Coordinate System 
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In LightLike, all input and output quantities are consistently expressed in MKS units. In particular, all distances are expressed in meters. This convention applies to all the AO tools functions as well. In particular, wavefront OPD values and DM actuator displacements will be expressed in meters, and wavefront slopes will be expressed in radians of tilt angle.
WFS/DM space and object spaceWhen modeling AO components (wavefront sensors, deformable mirrors, or beam steering mirrors), the most common waveoptics modeling practice is to project the adaptiveoptics geometry parameters to object space (i.e., beam dimensions outside the telescope). Using this approach, the AO component parameters can be easily related to the turbulence parameters of the propagation medium. For example, the WFS subaperture and DM actuator spacings are specified according the dimensions of their images in the entrance pupil of the telescope system. In connection with this procedure, it is important to note that, in constructing a LightLike system, we usually place all the optical system components in the same plane (the entrance pupil), with no physical propagation distance between any of the components. Of course, the order of operations carried out by various elements (e.g., splitting, attenuating, tilting, sensing, etc.) corresponds to the order in which the LightLike blocks are connected, and this can be made consistent with their actual positions in the physical system. In most LightLike modeling, there is no reason to carry out physicaloptics propagation using Fresnel propagators within the optical system. The one usual exception to this is the farfield image in (or near) a focal plane. The diffractive effects of the entrance pupil areaccounted for by propagations embedded in LightLike's camera or wavefront sensor modules. Defocused sensor planes can be accounted for as well in this framework. The omission of diffractive propagation between most elements of the optical system is consistent with the usual optical analysis of composite systems: the effects of diffraction are for practical purposes completely represented by one physical propagation from pupil to sensor plane. When using this projection modeling approach for the AO elements, users must ensure that the proper scaling and magnification is configured within the simulation. In particular, the specifications of LightLike sensor subsystems must be scaled to correspond to their projected dimensions.
Relations among LightLike propagation and AO meshesAs explained in the basic LightLike User Guide, LightLike's propagation mesh (the mesh on which the Fresnel propagations are performed) is determined by the location of sensors relative to sources. The propagation mesh is always centered on the local (x,y) origin of the pupil of a sensor module, and this applies to wavefront sensors as well. When specifying (x,y) coordinates for subapertures and actuators (using the aogeom tool), these coordinates should be interpreted as local coordinates relative to the pupil of the wavefront sensor or AO subsystem in question. This applies in particular if the LightLike system contains more than one wavefront sensor or AO subsystem that are displaced from each other using TransverseVelocity (displacement) blocks. This convention allows easy reuse of the AO coordinate specifications in a multiaperture system that has AO subsystems behind each aperture. In the AO configuration tools, three new meshes are defined. The points of these meshes correspond to WFS subaperture center positions, DM actuator positions, and points at which a wavefront OPD is to be evaluated. The AO tools allow considerable freedom in specifying the relative location of the mesh points, although there are certain constraints that may depend on the tools function in question. Whatever the exact specification method may be, the AO meshes are all referenced by means of specified offsets relative the local (x,y) origin. A LightLike simulation system will mate the AO setup information to the propagated wave by applying the necessary interpolation procedures. As one example, consider the size of a typical WFS subaperture compared to the propagation mesh. Given the practical constraints on propagation mesh point dimension, there will likely be very few propagation mesh points across one subaperture, and furthermore, the spacing may not be "nicely" related to the subaperture spacing. In order to adequately compute the spot shape in the WFS focal (sensor) plane, LightLike's HartmannWfsDft module will interpolate the incident optical field (which is defined on the propagation mesh) onto a mesh used for computing the Fourier Transforms that HartmannWfsDft performs for each subaperture. As a second example, consider the effect of a DM on an incident wavefront. The instantaneous deformation of the DM is defined on a mesh specified by the AO configuration tools, which is not required to have any exact relation to the propagation mesh. But of course, when LightLike applies the DM correction to the wavefront, it must do so on the propagation mesh, in preparation for a subsequent physical propagation operation. In this situation, LightLike also automatically performs the necessary interpolation.
Overall rescaling of an AO configurationSetting up a particular combination of AO geometry, influence function, and reconstructor is a fairly elaborate procedure. It may occur that one wants to rescale a given configuration to a different telescope aperture size. This arises in practice since one may have a given (expensive) DM that one wishes to use with various telescope apertures. LightLike provides a rescaling argument in the DMModel function, which allows the AO configuration results to be rescaled to a different aperture size without redoing the configuration procedures.
