.mat Interface File Contents

Output file of aogeom contains:

nact   Total number of DM actuators.

nslav   Number of slave actuators.

nmas   Number of master actuators.

The number of inert actuators is ninert = nact - nslav - nmas.  As discussed previously, the influence function and reconstructor calculations in the present release of the AO tools only work correctly forninert = 0, i.e., for nslav+nmas = nact.

xact    A column vector of dim (nact x1), containing the x-coordinates of the actuator locations. The actuator indexing convention has been described previously.

yact    A column vector of dim (nact x1), containing the y-coordinates of the actuator locations.

actype   A vector with length equal to nact. actype(i) determines whether the ith actuator is a master, slave, or an inert actuator. actype(i) = 1.0 if the ith actuator is a master actuator. actype(i) = -1.0 if the Ith actuator is a slave actuator. actype(i) = 0.0 if the Ith actuator is an inert actuator.

nmsmax   The maximum number of master actuators that any slave actuator is slaved to.

idxmas   A two-dimensional array which specifies which master actuators each slave responds to. The number of rows in idxmas is equal to nslav, the number of slave actuators, and the number of columns of idxmas is equal to nmsmax. The slave actuators are numbered from 1 to nslav in the same order as they appear in the numbering for all the actuators. If idxmas(i,1) = j, then the first master actuator (lowest numbered) that the ith slave actuator is slaved to is actuator number j. Actuator j must be a master actuator in this case. If a slave actuator is slaved to fewer than the maximum number of masters, the corresponding row of idxmas will contain some zeroes. For example, if the ith slave actuator is slaved to 2 masters and if nmsmax = 4, then idxmas(i,3) =idxmas(I, 4) = 0.

weight    A two dimensional array of the same size as idxmas. The ith slave actuator will be given a voltage command which is a linear combination of the voltage commands sent to one or more masters. The locations of those masters is specified in idxmas. The coefficients in that linear combination are in the ith row of the array weight. Normally, the sum of the numbers in any row ofweight would be unity. aoinf will fill the arrays idxmas and weight automatically using a very simple rule. If a slave actuator is adjacent to only one master, it is commanded with the same voltage as the master actuator. If it is adjacent to more than one master, it is commanded with the a weighted average of all the commands sent to the masters that it is adjacent to. The weights are proportional to the relative distance from the slave to each master.

nsub   The number of WFS subapertures.

xsub   A column vector of dim (nsub x1), containing the x-coordinates of the centers of the WFS subapertures.  The subaperture indexing convention has been described previously.

ysub   A column vector of dim (nsub x1), containing the y-coordinates of the centers of the WFS subapertures.

hs Subaperture center-center spacing.  Recall that the x and y spacings of subaperture centers must be equal.

U   This applies to Green's function influence functions only. A vector with length equal to nact. There are two parameters used in the clamped plate Green's function mirror model. One is the spring constant of the actuators, and the other relates the elongation of an actuator to the applied voltage. To determine these constants, an empirical influence function for the center actuator of an Itek mirror was used. The influence function was measured with 200 volts applied to the center actuator, all other actuators were not driven, and displacement of the mirror faceplate was recorded. The vector Ucontains the voltage commands for that test. It has zero entires for all except the center actuator which has 200 volts.

W   This applies to Green's function influence functions only. A vector containing the displacements of all the actuators when 200 volts were applied to the middle actuator, based on the Itek data. The displacement of the middle actuator is 3.3 micrometers, the displacement of the nearest neighbor actuators is 5% of the displacement of center actuator, and the displacement of neighboring actuators separated along a diagonal from the center actuator is 1% of the center actuator displacement. The vectors U and W are hardwired in aoinf.

rc    This applies to Green's function influence functions only. The radius at which the circular plate is assumed to be clamped in the Green's function model of the DM.

ninfl   This applies to Green's function influence functions only. This parameter specifies the region over which the localized DM influence functions are computed. ninfl is set by changing the Green's function Actuator Influence Reach in aogeom. The influence of an actuator is only calculated out toninfl actuator spacings and is assumed to be negligible beyond that distance.

nsi    Number of intervals used in the Simpson's rule quadrature along each side of a subaperture to compute G-tilts induced by the DM. The user can modify this be changing the parameter # of Integ. Steps/Side of Subap.

rmas   Radius of the master actuator circle.

rslav   Radius of the slave actuator circle.

ract   Radius of the circle containing all the actuators.

rsub    Radius of the circle containing all the subapertures.

Output file of aoinf contains:

All of the above, plus:

opdif   OPD influence function matrix, denoted A in the background discussion.  When stored in a sparse format, as it appears in the Matlab workspace, opdif is a 2D array with dims (nxreach * nyreach) x nact, where n{x,y}reach is the number of OPD mesh points that correspond to the influence function reach (the reach was determined by the aogeom setup specifications).

mvtov   A matrix that transforms a vector of voltage commands applied to the master actuators to voltage commands to all the actuators.  The (row, col) dimensions of mvtov are (nact x nmas).

vtod   A matrix that transforms a vector of voltages at all the actuators to displacements at all the actuators.  The (row, col) dimensions of vtod are (nact x nact).  As discussed previously, vtod is by default the unit matrix.

dtos    A matrix that transforms all actuator displacements to all WFS subaperture slopes induced by the DM on the sensed wavefront.  This is the DM slope influence matrix discussed in the background section, where it was designated S and defined by the relation s = S ddact .  The (row, col) dimensions of dtos are (2nsub x nact).

mvtos   A matrix that transforms a vector of voltages applied to the master actuators to all WFS subaperture slopes.  The (row, col) dimensions of mvtos are (2nsub x nmas). mvtos is equal to the matrix product dtos*vtod*mvtov.  As discussed previously, and as shown in a Matlab terminal session, the composite mvtos is usually the only one of these four matrices that the user needs to deal with explicitly.

Save file generated after execution of aorecon should contain:

All of the above, plus:

recon1, {recon2, ...}   Any number of reconstructor matrices.  The particular matrix to be used by any given subsystem in a LightLike system will be specified as an argument in the TasatDMModel function.  Unlike all the previously defined file variables, the actual names of recon1, {recon2, ...} are user-specified, as output argument names of the aorecon routine or its analogs.