Halftone spatial frequency domain imaging enables kilohertz high-speed label-free non-contact quantitative mapping of optical properties for strongly turbid media

Quantifying optical absorption and scattering in strongly turbid media is crucial for characterizing biological tissues and fluid fields. From absorption spectra, concentrations of structural and functional components (e.g., oxy-hemoglobin, deoxy-hemoglobin, water, lipids) can be computed via Beer's law, and their dynamics are hallmarks of physiological and disease states such as oxygenation, metabolism, cardiovascular disease, inflammation, diabetes, and cancer. In combustion flows, high-speed quantitative imaging of turbid media is important for aeronautical and astronautical engine design. However, photon scattering complicates direct measurement over macroscopic length scales, making wide-field, non-contact, and especially high-speed quantitative imaging challenging. Existing approaches either lack quantitative separation of absorption and scattering or are too slow for dynamic processes. This work addresses the need by introducing halftone-SFDI, enabling wide-field, label-free, non-contact quantitative mapping of optical properties at kilohertz rates.

Photoacoustic imaging can probe absorbers such as hemoglobin but cannot independently quantify absorption and scattering. Hyperspectral imaging is accessible but cannot reliably separate chromophore concentrations due to confounding absorption and scattering effects. Diffuse optical spectroscopy (DOS) and other diffuse optical techniques in the frequency or time domain separate absorption and scattering using modulated illumination and model-based analysis (e.g., diffusion approximation or Monte Carlo). Once absorption is measured at multiple wavelengths, chromophore concentrations can be solved from known extinction spectra using Beer's law. However, DOS is typically point-based, requires contact, and is slow for imaging (e.g., 10–20 minutes for 20×20 pixels, ~10^-3 Hz). Prior to this work, no diffuse optical technique provided kilohertz high-speed wide-field quantitative optical property mapping.

The proposed halftone spatial frequency domain imaging (halftone-SFDI) builds on SFDI but replaces 8-bit continuous-tone projection with 1-bit halftone binary patterns to exploit the maximum digital micromirror device (DMD) rate. Conventional SFDI uses 8-bit sinusoidal projections limited to ~290 Hz and requires 5 patterns per wavelength (DC illumination, dark frame, and three phase-shifted patterns at 0°, 120°, 240°). Halftone-SFDI converts these to 1-bit halftone patterns, increasing the maximum projection rate to ~23 kHz (~80× speedup) without hardware changes. The imaging setup projects the binary patterns via a DMD and projection lens onto the sample; a synchronized camera records remitted light. Cross-polarizers minimize specular reflection. Data processing includes demodulation of phase-shifted images and calibration using a phantom with known properties to obtain diffuse reflectance R at selected spatial frequencies. Optical properties (absorption μa and reduced scattering μs′) are extracted pixel-wise by mapping the calibrated diffuse reflectance at two spatial frequencies (e.g., 0 and 0.1 mm^-1) to μa and μs′ using a pre-computed Monte Carlo look-up table (LUT). The LUT is generated from Monte Carlo simulations of photon propagation, providing a unique mapping from measured R(0), R(0.1 mm^-1) to μa and μs′. Validation studies:

• Phantom study: 16 optical phantoms spanning μa = 0.005–0.04 mm^-1 and μs′ = 0.3–2 mm^-1. Diffuse reflectance measured at spatial frequencies 0, 0.05, 0.1, 0.2, and 0.4 mm^-1 at wavelengths 650–850 nm (50 nm steps). Optical properties extracted using the 0 and 0.1 mm^-1 combination.
• In vivo human tissue: Human hand imaged at 650–850 nm with spatial frequencies 0 and 0.1 mm^-1; μa and μs′ maps derived and hemoglobin concentrations computed from absorption spectra via Beer's law.
• In vivo rat cortex: Under ~2% isoflurane with a cranial window (exposed cortex ~11×7 mm). Imaged at 15 Hz using wavelengths 685 and 850 nm and spatial frequencies 0 and 0.1 mm^-1; speed limited by available near-infrared camera. The approach also supports kilohertz dual-wavelength monitoring, demonstrated for a dynamic flow field.

• Speed: Converting 8-bit sinusoidal patterns to 1-bit halftone increases maximum DMD projection rate from 290 Hz to 23 kHz (~80×), enabling kilohertz-rate quantitative mapping.
• Turbid media low-pass filtering ensures halftone-projected binary discontinuities do not appear in recorded images, preserving measurement fidelity.
• Phantom validation (16 phantoms; 650–850 nm; spatial frequencies 0–0.4 mm^-1):
  • Diffuse reflectance agreement across five spatial frequencies: percent difference 0.7 ± 0.9% (halftone-SFDI vs. continuous-tone SFDI).
  • Optical absorption μa: percent difference -1.6 ± 1.8%; measurement noise level 2.5%.
  • Reduced scattering μs′: percent difference 0.6 ± 0.6%; measurement noise level 1.3%.
• In vivo human hand (650–850 nm; 0 and 0.1 mm^-1):
  • Average μa percent difference 3.0 ± 0.9%; average μs′ percent difference -1.0 ± 0.3% (maps visually identical between methods).
  • Chromophore mapping from absorption spectra: HbO2 percent difference 1.9 ± 8.6% (noise 4.2%); HHb percent difference 4.8 ± 8.0% (noise 7.6%).
• In vivo rat cortex: Demonstrated quantitative hemodynamics monitoring at 15 Hz using two wavelengths; method supports kilohertz dual-wavelength monitoring as shown in a dynamic flow field experiment.

The study demonstrates that halftone-SFDI achieves quantitative equivalence to conventional continuous-tone SFDI while increasing projection speed by approximately two orders of magnitude. By leveraging the low-pass spatial filtering inherent to turbid media, 1-bit halftone patterns yield reflectance measurements indistinguishable from continuous-tone patterns, enabling rapid acquisition without sacrificing accuracy. The Monte Carlo LUT-based inversion from two spatial frequencies provides robust extraction of μa and μs′ across a broad range of optical properties. Validation on diverse phantoms and in vivo human tissue shows differences well within measurement noise, and derived chromophore concentrations agree closely. Application to rat cortex hemodynamics and kilohertz mapping of a dynamic flow field underscores the method’s potential for real-time, wide-field, label-free, non-contact quantification in biomedicine (e.g., brain functional monitoring) and engineering (e.g., combustion and fluid dynamics).

Halftone-SFDI introduces a 1-bit halftone projection strategy to SFDI, increasing projection speed from ~290 Hz to ~23 kHz and enabling kilohertz, wide-field, label-free, non-contact quantitative imaging of optical properties in strongly turbid media. Using Monte Carlo LUT inversion with two spatial frequencies, the method yields μa and μs′ values that agree with conventional SFDI within noise levels, and supports accurate chromophore quantification. Demonstrations include validation on a wide range of optical phantoms, in vivo human tissue measurements, rat cortex hemodynamics monitoring, and kilohertz dual-wavelength mapping of a dynamic flow field. Future research directions include extending in vivo applications to fully exploit kilohertz speeds with high-speed cameras, expanding wavelength sets for multiplexed chromophore mapping, optimizing spatial frequency selections for different tissues and media, and integrating real-time processing for closed-loop biomedical and engineering studies.

Although the method enables kilohertz projection rates, the in vivo rat cortex demonstration operated at 15 Hz due to limitations of the available camera, indicating that overall system speed may be constrained by detector hardware. The approach relies on calibration using phantoms with known properties and a pre-computed Monte Carlo LUT; accuracy depends on calibration quality and model assumptions. The optical property inversion in this study primarily used two spatial frequencies (0 and 0.1 mm^-1), which are effective for many tissues but may require adjustment for other sample types.