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\begin{document}

\title{Supporting Information for ``Intelligent Shape~Decoding of a Soft
Optical Waveguide Sensor''~~}



\author[1]{Chi Hin Mak}%
\author[1]{Yingqi Li}%
\author[1]{Kui Wang}%
\author[1]{Mengjie Wu}%
\author[1]{Justin Di-Lang Ho}%
\author[1]{Qi Dou}%
\author[1]{Kam-Yim Sze}%
\author[1]{Kaspar Althoefer}%
\author[1]{Ka-Wai Kwok}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 18, 2024}


\begingroup
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\sloppy


In this study, we utilize simple light-emitting diodes (LEDs) and
photodetectors (PDs) combined with an intelligent shape decoding
framework to enable 3D shape sensing of a self-contained flexible
substrate. Finite element analysis (FEA) is leveraged to optimize the
LED-PD layout and enrich ground-truth data from sparse to dense points
for model training. The mapping from light intensities to overall sensor
shape was achieved with an autoregression-based model that considers
temporal continuity and spatial locality. The sensing framework was
evaluated on an A5-sized flexible sensor prototype and a fish-shaped
prototype, where sensing accuracy (RMSE = 0.27 mm) and repeatability (\selectlanguage{greek}Δ
\selectlanguage{english}light intensity \textless{} 0.31\% over 1000 cycles) were tested
underwater. We validate an affordable alternative to FBG sensors with
high-order sensing outputs, where demonstrations are supplemented in the
below videos.



\section*{Supplementary Figures}

{\label{705958}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/temp/temp}

\end{center}
\end{figure}

\textbf{Figure S1. (A)} LED \& PD placement of the fish-shaped waveguide
sensor. \textbf{(B)} Sandwiched PDMS structure of the soft waveguide
sensor, where opaque and semi-opaque layers are silicone-dyed to enable
internal reflection.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/temp1/temp}

\end{center}
\end{figure}

\textbf{Figure S2.} Nodal Displacement error of four models in the
ablation study, which do not include three key components, namely
time-window (TW), history (HX) module and patch-wise (PW) processing.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.56\columnwidth]{figures/temp2/temp2}

\end{center}
\end{figure}

\textbf{Figure S3. ~}Schematic of the FPGA PCB used for both A5-sized
and fish-shaped waveguide sensors, sufficient for 30min consecutive
wireless sensing.~





\section*{Supplementary Videos}

{\label{888270}}

\subsection*{Supplementary Video V1}

{\label{814550}}

Rich media available at \url{https://youtu.be/50yvIG0ELWs}

\subsection*{Supplementary Video V2 ~}

{\label{221956}}

Rich media available at \url{https://youtu.be/PdNCJWE-fqI}

\subsection*{Supplementary Video V3}

{\label{477074}}

Rich media available at \url{https://youtu.be/1ER9xcBRkcw}

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