# A Differential Measurement System for Surface Topography Based on a Modular Design
## 6 Conclusions and Discussion  
In this paper, a concept of modular design for a high-accuracy measurement system is proposed. In the presented system, all of the components were standard components and easily available in the market. Instead of customizing high-accuracy built-in references, optical flats were applied in the proposed system to separate the geometric error caused by the mechanical components. The DoF analysis showed that this system could be easily assembled without special adjustment process. This system could also be easily scaled up for a bigger measurement range by introducing sliders with longer travel lengths. The experimental results showed that the developed system was able to achieve nanometer repeatability and reproducibility for a surface topography measurement in the range of 100 mm \(\times\) 100 mm. The motivation for developing this system was to explore a generic methodology of setting up systems for high-accuracy topography measurements in a large area. Table 4 is the comparison between the presented system and other topography measurement technologies. As shown in Table 4, the optical topography measurement technologies, such as confocal microscopy, coherence scanning interferometry and focus variation are able to achieve nanometer vertical resolution in a millimeter measurement area. The measurement resolution and area are determined by the optical DOV (depth of view) and FOV (field of view) respectively. Stylus profilometry is able to perform the high-resolution measurements in a larger area but the contact probing mechanism limited its applications if the target surfaces are soft or have cleanliness requirements. Compared with the measurement systems based on scanning tunneling microscopy (STM) or atomic force microscopy (AFM) [19; 20], The proposed system is not an ideal solution for ultra-precision applications. The objective of this study was to develop a measurement system with sub-micron level accuracy in a measurement area up to 100 mm \(\times\) 100 mm. Targeted applications of the proposed system include the metrological tasks in advanced manufacturing industries, such as semiconductor, consumer electronics, aerospace, etc. This system is now working as a research platform for the authors' team. The authors' team has published some relevant work, including a confocal measurement system with expanded vertical measurement range [36], fast chromatic confocal sensor development [37], and image grating development for displacement measurement as an alternative of linear encoders [38]. These in-house developed technologies will be integrated into the prototype presented in this paper. Conceptualization, F.C. ; Methodology, F.C. ; Software, J.Z. and H.S. ; Validation, F.C., Y.W. and Q.Y. ; Formal Analysis, F.C., J.Z. and H.S. ; Investigation, J.Z. and H.S. ; Resources, Q.Y. and Y.W. ; Data Curation, J.Z. ; Writing-Original Draft Preparation, F.C. ; Writing-Review & Editing, F.C. ; Visualization, J.Z. ; Supervision, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Technologies**} & **Measurement** & **Measurement** & \multirow{2}{*}{**Probe**} & **Motion Error** \\  & **Resolution** & **Area** & & **Compensation** \\ \hline Confocal microscopy & \(\sim\)10 nm & \(\sim\)1 mm & Optical & No \\ coherence scanning interferometry & \(\sim\)1 nm & \(\sim\)1 mm & Optical & No \\ Focus variation & \(\sim\)20 nm & \(\sim\)1 mm & Optical & No \\ Stylus profilometry & \(\sim\)1 nm & \(\sim\)100 mm & Contact & No \\ HQU developed system & \(\sim\)10 nm & 100 mm & Optical & Yes \\ STM with high-precision stage [19] & Sub-nanometer & \(\sim\)1 mm & STM & Not stated \\ AFM with high-precision stage [20] & Sub-nanometer & \(\sim\)1 mm & AFM & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Technology comparison. F.C. ; Project Administration, Y.W. and Q.Y. ; Funding Acquisition, Q.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (Grant No.