Microscopic characterizations, such as Scanning Electron Microscopy (SEM), are widely used in scientific research for visualizing and analyzing microstructures. Determining the scale bars is an important first step of accurate SEM analysis; however, currently, it mainly relies on manual operations, which is both time-consuming and prone to errors. To address this issue, we propose a multi-modal and automated scale bar detection and extraction framework that provides concurrent object detection, text detection and text recognition with a Large Language Model (LLM) agent. The proposed framework operates in four phases; i) Automatic Dataset Generation (Auto-DG) model to synthesize a diverse dataset of SEM images ensuring robust training and high generalizability of the model, ii) scale bar object detection, iii) information extraction using a hybrid Optical Character Recognition (OCR) system with DenseNet and Convolutional Recurrent Neural Network (CRNN) based algorithms, iv) an LLM agent to analyze and verify accuracy of the results. The proposed model demonstrates a strong performance in object detection and accurate localization with a precision of 100%, recall of 95.8%, and a mean Average Precision (mAP) of 99.2% at IoU=0.5 and 69.1% at IoU=0.5:0.95. The hybrid OCR system achieved 89% precision, 65% recall, and a 75% F1 score on the Auto-DG dataset, significantly outperforming several mainstream standalone engines, highlighting its reliability for scientific image analysis. The LLM is introduced as a reasoning engine as well as an intelligent assistant that suggests follow-up steps and verifies the results. This automated method powered by an LLM agent significantly enhances the efficiency and accuracy of scale bar detection and extraction in SEM images, providing a valuable tool for microscopic analysis and advancing the field of scientific imaging.