# Frequency–domain optical imagimg of absorption and scattering distributions by a Born
iterative method

### Y. Yao *et al.* (1997)

#### Summary

We present a Born iterative method for reconstructing optical properties of turbid media by
means of frequency–domain data. The approach is based on iterative solutions of a linear
perturbation equation, which is derived from the integral form of the Helmholtz equation for
photon–density waves. In each iteration the total field and the associated weight matrix are
recalculated based on the previous reconstructed image. We then obtain a new estimate by
solving the updated perturbation equation. The forward solution, also based on a Helmholtz
equation, is obtained by a multigrid finite difference method. The inversion is carried out
through a Tikhonov regularized optimization process by the conjugate gradient descent method.
Using this method, we first reconstruct the distribution of the complex wave numbers in a test
medium, from ehich the absorption and scattering distributions are then derived. Simulation
results with two–dimensional test media have shown that this method can yield quantitatively
(in terms of coefficient values) as well as qualitatively (in terms of object location and shape)
accurate reconstructions of absorption and scattering distributions in cases in which the
first–order Born approximation can not work well. Both full–angle and limited–angle measurement
schemes have been simulated to examine the effect of the location of detectors and sources. The
robustness of the algorithm to noise has also been evaluated.