The Conjugate Gradient Least Square Algorithm in Terahertz Tomography

Abstract

Terahertz tomography allows for non-contact tomographic inspection of dielectric materials without the need for radiation protection measures. Terahertz tomography offers the opportunity to inspect such objects from multiple angles not only by measuring the absorption but also by acquiring the time-of-flight of the radiation. Hence, this technique facilitates the reconstruction of the complete complex refractive index of a sample under test. Even complicated surface structures can be imaged, provided the feature size is above the diffraction limit roughly given by the wavelength of the terahertz radiation in use. For industrial applications, computational efficiency and imaging performance are crucial. Therefore, we apply the iterative conjugate gradient least square (CGLS) algorithm to reconstruct images from terahertz tomography data. To ensure reliable convergence of this semi-convergent CGLS algorithm a stopping mechanism based on the L-curve criterion is implemented. The result is a fast-converging, parallelizable method, which offers the flexibility to adapt to the specifics of terahertz tomography. As an example of this adaptability, we implement a non-negativity constraint, suppressing noise in the image and significantly enhancing reconstruction quality.

Keywords

• Terahertz radiation
• computed tomography
• nondestructive testing
• reconstruction algorithms
• imaging
• conjugate gradient least square (CGLS)