# Focus Estimation Methods for Use in Industrial SFF Imaging Systems
## 5 Conclusions  
What sets this study apart is incorporating actual interference instead of digitally introduced noise. This type of interference is implemented through supplementary industrial illuminators, adjustments to acquisition parameters, and imaging of the surfaces of actual industrial products. An industrial-grade camera is employed, and a tunable liquid lens carries out the image plane displacement.  
The results have identified the DSLT and DPTT operators as the primary candidates for further research and testing of the SFF method. These operators yield the best results in terms of error reduction and exhibit robustness to the disturbances considered in the study. Moreover, they demand lower computational power compared to other operators.  
This paper pursued a different approach for focus plane selection methods, diverging from solutions found in the literature [17]. The three-point interpolation with a Gaussian function has been dismissed, and the proposed alternatives include the maximum and centre of gravity (CoG) methods.  
This study confirms the applicability of both proposed focus plane selection methods. The method based on the maximum function proves sufficient for most cases considered. The absence of floating-point calculations results in less computing power and the possibility of using hardware acceleration methods [33; 34; 35]. The CoG method allows for the increased resolution in the \(z\)-axis. RMSE errors for the CoG method have been lower than for the maximum method.  
The research presented in this paper can be expanded to include multi-channel images. We are currently working on incorporating data from the R, G, and B channels into the SFF method. This will allow for the generation of a 3D image that can be further enhanced with RGBD (red, green, blue, depth) information.  
The next phase of the presented research could also involve an extension to 3D scene reprojection and spatial scene imaging.  
Conceptualization, B.L. and A.S.; methodology, B.L. and A.S.; software, B.L. and A.S.; validation, B.L. and A.S.; formal analysis, B.L. and A.S.; investigation, B.L. and A.S.; resources, B.L. and A.S.; data curation, B.L. and A.S.; writing--original draft preparation, B.L. and A.S.; writing--review and editing, B.L. and A.S.; visualization, B.L. and A.S.; supervision, A.S.; project administration, A.S.; funding acquisition, A.S. All authors have read and agreed to the published version of the manuscript.  
Funding: This study was funded by the AGH University of Krakow within the scope of subsidy funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: SFF Shape-From-Focus QC Quality control ToF Time of flight DL Some light BL Bar light DRL Direct ring light HRL Horizontal ring light CL Collimated light CoG Centre of gravity RMSE Root mean square error AFE Absolute fit error HM Height map