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yaokl.i
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/*
* yaokl.i
*
* A collection of routines related to Karhuenen Loeve modes.
*
* This file is part of the yao package, an adaptive optics simulation tool.
*
* Copyright (c) 2002-2017, Francois Rigaut
* Copyright (c) 2006, Damien Gratadour
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation; either version 2 of the License, or (at your
* option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details (to receive a copy of the GNU
* General Public License, write to the Free Software Foundation, Inc., 675
* Mass Ave, Cambridge, MA 02139, USA).
*
*/
local yaokl;
/* yaokl
Collection of routines for building the KL of a Kolmogorov statistics
Derived from a collection of routines developped both at ESO and ONERA
The main routine is the last one ...
for a Kolmogorov statistics :
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64);
or
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="kolmo");
for a Von Karman statistics :
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="karman");
or
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="karman",outscl=3);
default is : an outter scale of 3 times the size of the telescope
res is a 128x128x150 array containing the 150 first KL
of a kolmogorov or Von Karman stat
D. Gratadour Feb 2006
Available functions:
func dblindgen(n)
func polar_coord(r,&mask,&rho,&phi,&pts,occ=,xcent=,ycent=,\
func radii(nr,np,ri)
func polang(r)
func setpincs(ax,ay,px,py,ri,&pincx,&pincy,&pincw)
func pcgeom (nr,np,ncp,ri,ncmar,ap)
func set_pctr(bas, ncp =, ncmar=)
func pol2car(cpgeom,pol,mask=)
func kolstf(dvec)
func karmanstf(dvec,outscl=)
func gkl_radii(nr,ri)
func gkl_mkker(ri,nr,rad,funct=,outscl=)
func piston_orth(nr)
func gkl_fcom(kers,ri,nf,&evals,&nord,&npo,&ord,&rabas)
func gkl_mkazi(nord, np)
func gkl_bas(ri=,nr=,np=,nfunc=,verbose=,funct=,outscl=)
func gkl_sfi(bas, i)
func make_kl(nmax,dim,&var,&outpolarbase,&pupil,oc=,nr=,nopup=,\
func kl_basis_in_dm_space_4extrap(nm, n_rm_modes);
func kl_basis_in_dm_space(nm,n_rm_modes,&eigen_val);
*/
//require,mcao_i_dir+"lib/libgenutil.i";
//require,"digit2.i";
func dblindgen(n)
/*DOCUMENT res=dblindgen(size)
D. Gratadour Feb 2006
This routine returns a size x size array containing increasing indices
from 1 to size x size.
SEE ALSO : indgen, indices
*/
{
n=long(n);
return reform(indgen(n*n),[2,n,n]);
}
func polar_coord(r,&mask,&rho,&phi,&pts,occ=,xcent=,ycent=,\
verbose=,leq=,btw4pix=,sizemin=,dbprec=)
/* DOCUMENT polar_coord,radius,mask,rho,phi;
or polar_coord,radius,mask,rho,phi,pts,sizemin=1;
D. Gratadour Jan 2006
Calculation of polar coordinates rho and phi and an intensity mask
(the pupil) of a telescope of radius r
Derived from an IDL routine (polaire2.pro) written by L. Mugnier
INPUTS :
r = the radius of the mask
OUTPUT :
mask = the intensity mask (2d image)
rho = the width coordinate (2d image)
phi = the angle coordinate (rad) (2d image)
pts = (optional) indices of valid (non null) points of the
pupil (1d vector) if flag sizemin is set
OPTIONAL :
occ = the occultation level (<=1)
xcent = the x position of the center point of the mask
xcent = the y position of the center point of the mask
verbose = flag to get info on the process (0/1)
leq = flag to set the limits of the mask (<= radius or < radius)
btw4pix = flag to set the center of the mask on 1 pixel or
in between 4 pixels (0/1)
sizemin = flag to set the outputs in a minimum size arrays (null points
are eliminated) (0/1)
SEE ALSO : ...
*/
{
if (r==[]) r=128;
if (!is_set(occ)) occ=0.0;
if (!btw4pix) diam=long(2*floor(r)+1);
else diam=long(2*round(r));
if (!is_set(xcent)) xcent=float((diam-1)/2.);
if (!is_set(ycent)) ycent=float((diam-1)/2.);
if (verbose) {
write,format="Pupil diameter : %d\n",diam;
if (xycent!=[]) {
write,format="Pupil X center : %f\n",xycent(1);
write,format="Pupil Y center : %f\n",xycent(2);
}
}
x=float(((indices(diam))(,,1)-1.0) % diam);
y=transpose(x);
x-=xcent;
y-=ycent;
if (dbprec) {
rho=double(sqrt(x^2+y^2))/double(r);
phi=double(atan(y,x+(rho==0)));
} else {
rho=float(sqrt(x^2+y^2))/float(r);
phi=float(atan(y,x+(rho==0)));
}
if (leq) mask=((rho<=1) & (rho>=occ));
else {
if (dbprec) mask=double((rho<1) & (rho>=occ));
else mask=float((rho<1) & (rho>=occ));
}
if (sizemin) {
if (verbose) write,"We will keep only the non-null points";
pts=where(mask != 0.);
if (dimsof(pts) != []) {
sizepts=(dimsof(pts))(2);
if (verbose) write,"Number of null points : ",sizepts;
rho=rho(pts);
phi=phi(pts);
mask=mask(pts);
} else {
if (verbose) write,"All points are non-null !";
}
}
}
struct gkl_basis_struct
{
long nr;
long ni;
long np;
long nfunc;
float ri;
pointer radp;
pointer evals;
long nord;
pointer npo;
pointer ord;
pointer rabas;
pointer azbas;
};
struct geom_struct
{
pointer px;
pointer py;
pointer cr;
pointer cp;
pointer pincx;
pointer pincy;
pointer pincw;
pointer ap;
long ncp;
long ncmar;
};
func radii(nr,np,ri)
/*DOCUMENT res=radii(NumberOfR,NumberOfPhi,Dim)
D. Gratadour Feb 2006
This routine generates an nr x np array with np copies of the
radial coordinate array. Radial coordinate span the range from
r=ri to r=1 with successive annuli having equal areas (ie, the
area between ri and 1 is divided into nr equal rings, and the
points are positioned at the half-area mark on each ring). There
are no points on the border.
SEE ALSO : polang
*/
{
r2 = ri^2 +(float(indgen(nr)-1)+0.)/nr*(1.0 - ri^2);
rs = sqrt(r2);
return rs*array(1.,np)(-,);
}
func polang(r)
/*DOCUMENT res=polang(RadialCoordArray)
D. Gratadour Feb 2006
This routine generates an array with the same dimensions as r,
but containing the azimuthal values for a polar coordinate system.
SEE ALSO : radii
*/
{
s = dimsof(r);
nr = s(2);
np = s(3);
phi1 = float(indgen(np)-1)/float(np)*2.*pi;
return phi1(-,)*array(1.,nr);
}
func setpincs(ax,ay,px,py,ri,&pincx,&pincy,&pincw)
/*DOCUMENT res=polang(RadialCoordArray)
D. Gratadour Feb 2006
This routine determines a set of squares for interpolating
from cartesian to polar coordinates, using only those points
with ri < r < 1
SEE ALSO : pcgeom
*/
{
s = dimsof(ax);
nc = s(2);
s = dimsof(px);
nr = s(2);
np = s(3);
dcar = (ax(nc) - ax(1)) / (nc-1);
ofcar = ax(1,1);
rlx = (px - ofcar)/dcar;
rly = (py - ofcar)/dcar;
lx = long(rlx);
ly = long(rly);
shx = rlx - lx;
shy = rly - ly;
pincx=[lx,lx+1,lx+1,lx]+1;
pincy=[ly,ly,ly+1,ly+1]+1;
pincw=[(1-shx)*(1-shy),shx*(1-shy),shx*shy,(1-shx)*shy];
axy = ax^2 + ay^2;
axyinap = clip(axy,ri^2.+1.e-3,0.999);
sizeaxyinap=(dimsof(axyinap))(2);
pincw = pincw*axyinap(pincx+(pincy-1)*sizeaxyinap);
pincw = pincw*(1.0/pincw(,,sum))(,,-);
}
func pcgeom (nr,np,ncp,ri,ncmar,ap)
/*DOCUMENT geom=pcgeom(nr, np, ncp, ri, ncmar,ap)
D. Gratadour Feb 2006
This routine builds a geom_struct. px and py are the x and y
coordinates of points in the polar arrays. cr and cp are the
r and phi coordinates of points in the cartesian grids. ncmar
allows the possibility that there is a margin of ncmar points
in the cartesian arays outside the region of interest
SEE ALSO : setpincs, set_pctr
*/
{
nused = ncp - 2*ncmar;
ff = 0.5 * nused;
hw = float(ncp-1)/2;
r = radii(nr,np,ri);
p = polang(r);
px0 = r * cos(p);
py0 = r * sin(p);
px = ff * px0 + hw;
py = ff * py0 + hw;
ax = float(dblindgen(ncp)-1) % ncp - 0.5 * (ncp-1);
ax = ax / (0.5 * nused);
ay = transpose(ax);
setpincs, ax, ay, px0, py0, ri,pincx, pincy, pincw;
dpi = 2 * pi;
cr2 = (ax^2 + ay^2);
ap = clip(cr2,ri^2+1.e-3,0.999);
//cr = (cr2 - ri^2) / (1 - ri^2) * nr - 0.5;
cr = (cr2 - ri^2) / (1 - ri^2) * nr;
cp = (atan(ay, ax) + dpi) % dpi;
cp = (np / dpi) * cp;
cr = clip(cr,1.e-3,nr-1.001);
//fudge -----, but one of the less bad ones
cp = clip(cp,1.e-3,np -1.001);
//fudge ----- this is the line which
//gives that step in the cartesian grid
//at phi = 0.
geom = geom_struct();
geom.px=&px;
geom.py=&py;
geom.cr=&cr;
geom.cp=&cp;
geom.pincx=&pincx;
geom.pincy=&pincy;
geom.pincw=&pincw;
geom.ap=≈
geom.ncp=ncp;
geom.ncmar=ncmar;
return geom;
}
func set_pctr(bas, ncp =, ncmar=)
/*DOCUMENT geom=set_pctr(bas, ncp =, ncmar=)
D. Gratadour Feb 2006
This routine calls pcgeom to build a geom_struct with the
right initializations. bas is a gkl_basis_struct built with
the gkl_bas routine.
SEE ALSO : pcgeom, setpincs, gkl_bas
*/
{
if (!is_set(ncmar)) ncmar = 2;
if (!is_set(ncp)) ncp = 128;
return pcgeom(bas.nr,bas.np,ncp,bas.ri,ncmar,ap);
}
func pol2car(cpgeom,pol,mask=)
/*DOCUMENT cart=pol2car(cpgeom, pol, mask=)
D. Gratadour Feb 2006
This routine is used for polar to cartesian conversion.
pol is built with gkl_bas and cpgeom with pcgeom.
However, points not in the aperture are actually treated
as though they were at the first or last radial polar value
-- a small fudge, but not serious ?*******
SEE ALSO : pcgeom, gkl_bas
*/
{
if (sae) error;
cd = bilinear(pol, *cpgeom.cr+1, *cpgeom.cp+1);
if (mask!=[]) cd = cd*(*cpgeom.ap);
return cd;
}
func kolstf(dvec)
/*DOCUMENT var=kolstf(dvec)
D. Gratadour Feb 2006
This routine returns the kolmogorov phase variance at spatial
dimension (inverse of the spatial frequency) dvec
SEE ALSO :
*/
{
return 6.88 * dvec^(5./3.);
}
func karmanstf(dvec,outscl=)
/*DOCUMENT var=kolstf(dvec)
D. Gratadour Feb 2006
This routine returns the Von Karman phase variance at spatial
dimension (inverse of the spatial frequency) dvec. Same as kolstf
but with a correcting factor to account for the outter scale.
The latter should be in units of telescope diameter
SEE ALSO :
*/
{
if (dimsof(outscl)==[]) outscl = 3.;
return 6.88 * dvec^(5./3.)*(1-1.485*(dvec/outscl)^(1./3.)+\
5.383*(dvec/outscl)^(2)-6.281*\
(dvec/outscl)^(7./3.));
}
func gkl_radii(nr,ri)
/*DOCUMENT rad=gkl_radii(nr,ri)
D. Gratadour Feb 2006
This routine generates an array of radial polar coordinates along
which the KL are generated. nr is the number of elements and ri is
the maximum radius.
SEE ALSO :
*/
{
d = (1.-ri*ri)/nr;
// rad2 = ri^2 + d/2. + d * float(indgen(nr)-1);
// rad2 = ri^2 + d * float(indgen(nr)-1);
rad2 = ri^2 +d/16.+ d * float(indgen(nr)-1);
// rad2 = ri^2 +d/14.+ d * float(indgen(nr)-1); // nr=64,128
// rad2 = ri^2 +d/10.+ d * float(indgen(nr)-1);
rad = sqrt(rad2);
return rad;
}
func gkl_mkker(ri,nr,rad,funct=,outscl=)
/*DOCUMENT
D. Gratadour Feb 2006
This routine generates the kernel used to find the KL modes.
The kernel constructed here should be simply a discretization
of the continuous kernel. It needs rescaling before it is treated
as a matrix for finding the eigen-values. The outter scale
should be in units of the diameter of the telescope.
SEE ALSO :
*/
{
nth = 5*nr;
kers = array(float,[3,nr, nr, nth]);
cth = cos(float(indgen(nth)-1)*(2.*pi/nth));
dth = 2.*pi/nth;
fnorm = -1./(2*pi*(1.-ri^2))*0.5;
//the 0.5 is to give the r^2 kernel, not
//the r kernel
for (i =1;i<=nr;i++) {
for (j=1;j<=i;j++) {
te = 0.5*sqrt(rad(i)^2+rad(j)^2-(2*rad(i)*rad(j))*cth);
//te in units of the diameter, not the radius
if (funct=="kolmo") te = kolstf(te);
if (funct=="karman") te = karmanstf(te,outscl=outscl);
if ((funct!="kolmo") & (funct!="karman")) {
write,"The statistics is not known !";
error;
}
kelt = fnorm * dth * float (fft(te,-1));
kers (i, j,) = kelt;
kers (j, i,) = kelt;
}
if (is_set(verbose)) write, i;
}
if (is_set (verbose)) write," ";
return kers;
}
func piston_orth(nr)
{
s = array(float,[2,nr,nr]);
for (j=1;j<=nr-1;j++) {
rnm = 1./sqrt (float((j)*(j+1)));
s(1:j,j) = rnm;
s(j+1,j)= -1*(j)*rnm;
}
rnm = 1./sqrt (nr);
s(,nr) = rnm;
return s;
}
func gkl_fcom(kers,ri,nf,&evals,&nord,&npo,&ord,&rabas)
/*DOCUMENT
D. Gratadour Feb 2006
This routine does the work : finding the eigenvalues and
corresponding eigenvectors. Sort them and select the right
one. It returns the KL modes : in polar coordinates : rabas
as well as the associated variance : evals. It also returns
a bunch of indices used to recover the modes in cartesian
coordinates (nord, npo and ord).
SEE ALSO : gkl_bas
*/
{
s = dimsof(kers);
nr = s(2);
nt = s(4);
nxt = 1;
fktom = (1.-ri^2)/nr;
fevtos = sqrt(2*nr);
evs = array(float,[2,nr,nt]);
//ff isnt used - the normalisation for
//the eigenvectors is straightforward:
//integral of surface^2 divided by area = 1,
//and the cos^2 term gives a factor
//half, so multiply zero order by
//sqrt(n) and the rest by sqrt (2n)
//zero order is a special case...
//need to deflate to eliminate infinite eigenvalue - actually want
//evals/evecs of zom - b where b is big and negative
zom = kers(,,1);
s = piston_orth(nr);
ts =transpose(s);
b1 = ((ts(,+)*zom(+,))(,+)*s(+,))(1:nr-1, 1:nr-1);
newev = SVdec(fktom*b1,v0,vt);
v1 = array(float,[2,nr, nr]);
v1(1:nr-1,1:nr-1) = v0;
v1(nr,nr) = 1;
vs = s(,+)*v1(+,);
grow,newev,0;
evs(,nxt) = float(newev);
kers (,, nxt) = sqrt(nr)*vs;
// the rest are more straightforward
nxt = 2;
do {
newev = SVdec(fktom*kers(,,nxt),vs,vt);
evs(,nxt) = float(newev);
kers (,,nxt) = sqrt(2.*nr)*vs;
mxn = max(float(newev));
egtmxn = floor(evs(, 1:nxt)>mxn);
nxt = nxt + 1;
} while ((2*sum(egtmxn)-sum(egtmxn(,1))) < nf);
nus = nxt - 1;
kers = kers (,,1:nus);
evs = reform (evs (, 1:nus), nr*nus);
a = (sort(-1.*evs))(1:nf);
//every eigenvalue occurs twice except
//those for the zeroth order mode. This
//could be done without the loops, but
//it isn't the stricking point anyway...
no = 1;
ni = 1;
oind = array(long,nf+1);
do {
if (a(ni) < nr+1) {
oind(no) = a(ni);
no = no + 1;
} else {
oind(no) = a(ni);
oind(no+1) = a(ni);
no = no + 2;
}
ni = ni + 1;
} while (no < (nf+1));
oind = oind (1:nf);
tord = (oind-1)/nr+1;
odd = ((long(indgen(nf)-1) % 2) == 1);
pio = (oind-1) % nr +1;
evals = evs(oind);
ord = 2 *(tord-1) - floor(tord>1 & (odd))+1;
nord = max(ord);
rabas = array(float,[2,nr, nf]);
sizenpo=long(max(ord));
npo = array(long,sizenpo);
for (i=1;i<=nf;i++) {
npo(long(ord(i))) = npo(long(ord(i))) + 1;
rabas(, i) = kers (, pio(i), tord(i));
}
}
func gkl_mkazi(nord, np)
{
gklazi = array(float,[2,long(1+nord), np]);
th = float(indgen(np)-1)*(2.*pi/ np);
gklazi (1,) = 1.0;
for (i = 2; i<=nord;i+=2) gklazi (i,) = cos (((i-1)/2+1) * th);
for (i = 3; i<=nord;i+=2) gklazi (i,) = sin (((i-1)/2) * th);
return gklazi;
}
func gkl_bas(ri=,nr=,np=,nfunc=,verbose=,funct=,outscl=)
/*DOCUMENT
D. Gratadour Feb 2006
This routine uses the output of gkl_fcom to fill the gkl_base_struct.
SEE ALSO : gkl_fcom
*/
{
if (!is_set(ri)) ri = 0;
if (!is_set(nr)) nr = 40;
if (!is_set(np)) np = long(5*nr);
if (!is_set(nfunc)) nfunc = 500L;
nr = long(nr);
np = long(np);
if ((nr * np)/ nfunc < 8) {
if (is_set(verbose)) write,"warning: you may need a finer ",\
"radial sampling ";
if (is_set(verbose)) write, "(ie, increased nr) to generate ",\
nfunc, " functions";
} else if ((nr * np)/ nfunc > 40) {
if (is_set(verbose)) write,"note, for this size basis ",\
"radial discretization on ", nr;
if (is_set(verbose)) write, "points is finer than necessary",\
"-it should work, but you ";
if (is_set(verbose)) write, "could take a smaller nr without",\
"loss of accuracy";
}
radp = gkl_radii(nr, ri);
kers = gkl_mkker(ri, nr, radp,funct=funct,outscl=outscl);
gkl_fcom,kers,ri,nfunc,evals,nord,npo,ord,rabas;
azbas = gkl_mkazi(nord, np);
gklbasis = gkl_basis_struct();
gklbasis.nr=nr;
gklbasis.np=np;
gklbasis.nfunc=nfunc;
gklbasis.ri=ri;
gklbasis.radp=&radp;
gklbasis.evals=&evals;
gklbasis.nord=nord;
gklbasis.npo=&npo;
gklbasis.ord=⩝
gklbasis.rabas=&rabas;
gklbasis.azbas=&azbas;
return gklbasis;
}
func gkl_sfi(bas, i)
/*DOCUMENT
D. Gratadour Feb 2006
This routine returns the i'th function from the generalised KL
basis bas. bas must be generated first with gkl_bas.
SEE ALSO : gkl_bas
*/
{
if (i>bas.nfunc) {
write, "the basis only contains ", nfunc, "functions";
return 0;
}
nr = bas.nr;
np = bas.np;
ordp = *bas.ord;
ord=long(ordp(i));
rabasp=*bas.rabas;
rabas=rabasp(,i);
azbasp=*bas.azbas;
azbas=azbasp(ord, );
sf1=array(double,[2,nr,np]);
sf1(,*)=rabas;
sf2=array(float,[2,np,nr]);
sf2(,*)=azbas;
sf = sf1*transpose(sf2);
return sf;
}
func make_kl(nmax,dim,&var,&outpolarbase,&pupil,oc=,nr=,nopup=,funct=,outscl=,verbose=)
/* DOCUMENT
for a Kolmogorov statistics :
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64);
or
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="kolmo");
for a Von Karman statistics :
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="karman");
or
res=make_kl(150,128,varkl,outbas,pup1,oc=0.12,nr=64,funct="karman",outscl=5);
the outter scale is in units of the telescope diameter
default is : an outter scale of 3 times the size of the telescope
D. Gratadour Feb 2006
This routine is the main program. It returns nmax generalized
KL in an array dim x dim x nmax. It also returns the associated
variance as well as the pupil and the polar base used for their
calculation. Optional keywords includes any occultation, the
number of samples for the radial coordinate and a flag to avoid
pupil multiplication.
SEE ALSO : polar_coord, gkl_bas, set_pctr
*/
{
if (pupil==[]) polar_coord,dim/2.,pup,rho,phi,occ=oc,btw4pix=1;
else pup=pupil;
if (!is_set(nr)) nr=64;
if (dimsof(funct)==[]) {
if (verbose) write,"make_kl: Using the Kolmogorov model";
funct="kolmo";
} else if (funct=="karman") {
if (verbose) write,"make_kl: Using the von-Karman model";
}
polarbase = gkl_bas(ri=oc,nr=nr,np=(2*pi*nr),nfunc=nmax,\
funct=funct,outscl=outscl,verbose=verbose);
outpolarbase = polarbase;
pc1 = set_pctr(polarbase, ncp= dim);
kl = array(float,[3,long(dim),long(dim),nmax]);
if (is_set(nopup)) {
for (i=1;i<=nmax;i++) kl(,,i)=pol2car(pc1, gkl_sfi(polarbase,i));
} else {
for (i=1;i<=nmax;i++) {
sae=0;
// if (i==8) sae=1;
kl(,,i)=pol2car(pc1, gkl_sfi(polarbase,i))*pup;
}
}
pupil = pup;
var = *polarbase.evals;
return kl;
}
func kl_basis_in_dm_space(nm,n_rm_modes,&eigen_val,extrap=)
/* DOCUMENT
calcule la base optimale vis a vis des fonctions d'influence
du mirroir deformable et des conditions de turbulence.
To be used then for instance to compute MMSE reconstructors.
kl2dm = array(pointer,3);
ei_val = array(pointer,3);
filt_tab = [3,3,3];
for(nm=1;nm<=3;nm++) {
b=kl_basis_in_dm_space(nm, filt_tab(nm),eigen,extrap="extrap_kl.mat");
kl2dm(nm) = &(b);
ei_val(nm) = &(eigen);}
mat_kl2dm = array(float, [2,684,684]);
mat_kl2dm(1:240,1:240) = *kl2dm(1);
mat_kl2dm(241:564,241:564) = *kl2dm(2);
mat_kl2dm(565:,565:) = *kl2dm(3);
yao_fitswrite, "mat_kl2dm_filt111.fits",mat_kl2dm;
tab_ei_val = float(684);
tab_ei_val = _(*ei_val(1),*ei_val(2),*ei_val(3));
yao_fitswrite, "tab_ei_val_filt111.fits",tab_ei_val;
b = kl_basis_in_dm_space(1, 3,eigen,extrap="extrap_kl.mat");
will return a 240x240 array
plot, b(,1); //first mode = Astig (piston/TT have been filtered)
to see the modes:
inf_fun = yao_fitsread("KLDMmodes_DM1_IF_nrmodes3.fits");
if_nb = dimsof(inf_fun)(4);//nb of IF
dim = dimsof(inf_fun)(2);//size of the support
dm_mode = b(+,)*(inf_fun(*,))(,+);
dm_mode2 = reform(dm_mode,if_nb,dim,dim);
tv,dm_mode2(1,,);
nmodes = 40;
aff_kldm_basis,dm_mode2,nmodes,puptel=[];
eigen = eigenvalues associated with each mode
window,1;nm=1;
xx = indgen(mcaodm(nm).nvalid);
plot,eigen,xx;
plg,xx^(-11./6.)*45.,xx,color="red";
logxy,1,1;
*/
{
coeffi = [1.,1.24,1.47];//factor to take into account D vs h
L0 = 25.;
r0 = 0.4;
k = 2;//oversampling factor for fft of IF
//2 should be enough, larger than 2 takes a while
//inf_fun = 3D array of influence functions
inf_fun = get_mInfluence_withextrap(nm,extrap=extrap);
if_nb = dimsof(inf_fun)(4);//nb of IF
dim = dimsof(inf_fun)(2);//size of the support
//----Step0 : Modes Filtering-----------------
nnn = dimsof(ipupil)(2);
if(nm == 1) {
puptel = ipupil(nnn/2-dim/2+1:nnn/2+dim/2,nnn/2-dim/2+1:nnn/2+dim/2);
prepzernike,dim,sim.pupildiam,dim/2+0.5,dim/2+0.5;
pupkl = zernike(1);
}
if(nm > 1) {
pup = inf_fun(,,sum);
wp = where(pup >= max(pup)*0.75);
pup2 = pup*0.;pup2(wp)=1.;
dim2=(where(pup2(,dim/2)==1)(0)-where(pup2(,dim/2)==1)(1)+1);
prepzernike,dim,dim2,dim/2+0.5,dim/2+0.5;
pupkl = zernike(1);
puptel = pupkl;
}
//define IF on the pupil only
for(cpt=1;cpt<=if_nb;cpt++){
inf_fun(,,cpt) = inf_fun(,,cpt)*puptel;
}
if (numberof(n_rm_modes) != 0) {
if(n_rm_modes > 0) {
for(cpt=1;cpt<=if_nb;cpt++){
cmpnt = 0.0;
for(kj=1;kj<=n_rm_modes;kj++){
polz = zernike(kj);
coef = sum(inf_fun(,,cpt)*polz)/sum(polz*polz);
cmpnt = cmpnt + polz*coef;
}
inf_fun(,,cpt) = inf_fun(,,cpt) - cmpnt;
}
}
}
//save influence functions for latter:
if(n_rm_modes == []) n_rm_modes = 0;
name=swrite(format="KLDMmodes_DM%d_IF_nrmodes%d.fits",nm,n_rm_modes(1));
yao_fitswrite,name,inf_fun;
//-------------------------------------------------------
//Step1 : Computing geometrique covariance matrix ...
Delta_IF = array(float,[2,if_nb, if_nb]);
Spup = numberof(where(puptel));
nrm = Spup;//pupil surface in pixel;
tmp = inf_fun(*,);
Delta_IF = (tmp(+,)*tmp(+,))/nrm;
tmp = [];
write, "-> Géometrique Covariance, DONE !";
//---------------------------------------------------------
//Step2 : Calcul des TF des fction d'influence
phase_variance = (gamma(11./6.)*gamma(5./6.)/(2.*pi^(8./3.)))*
(24.*gamma(6./5.)/5.)^(5./6.)*
(L0/r0)^(5./3);
kdpix = long(dim/2.+10.)*k;//at least 2 times pupil size !
if(kdpix <= dim) write, "ATTENTION!"
//-------------------------------------
D = 8.*coeffi(nm);
//sp_freq = dist(kdpix)/(k*D*float(dim2)/float(sim.pupildiam));//FIXME
//This is not good! should be in real pix/m
sp_freq = dist(kdpix)/(k*D);
//------------------------------------
f = sp_freq;
cst = (gamma(11./6.)^2/(2.*pi^(11./3.)))*(24.*gamma(6./5.)/5.)^(5./6.) ;
phase_spectrum = eclat(cst*r0^(-5./3.)*(f^2+(1/L0)^2)^(-11./6.)) ;
print, "Variance theorique [rd^2]: ", (phase_variance);
phase_variance_from_spectrum = sum(double(phase_spectrum))/(k*D)/(k*D);
print, "Variance from dsp [rd^2]: ", (phase_variance_from_spectrum);
support = array(float,[2,kdpix, kdpix]);
FT_inf_fun = array(complex,[3,kdpix, kdpix, if_nb]);
for(i=1;i<=if_nb;i++){
support(1:dim,1:dim) = inf_fun(,,i);
FT_inf_fun(,,i) = fft(support,1)*sqrt(phase_spectrum);
}
write, "-> TF des IF, DONE !";
inf_fun = support = [];
//---------------------------------------------------------
//Step3 : correlation statistique des fonctions d'influence
H_IF = array(float,[2,if_nb, if_nb]);
nrm = (Spup*Spup)*(k*D)*(k*D);
tmp = FT_inf_fun(*,);
FT_inf_fun = [];
H_IF = float(tmp(+,)*conj(tmp)(+,))/nrm;
write, "-> Correlation Statistiques, DONE !";
//-------------------------------------------------------------
//Step4 : Double Diagonalisation
D2 = SVdec(Delta_IF, Mp);
print,"conditionning:",max(D2)/min(D2);
M = transpose(Mp/sqrt(D2)(-,));
Hp = M(,+)*(H_IF(,+)*M(,+))(+,);
Lp = SVdec(Hp,A);
print,"conditionning:",max(Lp)/min(Lp);
Bp = M(+,)*A(+,);
eigen_val = Lp;
write, "-> Double Diago, DONE !";
return Bp;
/*
//-----------------------------------
mcao_restore_dm,mysttop+"/mystInitFiles/mcao-prod.ybin";
nnm = 1;
spup=ipupil(dm(nnm)._n1:dm(nnm)._n2,dm(nnm)._n1:dm(nnm)._n2);
i=1;
tv,comp_dm_shape(nnm,&(float((*kl2dm(nnm))(,i))),extrap=0);
*/
}
func kl_basis_in_dm_space_4extrap(nm, n_rm_modes)
/* DOCUMENT
calcule la base optimale vis a vis des fonctions d'influence
du mirroir deformable et des conditions de turbulence.
To be used then for instance with gen_extrap_klopt
b = kl_basis_in_dm_space_4extrap(1, 1);
will return a 293x293 array
*/
{
//-----------------------------------
//Get Influence Functions WITH extrapolated
//and on a large array
inf_fun = get_mInfluence_large(nm);//it includes extrap and valids
if_nb = dimsof(inf_fun)(4);//nb of IF
dim = dimsof(inf_fun)(2);//size of the support
def1 = def2 = def3 = def4 = def5 = [];
edef1 = edef2 = edef3 = edef4 = edef5 = [];
dm(1)._def = &def1;dm(2)._def = &def2;dm(3)._def = &def3;
dm(4)._def = &def4;dm(5)._def = &def5;dm(1)._edef = &edef1;
dm(2)._edef = &edef2;dm(3)._edef = &edef3;
//--------------------------------------------
//Step0 : Modes Filtering
//First, we have to define a pupil...
pup = inf_fun(,,sum);
pup = sign(pup(wheremax(abs(pup))(1)))*pup;
pup = (pup > 0.8*max(pup));
dim2=where(pup(,dim/2)==1)(0)-where(pup(,dim/2)==1)(1)+1;
prepzernike,dim,dim2,dim/2+0.5,dim/2+0.5;
pupkl = zernike(1);
//define IF on the pupil only
for(cpt=1;cpt<=if_nb;cpt++){
inf_fun(,,cpt) = inf_fun(,,cpt)*pupkl;
}
if (numberof(n_rm_modes) != []) {