Iterative optical diffraction tomography (iODT) method and applications
A non-destructive iterative interferometric tomographic technique for imaging and reconstruction of phase objects as well as objects with complex permittivity and, particularly, to iterative optical diffraction tomographic (iODT) imaging and reconstruction of phase objects with high refractive index (RI) contrast, complex structures, and/or large optical path differences (OPDs) against the background, which cause multiple scattering, and applications thereof.
1. A method for performing iterative Optical Diffraction Tomography (iODT) to reconstruct an object, comprising the ordered steps of:
a) providing an object to be optically reconstructed, wherein said object is a multiply-scattering two-dimensional or three-dimensional phase object exhibiting a high refractive index contrast, a complex structure, or a large optical path difference against a background;
b) selecting initial parameter values θ: illumination angle, u 0 : known incident wave, u t : true diffracted field;
c) selecting a constraint operator, C, and a propagation solver, S;
d) applying the constraint operator, C, to the current estimated object function, as Cƒ (m) ;
e) applying the propagation solver, S, to the known incident wave, u 0 , through Cƒ (m) for each illumination angle, θ, to generate a first forward propagating field, u (m) fwd (θ);
f) applying an inverse of the propagation solver, S −1 , to the true diffracted field, u t , through Cƒ (m) for each illumination angle, θ, to generate a first backward propagating field, u (m) bwd (θ);
g) computing the perturbative Rytov phase Δφ (m) R (θ) as ln[u (m) fwd (θ)/u (m) bwd (θ)];
h) computing a correction, Δƒ (m) , to the current estimate of the object function using the perturbative Rytov phase;
i) updating the estimate of the object function to ƒ (m) -Δƒ (m)
j) increasing the iteration number from m to m+1;
k) repeating steps (c-i) until a selected stop condition is met or a predetermined maximum number of iterations is reached; and
l) obtaining an image or optical reconstruction of the object.
2. The method of claim 1 , wherein the constraint operator, C, is unity (i.e., a non-constraint), non-negativity, non-positivity, or reality (i.e., non-imaginary).
3. The method of claim 1 , wherein the propagation solver, S, is the wide-angle beam propagation method (WABPM) or finite difference time domain (FDTD).
4. The method of claim 1 , wherein computing the correction Δƒ (m) involves the following steps:
a) obtaining a Π-image in the Fourier domain, ΔΠ (m) (θ), by applying a filter to the Fourier transform of the perturbative Rytov phase Δφ (m) R (θ);
b) obtaining the correction, Δƒ (m) by summing the inverse Fourier transform of the Π-images over all illumination angles, θ.
5. The method of claim 4 , wherein the filter is a ramp filter or a Shepp-Logan-Gaussian filter.
6. The method of claim 1 , wherein the known incident wave, u 0 , is a plane wave.
7. A method for performing iterative Optical Diffraction Tomography (iODT) for the reconstruction of a refractive index (RI) profile of a multiply-scattering object, comprising: providing an object to be imaged or optically reconstructed, wherein said object is a multiple-scattering two-dimensional or three-dimensional phase object exhibiting a high refractive index contrast, a complex structure, or a large optical path difference against a background;
iteratively minimizing an error between an optical field diffracted by a a reconstructed object and an optical field;
computing a perturbative correction to the RI profile based on the error calculated from a previous estimate of the RI profile;
forming a new estimate for a next iteration;
computing a new perturbative correction to the RI profile based on the error calculated from the previous estimate of the RI profile; and
stopping the process when a convergence criterion is met and a reconstructed object image is formed or a stopping criterion is met and no reconstructed object image is formed.