To start the aogeom GUI enter the Matlab command:
» aogeom
This command brings up a figure window containing a diagram of a default AO system:
(NOTE: it may be necessary for the user to enlarge the default window (using the mouse) to avoid clipping the axis labels)
The default AO system is a 21x21actuator mesh designed for an unobscured aperture of 1-meter diameter. The following bullets list the graphical components of the above diagram, and specify the coordinate system:
•The white diamonds are master actuators as superposed on the deformable mirror.
•The red squares represent the areas of wavefront sensor subapertures, usually configured so the corners fall on actuators.
•The white circle shows the outer radius of master actuators.
•The red circle shows the outer radius of subapertures. The circle goes through some of the red squares, because the option is selected which keeps any subaperture whose area falls mostlyinside the outer subaperture radius.
•The axes show the coordinates of the actuators and subapertures, in units of meters. The horizontal axis in the AOGeom window is the x-axis, and the vertical axis is the y-axis.
In LightLike these coordinates are usually, but not necessarily, defined in "object space" (i.e., the actuator and subaperture dimensions are geometrically scaled up to the space of the primary projecting or collecting aperture).
For any wavefront sensor or AO subsystem, the x-y origin is the local origin of the subsystem in question. This local origin is the center of the pupil of the subsystem in question. This rule applies no matter what static or dynamic offset the AO subsystem may have due to any TransverseVelocity (displacement) blocks. See the coordinates section for a general review of the AO coordinate concepts.
•Other potential components of the diagram (inner boundaries, slave, and inert actuators) are not present in this default system, but will be introduced below.
Starting with the default configuration or another previously saved configuration, the user can employ the features of aogeom to define a new system and save it for influence function and reconstructor computation.
Specifying actuator and subaperture geometry
The main window of aogeom is a graphical representation of the current configuration. To change the configuration, the user employs the File
Load... or FileDefine Geometry... menu items. FileLoad... allows the user to load a .mat file which was saved during a previous run of aogeom, or which was created by an independent procedure. If created independently, the file variables must conform to the list in the section titled .mat Interface File Format. Once the file is loaded, the main window graphic is updated to reflect the geometry of the loaded system.
When the user employs the FileDefine Geometry... item, the AO Geometry Parameters window appears.
(NOTE: it may be necessary for the user to enlarge the default window (using the mouse) to avoid clipping some of the text fields).
The example window immediately below contains the actuator and subaperture numerical parameters that correspond to the previous geometry picture. Note in particular that all inner radii are 0, corresponding to the absence of inner boundaries in the geometry picture.
It is in this window that most of the activity of aogeom occurs. The user edits the various entries to modify the characteristics of the AO system geometry. While working with these items, the main window diagram is not automatically updated. Instead the user must press the 
, 
, or 
buttons. The button causes all changes to window to be committed and closes the window. commits the changes but leaves the window open and reloads the default configuration and leaves the window open. 
closes the window while discarding the changes that were made since the last apply.
In the AO Geometry Parameters window, the user specifies meshes of actuators and subapertures by specifying
(1) actuator and subaperture mesh offsets and dimensions;
(2) the radii of a series of concentric circles that restrict the meshes to specified annuli.
The user usually creates a configuration which consists of an array of subapertures whose corners coincide with an array of master actuators (the Fried geometry). The master actuators are intended to be directly driven by the inversion of a wavefront measurement over the subapertures. The user can also set up inner and outer rings of "slave" actuators. The slave commands are constructed as fixed linear combinations of neighboring master actuators, rather than from the slope pseudo-inversion procedure directly. Finally, aogeom also has a provision for rings of "inert" actuators (BUT see the WARNING below).
The following two figures illustrate the setup of an AO system geometry which includes master, slave, and inert actuators superposed on an annular aperture. For graphical completeness, a non-zero number of inert actuators have been included in this picture, despite the WARNING below. This new system geometry was obtained by editing the default geometry of the previous Geometry Parameters window.
The two red circles show the inner and outer boundaries of the subapertures. In the above example, any subaperture that falls mostly between the inner and outer subaperture radii is included. The "Full Subapertures Only" option (AO Geometry Parameters window, Subaperture Geometry box) will result in inclusion of only those subapertures that fall completely between the inner and outer subaperture radii.
The two white circles show the inner and outer boundaries of the master actuators.
The two magenta circles show the inner and outer boundaries of the slave actuators.
The two green circles show the inner and outer boundaries of inert actuators.
The outermost, cyan circle shows the clamping radius for the Green's function method (if that influence function is selected).
WARNING regarding inert actuators: the purpose of defining "inert" actuators was to model an unfortunate but potentially important event that occurs with physical DMs. Component failures can cause individual actuators to become inactive, in the sense that applying a voltage to that actuator produces no displacement. Since a DM is generally a high-value component, a working optical system that contains a DM with some dead actuators will usually continue to be used as is, at least for some time. Therefore, simulating the performance impact of dead actuators may be an important task. However, at present, the AO tools lack a consistent treatment of this issue in two respects. First, since dead actuators can occur anywhere in any grouping, the "ring" geometry currently provided by aogeom is inappropriate. Second, the present reconstructor calculations do not correctly handle the behavior of the dead actuators. We intend to add the required extensions to the AO tools,but, for the time being, users should only create DM configurations with zero inert actuators. (This is done by making the circle radii for inerts and slaves equal, i.e., specifying zero-width inert rings).
Note that the View menu in the aogeom window must be used to turn on/off display options such as the text labels and boundary circles. The colored legend at the upper right of the geometry picture indicates the total count of each type of actuator and the number of subapertures. The rings of actuators and subapertures shown in the previous picture were generated by specifying the eight radii contained in the Geometry Parameters window located immediately below.
The number of actuators and subapertures per axis define an initial rectangular array which is circumscribed by the circles. The precise values of circle radii are only important insofar as they exclude or include particular actuators or subapertures. As a matter of convention, we usually place an actuator at the origin, and we make the number of actuators along an axis odd so that the system is symmetric. The number of subapertures per axis is usually even and one less than the number of actuators. These conventions are not limitations of the underlying mechanisms; they simply set out a standard way of setting up the systems. The x-dimension is the horizontal axis in the aogeom diagram, and the y-dimension is the vertical axis.
Also specified are the actuator and subaperture spacing. These values indicate the distance between actuators and the distance between centers of subapertures. Actuators can be spaced differently in x and y, but subapertures cannot (note there are no separate x and y subap spacing specs in the above diagram). Usually the x and y spacing of actuators and subapertures are equal (as illustrated). See the background section for further comments on asymmetry and misregistration. The actuators, subapertures, and circle centers are normally symmetric with respect to the origin of the coordinate system. However, the user can specify offsets to any of these. For the definitions of each offset, see the subsequent section on aogeom details.
The yellow lines connecting the magenta and white diamonds illustrate the slaving relationship between master and slave actuators. The yellow lines drawn from the slaves to the masters show upon which masters the slave actuators depend. In the illustrated case, a master-slave connection algorithm which connects slaves to only one or two masters is used. The Slave Corners Three Ways option can be used to cause slaves to be connected to up to three adjacent masters.
Actuator and subaperture numbering convention
If the user wishes to work with some of the intermediate variables in the AO configuration process, it will be necessary to understand the 1-dimensional numbering convention for actuators and subapertures that is used by the AO tools. For actuators, the convention is that actuator 1 is at the left end of the bottom row of actuators (as seen in aogeom diagram). The actuator number increases going from left to right across the rows, and then up the rows from bottom to top. By using the menu option View - Show Actuator Numbers in the aogeom window, the numbers can be displayed.
The numbering of subapertures follows a different pattern than the actuators. For subapertures, the convention is that subaperture 1 is at the bottom of the left-most column. Then subaperture number increases going from bottom to top along the columns, and then across the columns from left to right.
Awareness of the numbering scheme is not required for working with the aogeom GUI, but the data vectors saved to file by aogeom are ordered according to these conventions. For example, there are vectors that contain the x and y coordinates of actuators and subapertures. To work with some of the intermediate variables in the AO tools, the user should be aware of the numbering conventions.
Specifying the actuator influence function and its parameters
Finally, the characteristics of the actuator influence function are also specified in the AO Geometry Parameters window. These specifications do not affect the display of the geometry, so there is no graphical feedback. The user simply selects one of five different influence functions, and specifies the extent of the influence function in a manner unique to each influence function type. The option details are described later.
Saving the results of aogeom
When users are satisfied with the specified AO system geometry, they can store the configuration to a.mat file, using the FileSave As... command in the file menu of the main aogeom window. The file can be loaded into a later run of aogeom (using FileLoad ...) for further editing, and/or provided as input to aoinf and/or other AO tools procedures. The save file name is entirely user-specifiable. Contents of the save file are detailed in .mat Interface File Contents.