2L phantoms had a constant top layer and varying absorption in the bottom layer. The top layer was prepared with a thickness of 5.5 mm and constant absorption concentration and scattering concentration. The bottom layer of the phantom (10 mm thick) had the same scattering concentration as the top layer and varying absorption concentrations. 1L phantoms were prepared, according to the optical properties corresponding to the top and bottom layers of the 2L phantoms, with a thickness of 10 mm. The absorption coefficient according to wavelengths was measured before adding IL and agar using a spectrophotometer. Reduced scattering coefficient according to wavelengths was measured using an integrating sphere.

We prepared 2L phantoms in that the bottom layer was prepared at first with different absorption concentrations (Indian ink: $0.1\times {10}^{-5}$, $0.2\times {10}^{-5}$, $0.3\times {10}^{-5}$, and $0.4\times {10}^{-5}$) with a constant scattering concentration (3% Intralipid). Here, Indian black ink (Royal Talens-490 ml) was utilized as an absorbing component and Intralipid (Intralipid 20% Emulsion, Sigma-Aldrich, Israel) as a scattering component. Again 1% agarose powder was used to convert the solution into gel. DDW was heated to the temperature of $\sim 65°\mathrm{C}$ while the 2% agarose was slowly added to distilled water. Once the agarose melted completely, ink, Intralipid, and additional DDW were added to the solution and mixed for 1 min with a continuous stir and at a mixing temperature of $\sim 40°\mathrm{C}$ to make a homogeneous solution. The homogeneous solution was poured into crystallizing dishes (with a diameter of 65 mm and a thickness of 20 mm) and cooled under vacuum conditions (to avoid air bubbles). The top layer (thickness denoted as $T$) solution (3% IL, and Indian ink: $0.5\times {10}^{-5}$) and 1% agarose solution were prepared and added on top of the solid bottom layer at room temperature; the thickness of the top layer was maintained as 5.5 mm. Finally, the 2L phantoms were cooled under vacuum conditions to receive solid 2L phantoms.

The same preparation procedure was carried out for single-layer phantoms with different absorption concentrations (Indian ink: $0.1\times {10}^{-5}$, $0.2\times {10}^{-5}$, $0.3\times {10}^{-5}$, and $0.4\times {10}^{-5}$) with a constant scattering concentration (3% IL). The solution was poured into tissue culture plates (with a diameter of 60 mm and a height of 10 mm) then cooled under vacuum conditions.

We prepared synthetic silicone-based phantoms using a P4 silicone rubber base and a p4 silicone activator (Eager Polymers, Chicago, Illinois), along with anatase titanium (IV) oxide and water-soluble nigrosin ink (Sigma-Aldrich, St. Louis, Missouri), for scattering and absorption features, respectively. Components were mixed together to achieve optimal homogeneity: 7 g of titanium (IV) oxide was stirred into the silicone activator by hand. The mixture was placed in a Branson 1200 ultrasonic cleaner (Branson Ultrasonics, Danbury, Connecticut) for 2 h to break apart coagulated titanium (IV) oxide particles. In a separate container, 1 ml of nigrosin solution ($1.5\mathrm{g}/1{\mathrm{H}}_2\mathrm{O}$) was added to the silicone base and mixed at 2000 to 2500 RPM with a plunge mixer (Freeman Manufacturing & Supply Company, Avon, Ohio) for 5 min. The titanium (IV) oxide suspension was mixed into the nigrosin and silicone base mixture. All components were then mixed for an additional 2 min with the plunge mixer and immediately placed into a Gas Vac II industrial vacuum degassing unit (Freeman Manufacturing & Supply Company, Avon, Ohio). The phantom mixture sat in the degassing chamber for $\sim 2\min$ until a pressure of $-29\mathrm{mmHg}$ was achieved and bubbles began to collapse.²⁵ Then, the mixture was returned to normal atmospheric pressure, the chamber was vented, and the containers were removed and placed on a flat surface [Fig. 2(a)]).

Fig. 2

Prepared agar and silicone-based phantoms. (a) Silicone-based phantom, (b) Indian black ink concentrations of 70% and 100% ink introduced by writing the university logo BIU on top of the silicone phantom. (c) 2L phantom made by placing an agar-based phantom on top of silicone phantom, the thickness of the top layer (agar-based phantom) was 5.5 mm.

We wrote the university logo “BIU” from Indian black ink concentrations of 70% and 100% ink on top of the prepared silicone phantom [Fig. 2(b)] using a painting brush. Once the ink was dried completely, the agar-based top layer phantom [Fig. 2(c) top layer: 3% IL and $0.5\times {10}^{-5}$ ink, thickness 5.5 mm] was placed carefully on top of the silicone phantom.

3.1.

Extracted Reduced Scattering Coefficients From 1L Phantoms

A fiber-based DR measurement was performed on five solid phantoms made with different IL concentrations, to extract the reduced scattering coefficients using three fiber core diameters (400, 600, and $1500\mu \mathrm{m}$).

The collected diffusely reflected intensity from the three fibers shown in Figs. 3(a)–3(c) is the logarithmic of the product between the measured intensity and square distance $[\ln (I\times D^2)]$ against distance, at 650 nm, for five IL concentrations (0.75%, 1%, 1.25%, 1.5%, and 1.75%). Figures 3(a)–3(c) correspond to the collected DR intensity from the fiber core diameter 400, 600, and $1500\mu \mathrm{m}$, respectively. DR experiments were done to calibrate the intensity collected by different fiber core diameters with a constant NA.

Fig. 3

Extracted reduced scattering coefficient as a function of different Intralipid concentrations using different fiber core diameters. Measured diffuse reflection from phantoms made with different IL concentrations (0.75%, 1%, 1.25%, 1.5%, and 1.75% represented by a line with the color dark blue, blue, aqua, green, and light green) as a function of the distance ($r$) at a wavelength 650 nm using fiber with core of (a) 400, (b) 600 and (c) $1500\mu \mathrm{m}$. (d) Calculated ${{\mu }_s}^{\prime }$ from the slopes, extracted from the curves in (a)–(c) as a function of different IL concentrations with a fiber core diameter of 400, 600, $1500\mu \mathrm{m}$ (square, diamond, and filled circle) compared the reduced scattering coefficient to integrating sphere (solid lines) data at different wavelengths: 550, 650, and 750 nm correspond to green, red, and blue. Error bar indicates the standard deviation ($<0.1{\mathrm{mm}}^{-1}$).

The slope was extracted from the linear region of the intensity profile from each phantom, where the slope increases with the IL concentrations. From the obtained slope, we calculated the reduced scattering coefficient for each phantom using Eq. (2) with the knowledge of absorption coefficient (here, IL and water are the absorbing components). Figure 3(d) shows the extracted reduced scattering coefficient from five IL concentrations using three fiber core diameters 400, 600, $1500\mu \mathrm{m}$ (square, diamond, and filled circle) at wavelengths of 550, 650, and 750 nm (green, red, and blue). The extracted ${{\mu }_s}^{\prime }$ values from three fiber core diameters at 650 nm are shown in Table 1.

Table 1

Extracted μs′ using three fiber core diameters at 650 nm.

The extracted reduced scattering coefficient values are in good agreement with the integrating sphere data [solid line in Fig. 3(d)]. We calculated the correlation coefficients for the ${{\mu }_s}^{\prime }$ from the different fiber core diameters. The values are $400\mu \mathrm{m}$: 0.990758, $600\mu \mathrm{m}$: 0.996158, and $1500\mu \mathrm{m}$: 0.999251. However, the closest fit between integrating sphere values and extracted values from the DR system is for a fiber core of 600 and $1500\mu \mathrm{m}$. Hence, we used these fibers for the next 2L phantoms study.

3.2.

Crossover Point Determination in Two-Layer Phantoms

DR measurements were performed on four 2L tissue-mimicking solid phantoms to extract the optical properties from 2L structures. We kept a constant top layer absorption and reduced scattering coefficients. The reduced scattering coefficient of the bottom layer was the same as the top layer but varying the bottom layer absorption coefficients (typical biological tissue case: top-layer absorption coefficient is greater than the bottom layer absorption coefficient). The total thickness of the 2L phantoms was 15.5 mm, where the top-layer thickness was maintained 5.5 mm and the bottom layer was 10 mm for all four phantoms. The sample preparation procedure is detailed in Sec. 2.3.

Figures 4(a)–4(d) show the logarithm of the product of collected diffuse reflectance (DR) intensity and square distance [ln ($\text{intensity}\times {\text{distance}}^2$)] versus distance. The 2L (red line) phantoms were compared with the 1L phantoms with the optical properties corresponding to the top layer (black line) and bottom layer (blue line) with a thickness of 10 mm. The optical properties of the top layer are ${{\mu }_{s1}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a1}=0.045{\mathrm{mm}}^{-1}$, and the bottom layer have the same scattering ${{\mu }_{s2}}^{\prime }=2.622{\mathrm{mm}}^{-1}$ and absorption of: ${\mu }_{a2}=0.014{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.022{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.029{\mathrm{mm}}^{-1}$, and ${\mu }_{a2}=0.037{\mathrm{mm}}^{-1}$ corresponding to Figs. 4(a)–4(d). The distance at which the 2L phantom intersects the top layer phantom is called the crossover point (Cp). In 2L phantoms, the DR intensity profile shows two different slopes before the Cp and after the Cp.

Fig. 4

Diffuse reflected intensity profile and crossover point in 2L phantoms (red lines) compared to the 1L phantoms corresponding to the top and bottom layers (black and blue lines) at 650 nm. 2L phantoms are made with constant absorption concentration ($0.5\times {10}^{-5}$) and scattering concentration (3% IL) in the top layer, and the bottom layers are made with different absorption concentrations (Indian ink: $0.1\times {10}^{-5}$, $0.2\times {10}^{-5}$, $0.3\times {10}^{-5}$, and $0.4\times {10}^{-5}$) with a scattering concentration (3% IL) the same as the top layer. The thickness of the top layer was 5.5 mm, and the bottom layer was 10 mm. The optical coefficients of the 2L phantoms and determined crossover points are: (a) ${{\mu }_{s1}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a1}=0.045{\mathrm{mm}}^{-1}$, ${{\mu }_{s2}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.014{\mathrm{mm}}^{-1}$, and Cp is $15.8\pm 0.2\mathrm{mm}$, (b) ${{\mu }_{s1}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a1}=0.045{\mathrm{mm}}^{-1}$, ${{\mu }_{s2}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.022{\mathrm{mm}}^{-1}$, and Cp is $13.6\pm 0.4\mathrm{mm}$, (c) ${{\mu }_{s1}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a1}=0.045{\mathrm{mm}}^{-1}$, ${{\mu }_{s2}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.029{\mathrm{mm}}^{-1}$, and Cp is $12.4\pm 0.3\mathrm{mm}$, and (d) ${{\mu }_{s1}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a1}=0.045{\mathrm{mm}}^{-1}$, ${{\mu }_{s2}}^{\prime }=2.622{\mathrm{mm}}^{-1}$, ${\mu }_{a2}=0.037{\mathrm{mm}}^{-1}$, and Cp is $11.4\pm 0.6\mathrm{mm}$.

The Cp depends on the absorption coefficients of the top and bottom layers in addition to the thickness of the top layer [according to Eq. (1)]. We use the thickness of the top layer of 5.5 mm and calculate the crossover point from the top and bottom layer’s absorption coefficient (line in Fig. 5). We compare the measured crossover points (red circles in Fig. 5) from Figs. 4(a)–4(d) to the calculated Cp (black line in Fig. 5) according to Eq. (1). The extracted Cps from DR measurements are in good agreement with the calculated values. As the absorption of the top layer increases, the Cp decreases.

Fig. 5

The extracted crossover point from 2L phantoms with varying absorption in the bottom layer at 650 nm. The crossover point was determined using DR measurements (filled red circles) from 2L phantoms compared with the 1L phantoms from Figs. 4(a)–4(d) and the calculated Cp (black line) using Eq. (1). The error bar indicates the standard deviation ($<0.0014\mathrm{mm}$).

Next, we examined the slopes before and after the Cp. In the DR intensity profile, we took a linear fit before the Cp point (first line in Table 2) and after the Cp (second line in Table 2). From these slopes, we calculated the absorption coefficient according to Eq. (2). The third and fourth lines in Table 2 are the extracted ${\mu }_a$ from the slopes in the first and second lines, respectively. The extracted ${\mu }_a$ from the experiments compared to the measured values from the spectrophotometer before the Cp (third and fifth lines in Table 2) are in good agreement. The extracted ${\mu }_a$ after the Cp in Figs. 4(a)–4(d) was not the same as the top layer (fourth and sixth lines in Table 2). For large SDDs (11.0 to 17.0 mm), there is a high chance that the majority of the photon migration occurs within the bottom layer due to longer trajectories, and the re-emitted photons were from the deeper layer. This crossover point can be used as a diagnostic fingerprint of in vivo biological systems.

Table 2

Calculated μa from 2L phantom at 650 nm.

3.3.

Determination of Indian Black Ink Concentrations in Two-Layer Phantom

A DR measurement was performed to determine the ink concentrations in the 2L phantom. The phantom preparation procedure was explained in Sec. 2.3 (Fig. 2). Fiber-based DR experiments were done on the 1L phantoms made with the optical properties equal to the top layer (agar-based) phantom and bottom layer (silicone-based) phantom. The DR intensity was collected from the 2L (agar and silicone-based) phantom before introducing the ink concentrations (red squares in Fig. 6). Then they were collected again after the introduction of ink concentrations at the junction between the 2L phantom (blue upward-pointing triangles for 70% ink and magenta downward-pointing triangles for 100% ink). The plot is the logarithm of the product of collected DR intensity and square distance [ln ($\text{intensity}\times {\text{distance}}^2$)] versus distance compared to a 1L (optical properties equal to the top layer agar-based) phantom (black filled circles). We saw different crossover points for 70% ink (blue upward-pointing triangles) and 100% ink (magenta downward-pointing triangles). The bottom layer data is not shown in Fig. 6.

Fig. 6

DR intensity profile for 2L (agar and silicone-based) phantom. The obtained crossover points for different ink concentrations at 650 nm. The DR intensity plotted as a logarithm of the product of collected intensity and the square distance versus distance; The top-layer agar-based phantom (black-filled circles). Agar and the silicone-based 2L phantom formed by placing an agar phantom on top of the silicone phantom (red squares). Ink concentrations of 70% ink (blue upward-pointing triangles) and 100% ink (magenta downward-pointing triangles) were introduced (university logo BIU) between the agar and silicone-based 2L phantom.

The red Cp between the top layer phantom and the 2L phantom is at a distance of $13.4\pm 0.1\mathrm{mm}$. The Cp for the phantom with 70% and 100% ink are at a distance of $12.14\pm 0.11\mathrm{mm}$ (blue Cp) and $11.73\pm 0.15\mathrm{mm}$ (magenta Cp), respectively. From Fig. 5, the crossover point and absorption coefficient relation suggest that as the absorption coefficient increases (ink concentration), the crossover point decreases. A decrease in crossover point verifies the presence of higher ink concentrations in the phantom. It confirms the presence of different ink concentrations at the bottom layer. The photons arrived at the bottom layer in the 2L phantom. In typical biological tissue cases such as skin, stomach, bladder brain, esophagus, intestine, etc, this Cp may be used as a diagnostic fingerprint.