# Sensitivity studies for imaging a spherical object embedded in a spherically symmetric,
two-layer turbid medium with photon-density waves

### Y. Yao *et al.* (1996)

#### Summary

We present analytic expressions for the amplitude and phase of phase of photon-density waves
in strongly scattering, spherically symmetric, two-layer media containing a spherical object.
This layered structure is a crude model of multilayered tissues whose absorption and scattering
coefficients lie within a range reported in the literature for most tissue types. The embedded
object simulates a pathology, such as a tumor. The normal-mode-series method is employed to
solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary
conditions. By comparing the total field at points in the outer layer at a fixed distance from
the origin when the object is present and when it is absent, we evaluate the potential
sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For
four types of background media with different absorption and scattering properties, we determine
the modulation frequency that achieves an optimal compromise between signal-detection reliability
and sensitivity to the presence of an object, the minimum detectable object radius, and the
smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our
results indicate that (1) enhanced sensitivity to the object is achieved when the outer layer is
more absorbing or more scattering than the inner layer; (2) sensitivity to the object increases
with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude
measurements are proportionally more sensitive to a change in absorption, phase measurements are
proportionally more sensitive to a change in scattering, and phase measurements exhibit a much
greater capacity for distinguishing an absorption perturbation from a scattering perturbation.