# Estimating Thermal Material Properties Using Solar Loading Lock-in Thermography
## 5 Conclusions and Further Work  
The presented algorithm has shown good measurement results, albeit non-optimal measurement conditions in the field experiment. It can not only obtain qualitative measurement results on the retaining wall structure but also identify thermal thickness differences using the phase angle information. The application of the presented algorithm can be extended to other kinds of infrastructure for inspection and monitoring purposes.  
Further work has to be done to bring the measured results closer to the actual thermal material properties of the structure; this involves separating thermal effects to get a better understanding on the exact heat flow acting on the test subject. How phase angle information can be used to estimate thermal thickness and do quantitative analysis in specific setups is subject to ongoing research as well.  
The calibration approximation has to verified under other conditions like other materials or other excitation conditions (i.e., more Sun, another season). If the approximation and regression fit holds for the other conditions, it can be shown to be sufficiently robust to investigate further on how this exact finding can be explained considering the physical effects acting on the test subjects.  
Furthermore, increasing accuracy by isolating singular systematic error sources and developing a more sophisticated correction term based on physical properties can be done. For example, measuring apparent ambient temperature with a pyrgeometer and estimating radiative heat flux directly. Using a pyranometer to measure radiative heat input the remaining heat in-/output can be inferred to be convective. Finally, all heat in- and outputs are known and a more accurate model can be set up.  
Lastly, a novel method could be devised to include amplitude information from various other frequencies. This work focusses solely on the fundamental 1/24 h frequency, where as other frequency bins are sure to contain additional information.  
Figure 11: Phase image of the fundamental 24 h period. This image depicts the 24 h phase information every pixel over the 96 h measurement period \(arctan\big{(}\Im\{S_{xy}\}/\Re e\{S_{xy}\}\big{)}\). Note that 90\({}^{\circ}\) phase would correlate to an angle of a sine wave, which has its origin at the time of the experiment start (8:00) and maximum 6 h later at 14:00. Note that higher angle values mean ’earlier’ thermal responses to the input. If the phase angle value is lower, that corresponds to a ’slower’ response to the periodic heat input.  
Author Contributions:Conceptualization, S.K. and H.-G.H.; methodology, S.K.; software, S.K.; validation, S.K., H.F., H.-G.H.; writing--original draft preparation, S.K.; writing--review and editing, S.K., H.F., H.-G.H.; visualization, S.K.; supervision, H.-G.H.; project administration, H.-G.H.; funding acquisition, H.-G.H. All authors have read and agreed to the published version of the manuscript.  
We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) and Saarland University within the funding programme Open Access Publishing: This research was funded by the European Regional Development Fund (ERDF), especially grant number 14.2.1.4-2016-1.  
Informed Consent Statement:Informed consent was obtained from all subjects involved in the study.  
Most data presented in this study are available on request from the corresponding author, including scripts and embedded software. Some data are not publicly available due to privacy reasons of the property owners.  
Gratitude goes to the RAG Montan Immobilien for access to the experiment site. Furthermore, the authors thank [PERSON], [PERSON], [PERSON] and [PERSON] for their help with experimental setup and conduction.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.