Statistical estimation theory detection limits for label-free imaging.

Significance: The emergence of label-free microscopy techniques has significantly improved our ability to precisely characterize biochemical targets, enabling non-invasive visualization of cellular organelles and tissue organization. However, understanding each label-free method with respect to the specific benefits, drawbacks, and varied sensitivities under measurement conditions across different types of specimens remains a challenge.

Aim: We link all of these disparate label-free optical interactions together and compare the detection sensitivity within the framework of statistical estimation theory.

Approach: To achieve this goal, we introduce a comprehensive unified framework for evaluating the bounds for signal detection with label-free microscopy methods, including second-harmonic generation, third-harmonic generation, coherent anti-Stokes Raman scattering, coherent Stokes Raman scattering, stimulated Raman loss, stimulated Raman gain, stimulated emission, impulsive stimulated Raman scattering, transient absorption, and photothermal effect. A general model for signal generation induced by optical scattering is developed.

Results: Based on this model, the information obtained is quantitatively analyzed using Fisher information, and the fundamental constraints on estimation precision are evaluated through the Cramér-Rao lower bound, offering guidance for optimal experimental design and interpretation.

Conclusions: We provide valuable insights for researchers seeking to leverage label-free techniques for non-invasive imaging applications for biomedical research and clinical practice.