Abstract
A height estimating function is proposed based on geometric analysis for a three-dimensional (3-D) measurement system using a digital light processing (DLP) projector and a camera. The proposed 3-D shape measurement method is a hybrid method that combines the geometric parameter measuring method and the least squares method. This method uses the phase-to-height relationship for one line by plane analysis, and the related parameters are estimated using the least squares method. The proposed method has one function per image line instead of one function per image pixel. Sinusoidal fringe patterns of the projector are projected on the object, and the phase of the measuring point is calculated from the camera image. Then, the relationship between the phase by fringe patterns and the height of the measuring point is described as a parameter of the horizontal coordinate on the image plane. Thus, the 3-D shape of the object can be obtained. Our experiments show that the error of the modeling function is within ±0.1 mm when the x-z working range is 100×50 mm. Therefore, the proposed method can dramatically reduce the number of mapping functions needed for 3-D measurement using the geometric relationship between the projector and camera.
Similar content being viewed by others
References
Chen, F., Brown, G. M., and Song, M., “Overview of Three-Dimensional Shape Measurement using Optical Methods,” Optical Engineering. Vol. 39, No. 1, pp. 10–22, 2000.
Hu, Y., Xi, J., Li, E., Chicharo, J., and Yang, Z., “Three-Dimensional Profilometry based on Shift Estimation of Projected Fringe Patterns,” Applied Optics, Vol. 45, No. 4, pp. 678–687, 2006.
Su, W., Shi, K., Liu, Z., Wang, B., Reichard, K., and Yin, S., “A Large-Depth-of-Field Projected Fringe Profilometry using Super-Continuum Light Illumination,” Optics Express, Vol. 13, No. 3, pp. 1025–1032, 2005.
Baumbach, T., Osten, W., Kopylow, C., and Jüptner, W., “Remote Metrology by Comparative Digital Holography,” Applied Optics, Vol. 45, No. 5, pp. 925–934, 2006.
Purcell, D., Davies, A., and Farahi, F., “Effective Wavelength Calibration for Moiré Fringe Projection,” Applied Optics, Vol. 45, No. 34, pp. 8629–8635, 2006.
Chung, B., So, B. and Lee, S., “Flexible Vision Inspection for Seat Frame of Automobile using Slit Beam,” Int. Journal of Precision Engineering and Manufacturing, Vol. 12, No. 4, pp. 605–611, 2011.
Sansoni, G., Carocci, M., and Rodella, R., “Three-Dimensional Vision based on a Combination of Gray-Code and Phase-Shift Light Projection: Analysis and Compensation of the Systematic Errors,” Applied Optics, Vol. 38, No. 31, pp. 6565–6573, 1999.
Tian, A., Jiang, Z., and Huang, Y., “A Flexible New Three-Dimensional Measurement Technique by Projected Fringe Pattern,” Optics and Laser Technology, Vol. 38, No. 8, pp. 585–589, 2006.
Da, F. and Gai, S., “Flexible Three-Dimensional Measurement Technique based on a Digital Light Processing Projector,” Applied Optics, Vol. 47, No. 3, pp. 377–385, 2008.
Choi, Y. B. and Kim, S. W., “Phase-Shifting Grating Projection Moiré Topography,” Optical Engineering, Vol. 37, No. 3, pp. 1005–1010, 1998.
Huang, L., Chua, P. S., and Asundi, A., “Least-Squares Calibration Method for Fringe Projection Profilometry Considering Camera Lens Distortion,” Applied Optics, Vol. 49, No. 9, pp. 1539–1548, 2010.
Liu, H., Su, W. H., Reichard, K., and Yin, S., “Calibration-based Phase-Shifting Projected Fringe Profilometry for Accurate Absolute 3D Surface Profile Measurement,” Optics Communications, Vol. 216, No. 1, pp. 65–80, 2003.
Takeda, M. and Mutoh, K., “Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shape,” Applied Optics, Vol. 22, No. 24, pp. 3977–3982, 1983.
Hu, Q., Huang, P. S., Fu, Q., and Chiang, F. P., “Calibration of a Three-Dimensional Shape Measurement System,” Optical Engineering, Vol. 42, No. 2, pp. 487–493, 2003.
Maurel, A., Cobelli, P., Pagneux, V., and Petitjeans, P., “Experimental and Theoretical Inspection of the Phase-to-Height Relation in Fourier Transform Profilometry,” Applied Optics, Vol. 48, No. 2, pp. 380–392, 2009.
Du, H. and Wang, Z., “Three-Dimensional Shape Measurement with an Arbitrarily Arranged Fringe Projection Profilometry System,” Optics Letters, Vol. 32, No. 16, pp. 2438–2440, 2007.
Guo, H., He, H., Yu, Y., and Chen, M., “Least-Squares Calibration Method for Fringe Projection Profilometry,” Optical Engineering, Vol. 44, No. 3, Paper No. 033603, 2005.
Li, W., Fang, S., and Duan, S., “3D Shape Measurement based on Structured Light Projection Applying Polynomial interpolation Technique,” Optik-International Journal for Light and Electron Optics, Vol. 124, No. 1, pp. 20–27, 2013.
Ganotra, D., Joseph, J., and Singh, K., “Profilometry for the Measurement of Three-Dimensional Object Shape using Radial Basis Function, and Multi-Layer Perceptron Neural Networks,” Optics Communications, Vol. 209, No. 4, pp. 291–301, 2002.
Zhang, S. and Yau, S. T., “Generic Nonsinusoidal Phase Error Correction for Three-Dimensional Shape Measurement using a Digital Video Projector,” Applied Optics, Vol. 46, No. 1, pp. 36–43, 2007.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chung, BM., Park, YC. Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection. Int. J. Precis. Eng. Manuf. 15, 407–413 (2014). https://doi.org/10.1007/s12541-014-0351-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12541-014-0351-8