  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. Each
label-free method has specific benefits, drawbacks, and varied varied
sensitivity under measurement conditions across different types of specimens.
To link all these disparate label-free optical interactions together and to
compare detection sensitivity of these modalities, we investigate their
sensitivity within the framework of statistical estimation theory. This paper
introduces a comprehensive unified framework for evaluating the bounds for
signal detection with label-free microscopy methods, including second harmonic
generation (SHG), third harmonic generation (THG), coherent anti-Stokes Raman
scattering (CARS), coherent Stokes Raman scattering (CSRS), stimulated Raman
loss (SRL), stimulated Raman gain (SRG), stimulated emission (SE), impulsive
stimulated Raman scattering (ISRS), transient absorption (TA), and photothermal
effect (PTE). A general model for signal generation induced by optical
scattering is developed. Based on this model, the information obtained is
quantitatively analyzed using Fisher information, and the fundamental
constraints on estimation precision are evaluated through the Cram\'er-Rao
Lower Bound (CRLB).
