
Spectroscopy applied to real-time biological imaging and medical diagnostics.Biomedical spectroscopy uses the interaction of light with biological tissues to obtain diagnostic information without invasive procedures. It encompasses a range of techniques, from Raman and fluorescence spectroscopy to optical coherence tomography, that can reveal the chemical composition, structure, and function of cells and tissues in real time. This field is transforming medicine by enabling early disease detection, image-guided surgery, and personalized treatment monitoring.
The roots of biomedical spectroscopy go back to the 19th century with the discovery of the absorption spectrum of hemoglobin. However, the modern era began in the 1970s and 1980s with the development of fiber-optic probes and sensitive detectors, which allowed in vivo measurements. The field has since grown rapidly with the advent of new laser sources and computational methods.
Different molecules absorb, scatter, or emit light at characteristic wavelengths. By shining light on a tissue and analyzing the spectrum of the returned light, one can identify specific biomolecules, such as hemoglobin, water, lipids, or proteins, and their concentrations. Advanced techniques like diffuse optical spectroscopy use multiple source-detector distances to map these concentrations in three dimensions, while time-resolved methods can separate absorption from scattering to probe deeper into the tissue.
Biomedical spectroscopy is used in clinical settings for non-invasive blood glucose monitoring, cancer detection during endoscopy, and real-time assessment of tissue oxygenation during surgery.
The technique of Raman spectroscopy can identify a single molecule by its unique vibrational fingerprint, which is why it is sometimes called 'molecular fingerprinting'.
| X_n | variable | random variable indexed by n — random variable |
| d_s | variable | spectral dimension — spectral dimension |
| Var | operator | statistical variance of a random variable — variance |
| ~ | operator | asymptotically proportional to (up to a constant factor) — asymptotic equivalence |
| f | operator | some function of the spectral dimension — function |
| B | variable | bispectrum — bispectrum cubic metre |
| k_1 | variable | first wavenumber — wavenumber reciprocal metre |
| k_2 | variable | second wavenumber — wavenumber reciprocal metre |
| k_3 | variable | third wavenumber — wavenumber reciprocal metre |
| \Delta | variable | spectral tilt — dimensionless |
| \omega | variable | oscillation frequency in log space — dimensionless |
| \propto | operator | indicates the left side equals the right side times a constant factor — proportionality |
| \ln | operator | logarithm to base e — natural logarithm |
| \cos | operator | trigonometric cosine — cosine |













