A novel method related to diffraction tomography is presented for imaging two-dimensional weak-scattering objects embedded in a lossy background with phaseless data.The proposed method requires only intensity measurements.Based on the information of the total field magnitudes the pseudo Fourier transformation of the object function can be determined

which is distributed along a fixed arc in the complex space.After expanding the object function by Fourier series the pseudo Fourier spectrum can be represented by the Fourier coefficients

which can be written in a form of system of equations.By means of regularization the ill-posed matrix can be solved and the object function is reconstructed.Numerical simulation results presented have proven the validity of the proposed method.Since this reconstruction algorithm needs only intensity information to rebuild the geometric and electromagnetic properties of objects embedded in a lossy background

it circumvents the difficulty of direct phase measurement.