Three-dimensional microscopic light field particle image velocimetry


A microscopic particle image velocimetry (\(\mu \text {PIV}\)) technique is developed based on light field microscopy and is applied to flow through a microchannel containing a backward-facing step. The only hardware difference from a conventional \(\mu\)PIV setup is the placement of a microlens array at the intermediate image plane of the microscope. The method combines this optical hardware alteration with post-capture computation to enable 3D reconstruction of particle fields. From these particle fields, we measure three-component velocity fields, but find that accurate velocity measurements are limited to the two in-plane components at discrete depths through the volume (i.e., 2C-3D). Results are compared with a computational fluid dynamics simulation.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. Belden J, Pendlebury J, Jafek A, Truscott TT (2014) Advances in light field imaging for measurement of fluid mechanical systems. Dynamic data-driven environmental systems science (DyDESS) conference

  2. Belden J, Truscott TT, Axiak MC, Techet AH (2010) Three-dimensional synthetic aperture particle image velocimetry. Meas Sci Technol 21:125403

    Article  Google Scholar 

  3. Bown MR, MacInnes JM, Allen RWK, Zimmerman WBJ (2006) Three-dimensional, three-component velocity measurements using stereoscopic micro-piv and ptv. Meas Sci Technol 17:2175–2185

    Article  Google Scholar 

  4. Chen S, Angarita-Jaimes N, Angarita-Jaimes D, Pelc B, Greenaway AH, Towers CE, Lin D, Towers DP (2009) Wavefront sensing for three-component three-dimensional flow velocimetry in microfluidics. Exp Fluids 47(4–5):849–863

    Article  Google Scholar 

  5. Cierpka C, Segura R, Hain R, Kähler C (2010) A simple single camera 3c3d velocity measurement technique without errors due to depth of correlation and spatial averaging for microfluidics. Meas Sci Technol 21(4):045401

    Article  Google Scholar 

  6. Cierpka C, Kaehler CJ (2012) Particle imaging techniques for volumetric three-component (3d3c) velocity measurements in microfluidics. J Vis 15:1–31

    Article  Google Scholar 

  7. Elsinga GE, Scarano F, Wieneke B (2006) Tomographic particle image velocimetry. Exp Fluids 41(6):933–947

    Article  Google Scholar 

  8. Fouras A, Jacono DL, Nguyen CV, Hourigan K (2009) Volumetric correlation piv: a new technique for 3d velocity vector field measurement. Exp Fluids 47:569

    Article  Google Scholar 

  9. Galbraith W (1955) The optical measurement of depth. Q J Microsc Sci 3(35):285–288

    Google Scholar 

  10. Kähler CJ, Scharnowski S, Cierpka C (2012) On the uncertainty of digital piv and ptv near walls. Exp Fluids 52:1641–1656

    Article  Google Scholar 

  11. Kim H, Grosse S, Elsinga G, Westerweel J (2011) Full 3d–3c velocity measurement inside a liquid immersion droplet. Exp Fluids 51:395–405

    Article  Google Scholar 

  12. Kim H, Westerweel J, Elsinga GE (2012) Comparison of tomo-piv and 3d-ptv for microfluidic flows. Meas Sci Technol 24(2):024007

    Article  Google Scholar 

  13. Levoy M (2006) Light fields and computational imaging. IEEE Comput 39(8):46–55

    Article  Google Scholar 

  14. Levoy M, Hanrahan P (1996) Light field rendering. ACM SIGGRAPH, pp 31–42

  15. Levoy M, Ng R, Adams A, Footer M, Horowitz M (2006) Light field microscopy. ACM Trans Graph 25(3):924–934

    Article  Google Scholar 

  16. Lima R, Wada S, Tanaka S, Takeda M, Ishikawa T, Tsubota KI, Imai Y, Yamaguchi T (2007) In vitro blood flow in a rectangular pdms microchannel: experimental observations using a confocal micro-piv system. Biomed Microdev 10(2):153–167

    Article  Google Scholar 

  17. Lindken R, Westerweel J, Wieneke B (2006) Stereoscopic micro particle image velocimetry. Exp Fluids 41:161–171

    Article  Google Scholar 

  18. Lindken R, Rossi M, Grosse S, Westerweel J (2009) Micro-particle image velocimetry: recent developments, applications, and guidlines. Lab Chip 9:2551–2567

    Article  Google Scholar 

  19. Lynch K (2011) Development of a 3-d fluid velocimetry technique based on light field imaging. Master’s thesis, Auburn University

  20. Lynch K, Fahringer T, Thurow B (2012) Three-dimensional particle image velocimetry using a plenoptic camera. In: 50th AIAA Aerospace Sciences Meeting. Nashville, TN

  21. Ng R, Levoy M, Bredif M, Duval G, Horowitz M, Hanrahan P (2005) Light field photography with a hand-held plenoptic camera. Stanford Tech Report

  22. Ooms T, Lindken R, Westerweel J (2009) Digital holographic microscopy applied to measurement of a flow in a t-shaped micromixer. Exp Fluids 47(6):941–955

    Article  Google Scholar 

  23. Park JS, Choi CK, Kihm KD (2004) Optically sliced micro-piv using confocal laser scanning microscopy (clsm). Exp Fluids 37:105–119

    Article  Google Scholar 

  24. Pereira F, Gharib M (2002) Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows. Meas Sci Technol 13(5):683

    Article  Google Scholar 

  25. Pereira F, Gharib M, Dabiri D, Modarress D (2000) Defocusing digital particle image velocimetry: a 3-component 3-dimensional dpiv measurement technique. Application to bubbly flows. Exp Fluids 29(1):S078–S084

    Google Scholar 

  26. Pereira F, Lu J, Castano-Graff E, Gharib M (2007) Microscale 3d flow mapping with \(\mu\)ddpiv. Exp fluids 42(4):589–599

    Article  Google Scholar 

  27. Peterson SD, Chuang H-S, Wereley ST (2008) Three-dimensional particle tracking using micro-particle image velocimetry hardware. Meas Sci Technol 19(11):115406

    Article  Google Scholar 

  28. Sveen KJ (2004) An introduction to MatPIV v.1.6.1 Preprint series. Mechanics and Applied Mathematics

  29. Sheng J, Malkiel E, Katz J (2006) Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl Opt 45(16):3893–3901

    Article  Google Scholar 

  30. Sibarita J-B (2005) Deconvolution microscopy. Adv Biochem Eng/Biotechnol 95:1288–1292

    Google Scholar 

  31. SplashLab (2014) Synthetic aperture imaging.

  32. Tien W-H, Kartes P, Yamasaki T, Dabiri D (2008) A color-coded backlighted defocusing digital particle image velocimetry system. Exp Fluids 44(6):1015–1026

    Article  Google Scholar 

  33. Tien W-H, Dabiri D, Hove JR (2014) Color-coded three-dimensional micro particle tracking velocimetry and application to micro backward-facing step flows. Exp Fluids 55(3):1–14

    Article  Google Scholar 

  34. Yoon SY, Kim KC (2006) 3d particle position and 3d velocity field measurement in a microvolume via the defocusing concept. Meas Sci Technol 17:2897

    Article  Google Scholar 

  35. Zhang Z (2010) A practicle introduction to light field microscopy. Computer Graphics Laboratory. Electrical Engineering, Stanford University, pp 1–15

Download references


This material is based upon work supported by the National Science Foundation under Grant No. 1126862. JB gratefully acknowledges funding from the Office of Naval Research under task number N0001413WX20545 monitored by program officer Dr. Ronald Joslin (ONR Code 333).

Author information



Corresponding author

Correspondence to Tadd T. Truscott.



We now derive the relationship between the synthetic image plane displacement, d and the corresponding object plane displacement, \(\delta,\) as given by Eq. 2 and shown schematically in Fig. 1a. The object plane is located at a distance

$$\begin{aligned} s_o^o = \delta +f_o \end{aligned}$$

to the left of the objective. The location of the image formed by the objective is found using the thin lens equation to give

$$\begin{aligned} s_i^o=\frac{f_o s_o^o}{s_o^o - f_o}, \end{aligned}$$

where \(s_i^o\) is positive to the right of the objective as drawn in Fig. 1a. The image formed by the objective becomes the object for the tube lens and is at a distance

$$\begin{aligned} s_o^t =\, & {} f_t+f_o-s_i^o\nonumber \\ =\, & {} f_t+f_o-\frac{f_o s_o^o}{s_o^o-f_o} \end{aligned}$$

from the tube lens (\(s_o^t\) is positive to the left of the tube lens). The thin lens equation is then applied to the tube lens to give the distance to the image plane, which coincides with the displaced \(s't'\) plane,

$$\begin{aligned} s_i^t = \frac{f_t\left( \frac{-f_o^2}{s_o^o-f_o}\right) +f_t^2}{\frac{-f_o^2}{s_o^o-f_o}} \end{aligned}$$

Inserting the relation for object plane displacement given in Eq. 11, Eq. 14 can be solved to give

$$\begin{aligned} s_i^t= & {} f_t-\left( \frac{f_t^2}{f_o^2}\right) \delta \nonumber \\= & {} f_t-M^2\delta, \end{aligned}$$

where the definition for magnification has been inserted. Finally, inserting the relation \(s_i^t = f_t-d\) into Eq. 15 and rearranging yields,

$$\begin{aligned} \delta = \frac{d}{M^2} \end{aligned}$$

As described in Sect. 2.1, the object plane displacements must be corrected to account for the fact that the index of refraction of the object medium differs from the medium in which the objective is immersed. Pereira and Gharib (2002) derived the correction for the apparent object depth Z, measured from the objective lens plane to the location at which the object would exist if there were no index of refraction changes. The actual object depth is given by

$$\begin{aligned} Z^\prime = D + w + \Omega \left( n_f \right) \left[ Z - D - \frac{w}{\Omega \left( n_w \right) } \right], \end{aligned}$$

where D is the distance from the objective plane to the channel wall, w is the thickness of the channel wall, \(n_w\) is the index of refraction of the channel wall and the function \(\Omega \left( \nu \right)\) is defined as

$$\begin{aligned} \Omega \left( \nu \right) = \sqrt{\frac{R^2}{Z^2} \left[ \left( \frac{\nu }{n}\right) ^2 - 1 \right] + \left( \frac{\nu }{n}\right) ^2} \end{aligned}$$

where \(R^2 = X^2 + Y^2\) is the radial coordinate of the object point with respect to the main optical axis and n is the index of refraction of the medium in which the objective is immersed (\(n = 1\) herein). For rather extreme values in our setup of \(R = 400\,\upmu\)m and \(Z = 1000\,\upmu\)m, we have \(\Omega (n_f ) = 1.353,\) which is approximately equal to \(n_f/n = 1.333.\) Therefore, we make an approximation that is often made (Tien et al. 2008; Galbraith 1955) and assume that \(\Omega (n_f ) \approx n_f/n,\) which conveniently removes the dependence of the depth correction on the radial coordinate. Thus, Eq. 17 reduces to

$$\begin{aligned} Z^\prime = \frac{n_f}{n} Z + \left( 1-\frac{n_f}{n} \right) D + \left( 1-\frac{n_f}{n_w} \right) w \end{aligned}$$

where we have also assumed that \(\Omega \left( n_w\right) \approx n_w/n.\) Therefore, the actual corrected depth distance between any two planes is given as:

$$\begin{aligned} \Delta Z^\prime = Z^\prime _2 - Z^\prime _1 = \frac{n_f}{n} \left( Z_2-Z_1\right) = \frac{n_f}{n} \Delta Z \end{aligned}$$

Substituting for \(\Delta Z\) the apparent object plane displacement \(\delta,\) we get

$$\begin{aligned} \delta ^\prime = \frac{n_f}{n} \delta \end{aligned}$$

which is Eq. 8.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Truscott, T.T., Belden, J., Ni, R. et al. Three-dimensional microscopic light field particle image velocimetry. Exp Fluids 58, 16 (2017).

Download citation


  • Particle Image Velocimetry
  • Point Spread Function
  • Light Field
  • Particle Tracking Velocimetry
  • Microlens Array