  As the aerospace industry becomes increasingly demanding for stronger
lightweight materials, the ultra-strong carbon nanotube (CNT) composites with
highly aligned CNT network structures could be the answer. In this work, a
novel methodology applying topological data analysis (TDA) to the scanning
electron microscope (SEM) images was developed to detect CNT orientation. The
CNT bundle extensions in certain directions were summarized algebraically and
expressed as visible barcodes. The barcodes were then calculated and converted
into the total spread function $V(X,\theta)$, from which the alignment fraction
and the preferred direction could be determined. For validation purposes, the
random CNT sheets were mechanically stretched at various strain ratios ranging
from $0-40\%$, and quantitative TDA analysis was conducted based on the SEM
images taken at random positions. The results showed high consistency
($R^2=0.975$) compared to the Herman's orientation factors derived from the
polarized Raman spectroscopy and wide-angle X-ray scattering analysis.
Additionally, the TDA method presented great robustness with varying SEM
acceleration voltages and magnifications, which might alter the scope in
alignment detection. With potential applications in nanofiber systems, this
study offers a rapid and simple way to quantify CNT alignment, which plays a
crucial role in transferring the CNT properties into engineering products.
