8.1. INTRODUCTION

Ideally, ballistic imaging is based on unscattered or singly backscattered ballistic
photons. In reality, however, more-scattered quasiballistic photons are often measured
as well to increase the signal strength. For brevity, subsequent use of the
term ballistic photons in this chapter also refers to quasiballistic photons unless
otherwise noted. Ballistic imaging provides high spatial resolution but suffers
from limited imaging depth.

8.2. CHARACTERISTICS OF BALLISTIC LIGHT

The intensity of unscattered light I_T attenuates according to Beer’s law:

Here, z denotes the ballistic path length in the scattering medium, μ_t denotes
the extinction coefficient, and I₀ denotes the fluence rate of the incident light
if specular reflection is negligible. The intensity of singly backscattered light is
given by

where R_bdenotes the percentage of the backscattered light to be received by the
detector, and the factor of 2 in the exponent is due to round-trip propagation. In
both cases, the strictly ballistic signals decay exponentially with the path length.

The objective of ballistic imaging is to reject nonballistic photons and to retain
ballistic photons on the basis of the following characteristic differences between
them:

1. Time of Flight. Transmitted ballistic photons take shorter paths and arrive
   at the detector earlier than do nonballistic photons. Time-gated imaging
   and coherence-gated holographic imaging are based on this difference.
2. Collimation. Transmitted ballistic light has better collimation (smaller
   divergence) than does nonballistic light. Spatial-frequency filtered imaging
   and optical heterodyne imaging are based on this difference.
3. Polarization. Ballistic light retains the incident polarization in a nonbirefringent
   scattering medium better than does nonballistic light. Polarizationdifference
   imaging is based on this difference.
4. Wavefront. Ballistic light possesses a better-defined wavefront than does
   nonballistic light and hence can be better focused. Confocal microscopy and
   two-photon microscopy are based on this difference. Note that wavefront
   and collimation are related.