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slopesLinearMMSE.m
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classdef slopesLinearMMSE < handle
%% SLOPESLINEARMMSE MMSE wavefront estimation from slopes
%
% mmse = linearMMSE(sampling,diameter,atmModel,guideStar)
% mmse = linearMMSE(sampling,diameter,atmModel,guideStar,mmseStar)
% mmse = linearMMSE(...,'pupil',pupilMask,'unit',unit)
% mmse = linearMMSE(...,'model','modal','zernikeMode',zMode)
% Results are given at the wavelength of the mmseStar
%
% Example:
% sampling = 11;
% diameter = 8;
% atmModel = atmosphere(photometry.V,15e-2,60,'altitude',10e3);
% gs = source('asterism',{[3,arcsec(30),0]},'wavelength',photometry.R);
% ss = source('wavelength',photometry.H);
% mmse = linearMMSE(sampling,diameter,atmModel,gs,ss,'pupil',utilities.piston(sampling,'type','logical'),'unit',-9);
properties
tag = 'slopesLinearMMSE';
% pupil sampling
sampling
% pupil resolution
resolution
% pupil diameter
diameter
% slopes pupil mask
slopesMask
% wavefront pupil mask
wavefrontMask
% wavefront array size
wavefrontSize;
% atmosphere mode
atmModel
% guide star covariance matrix
Cxx
% mmse star covariance matrix
Cox
% guide star direction
guideStar
% Fourier spectrum resolution
NF;
% Fourier spectrum oversampling factor
sf;
% MINRES relative tolerance
RTOL = 5e-2;
% MINRES maximum number of iteration
MAXIT = 200;
% MINRES initial guess
x0
% warm start flag
warmStart = false;
% bilinear sparse operator
B = [];
end
properties (Dependent)
% mmse estimates directions
mmseStar
% noise variance
noiseVar;
end
properties (Access=private)
log
p_mmseStar
p_noiseVar = 0;
fun;
funp;
c;
wavefrontToMeter;
end
methods
%% Constructor
function obj = slopesLinearMMSE(wfs,tel,atmModel,guideStar,varargin)
inputs = inputParser;
inputs.addRequired('wfs',@(x) isa(x,'shackHartmann') );
inputs.addRequired('tel',@(x) isa(x,'telescope'));
inputs.addRequired('atmModel',@(x) isa(x,'atmosphere'));
inputs.addRequired('guideStar',@(x) isa(x,'source'));
inputs.addOptional('mmseStar',[],@(x) isa(x,'source'));
inputs.addOptional('NF',1024, @isnumeric );
inputs.addOptional('sf',4, @isnumeric );
inputs.parse(wfs,tel,atmModel,guideStar,varargin{:});
obj.resolution = inputs.Results.wfs.lenslets.nLenslet;
obj.diameter = inputs.Results.tel.D;
obj.sampling = obj.diameter/obj.resolution;
obj.wavefrontMask = ~inputs.Results.wfs.validActuator;
obj.atmModel = inputs.Results.atmModel;
obj.guideStar = inputs.Results.guideStar;
obj.slopesMask = repmat( repmat( inputs.Results.wfs.validLenslet(:) , 2, 1), 1, length(obj.guideStar) );
obj.p_mmseStar = inputs.Results.mmseStar;
if isempty(obj.p_mmseStar)
obj.p_mmseStar = obj.guideStar;
end
obj.NF = inputs.Results.NF;
obj.sf = inputs.Results.sf;
obj.log = logBook.checkIn(obj);
obj.log.verbose = false;
add(obj.log,obj,'atmosphere wavelength set to mmse star wavelength!')
atmWavelength = obj.atmModel.wavelength;
obj.atmModel.wavelength = obj.p_mmseStar(1).wavelength;
if isinf(obj.guideStar(1).height)
add(obj.log,obj,'Computing the covariance matrices for NGS')
tic
dv = [obj.guideStar.directionVector];
ddv_x = bsxfun( @minus, dv(1,:), dv(1,:)' );
ddv_y = bsxfun( @minus, dv(2,:), dv(2,:)' );
m_Cxx = arrayfun( @(dx,dy) slopestoSlopesCovariance(obj, dx, dy), ...
ddv_x, ddv_y, 'UniformOutput', false );
obj.Cxx = m_Cxx;
deltaSrc = bsxfun( @minus ,dv , obj.p_mmseStar.directionVector );
m_Cox =...
arrayfun( @(dx,dy) phaseToSlopesCovarianceFiniteHeight(obj,0,obj.atmModel,dx,dy,1) ,...
deltaSrc(1,:), deltaSrc(2,:), ...
'UniformOutput', false );
obj.Cox{1} = cell( 1 , 1 );
obj.Cox{1}{1} = m_Cox;
% obj.Cox{1} = { { phaseToSlopesCovariance(obj,0,obj.atmModel,0,0,1) } };
toc
else
add(obj.log,obj,'Computing the covariance matrices for LGS')
tic
dv = [obj.guideStar.directionVector];
ddv_x = bsxfun( @minus, dv(1,:), dv(1,:)' );
ddv_y = bsxfun( @minus, dv(2,:), dv(2,:)' );
m_Cxx = arrayfun( @(dx,dy) slopestoSlopesCovariance(obj, dx, dy), ...
ddv_x, ddv_y, 'UniformOutput', false );
obj.Cxx = m_Cxx;
obj.Cox{1} = cell( obj.atmModel.nLayer , 1 );
for kLayer = 1:obj.atmModel.nLayer
% fprintf('. Layer #%d\n',kLayer);
atmLayer = slab(obj.atmModel,kLayer);
g = 1 - atmLayer.layer.altitude./[obj.guideStar.height];
pad = ceil( 0.5*obj.resolution*(1-g)./g );
deltaSrc = bsxfun( @minus ,dv , obj.p_mmseStar.directionVector );
deltaSrc = atmLayer.layer.altitude.*deltaSrc;
m_Cox =...
arrayfun( @(x,dx,dy,gl) phaseToSlopesCovariance(obj,x,atmLayer,dx,dy,gl) ,...
pad , deltaSrc(1,:), deltaSrc(2,:), g, ...
'UniformOutput', false );
obj.Cox{1}{kLayer} = m_Cox;
NI = obj.resolution+1;
NP = NI + 2*pad(1);
obj.B{kLayer} = tools.bilinearSparseInterpolator(NI,NP,1,g(1));
end
obj.B = cell2mat( obj.B );
toc
end
obj.fun = @(x) mtimes4squareBlocks(obj.Cxx,x,wfs.validLenslet(:));
obj.funp = @(x) mtimes4precond(obj.Cxx,x,obj.slopesMask);
obj.c = zeros(obj.resolution^2*2*length(obj.guideStar),1 );
obj.wavefrontToMeter = ...
obj.guideStar(1).wavelength*obj.atmModel.wavelength/2/pi/(obj.sampling*wfs.lenslets.fftPad)/wfs.lenslets.nyquistSampling;
obj.wavefrontSize = ones(1,2)*(obj.resolution+1);
obj.x0 = zeros(size(obj.c));
obj.log.verbose = true;
obj.atmModel.wavelength = atmWavelength;
end
%% Destructor
function delete(obj)
if ~isempty(obj.log)
checkOut(obj.log,obj)
end
end
%% Set/Get mmseStar
function set.mmseStar(obj,val)
obj.p_mmseStar = val;
add(obj.log,obj,'Computing the mmse/guide stars covariance matrix')
phaseToSlopesCovariance(obj);
end
function val = get.p_mmseStar(obj)
val = obj.p_mmseStar;
end
%% Set/Get noiseVar
function set.noiseVar(obj,val)
obj.p_noiseVar = val;
slopestoSlopesCovariance(obj);
end
function val = get.noiseVar(obj)
val = obj.p_noiseVar;
end
%% Wavefront reconstruction
function out = mtimes(obj,wfs)
if isa(wfs,'shackHartmann')
obj.c( obj.slopesMask ) = wfs.slopes(:);
else
obj.c( obj.slopesMask ) = wfs;
end
[yy,~] = minres(obj.fun,obj.c(:),obj.RTOL,obj.MAXIT,[],[],obj.x0*obj.warmStart);
obj.x0 = yy;
m_Cox = obj.Cox{1};
n = length(m_Cox);
m = length(m_Cox{1});
out = cell( n , 1 );
ns = obj.resolution^2*2;
% nFig = 100 + randi(100);
for kn=1:n
out{kn} = zeros( m_Cox{kn}{1}{1}.nRow^2 , 1 );
u = 1:ns;
for km=1:m
yyy = yy(u);
out{kn} = out{kn} + ...
m_Cox{kn}{km}{1}*yyy(1:end/2) + m_Cox{kn}{km}{2}*yyy(1+end/2:end);
u = u + ns;
end
% figure(nFig)
% subplot(1,n,kn)
% imagesc( reshape( out{kn} , ones(1,2)*m_Cox{kn}{1}{1}.nRow ) )
% axis square
% colorbar
end
out = cell2mat( out );
if ~isempty(obj.B)
out = obj.B*out;
end
if length(out)>prod(obj.wavefrontSize)
out(obj.wavefrontMask) = [];
else
if numel(out)==numel(obj.wavefrontMask)
out(obj.wavefrontMask) = 0;
end
out = reshape(out,obj.wavefrontSize);
end
out = out*obj.wavefrontToMeter;
end
function out = estimation(obj,wfs)
% [yy,flag,relres,iter,resvec] = minres(fun,c,1e-3,50);
if isa(wfs,'shackHartmann')
obj.c( obj.slopesMask ) = wfs.slopes;
else
obj.c( obj.slopesMask ) = wfs;
end
yy = minres(obj.fun,obj.c,obj.RTOL,obj.MAXIT,[],[],obj.x0);
if obj.warmStart
obj.x0 = yy;
end
out = obj.Cox{1}*yy(1:end/2) + obj.Cox{2}*yy(1+end/2:end);
if length(out)>prod(obj.wavefrontSize)
out(obj.wavefrontMask) = [];
else
out(obj.wavefrontMask) = 0;
out = reshape(out,obj.wavefrontSize);
end
out = out*obj.wavefrontToMeter;
end
function varargout = imagesc(obj)
% n = length(obj.Cxx);
m_Cxx = cellfun( ...
@(x) [x{1,1}.elements, x{1,2}.elements x{2,1}.elements, x{2,2}.elements] ,...
obj.Cxx,'UniformOutput',false);
m_Cxx = cell2mat( m_Cxx );
m_Cox = cellfun( ...
@(x) [x{1,1}.elements, x{1,2}.elements] ,...
obj.Cox{1},'UniformOutput',false);
% m_Cox = cell2mat( m_Cox );
% subplot(2*n+1,2*n,[1,4*n^2])
% imagesc(m_Cxx)
% axis square
% colorbar
% subplot(2*n+1,2*n,[1+4*n^2,(2*n+1)*(2*n)])
% imagesc(m_Cox)
% axis equal tight
% colorbar
if nargout>0
varargout{1} = m_Cxx;
varargout{2} = m_Cox;
end
end
end
methods (Access=private)
function m_Cxx = slopestoSlopesCovariance(obj,deltaSrc_x,deltaSrc_y)
%% slopes-to-slopes covariance matrix
% fprintf(' ==> Computing slopes-to-slopes covariance matrix ...\n');
nLenslet = obj.resolution;
atm = obj.atmModel;
lambda = atm.wavelength;
d = obj.diameter/nLenslet;
covxx = zeros( obj.NF);
covyy = zeros( obj.NF);
cov = zeros( obj.NF);
nm = ones(1,2)*nLenslet;
b0 = obj.NF/2+1;
b = (1-nLenslet:nLenslet-1)*obj.sf + b0;
[fx0,fy0] = freqspace(obj.NF,'meshgrid');
% tic
% fprintf(' . Layer # ');
for kLayer = 1:obj.atmModel.nLayer
% fprintf('\b\b%2d',kLayer);
atmLayer = slab(obj.atmModel,kLayer);
h = atmLayer.layer.altitude;
g = 1-h/obj.guideStar(1).height;
lf = obj.sf/(d*2*g);
fx = lf*fx0;
fy = lf*fy0;
delta = 2*lf/obj.NF;
phasor = exp( 2*1i*pi.*h*( deltaSrc_x*fx + deltaSrc_y*fy ) );
spectrum = @(fx,fy,u,v) lambda.^2*(fx.*u(1) + fy.*u(2)).*(fx.*v(1) + fy.*v(2)).*...
delta.^2.*phaseStats.spectrum(hypot(fx,fy),atmLayer).*...
(tools.sinc(g*d*fx).*tools.sinc(g*d*fy)).^2.*phasor;
covxx = covxx + fft2( fftshift( spectrum(fx,fy,[1,0],[1,0]) ) );
covyy = covyy + fft2( fftshift( spectrum(fx,fy,[0,1],[0,1]) ) );
cov = cov + real( fftshift( fft2( fftshift( spectrum(fx,fy,[0,1],[1,0]) ) ) ) );
end
% fprintf('\n');
covxx(1) = covxx(1) + obj.p_noiseVar;
covxx = real( fftshift( covxx ) );
T = toeplitzBlockToeplitz( nm, nm, covxx(b,b) );
m_Cxx{1,1} = T;
covyy(1) = covyy(1) + obj.p_noiseVar;
covyy = real( fftshift( covyy ) );
T = toeplitzBlockToeplitz( nm, nm, covyy(b,b) );
m_Cxx{2,2} = T;
T = toeplitzBlockToeplitz( nm, nm, cov(b,b) );
m_Cxx{1,2} = T;
m_Cxx{2,1} = T';
% elapsedTime = toc;
% fprintf(' ==> slopes-to-slopes covariance matrix computed in %5.2fs\n',elapsedTime);
end
function m_Cox = phaseToSlopesCovariance(obj,pad,m_atm,deltaSrc_x,deltaSrc_y, gl)
%% phase-to-slopes covariance matrix
% fprintf(' ==> Computing phase-to-slopes covariance matrix ...\n');
alpha = 1;
[fx,fy] = freqspace(obj.NF,'meshgrid');
nLenslet = obj.resolution;
lambda = m_atm.wavelength;
d = obj.sampling;
lf = obj.sf/(d*2*gl);
fx = lf*alpha*fx;
fy = lf*alpha*fy;
delta = 2*lf*alpha/obj.NF;
phasor = exp( 2*1i*pi.*( (deltaSrc_x+0.5*d)*fx + (deltaSrc_y+0.5*d)*fy ) );
spectrum2 = @(u) lambda.*1i*(fx.*u(1) + fy.*u(2)).*...
delta.^2.*phaseStats.spectrum(hypot(fx,fy),m_atm).*...
tools.sinc(gl*d*fx).*tools.sinc(gl*d*fy).*phasor./gl;
nm = [nLenslet+1+2*pad nLenslet];
b0 = obj.NF/2+1;
b = (1-nLenslet-pad:nLenslet+pad)*obj.sf + b0;
% tic
covx = fftshift(real( fft2( fftshift( spectrum2([1,0]) ) ) ) );
covy = fftshift(real( fft2( fftshift( spectrum2([0,1]) ) ) ) );
m_Cox{1} = toeplitzBlockToeplitz( nm, nm, covx(b,b) );
m_Cox{2} = toeplitzBlockToeplitz( nm, nm, covy(b,b) );
% elapsedTime = toc;
% fprintf(' ==> phase-to-slopes covariance matrix computed in %5.2fs\n',elapsedTime);
end
function m_Cox = phaseToSlopesCovarianceFiniteHeight(obj,pad,m_atm,deltaSrc_x,deltaSrc_y, gl)
%% phase-to-slopes covariance matrix
% fprintf(' ==> Computing phase-to-slopes covariance matrix ...\n');
alpha = 1;
[fx,fy] = freqspace(obj.NF,'meshgrid');
nLenslet = obj.resolution;
lambda = m_atm.wavelength;
d = obj.sampling;
lf = obj.sf/(d*2*gl);
fx = lf*alpha*fx;
fy = lf*alpha*fy;
delta = 2*lf*alpha/obj.NF;
covx = zeros( obj.NF );
covy = zeros( obj.NF );
for kLayer=1:m_atm.nLayer
atmLayer = slab(m_atm,kLayer);
h = atmLayer.layer.altitude;
phasor = exp( 2*1i*pi.*( (deltaSrc_x*h+0.5*d)*fx + (deltaSrc_y*h+0.5*d)*fy ) );
spectrum2 = @(u) lambda.*1i*(fx.*u(1) + fy.*u(2)).*...
delta.^2.*phaseStats.spectrum(hypot(fx,fy),atmLayer).*...
tools.sinc(gl*d*fx).*tools.sinc(gl*d*fy).*phasor./gl;
nm = [nLenslet+1+2*pad nLenslet];
b0 = obj.NF/2+1;
b = (1-nLenslet-pad:nLenslet+pad)*obj.sf + b0;
% tic
covx = covx + fftshift(real( fft2( fftshift( spectrum2([1,0]) ) ) ) );
covy = covy + fftshift(real( fft2( fftshift( spectrum2([0,1]) ) ) ) );
end
m_Cox{1} = toeplitzBlockToeplitz( nm, nm, covx(b,b) );
m_Cox{2} = toeplitzBlockToeplitz( nm, nm, covy(b,b) );
% elapsedTime = toc;
% fprintf(' ==> phase-to-slopes covariance matrix computed in %5.2fs\n',elapsedTime);
end
end
end
function out = mtimes4squareBlocks( OO, w, mask )
n = length(OO);
nw = length(w);
u = 1:nw/n;
out = zeros( size(w) );
if nargin>2
for ii=1:n
v = 1:nw/n;
for jj=1:n
ww = w(v);
x = ww(1:end/2);
y = ww(1+end/2:end);
O = OO{ii,jj};
out(u) = out(u) + [...
maskedMtimes(O{1,1},x,mask) + maskedMtimes(O{1,2},y,mask)
maskedMtimes(O{2,1},x,mask) + maskedMtimes(O{2,2},y,mask)
];
v = v + nw/n;
end
u = u + nw/n;
end
else
for ii=1:n
v = 1:nw/n;
for jj=1:n
ww = w(v);
x = ww(1:end/2);
y = ww(1+end/2:end);
O = OO{ii,jj};
out(u) = out(u) + [...
mtimes(O{1,1},x) + mtimes(O{1,2},y)
mtimes(O{2,1},x) + mtimes(O{2,2},y)
];
v = v + nw/n;
end
u = u + nw/n;
end
end
end
function out = mtimes4precond( OO, w, mask)
x = w(1:end/2);
y = w(1+end/2:end);
O = OO{1};
A = O{1,1};
B = O{2,2};
out = [medfilt1( A\x ) ; medfilt1( B\y )];
end