2.3 Light scattering, absorption, and reflection in biological media

Light scattering, absorption, and reflection shape how light interacts with biological tissues. These processes determine how far light penetrates, where it goes, and what information we can gather from it. Understanding these interactions is crucial for developing effective optical diagnostic and therapeutic techniques in medicine.

Rayleigh and Mie scattering explain how particles of different sizes affect light's path. The Beer-Lambert law describes light absorption, while reflection and transmission coefficients quantify how light behaves at tissue interfaces. These concepts form the foundation for interpreting optical signals from biological systems.

Scattering Mechanisms

Rayleigh and Mie Scattering

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  Limits of Resolution: The Rayleigh Criterion | Physics View original

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• Rayleigh scattering occurs when light interacts with particles much smaller than its wavelength
  • Intensity of scattered light proportional to the inverse fourth power of the wavelength ($I \propto \frac{1}{\lambda^4}$)
  • Explains why the sky appears blue (shorter wavelengths scattered more)
  • Predominant in gases and very small particles (dust, smoke)
• Mie scattering takes place when particle size comparable to or larger than the wavelength of light
  • More uniform scattering across wavelengths
  • Responsible for the white appearance of clouds and milk
  • Applies to larger particles in biological tissues (cell organelles, collagen fibers)
• Scattering efficiency depends on the ratio of particle size to wavelength
  • Rayleigh scattering dominates when particle size << wavelength
  • Mie scattering becomes significant as particle size approaches wavelength

Multiple Scattering and Its Effects

• Multiple scattering occurs when light undergoes repeated scattering events in a medium
  • Common in biological tissues due to their complex structure
  • Results in diffuse light propagation
• Effects of multiple scattering on light propagation
  • Increases effective optical path length
  • Reduces directionality of light
  • Complicates analysis of light-tissue interactions
• Modeling multiple scattering
  • Radiative transfer theory used to describe light propagation in scattering media
  • Monte Carlo simulations often employed to model complex scattering scenarios

Absorption and Transmission

Beer-Lambert Law and Its Applications

• Beer-Lambert law describes the attenuation of light as it passes through an absorbing medium
  • Expressed as $I = I_0 e^{-\mu_a d}$, where I is transmitted intensity, I_0 is incident intensity, μa is absorption coefficient, and d is path length
  • Assumes negligible scattering and homogeneous absorption
• Applications of Beer-Lambert law in biophotonics
  • Determination of chromophore concentrations (hemoglobin, melanin)
  • Spectrophotometry for quantitative analysis of solutions
  • Basis for many optical sensing techniques (pulse oximetry)
• Limitations of Beer-Lambert law in biological tissues
  • Scattering often significant, leading to deviations from the law
  • Inhomogeneities in tissue composition affect absorption

Optical Path Length and Its Significance

• Optical path length represents the effective distance light travels through a medium
  • Influenced by refractive index and physical path length
  • Expressed as $OPL = n \cdot d$, where n is refractive index and d is physical path length
• Importance of optical path length in biophotonics
  • Determines the extent of light-tissue interactions
  • Affects the depth of penetration of light in tissue
  • Critical for designing optical imaging and sensing systems
• Factors influencing optical path length in biological media
  • Tissue structure and composition
  • Wavelength of light
  • Scattering properties of the medium

Reflection and Transmission Coefficients

Reflection and Transmission at Interfaces

• Reflection coefficient (R) quantifies the fraction of incident light intensity reflected at an interface
  • Calculated using Fresnel equations
  • Depends on refractive indices of media and angle of incidence
  • For normal incidence: $R = (\frac{n_1 - n_2}{n_1 + n_2})^2$, where n1 and n2 are refractive indices
• Transmission coefficient (T) represents the fraction of incident light intensity transmitted through an interface
  • Related to reflection coefficient by T = 1 - R (for non-absorbing media)
  • Crucial for understanding light penetration into tissues
• Applications of reflection and transmission coefficients
  • Designing optical coupling systems for medical devices
  • Optimizing light delivery in phototherapy
  • Analyzing tissue-air interfaces in optical imaging

Diffuse Reflectance and Its Implications

• Diffuse reflectance occurs when light is scattered multiple times before exiting a medium
  • Characteristic of many biological tissues
  • Results in a more uniform angular distribution of reflected light
• Factors influencing diffuse reflectance
  • Scattering properties of the medium (scattering coefficient, anisotropy factor)
  • Absorption properties of the medium
  • Tissue structure and composition
• Applications of diffuse reflectance in biophotonics
  • Non-invasive tissue characterization
  • Optical diagnosis of skin conditions
  • Monitoring of tissue oxygenation and perfusion
• Modeling diffuse reflectance
  • Diffusion approximation often used for highly scattering media
  • Monte Carlo simulations provide more accurate results for complex geometries