Transverse Displacement and Size of Propagation Mesh

An important feature of LightLike is that the required size of the optical propagation mesh is, in one important aspect, decoupled from the transverse displacement or motion of sources and sensors.  This feature is closely connected with LightLike's methods of modeling overall wavefront tilt.  Before continuing with the present section, the reader should quickly review the previous section on tilt modeling, whose essentials form the background for the present section.

Consider again one of the LightLike systems used previously to illustrate transverse motion and slew.  Suppose that:

(a)  the transmitter-receiver z-separation is 100 km, and the receiver velocity relative to the transmitter is vRy = +100m/s;

(b)  the aperture radii of both the Gaussian laser and the receiver telescope are 0.5 m;

(c)  at t = 0, the receiver and transmitter local origins have zero transverse offset (x0 = 0 = y0 in both TransverseVelocity modules);

(d)  we wish to simulate the receiver signals until t = 0.1s .

At the end of this time interval, the target subsystem center will have a y-offset of 10 m and 100 mrad relative to the source center.  In accordance with LightLike's modeling of overall wavefront tilt, the transmitter-end Slew module does not multiply the exiting complex field by a tilt phasor.  Therefore, it is not necessary for the optical propagation mesh to sample the 100 mrad initial tilt or to contain the 10-m final offset between source and sensor.  It is only necessary for the propagation mesh to satisfy the sampling requirements of the zero-offset geometry.  The zero-offset mesh equirements are influenced by the transmitter and receiver aperture diameters, the propagation distance, the wavelength, the integrated turbulence strength, and the spatial spectrum of the initial complex field, but not by the motion-induced offsets in the system.  The time-varying offsets are all handled internally by appropriate transverse shifts, and by application of tilt phasors just prior to sensing, if the sensor type requires it.  

Notice in the preceding sentences that we said the propagation mesh requirements are influenced by the spatial spectrum of the initial complex field.  In particular, if for some reason the initial complex field contains a large overall tilt, then the mesh must be dense and large enough to be able to adequately sample this field for input to the propagator.  But, the point is that LightLike's method of handling motion offsets and slew is designed to avoid the impractically large propagation mesh dimensions that would be needed if the associated tilt factors were always represented in the pre-propagation complex field.

CAUTION:  LightLike's "applyToField"="false" method cannot by itself solve all tilt-related sampling problems.  We stated above that the tilt carried in the so-called "tilt register" is finally put into the complex field just before sensing occurs.  Now if the sensor is of a type that is sensitive to the incident phase in the sensor pupil (e.g.,SimpleFieldSensor or Camera), then of course inadequate sampling of that phase will produce incorrect phase results.  However, this problem is usually easy to circumvent, because a pre-sensor Slew can be used to orient the sensor so that the pupil plane is more or less parallel to the incident tilt.  This issue was already discussed in a somewhat different form in one sub-section of the transverse-motion and slew introduction.