Longitudinal (z) Displacement and Motion

LightLike has no facility for representing longitudinal motion comparable to the modules provided for representing transverse motion.  In most LightLike applications of interest, the longitudinal component of motion does not produce any noticeable change to the measured quantities of interest: it is only the transverse components of the physical velocities that generate the turbulence-related time dependences of modeling interest.  The longitudinal components are insignificant because of the combination of the relatively large propagation distances involved, and the relatively short time spans over which we need to perform the wave-optics simulation.  These approximations are tied to the conventional way in which the frozen turbulence approximation is applied to optical turbulence calculations.

There are several limitations to this physical model.  The first limitation has nothing to do with turbulence, but arises simply because various magnification factors change if the distance changes significantly during the simulation time.  A second limitation is that, as the motion progresses, phase screens nearest the target or platform should drop out of the problem when that part of the air mass is no longer between the platform and target.  Modeling such changes may become important, for example, in simulating a long-enough engagement against a nearby missile moving more or less directly at the platform.  At present, if such effects are important in a LightLike simulation, the user must break up the problem into time segments such that the z-range can be treated as approximately constant during each segment.

Despite the absence of longitudinal-motion library modules, there is a significant aspect of longitudinal motion thatcan be modeled in LightLike.  Depending on the range and time scales involved, the principal effect of longitudinal motion may be a Doppler shift.  A physical example is the problem of remote Doppler vibrometry through a turbulent medium.  In problems of this type, we can model the longitudinal motion in terms of temporally-varying phase shifts.  This produces effects such as walking fringes, for example, and LightLike does contain modules that can generate these effects.  An auxiliary document contains a detailed explanation of how to model such effects in LightLike.  The auxiliary document also discusses in general the extent to which the interference of polychromatic fields can be modeled in LightLike.