2.1.

Hardware

For this proof-of-concept system, three wavelengths of light were used: 519, 652, and 740 nm. One high-power LED per wavelength (Cree XLamp, Cree, Inc. Durham, North Carolina) was driven at 700 mA (652 and 740 nm) or 1000 mA (519 nm) with independent constant current sources. Light from the LEDs was modulated in time using a pulse-width modulation sequence controlled by a microcontroller (Arduino UNO). Modulation frequencies were set at 5.21, 8.68, and 12.15 Hz, each of which falls into a single bin of a 32 point discrete Fourier transform when a sampling period of 18 ms ($55.6\text{frames}/\mathrm{s}$) is used. Frequencies occupying a single bin were important for reducing cross-talk between wavelengths. These frequencies were also chosen to avoid harmonic content from lower frequencies influencing higher frequency modulation. Light from the LEDs was roughly collimated by a lens over each emitter and sent through a transparency printed with a sine wave pattern using a laser jet printer [Fig. 1(a)]. The spatiotemporally modulated light was directed onto a sample, and the reflected light was recorded by a 16 bit scientific CCD camera (Zyla 4.2, Andor, Inc.) with an $8.5\times 6.4\mathrm{cm}$ field-of-view (FoV). Crossed polarizers were used to minimize the effect of specular reflection. Modulation and acquisition timings were controlled by a custom Arduino program.

Fig. 1

(a) System diagram. Three LEDs were driven by independent constant current sources (D1, D2, D3) and were temporally modulated by a microcontroller. The light was roughly collimated by three lenses (CL) and polarized (P1) before passing through a patterned transparency (T). Before being imaged by the camera, reflected light passed through a second polarizer (P2) set at 90 deg to P1 to reject specular reflection. Camera FoV is indicated by dashed lines. (b) Schematic of data processing. A video was captured from the camera and the variation of each pixel in time was plotted. An FFT of this time series was taken and the strength of the signal at the frequencies corresponding to the modulation of the LEDs was used to build up a 2-D image for each wavelength. These temporally demodulated images were then processed using the SSOP technique as in Ref. 14.

2.2.

Processing

Videos of temporally modulated light reflected from the sample were acquired at $55.6\text{frames}/\mathrm{s}$ for 2.3 s (128 frames) for offline processing. A Fourier transform in time of each pixel of the image was performed to separate the wavelengths. The amplitude of the spectrum at each modulation frequency corresponded to the intensity of the light reflected by that specific wavelength at that specific spatial location [Fig. 1(b)]. Recording the strength of the peaks at each pixel effectively separates each wavelength, while simultaneously rejecting background light (Fig. 2). Once an image of each wavelength was extracted, the images were rotated to ensure that the stripes were parallel to the top and bottom of the frame, and the optical properties were determined by previously published techniques.¹⁴ Briefly, each image was split into a DC and AC component by taking a spatial Fourier transform of each line of the image and filtering in the spatial frequency domain. The DC image was generated by removing a band of frequencies surrounding the projected AC frequency, leaving the high and low frequency content intact. The inverse Fourier transform of this spectrum was used to determine the diffuse reflectance of the sample under planar illumination. The AC image was obtained via Hilbert transform followed by inverse Fourier transform of the high frequency content. The demodulated AC and DC images were compared with a reference standard to obtain the calibrated reflectance of each pixel in the image. Optical properties were calculated by interpolating a look-up table relating calibrated reflectance values to optical properties, which was generated by scaling of a single Monte Carlo simulation.^12,18

Fig. 2

Comparison of normalized images taken of the spatial pattern when the LEDs were individually illuminated without temporal modulation (top row) versus temporally demodulated images of each wavelength using the TM-SFDI system (bottom row). The images closely match, showing the ability of temporal demodulation to separate different wavelengths. The scale bar applies to all images.

2.3.

Accuracy and Drift

To test the accuracy of the TM-SFDI system, a set of 13 tissue mimicking phantoms with varying optical properties were imaged three times over 3 days with a commercial SFDI system (OxImager RS, Modulated Imaging, Inc.) at wavelengths of 526, 659, and 729 nm to establish the “gold standard” measurements of the phantom optical properties. The same set of phantoms was also imaged three times over 3 days with the TM-SFDI system at wavelengths of 519, 652, and 740 nm. Both systems used measurements of a reference standard with known optical properties for instrument response calibration. To account for variability in the TM-SFDI system, the reference standard was imaged five times per day and the temporally demodulated images were averaged together before being used to calculate ${\mu }_{\mathrm{a}}$ and ${\mu }_{\mathrm{s}}^{\prime }$ at each wavelength. Optical properties of the phantoms from both the commercial system and the TM-SFDI system were calculated using the same SSOP algorithm and compared against each other. Because the same wavelengths were not available for both systems, a correction factor was implemented to estimate the optical properties calculated by the commercial system at the wavelengths used in the TM-SFDI system. To construct the correction factor for ${\mu }_{\mathrm{a}}$, the absorption spectrum of nigrosin, the chromophore used to make the tissue mimicking phantoms, was measured using a spectrophotometer. The correction factor for absorption was defined as ${\mu }_{\mathrm{a}}({\lambda }_{\mathrm{TM}})=\frac{{\mu }_{\mathrm{a}}({\lambda }_{\mathrm{Com}})\epsilon ({\lambda }_{\mathrm{TM}})}{\epsilon ({\lambda }_{\mathrm{Com}})}$, where ${\mu }_{\mathrm{a}}({\lambda }_{\mathrm{TM}})$ is the estimated absorption coefficient at the TM-SFDI wavelength ${\lambda }_{\mathrm{TM}}$, ${\mu }_{\mathrm{a}}({\lambda }_{\mathrm{Com}})$ is the measured absorption coefficient at the wavelength of the commercial system (${\lambda }_{\mathrm{Com}}$), and $\epsilon (\lambda )$ is the extinction coefficient of nigrosin at the wavelength $\lambda$ measured with the spectrophotometer. To estimate how ${\mu }_{\mathrm{s}}^{\prime }$ changes with wavelength, we assumed a Rayleigh scattering (${\mu }_{\mathrm{s}}^{\prime }\propto {\lambda }^{-4}$) relationship and defined the correction factor as ${\mu }_{\mathrm{s}}^{\prime }({\lambda }_{\mathrm{TM}})=\frac{{\mu }_{\mathrm{s}}^{\prime }({\lambda }_{\mathrm{Com}}){\lambda }_{\mathrm{Com}}^{-4}}{{\lambda }_{\mathrm{TM}}^{-4}}$, where ${\mu }_{\mathrm{s}}^{\prime }({\lambda }_{\mathrm{Com}})$ is the reduced scattering coefficient calculated by the commercial system at ${\lambda }_{\mathrm{Com}}$. Rayleigh scattering was assumed because scattering in the phantoms is controlled by altering the concentration of titanium dioxide nanoparticles, the diameters of which are much smaller than the wavelengths of light used. The maximum change in optical properties using these correction factors was slightly over 5%. Each TM-SFDI scan consisted of 128 $2048\times 1536\text{pixel}$ images, with an FoV of $8.5\times 6.4\mathrm{cm}$. To improve the signal-to-noise ratio, the temporally demodulated images were downsampled using $2\times 2$ averaging.

To assess the stability of the TM-SFDI system, a single tissue mimicking phantom was scanned every 10 min for 2 h following a 30-min warm up period, and the variations in calibrated reflectance and optical properties at each wavelength over that time were calculated based on comparison with a reference standard imaged at the start and end of the drift test. Each scan consisted of 128 images.

2.4.

Effect of Ambient Light

To test the effect of ambient light on TM-SFDI, a calibration phantom was imaged in complete darkness. TM-SFDI videos were then acquired at various levels of ambient light controlled by changing the distance between the bulb of a standard desk lamp and the sample. Images of a single wavelength not modulated in time were also acquired to compare the TM-SFDI technique with the SSOP method.

3.1.

Accuracy

We found that there was a good agreement in optical property extractions between the gold standard commercial instrument and the proof-of-concept TM-SFDI system (Fig. 3). The average error in absorption between the TM-SFDI and the gold standard was 13%. The TM-SFDI system was more accurate at extracting reduced scattering, with an average error of 8% compared with the gold standard. The absorption measurements were biased, consistently underestimating the actual absorption coefficient by an average of $0.003{\mathrm{mm}}^{-1}$, while the scattering measurements were biased in the other direction, overestimating ${\mu }_{\mathrm{s}}^{\prime }$ by an average of $0.088{\mathrm{mm}}^{-1}$.

Fig. 3

Comparison of TM-SFDI with gold standard in terms of (a) scattering and (b) absorption. The identity line is shown in gray. Error bars indicate $\pm 1$ standard deviation of the average measured optical property across the 3 days. Acquisition time was 2.3 s for the TM system versus $\sim 30\mathrm{s}$ for the gold standard device.

In addition to homogeneous phantoms, a more complex tissue simulating phantom was imaged. The sample was a 3-D printed block of acrylonitrile butadiene styrene that featured a network of vascular like channels filled with a highly absorbing acrylic copolymer (P400SR, Stratasis, Inc.). The complex phantom was imaged with the TM-SFDI system, and a good correlation between the printed channel and the absorption map was noted (Fig. 4).

Fig. 4

(a) Photograph of the 3-D printed phantom with vessel-like inclusions under strong back illumination. (b) Temporally and spatially demodulated image of calibrated DC reflectance at 652 nm. (c) Map of the absorption coefficient and (d) map of the reduced scattering coefficient of the sample (d) at 652 nm. Scale bar applies to all images. Median filtering was used on panels (c) and (d) to remove artifacts.

3.2.

Drift

The drift of the TM-SFDI system was tested by allowing the system to warm up for 30 min and then repeatedly measuring the same phantom every 10 min for 2 h. The average changes in calibrated reflectance over this time period were less than 3% for the AC and DC components. However, these errors translated into a relatively large average variation in ${\mu }_{\mathrm{a}}$ of 13% about the mean. The average variation in ${\mu }_{\mathrm{s}}^{\prime }$ was 1%. There was no systematic rise or fall to the change but rather a random variation about the mean. To determine the source of the drift, we tested each LED individually with DC illumination and no temporal modulation and found a variation of 1% to 3% of output intensity over time. Though relatively small, this variation would also change the calibrated reflectance by the same 1% to 3%, which maps to a greater than 10% change in ${\mu }_{\mathrm{a}}$. The observed variation in optical properties is likely due to instability of the LEDs and driver electronics, which were both consumer grade. We expect that upgrading these components and implementing temperature control would reduce the variability in measured optical properties.

3.3.

Effect of Ambient Light

We found that the TM-SFDI system was almost entirely insensitive to the ambient light level. In Fig. 5, the calibrated reflectance for planar illumination is shown for SSOP (blue) and TM-SFDI (red) along with linear fits to the data at a variety of ambient light levels. The slope of the linear fit of the TM-SFDI DC reflectance was not significantly different from zero ($p=0.5$) using a two sided $t$-test, indicating that there was no relationship between ambient light level and calibrated reflectance. The change in calibrated reflectance using SSOP would result in extremely large errors in optical properties as ambient illumination changed. Future instruments using TM-SFDI will need to avoid frequencies near the AC power supply (typically 50 or 60 Hz) to avoid contamination from the flickering of room lights.

Fig. 5

Temporally modulated (blue) SFDI compared with single shot SFDI (red) under varying levels of ambient light. TM-SFDI is largely insensitive to the ambient light level while SSOP is highly sensitive. Error bars represent $\pm 1$ standard deviation of the pixels in the image.

3.4.

Discussion

The TM-SFDI system presented here allows for the rapid acquisition of diffuse optical images. At $56\text{frames}/\mathrm{s}$ and a typical video length of 128 frames, we were able to capture spectroscopic images of optical properties at three wavelengths in 2.3 s. The number of simultaneous wavelengths that can be collected is limited by the number of video frames acquired. The maximum number of wavelengths that can be unambiguously demodulated is no more than one per FFT bin (excluding DC). This means that a 128 frame scan could theoretically support 63 wavelengths, while a 256 frame scan could support 127, although practically, this number of wavelengths may be reduced due to spectral leakage. We experimented with using fewer video frames (64, 32, 16, etc.) and found an increased scan-to-scan variability. Using 64 images, there were only modestly higher errors (10% in scattering and 24% in absorption), meaning acquisition speeds of around 1 s with reasonable errors are possible. Since the maximum frame rate of the camera increases when fewer CCD lines need to be read, using a smaller FoV could also increase acquisition speed. For an image of $512\times 512\text{pixels}$, it would be possible to increase the frame rate from 55.6 to 80 fps, resulting in a minimum acquisition time of 800 ms for up to 16 wavelengths.

Recent work has utilized a similar temporal modulation of excitation wavelengths for single pixel SFDI.¹⁹ Despite advantages in simplicity of hardware, cost, and bandwidth, single pixel imaging scales poorly with resolution, requiring the projection of over 31,000 patterns for each spatial frequency and phase to acquire an image with a comparable number of pixels used in this study. For example, Torabzadeh et al.¹⁹ used single-pixel SFDI to acquire 400 samples in 80 ms, meaning a single high resolution image could be collected every 6.2 s. While a large number of pixels is not strictly necessary for low-resolution diffuse imaging, it allows for pixel binning to reduce the overall noise level. Greater numbers of pixels would also allow for the possibility of imaging larger FoVs without impacting resolution.

The TM-SFDI system has several limitations worth noting. The first is variability in ${\mu }_{\mathrm{a}}$ extractions. The errors in absorption are likely due to the fact that, at the chosen spatial frequencies, small changes in reflectance map to large changes in ${\mu }_{\mathrm{a}}$, meaning that the effects of noise and LED instability are amplified.⁴ It is likely that temperature variations of the LEDs and driver circuit led to instability of the LED output and resulted in uncertainty in the absorption estimates. We also found that the estimates for optical properties were biased with the absorption being underestimated and the scattering overestimated. We believe both biases are due to broadband noise contaminating the images, resulting in small, systematic errors in diffuse reflectance as well as nonlinearities in system response, which are not accounted for in the calibration step and result in increased errors for samples with optical properties that differ significantly from the calibration phantom. It is likely that improvements in the signal-to-noise ratio and careful choice of calibration phantom will help resolve this issue. Second, the acquisition time of 1 to 2 is relatively long compared with the SSOP method, and the sample must be held motionless for that entire time to achieve a clear image of the resulting optical properties. This could potentially be solved by adding an image registration step to align the frames of the video prior to processing. Third, although scans can be performed relatively quickly, processing of the data requires significant computational resources. Each scan requires over 300,000 FFTs to be performed as well as searching a nonlinear look-up-table for each pixel at each wavelength. On a relatively modern desktop computer (Intel i7-6700, 16 GB RAM), the time to process each scan was about 80 s. However, much of the processing is parallelizable and could likely be vastly sped up by offloading to a graphics processing unit.