## High-speed height measurement by a light-source-stepping method using a linear LED array |

Optics Express, Vol. 21, Issue 20, pp. 23169-23180 (2013)

http://dx.doi.org/10.1364/OE.21.023169

Acrobat PDF (4024 KB)

### Abstract

High-speed height measurement is required in industrial fields for analyzing the behavior of a breaking object, a vibrating object or a rotating object. A shape measurement performed using a phase-shifting method can measure the shape with high spatial resolution because the coordinates can be obtained pixel by pixel. A light-source-stepping method (LSSM) that uses a linear LED array by means of a whole-space tabulation method (WSTM) has been proposed. Accurate shape measurement can be performed using this method. The response speed of the LED array is greater than 12 kHz. In this paper, height measurement is performed using WSTM and LSSM with a linear LED array and a high-speed camera. It was verified that the response speed of the linear LED is greater than 200 kHz. The phase shifting was performed at 12 kHz, and the height measurement of the vibrating woofer was performed at 4 kHz using a 3-step phase-shifting method.

© 2013 OSA

## 1. Introduction

1. Y. Morimoto, M. Fujigaki, and H. Toda, “Real-time shape measurement by integrated phase-shifting method,” Proc. SPIE **3744**, 118–125 (1999). [CrossRef]

3. H. N. Yen, D. M. Tsai, and J. Y. Yang, “Full-field 3-D measurement of solder pastes using LCD-based phase shifting techniques,” IEEE Trans. Electron. Packag. Manuf. **29**(1), 50–57 (2006). [CrossRef]

4. C. S. Chan and A. K. Asundi, “Phase-shifting digital projection system for surface profile measurement,” Proc. SPIE **2354**, 444–452 (1994). [CrossRef]

5. P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. **42**(1), 163–168 (2003). [CrossRef]

7. Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express **18**(19), 19743–19754 (2010). [CrossRef] [PubMed]

8. T. Yoshizawa, T. Wakayama, and H. Takano, “Application of a MEMS scanner to profile measurement,” Proc. SPIE **6762**, 67620B (2007). [CrossRef]

10. S. Zwick, R. Fessler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express **20**(4), 3642–3653 (2012). [CrossRef] [PubMed]

11. M. Grosse, M. Schaffer, B. Harendt, and R. Kowarschik, “Fast data acquisition for three-dimensional shape measurement using fixed-pattern projection and temporal coding,” Opt. Eng. **50**(10), 100503 (2011). [CrossRef]

6. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express **18**(9), 9684–9689 (2010). [CrossRef] [PubMed]

7. Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express **18**(19), 19743–19754 (2010). [CrossRef] [PubMed]

11. M. Grosse, M. Schaffer, B. Harendt, and R. Kowarschik, “Fast data acquisition for three-dimensional shape measurement using fixed-pattern projection and temporal coding,” Opt. Eng. **50**(10), 100503 (2011). [CrossRef]

6. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express **18**(9), 9684–9689 (2010). [CrossRef] [PubMed]

*z*position. However, because the

*z*coordinate and the phase obtained using the phase-shifting method have a one-to-one relationship, accurate shape measurement can be realized using the whole-space tabulation method (WSTM) proposed previously [15,16

16. M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE **7066**, 706606, 706606-8 (2008). [CrossRef]

## 2. Light-source-stepping method (LSSM)

*ϕ*(

*x*

_{p},

*z*

_{p}) at point P(

*x*

_{p},

*z*

_{p}) on the object is equal to the phase at point G(

*x*

_{g},

*z*

_{g}) on the grating plate. Point G is the intersection of a line that connects light source S(

*x*

_{s},

*z*

_{s}) and point P with the grating plate.

*ϕ*on the grating plate is expressed in Eq. (1),where

*p*is the pitch of the grating and

*ϕ*

_{0}is the intercept value at

*x*= 0. The

*x*coordinate at point G is calculated from the coordinates of point S and point P using Eq. (2),The projected phase

*ϕ*(

*x*

_{p},

*z*

_{p}) at point P is obtained using Eq. (3),Figure 2 shows a schematic illustration of phase-shifted projected grating patterns using a light-source-stepping method. The projected grating pattern is changed by stepping the light source position, as shown in Fig. 2. The projected phase at point P on an object is also changed according to the position of the light source. When the position of the light source is stepped from S to S', which are separated by a distance Δ

*x*, the intersection of the line that connects the light source and point P on the grating plate is changed from G to G' and moves a distance Δ

*x*, which is given by Eq. (4),The projected phase at point P is shifted by Δ

_{g}*ϕ*, which is given in Eq. (5),This equation implies that the projected phase is shifted in proportion to the light source stepping distance Δ

*x*, and the proportionality coefficient is determined by the grating pitch of the grating plate and the

*z*positions of the light sources, grating plate and point P on the object. Because the grating pitch of the grating plate, the

*z*position of the light sources and the

*z*position of the grating plate are fixed, the proportionality coefficient corresponds to the

*z*position of the object surface.

*xz*-plane instead of a point light source, the same principle is available. The intensity of the projected grating can be increased using the linear light source. Figure 3 shows the schematic illustration of a projected grating using a linear light source. The direction of a linear light source is the

*y*-direction. When the direction of the linear light source is aligned with the direction of the grating slits, the projected grating patterns obtained by each point light source on the linear light source are overlapped. The grating alignment and the phase obtained by each point light source become conformable as shown in Fig. 3. As a result, the brightness of the projected grating pattern becomes higher.

## 3. Whole-space tabulation method (WSTM)

*z*position, as described above. The

*z*coordinate and the phase obtained using the phase-shifting method have a one-to-one relationship.

*z*-direction is translated in the

*z*-direction by small amount. A camera and a projector are fixed above the reference plane. The grating is projected from the projector onto the reference planes. The phase of the projected grating can be easily obtained using the phase-shifting method. A pixel of the camera obtains an imagealong the ray line L in Fig. 4(a). The pixel contains images of the points P

_{0}, P

_{1}, P

_{2}…P

*on the reference planes R*

_{N}_{0}, R

_{1}, R

_{2}…R

*, respectively. At each point, the grating phases*

_{N}*θ*

_{0},

*θ*

_{1},

*θ*

_{2}…

*θ*can be calculated using the phase-shifting method. Therefore, the correspondence between the heights

_{N}*z*

_{0},

*z*

_{1},

*z*

_{2}…

*z*and the phases

_{N}*θ*

_{0},

*θ*

_{1},

*θ*

_{2}…

*θ*, respectively, is obtained. From these phase-shifted images, calibration tables are formed to obtain the

_{N}*z*coordinate from the phase

*θ*at each pixel, as shown in Fig. 4(b). This table can be constructed in the range that the phase is changed within 2π. The range has some limitation. There are no disambiguation of phases in this method.

*z*coordinate can be obtained from the phase at each pixel using the calibration lookup tables, and this operation does not require any time-consuming complex calculation.

## 4. Linear LED device and response speed

## 5. Experiment for high-speed height measurement

### 5.1 Experimental setup

*z*direction. Before measuring an object, the reference plane set on the linear stage is placed on the measurement area to produce phase-height tables for the WSTM. The reference plane is translated from 0 to 6.0 mm in 0.4 mm increments. The relationship between the phases of the grating projected onto the reference plane and the

*z*position is recorded. The calibration tables are produced at every 2π/1000 of phase in a pixel-by-pixel manner. Figure 9 shows the phase-height table at the center pixel of the measurement area.

*θ*at a pixel is calculated using the relationship between phase and phase shifted intensities as shown in Eq. (6),where

*I*

_{0},

*I*

_{1}and

*I*

_{2}are intensities obtained at a pixel with 3-step phase shifting.

### 5.2 Confirmation of accuracy using the reference plane

### 5.3 High-speed height measurement for a vibrating woofer

## 6. Conclusions

## Acknowledgments

## References and links

1. | Y. Morimoto, M. Fujigaki, and H. Toda, “Real-time shape measurement by integrated phase-shifting method,” Proc. SPIE |

2. | M. Fujigaki, S. Matsumoto, A. Masaya, Y. Morimoto, and Y. Murata, “Development of shape measurement system using mirrors for metallic objects ,” J. JSEM |

3. | H. N. Yen, D. M. Tsai, and J. Y. Yang, “Full-field 3-D measurement of solder pastes using LCD-based phase shifting techniques,” IEEE Trans. Electron. Packag. Manuf. |

4. | C. S. Chan and A. K. Asundi, “Phase-shifting digital projection system for surface profile measurement,” Proc. SPIE |

5. | P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. |

6. | S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express |

7. | Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express |

8. | T. Yoshizawa, T. Wakayama, and H. Takano, “Application of a MEMS scanner to profile measurement,” Proc. SPIE |

9. | D. Asai, T. Miyagi, M. Fujigaki, and Y. Morimoto, “Application to bin-picking of shape measurement using whole-space tabulation method with MEMS scanner grating projector,” J. JSEM |

10. | S. Zwick, R. Fessler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express |

11. | M. Grosse, M. Schaffer, B. Harendt, and R. Kowarschik, “Fast data acquisition for three-dimensional shape measurement using fixed-pattern projection and temporal coding,” Opt. Eng. |

12. | Y. Oura, M. Fujigaki, A. Masaya, and Y. Morimoto, “Development of linear LED device for shape measurement by light source stepping method,” Opt. Meas. Mod. Metrol. |

13. | Y. Morimoto, A. Masaya, M. Fujigaki, and D. Asai, “Shape measurement by phase-stepping method using multi-line LEDs,” in |

14. | Y. Horikawa, Japanese Unexamined Patent Application Publication No. 2002–286432 (2002). |

15. | M. Fujigaki and Y. Morimoto, “Shape measurement with grating projection using whole-space tabulation method,” J. JSEM |

16. | M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE |

**OCIS Codes**

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.2830) Instrumentation, measurement, and metrology : Height measurements

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.7280) Instrumentation, measurement, and metrology : Vibration analysis

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: July 8, 2013

Revised Manuscript: September 2, 2013

Manuscript Accepted: September 6, 2013

Published: September 24, 2013

**Citation**

Motoharu Fujigaki, Yohei Oura, Daisuke Asai, and Yorinobu Murata, "High-speed height measurement by a light-source-stepping method using a linear LED array," Opt. Express **21**, 23169-23180 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23169

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### References

- Y. Morimoto, M. Fujigaki, and H. Toda, “Real-time shape measurement by integrated phase-shifting method,” Proc. SPIE3744, 118–125 (1999). [CrossRef]
- M. Fujigaki, S. Matsumoto, A. Masaya, Y. Morimoto, and Y. Murata, “Development of shape measurement system using mirrors for metallic objects,” J. JSEM 2, 194–197(2012).
- H. N. Yen, D. M. Tsai, and J. Y. Yang, “Full-field 3-D measurement of solder pastes using LCD-based phase shifting techniques,” IEEE Trans. Electron. Packag. Manuf.29(1), 50–57 (2006). [CrossRef]
- C. S. Chan and A. K. Asundi, “Phase-shifting digital projection system for surface profile measurement,” Proc. SPIE2354, 444–452 (1994). [CrossRef]
- P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng.42(1), 163–168 (2003). [CrossRef]
- S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express18(9), 9684–9689 (2010). [CrossRef] [PubMed]
- Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express18(19), 19743–19754 (2010). [CrossRef] [PubMed]
- T. Yoshizawa, T. Wakayama, and H. Takano, “Application of a MEMS scanner to profile measurement,” Proc. SPIE6762, 67620B (2007). [CrossRef]
- D. Asai, T. Miyagi, M. Fujigaki, and Y. Morimoto, “Application to bin-picking of shape measurement using whole-space tabulation method with MEMS scanner grating projector,” J. JSEM10(Special Issue), 186–191 (2010).
- S. Zwick, R. Fessler, J. Jegorov, and G. Notni, “Resolution limitations for tailored picture-generating freeform surfaces,” Opt. Express20(4), 3642–3653 (2012). [CrossRef] [PubMed]
- M. Grosse, M. Schaffer, B. Harendt, and R. Kowarschik, “Fast data acquisition for three-dimensional shape measurement using fixed-pattern projection and temporal coding,” Opt. Eng.50(10), 100503 (2011). [CrossRef]
- Y. Oura, M. Fujigaki, A. Masaya, and Y. Morimoto, “Development of linear LED device for shape measurement by light source stepping method,” Opt. Meas. Mod. Metrol.5, 285–291 (2011).
- Y. Morimoto, A. Masaya, M. Fujigaki, and D. Asai, “Shape measurement by phase-stepping method using multi-line LEDs,” in Applied Measurement Systems, Ed. M. Zahurul Haq (InTech, 2012), Chapter 7, 137–152.
- Y. Horikawa, Japanese Unexamined Patent Application Publication No. 2002–286432 (2002).
- M. Fujigaki and Y. Morimoto, “Shape measurement with grating projection using whole-space tabulation method,” J. JSEM8(4), 92–98 (2008) (in Japanese).
- M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” Proc. SPIE7066, 706606, 706606-8 (2008). [CrossRef]

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