Actuator-Subaperture Geometry

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The aogeom tool facilitates the specification of rectangular (in fact, mostly square) meshes of WFS subapertures and DM actuators.  Regions of active, slave and inert actuators are then defined by circles of various radii.  The routine aogeom differs from all the other AO tools in this sense:  by running aogeom, the user starts and then interacts with a graphical user interface (GUI).  All other routines discussed in this guide are ordinary functions that take input arguments from and return output arguments to the Matlab workspace.

WFS and DM alignment is specified with respect to the local coordinate origins of the wavefront sensor or AO subsystems.  In aogeom, the alignment is specified by an (x,y) offset for the subaperture mesh and another offset for the actuator mesh.  If these offsets are both (0,0), then the meshes are registered in the so-called Fried geometry, wherein the actuators lie at the corners of the subapertures. Figure 3 illustrates the Fried geometry.  Positioning the actuators at the subaperture corners allows the best match between DM deformation and subaperture WF slopes, and minimizes potential problems with unsensed wavefront modes.  Equal but non-zero offsets would still preserve the Fried geometry, but would offset the center of both meshes from the center of the propagation mesh.  An equal-offset specification is allowed, although it usually serves no purpose.

FriedGeom

Figure 3:  The Fried geometry (perfectly registered meshes)

Using aogeom, one may also create departures from the Fried geometry, by making the actuator mesh offset different from the subaperture mesh offset.  This is considered "misregistration" of the meshes.  Of course this can occur in practice, and it may be important to simulate and study the resulting performance effects.

CAUTION:  Before attempting to set up a misregistered system, the user should study the Guide section Working with Asymmetric and/or Misregistered Systems.  Note in particular that the aoinfroutine for computing influence functions does not work if there are departures from the Fried geometry.  In addition to a shift misregistration, aogeom also allows another form of misregistration, namely an actuator spacing not equal to the subaperture spacing.  This could arise in a physical system due to imperfect magnification match between the WFS and DM paths.

aogeom by itself does not perform any calculations that depend on the fill factor of the subapertures.  As will appear in the GUI discussion below, the only subaperture size specification in aogeom is the "subaperture spacing" (i.e., center-to-center spacing).  The implicit assumption is that the subapertures are square, with a 100% fill factor, which is typical for Hartmann-Shack lenslet arrays.  But this assumption is only used when LightLike's HartmannWfsDft subsystem segments an incident beam and computes the sensor-plane irradiance formed by each subaperture.  A LightLike system can model a more general fill factor, but to do so the user must create and insert a transmittance mask in the LightLike system in front of HartmannWfsDft.  The mask can be created by using LightLike's Apodizer system.  If a transmittance mask is added, the use of aogeom is unchanged.

 

Geometry specification when no DM is present

If we are interested solely in computing a reconstructed wavefront, with no DM and no correction loop in mind, then we still use aogeom to define the WFS subaperture geometry. Furthermore, defining "actuator" positions in aogeom can also still be useful, even though no DM will be present.  Given "actuator" position specifications, aogeom simply creates vectors that list the "actuator" x and y coordinates in a special ordering scheme.  Then later, when using some of the routines that produce reconstructed WF values, the so-called "actuator" position vectors can be used to specify the points at which one desires the evaluation of the reconstructed WF.