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Volumetric calibration for scheimpflug light-field PIV

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Abstract

This work presents a volumetric calibration method for Scheimpflug plenoptic camera in particle image velocimetry. To establish a prerequisite foundation for the Scheimpflug light-field PIV, the proposed technique makes use of the unique point-like pattern and plenoptic disc feature of particle light-field images to accurately determine affected pixels for a spatial voxel in a measurement volume. With Gaussian optics, an ideal projection model of the Scheimpflug plenoptic camera is derived to provide a basis for the calibration method. By taking lens defects, optical window’s imperfection, inaccurate tilted-angle and other practical application difficulties into account, the calibration method can establish the mapping relationship between a spatial voxel and its affected pixels correctly. The volumetric calibration method was validated by a classic vortex-ring PIV measurement where the correspondence between a voxel and its affected pixels was accurately determined and the volumetric velocity field was successfully acquired.

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Abbreviations

\(f_{m} ,\) :

 Focal length of the main lens

\(f_{\# } ,{ }f\) :

f-number of the main lens

\(p_{m} ,\) :

 Effective size of the main lens

\(S_{o} ,\) :

 Distance from the object focal plane to the main lens

\(S_{i} ,\) :

Distance between the main lens and the image focal plane

\(M,\) :

   Magnification of the plenoptic camera, \(M = - S_{o} /S_{i}\)

\(\theta ,{ }\) :

Tilted-angle, the angle between main lens plane and MLA plane

\(\alpha ,{ }\) :

The angle between main lens plane and focal plane, \(\tan \alpha = - M\tan \theta\)

\(f_{l} ,\) :

  Focal length of the lenslet

\(p_{l} ,\) :

Physical size of each lenslet pitch

\(p_{p} ,\) :

  Physical size of each pixel pitch

\(O,{ }\) :

Ideal optical centre

\(O_{m} ,{ }\) :

Intersection point between optical axis and MLA plane

\(O_{p} ,{ }\) :

Perpendicular projected point of \(O_{m}\) on sensor plane

\(A,{ }\) :

Aperture centre

\(A_{1} ,{ }\) :

Perpendicular projected point of \(A\)on MLA plane

\(A_{m} ,{ }\) :

Size of aperture

\(P,{ }\) :

Object point, a point light source

\(Q,{ }\) :

Converging image point

\(Q_{1} ,{ }\) :

Perpendicular projected point of \(Q\) on MLA plane

\(R,{ }\) :

Intersection point of the MLA plane and the line that pass through \(A\) and \(Q\)

\(p_{ci} ,\) :

 Centre of the \(i\)-th point-like pattern beneath \(i\)-th lenslet

\(h_{ci} ,{ }\) :

Centre of the \(i\)-th lenslet on the senor plane

\(g_{ci} ,{ }\) :

Centre of the \(i\)-th aperture projection point beneath \(i\)-th lenslet

\(l_{ci} ,{ }\) :

Centre of the \(i\)-th lenslet on MLA plane

\(EoC,{ }\) :

Ellipse of confusion formed on MLA plane

\(Center_{EoC} ,\) :

 Center of the \(EoC\) formed on MLA plane

\(D_{EoC}^{major} ,\) :

 Length of the \(EoC\)'s major axis

\(D_{EoC}^{minor} ,\) :

 Length of the \(EoC\)'s minor axis

\(CoC,{ }\) :

Circle of confusion formed on MLA plane

\(D_{CoC} ,{ }\) :

Dimeter of the \(CoC\)

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Acknowledgements

The authors are grateful to Dr. Yinshen Luan and Dr. Di Mei for their constructive suggestions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11772197, 11911530175 and 12172222).

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

    Zhou Zhao & Shengxian Shi

  2. Engineering Research Center of Gas Turbine and Civil Aero Engine, Ministry of Education, Shanghai, China

    Zhou Zhao & Shengxian Shi

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  1. Zhou Zhao
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  2. Shengxian Shi
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Correspondence to Shengxian Shi.

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Zhao, Z., Shi, S. Volumetric calibration for scheimpflug light-field PIV. Exp Fluids 62, 251 (2021). https://doi.org/10.1007/s00348-021-03350-0

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