2.1.

Hyperspectral SFDI Instrument

The hyperspectral SFDI system is based on a 5-ps diode pumped Yb fiber laser supercontinuum source (SC 400-2, Fianium, United Kingdom). Once spectrally broadened, the source generates picosecond pulses with a broadband spectrum of 400 to 2100 nm at a maximum total power of 2 W. Bandpass filtering of the broadband laser source is achieved by utilizing a folded prism Martinez compressor design. A prism (PS858, Thorlabs, Newton, New Jersey) spatially disperses the illumination beam on a Plössl lens.³³ The Plössl lens brings the illumination beam to a line focus onto a slit (VA100, Thorlabs, Newton, New Jersey), which is mounted on a linear stage (TLS13E, Zaber Technologies Inc., Vancouver, British Columbia), in front of a mirror to fold the design to be more compact. This configuration allows for tuning the spectral bandwidth and central wavelength of the broadband laser output. The Plössl lens is moved down from the optical axis to steer the beam so that it can be easily picked off with a D-mirror after the second pass through the prism. The Plössl lens consists of two achromatic doublet lenses in a symmetrical placement. This configuration ensures a flat-field curvature for the entire line focus where the slit selects the spectral output. The flat-field curvature then helps proper collimation of beam once spectrally selected. Another advantage of the Plössl lens is to help mitigate chromatic aberration.

The wavelength-tuned beam is then expanded. To reduce spatial heterogeneity, the beam is transmitted through a high grit diffuser (DG100-600-B, Thorlabs, Newton, New Jersey) prior to the DMD (CEL5500, Digital Light Innovation, Austin, Texas). The DMD produces 8-bit grayscale sinusoidal patterns through the time-sharing PWM method. The spatially modulated light is imaged onto the sample and the diffusely reflected light is captured via a high-speed sCMOS camera (ORCA-Flash 4.0 V2, Hamamatsu Photonics K.K., Japan). To increase the signal-to-noise ratio (SNR), pixels are binned by a factor of 4, which gives an image resolution of $512\times 512\text{pixels}$ over a $4\mathrm{cm}\times 6\mathrm{cm}$ FOV. The camera captures images using the internal running mode to achieve highest acquisition rate at a constant exposure time, 50 ms, which is adjusted to the pattern refresh rate of the DMD. The proposed setup has the flexibility to optimize light throughput by adjusting slit speed and camera integration time.

The start and end locations of the motorized stage are chosen with margins to allow for cruising at constant speed within the desired spectral range, 580 to 950 nm. The camera and DMD are controlled by trigger signals from the stage via Arduino Due microcontroller (Sparkfun Electronics, Niwot, Colorado) once the slit reaches both ends of the spectrum. Each scan of the moving slit provides 1000 images. A schematic of the instrument is shown in Fig. 1(a).

Fig. 1

(a) Schematic representation of the hs-SFDI instrument and tissue phantom: supercontinuum input is first dispersed via a prism and imaged onto a mirror placed at the focal point of a cylindrical lens. A slit mounted on a linear stage selects the spectral output, which is spatially modulated via a DMD and projected onto the tissue phantom. The tissue phantom is made of solid silicone background with four wells that are filled with solutions of absorptive dyes and IL. (b) Slit location-central wavelength plot. Each slit location of the hs-SFDI instrument corresponds to a tuned spectral bin from the broadband source. Spectral bins are measured using a spectrometer and are shown with color-coded sensor counts.

2.2.

Spectral Characterization

Figure 1(b) shows a plot of slit location as a function of wavelength. Intensity profile across the spectrum is also shown with a peak intensity at 740 nm. We chose 1000 slit locations corresponding to 1000 spectral bins in the 580- to 950-nm region and measured the output spectra using a spectrometer (Blue Wave, Stellar Net Inc., Tampa, Florida). Slit width was set to $200\mu \mathrm{m}$. Mean and standard deviation (SD) of full width at half maximum (FWHM) was calculated to be 17.25 and 5.69 nm, respectively. As expected, lower $\mathrm{d}n/\mathrm{d}\lambda$ ($n$, refractive index of prism material; $\lambda$, Wavelength) at longer wavelengths on the dispersive prism led to increasing spectral bandwidth, reaching 26.42 nm for the 950-nm spectral bin.

Most of the spectral features of the tissue main chromophores (oxy/deoxy/methemoglobin, fat, and water) in the first optical window (600 to 1000 nm) are broader than the instrument bandwidth using the hs-SFDI instrument.

2.3.

SFDI Processing

In this paper, we have used a single spatial frequency ($f_x=0.1{\mathrm{mm}}^{-1}$) sinusoidal pattern at three $2\pi /3$ rad-shifted phases, which were then inserted into the following SFDI demodulation Eq. (1):

The following procedure is then performed to calculate the optical properties of a sample.

3.1.

Multiconcentration Liquid Phantom

To experimentally validate the performance of the broadband hyperspectral imager, we performed a series of controlled tissue phantom measurements to demonstrate that the instrument can quantify absorption and reduced scattering over a wide spectral range. Solid tissue phantoms were fabricated from silicone, as described in Sec. 2.3. We then inserted 12.5-mm diameter cylindrical molds in the base phantom. Once the base phantom was cured, we removed the cylindrical molds and poured the liquid solutions in the resulting “wells.” A schematic of the tissue phantom is shown in Fig. 1(a).

Distilled water-based solutions of Naphthol Green B at multiple concentrations [0.25, 0.03125, 0.0375, 0.04275, and 0.05 gram per liter (g/L)] were prepared and measured with a custom-built spectrophotometer to calculate the absorption coefficients from 580 to 950 nm. Turbid versions of the same solutions were prepared by adding intralipid (IL) (Fresenius Kabi, Uppsala, Sweden): one milliliter (mL) of 20% IL was added to 19 mL of each solution, poured into the wells of the phantom, and measured with the hyperspectral SFDI instrument. The measurement was performed over 1000 spectral bins in the 580- to 950-nm region; however, we selected 208 linearly spaced bins for our final analysis.

Figure 2(a) shows absorption coefficient values of 5 Naphthol Green B solutions determined using the hyperspectral SFDI instrument and the spectrophotometer. The ${\mu }_a$ values of these solutions range from 0.015 to $0.087{\mathrm{mm}}^{-1}$, whereas ${\mu }_s^{\prime }$ range from 0.75 to $1.8{\mathrm{mm}}^{-1}$. Figure 2(b) shows reduced scattering plots for the five solutions. The optical properties in Fig. 2 are determined by averaging over a $6\mathrm{mm}\times 6\mathrm{mm}$ region of interest (ROI) in the center of each well. Average standard deviations in absorption and reduced scattering maps of these ROIs are 0.0019 and $0.0488{\mathrm{mm}}^{-1}$, which give coefficients of variation of 3.949% and 3.614%, respectively.

Fig. 2

(a) Plot of bulk ${\mu }_a$ spectra for five concentrations of Naphthol Green B in 1% IL. Each data point corresponds to the mean value of ${\mu }_a$ over a $6\mathrm{mm}\times 6\mathrm{mm}$ ROI. About 208 data points in the 580- to 950-nm region are plotted for each concentration. Colored lines are from the hs-SFDI instrument and black dashed lines are spectrophotometer measurements. Mean spatial standard deviation of hs-SFDI-derived ${\mu }_a$ values over specified ROIs is $0.0019{\mathrm{mm}}^{-1}$. (b) Plot of bulk ${\mu }_s^{\prime }$ spectra for five concentrations of Naphthol Green B solutions in 1% IL. The hs-SFDI reduced scattering values are compared to those obtained using a conventional SFDI instrument, Reflect RS^™. Mean standard deviation of hs-SFDI-derived ${\mu }_s^{\prime }$ values over specified ROIs is $0.0488{\mathrm{mm}}^{-1}$.

The average difference between recovered ${\mu }_a$ values determined using the hs-SFDI instrument and spectrophotometer values was 6.7% (SD 6.8%). We expected similar ${\mu }_s^{\prime }$ values for these solutions since the dominant scattering contribution originated from their comparable IL concentrations. We showed that the hs-SFDI-fitted ${\mu }_s^{\prime }$ values were within 12.3% (SD 6.9%) of 1% IL ${\mu }_s^{\prime }$ values measured by a conventional SFDI instrument. A commercially available SFDI measurement system, Reflect RS^™ (Modulated Imaging, Inc., Irvine, California), was used to image reduced scattering coefficients of 1% IL solutions at six wavelengths between 580 and 850 nm. We then fitted a power series to 6 data points and compared Reflect RS^™ reduced scattering values with hs-SFDI data at 208 spectral bins in the 580- to 950-nm region.

Although there is larger error in scattering at short wavelengths, the fact that precision of scattering spectra for different dye concentrations is acceptable (1% to 2.5% coefficient of variation in the 680- to 950-nm range) implies that there may be systematic errors that cause this discrepancy. One of our suspicions is the chromatic aberration on the h-SFDI setup, which can add more “blurring” to the fringes, thus jeopardizing the SFDI algorithm to report higher scattering values.

Figure 3(a) shows fit intervals for the expected ${\mu }_a$ values, spectrophotometer results, and those obtained using the hs-SFDI instrument for all five solutions at 208 wavelengths. Figure 3(b) shows Bland–Altman plots³⁹ of recovered optical absorption for the same data set. About 94% of hs-SFDI measurements are within $1.96\times \mathrm{SD}$ of the mean difference indicating a close agreement between the two approaches. The data points with errors larger than $1.96\times \mathrm{SD}$ are more significant for absorption coefficients $<0.02{\mathrm{mm}}^{-1}$, specifically for wavelengths longer than 750 nm, where the bandwidth of spectral bins becomes larger due to lower $\mathrm{d}n/\mathrm{d}\lambda$ imposed by the dispersive prism in our optical design. However, other factors, such as the partial volume effect from the surrounding medium at lower absorption values and low SNR at longer wavelengths, could also contribute to this result. Figure 3(c) shows fit intervals for the expected ${\mu }_s^{\prime }$ values from Reflect RS^™ and hs-SFDI results for the five solutions at 208 wavelengths. Figure 3(d) shows Bland–Altman plots of recovered reduced scattering.

Fig. 3

(a) Comparison between absorption coefficients extracted from spectrophotometer (expected ${\mu }_a$) and hs-SFDI (measured ${\mu }_a$). Scatter plot with regression fit and confidence intervals for slope and fit. (b) Bland–Altman plots of mean and percentage difference between spectrophotometer (expected ${\mu }_a$) and hs-SFDI data (measured ${\mu }_a$). Dashed lines show intervals for $+/-1.96$ times standard deviation of percentage difference. The absorption percentage differences are calculated by using the spectrophotometer values in the denominator. (c) Comparison between fitted reduced scattering coefficients extracted from Reflect RS^™ (expected ${\mu }_s^{\prime }$) and hs-SFDI (measured ${\mu }_s^{\prime }$). Scatter plot with regression fit and confidence intervals for slope and fit. (d) Bland–Altman plots of mean and percentage difference between Reflect RS^™ (expected ${\mu }_s^{\prime }$) and hs-SFDI data (measured ${\mu }_s^{\prime }$). Dashed lines show intervals for $+/-1.96$ times standard deviation of percentage difference. The reduced scattering percentage differences are calculated by using the fitted Reflect RS^™ values in the denominator.

3.2.

Multidye Phantom

To test spectral resolution, solutions of four compounds with absorption peaks at 636, 675/930, 730, and 910 nm were fabricated: blue food dye (Ateco, Glen Cove, New York), extra virgin olive oil, Naphthol Green B (Sigma Aldrich, St. Louis, Missouri), and FHI96716 dye (Fabricolor Holding Int’l, Paterson, New Jersey), respectively. We then made turbid versions of these solutions by adding 20% IL so that the resulting concentrations of IL were 1%, except for the olive oil, which was mixed with ${\mathrm{TiO}}_2$. The four solutions were then poured in wells of a silicone phantom built using the same method described in Sec. 3.1. The concentrations of Naphthol Green B solutions were chosen to be within the range of brain and skin tissues commonly measured with SFDI.^28,40 Also, at lower absorption values, there are limitations with accuracy of IAD. Therefore, in this study we measured phantoms in the absorption range where our calibration technique provided reliable values.

We measured these solutions using the hs-SFDI instrument and extract ${\mu }_a$ and ${\mu }_s^{\prime }$ for 1000 spectral bins in the 580- to 950-nm range. Figure 4 shows absorption spectra for the four solutions. The optical properties are determined by averaging over a $6\mathrm{mm}\times 6\mathrm{mm}$ ROI in the center of each well. The spectral shapes of these solutions agree with the expected absorption spectra trends for each. There is, however, some cross talk between the FHI96716 sample and the calibration phantom in the 890- to 910-nm region. The calibration phantom has an absorption peak in the 910-nm region that is consistent with the absorption of silicone. The contribution of the 910-nm peak is visible in the absorption spectra of the sample. Therefore, the calibration procedure, discussed in Sec. 2.3, has not completely corrected for instrument response and absorption features of the calibration phantom.

Fig. 4

Plot of bulk ${\mu }_a$ spectra for four solutions: three water-soluble dyes with 1% IL concentration. Olive oil is mixed with known concentration of ${\mathrm{TiO}}_2$ (0.65 g/L). Each data point corresponds to the mean value of an optical property over a $6\mathrm{mm}\times 6\mathrm{mm}$ ROI. About 208 data points in the 580- to 950-nm region are plotted for each concentration.

On the scattering values, however, there were increased deviations in reduced scattering values between the three solutions with 1% IL concentrations, compared to Sec. 3.1. This could be related to photons propagating through multiple media in the phantom with different refractive indices and optical properties or minor spatial variations in the calibrated reflectance. Therefore, scattering plot is not presented in this section.

Figure 5 shows a movie of the spectral cube ($x,y$, and $\lambda$) for absorption and reduced scattering coefficients of the multiwell phantom. While averaging over the center of each well gives a bulk optical property value, there are partial volume effects next to the edges as large path lengths allow photons from the solid medium to enter each well and contribute to the localization of optical properties.

Fig. 5

Spectral cube ($x,y$, and $\lambda$) for absorption and reduced scattering coefficients of the multiwell phantom. Schematic representation of the wells with the silicone-based solid background is shown (Windows Media Player, 782 KB).

3.3.

Beef Sample

To characterize a more realistic biological specimen, we measure a sirloin beef sample with distinct regions of the primary tissue chromophores: hemoglobin, water, and lipid. Figure 6 shows absorption and reduced scattering spectra for two $3\mathrm{mm}\times 3\mathrm{mm}$ ($15\text{pixels}\times 15\text{pixels}$) ROIs located on the fatty and muscle part of the sample. ROIs are chosen on smooth areas of the sample to avoid artifacts from very steep angles.

Fig. 6

Plot of (a) bulk ${\mu }_a$ spectra and (b) ${\mu }_s^{\prime }$ spectra at two ROIs ($3\mathrm{mm}\times 3\mathrm{mm}$): fat (red) and muscle (blue).

The absorption spectra have local maxima, as shown in Fig. 6(a), at 600 and 630 nm mostly due to deoxy/oxyhemoglobin and methemoglobin absorption, respectively. These peaks are noticeable for both ROIs since the diffuse light field samples a larger volume than the specified ROI and there is spatial heterogeneity in three dimensions (i.e., partial volume effect). An increase in absorption values at 850 nm and longer wavelengths is seen in both fatty and muscle components. There is also a distinct lipid absorption peak at about 920 nm in the spectrum acquired from the fat ROI. The overall trend and magnitude of absorption and reduced scattering spectra on the muscle ROI agree with previous studies.^41,42 The fat ROI ${\mu }_s^{\prime }$ values are consistently greater than muscle and, when fitted to a standard Mie theory model:⁴³ ${\mu }_{s\_\text{normalized}}^{\prime }=A\times {(\lambda /850\mathrm{nm})}^{-b}$, scattering prefactor (A), and scattering power (b) are, respectively, $1.259{\mathrm{mm}}^{-1}$ and 1.043 for fatty tissue and $0.5051{\mathrm{mm}}^{-1}$ and 1.248, for muscle tissue. These values are comparable with previous reports in Ref. 44 as average (standard deviation) of A and b parameters for fatty tissue from six studies are 1.288 $(0.630){\mathrm{mm}}^{-1}$ and 0.672(0.242), respectively. The average (standard deviation) of A and b parameters of muscle/heart tissue from four studies are 0.531 $(0.224){\mathrm{mm}}^{-1}$ and 1.609 (0.722), respectively.

Figure 7 shows absorption and reduced scattering maps at two wavelengths (600 and 930 nm).

Fig. 7

(a), (b) The ${\mu }_a$ and (c), (d) ${\mu }_s^{\prime }$ maps of the beef sample at 600 and 930 nm. The dominant spatial contrast between fat and muscle arises from oxy/deoxyhemoglobin absorption at 600 nm while increases in both lipid and water absorption at 930 nm reduces absorption contrast between these components. Higher A and lower b parameters in the fat region cause decrease in contrast between the fat and muscle regions in the reduced scattering map. Also, at longer NIR wavelengths, higher scattering-to-absorption ratios and therefore partial volume effect cause lower spatial resolution.

Finally, we fitted the absorption spectra at two $3\mathrm{mm}\times 3\mathrm{mm}$ ($15\text{pixels}\times 15\text{pixels}$) ROIs (fat and muscle regions) to five chromophores: oxyhemoglobin (${\mathrm{HbO}}_2$), deoxyhemoglobin (Hb), methemoglobin (MetHb), fat, and water using the Beer–Lambert law, published extinction coefficient values,⁴⁵ and MATLAB (Mathworks Inc., Natick, Massachusetts) linear least-squares solver. Table 1 shows calculated values and standard deviations for each chromophore.

Table 1

Chromophore concentration in micromolar (μM) and fraction values for two ROIs (fatty and muscle) in the beef sample. Standard deviations across pixel values within each ROI are included in parentheses.

The calculated values match with expected higher hemoglobin concentrations and water fraction in the muscle. Overlap of MetHb with fat and water absorption peaks and the large bandwidth of spectral bins in the 850- to 950-nm region decrease our ability to fully decouple these chromophores, thus causing a possible underestimation of MetHb and an overestimation of fat in the muscle ROI. We exclude spectral bins in the 580- to 600-nm region in the chromophore fitting procedure due to low SNR imposed by hemoglobin absorption in the sample. In general, there are many issues including type of skeletal muscle, date of harvesting, packaging, and the aging procedure that can cause variations in the sample’s constituents. Depth of interrogation also differs across the spectral bandwidth, which can prevent sampling the same volume of tissue. Full control over these parameters is out of the scope of this study but may allow for more accurate estimation of tissue constituents.