Experiments in Fluids

, 60:21 | Cite as

Volumetric calibration enhancements for single-camera light-field PIV

  • Shengxian ShiEmail author
  • Junfei Ding
  • T. H. New
  • You LiuEmail author
  • Hanmo Zhang
Research Article


This work presents a volumetric calibration method for single-camera light-field particle image velocimetry (light-field PIV or LF-PIV). The proposed technique makes use of the unique point-like feature of particle light-field images to accurately determine affected pixels for a spatial voxel over a relative large measurement volume. A calibration model is derived based on Gaussian optics, which relates a spatial point light source with its confusion circle produced on microlens array (MLA), and optical distortions are accounted for by introducing five calibration parameters. By taking lens defects and misalignment between MLA and image sensor into account, the calibration method can calculate weighting coefficient for particle image reconstruction more accurately than the theoretical ray-tracing method, especially for regions further away from focal plane where light ray deflections are significant due to optical distortions. The volumetric calibration method was validated by simulation tests using synthetic light-field images, and has been successfully applied to a classic vortex-ring LF-PIV measurement, where the measurable range in depth direction was successfully extended and the quality of reconstructed volumetric velocity field was greatly improved.

Graphical abstract

List of symbols


Object distance


Image distance


Focal length of the main lens

\({f_\# }\)

F-number of the main lens


Effective aperture of the main lens


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


Focal length of lenslet


Lenslet pitch


Lenslet centre (relative to optical axis)


Offset of a light ray from the lenslet centre


Intersection of a light ray made with the pixel plane


Intersection of a light ray made with the main lens, light ray passes lenslet centre


Intersection of a light ray made with the main lens


Coordinate of the ith lenslet centre in pixel plane


Lenslet pitch (in pixel plane), \({d_{\text{l}}}={p_{\text{l}}}\frac{{{S_{\text{i}}}+{f_{\text{l}}}}}{{{S_{\text{i}}}}}=\left| {{C_{{\text{l}}(i)}} - {C_{{\text{l}}(i - 1)}}} \right|\)

\(O\left( {X,Y,Z} \right)\)

3D coordinate of a point light source

\(E\left( {X,Y,Z} \right)\)

Intensity of a voxel at \(\left( {X,Y,Z} \right)\)


Pixel intensity of a light-field image at image coordinate \(({x_i},{y_i})\)

\(w={w_1} \times {w_2}\)

Weighting coefficient for MART reconstruction


Lenslet weighting coefficient


Pixel weighting coefficient


Coordinate of the confusion circle centre (in MLA plane)


Diameter of the confusion circle (in MLA plane)


Coordinate of the confusion circle centre (in pixel plane), \({C_{df}}=C{'_{df}}\frac{{{S_{\text{i}}}+{f_{\text{l}}}}}{{{S_{\text{i}}}}}\)


Diameter of the confusion circle (in pixel plane), \({D_{df}}=D{'_{df}}\frac{{{S_{\text{i}}}+{f_{\text{l}}}}}{{{S_{\text{i}}}}}\)

\({\mathcal{M}}_{4\times 3}\)

Mapping matrix that relates a spatial point \(O\left( {X,Y,Z} \right)\) with its corresponding \({C_{df}}\)


Centre of point-like feature beneath each lenslet


Particle per microlens



Financial support provided by National Natural Science Foundation of China (Grant nos. 11472175, 11772197) and Singapore Ministry of Education AcRF Tier-2 grant (Grant no. MOE2014-T2-1-002) are gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.College of Power and Energy EngineeringHarbin Engineering UniversityHarbinChina
  4. 4.Shanghai Aerospace Control Technology InstituteShanghai Key Laboratory of Space Intelligent Control TechnologyShanghaiChina

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