Assessing Absorption and Scattering in a Diffuse Phantom Using FD-NIRS and MATLAB-Based Slope Analysis

Abstract

In this lab report we employed frequency-domain near-infrared spectroscopy (FD-NIRS) to characterize optical properties of a diffuse optical phantom, demonstrating multi-distance scanning configuration for optical property recovery method. Utilizing a linear slope optical property retrieval method, with 690 nm and 830 nm wavelengths, we extracted absorption (μₐ) and reduced scattering (μ’s) coefficients. We visualized a diffuse reflectance obtained from our measurements, where the amplitude of this is the intensity (AC) measurement and the phase is the phase measurement. Then we extracted the slope of the linearized intensity and phase as a function of source-detector distance as needed to extract absolute optical properties. We found that absorption was higher at 830 nm (μₐ ≈ 0.00110 mm⁻¹) compared to 690 nm (μₐ ≈ 0.00074 mm⁻¹), while scattering was greater at 690 nm (μ’s ≈ 0.4914 mm⁻¹) than 830 nm (μ’s ≈ 0.3529 mm⁻¹). MATLAB scripts, provided with the measurement data, were used for all processing and visualization, enabling precise characterization of the phantom's optical properties and validating the FD-NIRS technique.

Introduction

The history of using diffuse optics and near-infrared light to measure the oxygen content of blood can be traced back to the late 1860s when Felix Hoppe-Seyler from Germany demonstrated that optical absorption changed when blood was mixed with oxygen. Further experiments into noninvasive pulse oximetry and the construction of instruments to measure blood oxygenation began in the late 1920s and 1930s. It wasn’t until 1974, when Takuo Aoyagi and the Nihon Kohden Corporation introduced the first commercial pulse oximeter, that doctors were able to easily measure saturated blood oxygen without the need for sampling. Later, in 1977, Frans Jöbsis published a paper that is universally cited as the study that introduced the use of near-IR light for brain imaging1. Today, near-IR light is continually used in brain imaging studies, as well as pulse oximeters in doctors offices around the globe.

Diffuse optics is a class of methods that involves measuring tissue optical properties noninvasively and nondestructively with near-infrared light. This method is reliant on the property that biological tissue and hemoglobin is least absorbing in the red or near-infrared spectrum.This type of spectroscopy is typically performed in the wavelength range from about 600 nm to 1000 nm.2 The instrumentation involved is lightweight and compact, making it ideal for use in every-day settings, worn by subjects while engaged in normal activities, in hospitals, at the bedside, any anywhere there might be a medical need3. The ease of use and wide variety of applications makes diffuse optics an ideal method for operation in food science, pharmaceutical manufacturing, archaeological soil analysis, art authentication, medical diagnostics, and physiological monitoring, among others2.

Biological tissue is defined as an optically diffuse medium, or a medium in which light is moved about by randomly changing the direction it is travelling. The measurement of diffuse optics can be defined by the absorption coefficient (μa) – the absorption probability per unit distance traveled by a photon – and the reduced scattering coefficient (μ′s) – the diffusion of photons in a medium. There are three domains of diffuse optics: continuous wave, frequency domain, and time domain. Continuous wave optics measures the change in intensity of plain light that is always on. Time domain optics measures the change in intensity as a function of the time of a light pulse. This lab focuses on frequency domain diffuse optics, which measures the change in intensity and phase of light oscillated at ~MHz.4 A phantom matrix was used to imitate human tissue for imaging and analysis purposes.

This report begins with an overview of the mechanisms of diffuse optics, followed by the measurement and analytic methods used in this lab. Results and associated quantitative and qualitative analyses are presented. Key findings, limitations, and advantages of this lab are summarized in the conclusion.

Background

In frequency-domain near-infrared spectroscopy (FD-NIRS), absolute optical properties can be measured from a turbid sample using the zero-boundary version of diffuse reflectance and the linear slopes method. In this framework, the light distribution in tissue is described in terms of fluence rate (𝜙), which represents the optical energy that flows per unit time per unit area along all possible directions at a given time and position. In this technique, the light source emits a power that is sinusoidally, temporally modulated at a frequency and the fluence rate resulting from a point source embedded in a homogeneous, infinite medium is calculated by:

In this equation, PFD(𝑤) is the amplitude of the optical power emitted from the source, and 𝑤 is the angular frequency that the optical power is sinusoidally modulated at. The expressions for the AC and phase components of the fluence rate are:

These expressions show that the phase and AC of the fluence rate depend on source-detector distance r, the modulation frequency of the source power 𝑤, and the absolute optical properties of the source medium itself. The properties of the source media are described as the absorption coefficient 𝜇a and the reduced scattering coefficient 𝜇’s. 

Because the matrix we are measuring is considered a homogenous medium, the linearized amplitude or intensity (I)(lnｐ2 I) and the phase (𝜙) are linear with respect to r. Source power, optical coupling, and coupling efficiency all affect the intercepts of these functions. For a fixed modulation frequency, the slopes of these lines are sensitive solely to the optical properties of the medium. 

Inverting these expressions can be done to solve for both the absorption and reduced scattering coefficients. In these equations, SӨ is the slope of the phase as a function of r, SAC is the slope of the linearized intensity as a function of r, and c is the speed of light in a vacuum. 

Methods

This lab utilized frequency-domain near-infrared spectroscopy (FD-NIRS) to extract the absolute optical properties of a silicone-based phantom designed to mimic biological tissue. The experimental setup involved a single fixed detector fiber and two co-localized source fibers. These were scanned across eleven positions using a linear stage to generate a multi-distance measurement range of 20 mm to 30 mm in 1 mm increments. At each position, measurements of amplitude (AC) and phase shift were collected at two wavelengths (690 nm and 830 nm) over a 30-second acquisition period. Proper optical contact was ensured by adjusting the vertical position of the fibers.

Data collection was managed through a graphical user interface (GUI), which allowed fine-tuned control of detector position and gain. Markers were automatically logged to indicate the start and end of each source-detector configuration. Following acquisition, the data were processed in MATLAB. Time-resolved plots of AC and phase data were first generated and segmented using the inserted markers to isolate each distance-specific measurement.

For each source-detector separation, the AC and phase data were averaged. The AC measurements were then transformed using the linearized intensity form ln(ρ2I), and both these values and the phase data were plotted as a function of distance. Linear regressions were used to extract the slopes of these relationships. The equations previously outlined in the background section were then used to calculate the absorption coefficient (μₐ) and reduced scattering coefficient (μ′ₛ) at each wavelength, using the derived slopes and known parameters such as the modulation frequency, speed of light, and refractive index of the medium.

All processing and visualization were conducted in MATLAB using scripts provided alongside the measurement data. These methods enabled characterization of the phantom’s optical properties with high precision, validating the FD-NIRS technique in a controlled environment.

Results and Analysis

As calculated in Matlab and visualized in the Figure 4 graphs above, the slopes are as follows:

Slope of ln(ρ² × Intensity) at 830 nm: −0.0534 per mm

Slope of ln(ρ² × Intensity) at 690 nm: −0.0603 per mm

Slope of Phase at 830 nm: +0.0410 radians/mm

Slope of Phase at 690 nm: +0.0505 radians/mm

The slope of the phase data is positive, while the slope of the linearized intensity data is negative, due to the different ways in which these measurements respond to increasing source-detector distance. As the distance between the source and detector increases, photons must travel longer paths through the scattering medium. This increased path length results in greater attenuation of the detected light intensity, since more photons are absorbed or scattered away from the detector. Consequently, the detected amplitude decreases, and the natural logarithm of the intensity (after being scaled by the square of the distance) shows a decreasing linear trend, leading to a negative slope. In contrast, the phase data reflects the average delay or shift in the photon-density wave as it travels through the tissue. As photons take longer and more circuitous paths at greater distances, the phase delay accumulates, resulting in an increasing phase value. This relationship produces a positive linear slope when phase is plotted against distance. Together, these complementary trends enable the extraction of the absorption and scattering properties of the medium.

The absolute optical properties calculated for the phantom revealed notable wavelength-dependent differences. At 830 nm, the absorption coefficient (μₐ) was found to be approximately 0.00110 mm⁻¹, while at 690 nm it was lower, at approximately 0.00074 mm⁻¹. This indicates that absorption is higher at the longer wavelength. Conversely, the reduced scattering coefficient (μₛ′) was greater at the shorter wavelength: approximately 0.4914 mm⁻¹ at 690 nm, compared to 0.3529 mm⁻¹ at 830 nm. These trends are consistent with the known optical behavior of biological tissues and tissue-mimicking phantoms. Specifically, scattering typically decreases with increasing wavelength due to reduced interaction between photons and microstructures at longer wavelengths. Meanwhile, absorption can vary depending on the chromophores present in the medium. In this case, the phantom was designed to mimic tissue properties using absorbers like India ink, and its absorption profile aligns with the general behavior of hemoglobin, which has relatively lower absorption in the near-infrared region but shows a slight rise near 830 nm. These results support the effectiveness of the FD-NIRS technique in resolving wavelength-dependent optical characteristics of turbid media.

Conclusion

Diffuse optics relies heavily on understanding light-tissue interactions, in which light undergoes many scattering events, behaving like a random walk. The combination of absorption, scattering, geometry and domain choice defines the system’s capability for non-invasive optical characterization, with implications for medical diagnostics and physiological measurements. In this lab report, we utilize the frequency-domain near-infrared spectroscopy (FD-NIRS) which employs intensity-modulated light and phase-sensitive optical detection, which has two degrees of freedom: intensity (amplitude) and phase. By systematically varying the source-detector separation we analyzed the amplitude and phase data at two discrete wavelengths (690 nm and 830 nm), which revealed higher absorption at 830 nm and greater scattering at 690 nm. Overall, this lab allowed us to measure the absolute optical properties of diffuse optical phantoms in the frequency-domain using the linear slopes optical property recovery method. By the end of this lab we were able to gain both technical and conceptual insight into quantitative tissue optics with a particular focus on frequency-domain diffuse optical measurements using a multi-distance scanning configuration.

Author Contributions: KS, JRS, and MZ equally contributed to the conceptualization, methodology, investigation, and drafting of the manuscript. JRS was responsible for coding and data analysis in MATLAB. JRS and MZ led the revision and editing process, while KS coordinated the final submission. MS provided guidance, supervision, and project oversight. All authors reviewed and approved the final version of the report.

Funding: This work was supported by the Tufts University School of Engineering and made possible through the use of facilities at the Diffuse Optical Imaging of Tissue (DOIT) Lab. We thank both institutions for providing access to the equipment and resources as part of the BME-0156: Biophotonics Laboratory course.

Acknowledgments: We extend our sincere gratitude to Dr. Maria Savvidou, Postdoctoral Researcher in the Department of Biomedical Engineering at Tufts University, for her mentorship, guidance, and support throughout the project, especially in advising and assisting with laboratory data collection. We also thank Jodee Frias, EG’2G, for her generous technical support with both software and hardware during the lab sessions, as well as for compiling the experimental data.

Conflicts of Interest: The authors declare no conflict of interest.

References

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