2.1.

Monte Carlo Method

The MC method²² was adopted to simulate the light propagation in a scattering medium and to visualize the absorption distribution inside the medium for two different boundary conditions. Briefly, the turbid medium was modeled as having layers with finite thickness (along the depth, $z$ axis) of specified optical properties in each layer. In our simulation, millions of photons were generated at each source location. Each photon was incident at the surface of the turbid medium and was assigned a unity weight $W$ , which is analogous to light intensity. Generally, the photon was incident normally to the surface. When an angled source was introduced, the photon was incident with the specified angle. Each photon went through many steps of absorption and scattering processes. After each step, part of the weight $\mathrm{\Delta }W$ was absorbed by the medium and the weight of the photon was decreased. The photon was scattered following the Henyey-Greenstein function. The medium anisotropy $g$ was chosen to be 0.9 in this simulation. The Roulette technique was used to terminate the photon when $W\le W_{th}$ , where $W_{th}$ was a threshold value. For each photon, it was either absorbed in the medium, or detected at the reflecting surface, or it exited the transmitting surface. After the migration of one particular photon halted, a new photon was launched into the medium at the source location. The MC simulation was performed in the time domain²³ and the resulting temporal data were Fourier transformed to give frequency domain amplitude and phase shift as a function of distance. In this simulation, the boundary condition can be easily controlled through the refractive indexes of the surface layer and the medium layer. If these two layers had matched refractive indexes then the absorption boundary condition was satisfied. If the refractive indexes of these two layers were mismatched, the possible total internal reflection was considered by calculating the Fresnel reflection coefficient.²⁴ The Fresnel reflection coefficient was compared with a random number, and the reflectance was decided statistically. Therefore, the reflection boundary condition or partial reflection boundary condition can be simulated.

To evaluate the contributions of different boundary conditions and their effects on image reconstruction of a target, the MC program was extended to include a target embedded inside the medium. The size, position, and optical properties of the target were controlled from an input file. The difference compared with the flat layer only MC simulation was the addition of complex reflection and refraction computation between target and medium interfaces.

2.2.

Green’s Function Solutions to the Diffusion Equation Under Different Boundary Conditions

The general photon density wave $\Phi (\mathit{r},t)$ at position $\mathit{r}$ and time $t$ is described by the diffusion equation:²⁵

Different boundary conditions can be modeled by taking different values of ${\xi }_{ext}$ : for a reflection boundary ${\xi }_{ext}\to \infty$ and for an absorption boundary ${\xi }_{ext}\to 0$ . Generally ${\xi }_{ext}$ can be expressed as

2.3.

Analytical Equation of an Angled Source Using an Absorption Boundary

An angled source was introduced to improve the light illumination in the transition region of 1.0- to $1.5\text{-}\mathrm{cm}$ depth. The diffusion Eq. 1 with an angled source in frequency domain can be modified as

2.4.

Probe Design and Experimental System

A frequency domain system was used in the phantom experiments. The system consists of three wavelengths of 690, 780, and $830\mathrm{nm}$ modulated at $140\mathrm{MHz}$ and one photomultiplier tube (PMT) detector. Each wavelength was switched to nine source locations on a probe using $3\times 1$ and $1\times 9$ optical switches, and the PMT detector was translated to eight detection locations connected to optical light guides. The clinical system used an identical source system but 10 parallel PMT detectors.²⁶ At each detector position, both amplitude and phase of the scattered wave were measured and were used to reconstruct the absorption distributions.

The probe configuration shown in Fig. 1 was used for simulation and experiments. An ultrasound transducer was located at the center to provide target size, shape, and depth information. Figure 1a is the photograph of the probe made of black plastic, which provides an absorption boundary. One angled source fiber tilted $55\mathrm{deg}$ from the incident plane was located next to a source fiber of normal incidence. In the comparison study, either the angled or the normal-incident source was connected to the source output. Thus the total number of sources was the same in each experiment. The probe can also be covered with an aluminum plate to provide a partial reflection boundary and the fitted $R_{eff}$ is 0.6. Figure 1b is the photograph when the aluminum cover is used for imaging shallower lesions and will be referred to as a partial reflection boundary in the following text.

Fig. 1

Photograph of the new probe that incorporates an absorption boundary with an angled source (a) or a partial reflection boundary using an aluminum cover (b). The ultrasound probe was located at the center and the optical source and detector fibers were distributed at the periphery of the ultrasound probe.

2.5.

Image Reconstruction

The dual-zone mesh scheme is used for imaging reconstruction.¹⁴ Briefly, the entire imaging volume was divided into the background region and the target region. The background region was divided into a relatively coarse mesh of voxel size $1.0\times 1.0\times 1.0{\mathrm{cm}}^3$ , and the target region was segmented into a fine mesh of voxel size $0.2\times 0.2\times 0.5{\mathrm{cm}}^3$ . As a result, the total number of voxels with an unknown absorption coefficient was significantly reduced. In addition, the total absorption distribution instead of absorption distribution per se was reconstructed, and the total absorption distribution was divided by different voxel sizes of target and background region. Because the absorption changes in background region were generally smaller than the lesion region, the total absorption distribution was maintained on the same order for voxels in both regions and the inversion was well conditioned for convergence. The Born approximation was used to relate the measured perturbation and the medium absorption distribution, and the conjugate gradient method was used for inverse reconstruction.

3.1.

Comparison of Absorption and Reflection Boundaries

Figure 2a shows the MC simulation of the absorption distribution ( $x\text{-}z$ projection) using an absorption boundary. An absorber of $0.5\text{-}\mathrm{cm}$ radius was located $0.7\text{-}\mathrm{cm}$ deep in the medium. Figure 2b shows the absorption distribution of the same target and the background using a reflection boundary of $R_{eff}=1$ . Both figures were normalized to the total number of photons and displayed in logarithmic scale. The total absorbed weight at the target region, defined as the summation of the absorbed weight in the target volume, in the absorption and reflection boundary cases was 0.0077 and 0.0505, respectively. About 6.5 times higher absorption was obtained with the reflection boundary and consequently larger perturbation could be expected in the measurements.

Fig. 2

Logarithmic scale display of absorption distributions inside the medium computed using an absorption boundary (a) and a reflection boundary (b). The medium has dimensions of $12\times 12\times 7{\mathrm{cm}}^3$ . The figure was displayed as $x\text{-}z$ projection; $x$ axis is the lateral dimension and $z$ is the depth. The medium background optical properties were ${\mu }_a=0.03{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.0{\mathrm{cm}}^{-1}$ ; the target optical properties were ${\mu }_a=0.3{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.0{\mathrm{cm}}^{-1}$ . The target was a $0.5\text{-}\mathrm{cm}$ radius sphere located at (0, 0, $0.7\mathrm{cm}$ ), and the source was located at ( $-1.7\mathrm{cm}$ , 0, 0).

Figure 3 shows the normalized perturbation distribution caused by a point absorption target as a function of the target depth for absorption $(R_{eff}=0)$ and reflection $(R_{eff}=1)$ boundaries. In the calculation, a small target with a diameter of $1\mathrm{mm}$ was used and the difference of the absorption and reduced scattering coefficients between the target and the background medium were 0.3 and $0{\mathrm{cm}}^{-1}$ , respectively. The center of the target was located at the middle between the source and the detector. For each depth, the photon density at the detector position was calculated and subtracted by the background photon density, which was calculated from the absence of the target. The result was further divided by the background photon density, which provided a percentage of the photon density change caused by the absorbing target. To compare the results of different boundary conditions, the percentage of photon density changes in each case was normalized to its maximum value. Two typical separation distances of 3 and $7\mathrm{cm}$ between the source and the detector were adopted. When the reflection boundary was used, the perturbation reached a maximum close to the boundary and reduced as the depth increased. When an absorption boundary was chosen, the maximum perturbation occurred at certain depth depending on the source-detector separation. These results suggest that a reflection boundary should be used for detecting shallow targets and an absorption boundary for deeper lesions.

Fig. 3

Perturbation distribution as a function of the target depth for an absorption boundary $(R_{eff}=0)$ and reflection boundary $(R_{eff}=1)$ . Two typical source-detector distances of 3 and $7\mathrm{cm}$ were selected.

3.2.

Comparison of Extrapolated Boundary and Partial-Current Boundary

As discussed in Sec. 2.2, an effective reflective coefficient $R_{eff}$ was introduced to account for partial reflection of photons from a boundary. For the thin aluminum plate used, the best fitted $R_{eff}$ is 0.6. It has been known that the extrapolated boundary condition fails when $R_{eff}$ is close to unity.^{12, 13} To evaluate the validity of the extrapolated boundary approximation when $R_{eff}=0.6$ , we numerically calculated the error of photon distribution caused by an absorbing target from Eqs. 2, 3, respectively. Figure 4a shows the amplitude error and 4b shows the phase error between the extrapolated and partial-current boundary conditions. The amplitude errors were about 1.26%, 1.58%, and 2.09% for typical source-detector pairs separated by 3, 4, and $6\mathrm{cm}$ , respectively, when $R_{eff}=0.6$ . Correspondingly, the phase errors were $-1.34$ , $-0.82$ , and $-0.47\mathrm{deg}$ , respectively. It is obvious that when $R_{eff}=0.6$ , the extrapolated boundary condition is very close to the partial-current boundary condition.

Fig. 4

Errors between two boundary conditions as a function of effective reflection coefficient. Three typical source-detector distances of 3, 4, and $6\mathrm{cm}$ were shown in figures. (a) Relative errors of amplitude. (b) Phase errors.

3.3.

Phantom Experiment Using Reflection and Absorption Boundaries

To validate the simulations, a set of phantom experiments was performed using the system described in Sec. 2.4. An Intralipid (Baxter, Deerfield, Illinois) solution was used to emulate typical breast tissue optical properties of ${\mu }_a=0.03{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.3{\mathrm{cm}}^{-1}$ . The high-contrast target was a $1.0\text{-}\mathrm{cm}$ diameter sphere made of polyester resin of calibrated values ${\mu }_a=0.23{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=5.45{\mathrm{cm}}^{-1}$ at $780\mathrm{nm}$ . The low-contrast target had the same size, but different optical properties of ${\mu }_a=0.07{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=5.50{\mathrm{cm}}^{-1}$ calibrated at the same wavelength. The data were collected separately using the black probe [Fig. 1a] with no angled source and the probe with the aluminum cover [Fig. 1b] when each target was located at 0.7, 1.0, and $1.5\mathrm{cm}$ in depth, respectively. The left and right columns of Fig. 5 show the reconstructed images using both boundary conditions at $780\mathrm{nm}$ . The color bar represents the reconstructed absorption coefficient. The left column [Figs. 5a, 5d, 5g] shows the reconstructed images obtained from the black probe; the right column [Figs. 5c, 5f, 5i] displays images obtained from the probe with the aluminum cover. The middle column [Figs. 5b, 5e, 5h] shows the reconstructed images using the probe shown in Fig. 1a with one angled source, which will be compared in the later section. The reconstructed maximum values and the mean values within full width at half maximum (FWHM) are given in Table 1 (first and third columns). At a shallower depth of $0.7\mathrm{cm}$ , the reconstructed target ${\mu }_a$ value and shape have been improved when the aluminum cover was used. When the depth was increased to $1\mathrm{cm}$ , the reconstructed target ${\mu }_a$ obtained from the black probe with the angled source was more accurate than that of using the black probe only and the aluminum cover. The ${\mu }_a$ obtained from the aluminum-covered probe was better than the black probe only. At the $1.5\text{-}\mathrm{cm}$ depth, the best result regarding to reconstructed target ${\mu }_a$ was obtained from the black probe with absorbing boundary condition.

Fig. 5

Images of the high-contrast absorber reconstructed from different boundary conditions. The left column was obtained using the absorption boundary; the middle column was obtained using the absorption boundary with one angled source; the right column was obtained using the partial reflection boundary. In (a), (b), and (c), the target center was located at $0.7\text{-}\mathrm{cm}$ depth. The first slice is the spatial $x\text{-}y$ image of $8\mathrm{cm}\times 8\mathrm{cm}$ obtained at $0.2\text{-}\mathrm{cm}$ depth, and the second and third cross-sections slice at 0.7- and $1.2\text{-}\mathrm{cm}$ depths. In (d), (e), and (f), the target center was located at $1.0\text{-}\mathrm{cm}$ depth. The first slice is obtained at $0.5\mathrm{cm}$ and the second and third at 1.0- and $1.5\text{-}\mathrm{cm}$ depths. In (g), (h), and (i), the target center was located at $1.5\text{-}\mathrm{cm}$ depth. The reconstructed maximum and mean values were shown in Table 1.

Table 1

The reconstructed maximum values and mean values of the high-contrast target (μa=0.23cm−1) under different conditions at 780nm .

Similar experiments were performed for the low-contrast target and the reconstruction results are shown in Fig. 6 for both boundary conditions at $780\mathrm{nm}$ . The reconstructed maximum and mean values are given in Table 2 (first and third columns). The middle column shows the results obtained from the black probe with the angled source. For the low-contrast target, the shape of the reconstructed image using the absorption boundary is better than the partial reflection boundary at 1- and $1.5\text{-}\mathrm{cm}$ depth, however, the image at $0.7\text{-}\mathrm{cm}$ depth is distorted. The reconstructed image at $0.7\text{-}\mathrm{cm}$ depth is improved under the partial reflection boundary condition. When the average target ${\mu }_a$ was used to compare three configurations, the black probe with the angled source provided a more accurate target ${\mu }_a$ at $1\text{-}\mathrm{cm}$ depth and the black probe with no-angled source was the best at $1.5\text{-}\mathrm{cm}$ depth.

Fig. 6

Images of the low-contrast absorber reconstructed from different boundary conditions. The left column was obtained using the absorbing boundary; the middle column using the absorption boundary with one angled source; the right column using the partial reflection boundary condition. In (a), (b), and (c), the target center was located at $0.7\text{-}\mathrm{cm}$ depth. In (d), (e), and (f), the target center was located at $1.0\text{-}\mathrm{cm}$ depth. In (g), (h), and (i), the target center was $1.5\text{-}\mathrm{cm}$ depth. The reconstructed maximum and mean values were shown in Table 2.

Table 2

The reconstructed maximum values and mean values of the low-contrast target (μa=0.07cm−1) under different conditions at 780nm .

To further validate the phantom experiments, we have performed one set of mouse tumor experiments. The excised tumor was heterogeneous with three lobular structures and was placed inside a transparent cuvette of $1\mathrm{cm}$ in size. The cuvette was located at 1.0- and $1.6\text{-}\mathrm{cm}$ depths within an Intralipid solution of fitted optical properties ${\mu }_a=0.023{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=7.0{\mathrm{cm}}^{-1}$ at $780\mathrm{nm}$ . For each target depth, two sets of data were acquired by using two probes: an absorbing probe without angled source [Fig. 1a] and the probe with aluminum cover [Fig. 1b]. Reference data were acquired using the corresponding probe. The absorption map obtained with the aluminum cover at $1\text{-}\mathrm{cm}$ depth [see Fig. 7b ] showed higher ${\mu }_a$ of maximum $0.122{\mathrm{cm}}^{-1}$ and improved target shape compared with the absorption map obtained at the same depth using the black absorbing probe [see Fig. 7a]. The reconstructed maximum ${\mu }_a$ obtained with the black probe was $0.088{\mathrm{cm}}^{-1}$ . At $1.6\text{-}\mathrm{cm}$ depth, the absorption map obtained with the black probe demonstrated a higher reconstructed ${\mu }_a$ of maximum $0.137{\mathrm{cm}}^{-1}$ [see Fig. 7c] and improved target definition compared with the map obtained with the aluminum cover [see Fig. 7d]. The reconstructed maximum ${\mu }_a$ obtained with the aluminum cover was $0.101{\mathrm{cm}}^{-1}$ . Thus, more uniform reconstruction can be achieved with the use of partial reflection boundary for a shallower depth, such as $1\mathrm{cm}$ , and an absorbing boundary at depths beyond $1.0\mathrm{cm}$ . This set of results agrees with phantom experiments shown in Fig. 5.

Fig. 7

Images of an excised mouse tumor reconstructed from different boundary conditions. The left column [(a) and (c)] was obtained using the absorbing boundary; the right column [(b) and (d)] using the aluminum cover. In (a) and (b), the tumor center was located at $1.0\text{-}\mathrm{cm}$ depth. The reconstructed maximums were 0.088 and $0.122{\mathrm{cm}}^{-1}$ , respectively. In (c) and (d), the tumor center was located at $1.6\text{-}\mathrm{cm}$ depth. The reconstructed maximums were 0.137 and $0.101{\mathrm{cm}}^{-1}$ , respectively.

3.4.

Simulation Results with Angled Source

Using the MC method, the forward data using sources with normal incidence and one angled source, referred to as the angled probe, were generated from the probe configuration shown in Fig. 1a. The reconstructed images for the $1.0\text{-}\mathrm{cm}$ diameter target are shown in Fig. 8 along with values for the simulation parameters. Figure 8a is the reconstructed image using the probe with sources at normal incidence, and Fig. 8b is the reconstructed image using the angled probe. The total number of sources used in obtaining the images [1(a)] and [1(b)] is the same. For both images, the first slice is the spatial $x\text{-}y$ image of $6\mathrm{cm}\times 6\mathrm{cm}$ obtained at $0.2\mathrm{cm}$ , and the second slice is at the depth of $0.7\mathrm{cm}$ with $0.5\text{-}\mathrm{cm}$ spacing between slices. In Fig. 8a, the image is blurred and shifted from the center position. The maximum reconstructed value is ${\mu }_a=0.162{\mathrm{cm}}^{-1}$ , which is about 54% of the true value, and the mean is $0.122{\mathrm{cm}}^{-1}$ , which is 41% of the true value. In Fig. 8b, both the reconstructed value and location of the target are improved compared with Fig. 8a. The maximum reconstructed value in Fig. 8b is ${\mu }_a=0.270{\mathrm{cm}}^{-1}$ , which is about 90% of the true value, and the mean is $0.196{\mathrm{cm}}^{-1}$ , which is about 65% of the true value. These results demonstrate that tilted sources may further improve the shallow region illumination. The experimental implementation of tilted sources, however, presents a limitation for clinical studies (see Sec. 4).

Fig. 8

The reconstructed image for a simulated target using the black probe with normal-incident sources (a) and the angled probe (b). The background optical properties of the medium were ${\mu }_a=0.03{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.0{\mathrm{cm}}^{-1}$ . The target was located at the center (0, 0, $0.7\mathrm{cm}$ ) with radius $0.5\mathrm{cm}$ and ${\mu }_a=0.3{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.0{\mathrm{cm}}^{-1}$ . For both images, the first slice is the spatial $x\text{-}y$ image of $6\mathrm{cm}\times 6\mathrm{cm}$ obtained at $0.2\mathrm{cm}$ , and the second slice is at the depth of $0.7\mathrm{cm}$ with $0.5\text{-}\mathrm{cm}$ spacing between slices. In (a), the maximum reconstructed value was ${\mu }_a=0.162{\mathrm{cm}}^{-1}$ (54% of the true value), and in (b), the maximum ${\mu }_a=0.27{\mathrm{cm}}^{-1}$ (90%).

Simulations of different target contrast were performed to evaluate the probe with one angled source. In the simulations, the background properties were kept as ${\mu }_a=0.03{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.0{\mathrm{cm}}^{-1}$ while the target ${\mu }_a$ varied from 0.1 to $0.3{\mathrm{cm}}^{-1}$ in $0.1{\mathrm{cm}}^{-1}$ increments. The target ${\mu }_s^{\prime }$ was kept as $6.0{\mathrm{cm}}^{-1}$ . The spherical target of $1\text{-}\mathrm{cm}$ diameter was located at (0, 0, $0.7\mathrm{cm}$ ). Figure 9 plots the reconstructed maximum values (dashed line) and the mean values (dotted line) with different probes. The blue solid line shows the true values. The black dashed line is the reconstructed maximum value from the angled probe with normal-incident sources and one angled source, and the black dotted line is the reconstructed mean value from this probe. The red dashed line is the reconstructed maximum value obtained from the probe with all normal-incident sources, and the red dotted line is the reconstructed mean value. The reconstructed values at low contrast region are close for both probes. For higher contrasts, the performance of the angled probe is superior to that with all normal-incident sources.

Fig. 9

Reconstruction results for a $1\text{-}\mathrm{cm}$ diameter spherical target at (0, 0, $0.7\mathrm{cm}$ ) from the probe with all normal-incident sources and the angled probe with normal-incident sources and one angled source.

3.5.

Phantom Experiments Using the Angled Probe

Phantom experiments were performed to validate the results obtained from the simulations. An Intralipid solution of optical properties ${\mu }_a=0.03{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=6.3{\mathrm{cm}}^{-1}$ was used. The high- and low-contrast targets were the same as used before. The data were collected using the probe shown in Fig. 1a with the angled source connected to the source fiber when the target was positioned at 0.7-, 1.0-, and $1.5\text{-}\mathrm{cm}$ depths. Figures 5b, 5e, 5h show the reconstructed images obtained from the high-contrast target. For the target located at $0.7\text{-}\mathrm{cm}$ depth, the angled probe improved the reconstruction accuracy by 16% compared with the probe of all normal-incident sources. At this target depth, the best result in terms of reconstruction accuracy was obtained from the probe with the aluminum cover [Fig. 5c]. Figure 5e is the reconstructed image when the target is located at 1.0-cm depth. For the high-contrast target, the probe with all normal-incident sources can reconstruct the image at the correct location, but the maximum reconstructed ${\mu }_a$ value is $0.149{\mathrm{cm}}^{-1}$ (65% of true value). The angled probe provides a similar result, but the reconstructed ${\mu }_a$ value is $0.180{\mathrm{cm}}^{-1}$ (78% of true value), which is better than the probe with the aluminum cover for which the reconstructed value was $0.163{\mathrm{cm}}^{-1}$ (71% of true value). It is clear that the angled probe can provide better target shape and improved reconstructed value compared with the probe with all normal-incident sources, especially in the range of 0.7 to $1.0\mathrm{cm}$ . At $1.5\text{-}\mathrm{cm}$ depth, the results obtained from the angled probe and the probe with normal-incident sources are comparable. For the high-contrast target at this depth, the maximum reconstructed ${\mu }_a$ value obtained from the probe with normal-incident sources is $0.204{\mathrm{cm}}^{-1}$ , which is 89% of the true value, and the maximum ${\mu }_a$ value of the angled probe is $0.20{\mathrm{cm}}^{-1}$ , which is 87% of the true value. The reconstructed maximum values and means within FWHM are listed in the second column of Table 1. For the low-contrast target, as we expected, both probes provided similar results. The reconstructed maximum values and means are listed in the second column of Table 2. It is clear that the tilted source in the angled probe increased the detection sensitivity to shallow targets located at approximately $1\text{-}\mathrm{cm}$ depth and improved the reconstruction results compared with the probe will all normal-incident sources.

3.6.

A Clinical Example

An example was obtained from our ongoing clinical study conducted at the University of Connecticut Health Center. The study protocol was approved by the local Institutional Review Board and the informed consent was obtained from the patient. The black angled probe without and with aluminum cover of absorption and partial reflection boundary condition (see Fig. 1) was used to evaluate a $6\text{-}\mathrm{mm}$ lesion of a 53-year-old patient prior to her ultrasound-guided core biopsy. Figures 10a and 10d show the coregistered ultrasound images of the $6\text{-}\mathrm{mm}$ lesion located at $1\text{-}\mathrm{cm}$ depth when the black angled probe with and without the aluminum cover were used, respectively. The corresponding absorption maps obtained at $780\mathrm{nm}$ as well as the computed total hemoglobin maps without and with the aluminum cover are shown in Figs. 10b and 10c and Figs. 10e and 10f, respectively. The maximum and mean lesion ${\mu }_a$ at $780\mathrm{nm}$ were 0.144 and $0.098{\mathrm{cm}}^{-1}$ for the angled probe and 0.088 and $0.064{\mathrm{cm}}^{-1}$ for the aluminum probe. The computed total hemoglobin maximum and mean were 62.0 and $44.3\mathrm{\mu }\mathrm{M}∕\mathrm{l}$ for the angled probe and 53.1 and $38.4\mathrm{\mu }\mathrm{M}∕\mathrm{l}$ for the aluminum probe, respectively. Based on the comparison studies shown in Figs. 5e and 5f and Fig. 6e and 6f (see Tables 1, 2), the mean values of the angled probe are more accurate than the aluminum probe at this target depth. Ultrasound-guided core biopsy revealed a benign fibroadenoma. The total hemoglobin levels obtained agree with the benign findings reported by us earlier.^{15, 17}

Fig. 10

(a) Coregistered ultrasound image, (b) the corresponding absorption map obtained at $780\mathrm{nm}$ , and (c) total hemoglobin map obtained from 53-year-old woman using the black angled probe shown in Fig. 1a. (d) Coregistered ultrasound image, (e) the corresponding absorption map obtained at $780\mathrm{nm}$ , and (f) total hemoglobin map using the same probe with the aluminum cover. In absorption and total hemoglobin maps, each slice corresponds to a spatial image of $9\mathrm{cm}\times 9\mathrm{cm}$ obtained at $0.3\mathrm{cm}$ underneath the skin surface to $3.3\mathrm{cm}$ deep toward the chest wall with $0.5\text{-}\mathrm{cm}$ spacing in depth. The fitted background absorption and reduced scattering coefficients from the normal side of the breast were 0.01, $3.78{\mathrm{cm}}^{-1}$ $\left(780\mathrm{nm}\right)$ , and 0.012, $4.23{\mathrm{cm}}^{-1}$ $\left(830\mathrm{nm}\right)$ , respectively. The core biopsy result revealed a benign fibroadenoma.