DERIVATION OF EXPRESSION FOR PHOTOCURRENT DENSITY FOR NON-DESTRUCTIVE TESTING OF 3D PRINTING FILAMENT BY MEANS OF TERAHERTZ SPECTROSCOPY

Abstract

This report presents a revised expression for the photocurrent density in terahertz spectroscopy, which is a non-destructive testing technique of particular interest to the authors in the context of 3D printed parts. 3D printing, also known as additive manufacturing, involves creating three-dimensional objects based on computer-aided design (CAD) models. The process entails depositing, joining, or solidifying material under computer control, layer by layer.
 
 Defects in 3D printing, such as weak infill, gaps in thin walls, inconsistent extrusion, layer separation, and bed drop, can lead to low printing quality and render some printed parts unfit and unsafe for use. Moreover, the ability to tamper with internal layers without altering the exterior could result in the production of maliciously defective parts without detection. Therefore, it is crucial to test 3D printed details and filaments at each stage of processing using non-destructive methods.
 
 A comprehensive review of the relevant literature indicates the potential for enhancing measurement accuracy through various improvements in terahertz spectrometer models. The mathematical model for the photocurrent involves a convolution integral of the current density and the laser radiation pulse that irradiates the surface of the material under study. The expression within the integral incorporates parameters such as the duration of the optical pulse, carrier lifetime, and momentum relaxation time. By evaluating the integral, the result can be obtained as two terms, each being a product of an exponent and a complementary error function with the same parameters mentioned earlier.
 
 The calculation involves several steps, including a change of variables during integration. Verification using Maple software demonstrates agreement with analytical calculations and suggests a pathway for further refinement of the expression for the photocurrent density. The Maple program influenced the results by means of repeating same calculation with aid of computer and allowing to compare if analytical results are same and true, also it could be use for simulation and example calculation, for results graphical representation. 
 
 The connection between the obtained mathematical expression and its relation to 3D printing (additive manufacturing) exists. The explanation is in that the 3D printer uses filament, filament has defects, defectoscopy of filament in the terahertz domain have models and methods. The research of defectoscopy models and methods is helpful to increase accuracy of measurement of filament defect parameters and account on it and improve the quality of 3D printed details.