## Line-defect calibration for line-scanning projection display

Optics Express, Vol. 17, Issue 19, pp. 16492-16504 (2009)

http://dx.doi.org/10.1364/OE.17.016492

Acrobat PDF (744 KB)

### Abstract

A method of line-defect calibration for line-scanning projection display is developed to accomplish acceptable display uniformity. The line scanning display uses a line modulating imaging and scanning device to construct a two-dimensional image. The inherent line-defects in an imaging device and optical lenses are the most fatal performance-degrading factor that should be overcome to reach the basic display uniformity level. Since the human eye recognizes line defects very easily, a method that perfectly removes line defects is required. Most line imaging devices are diffractive optical devices that require a coherent light source. This particular requirement makes the calibration method of sequential single pixel measurement and correction insufficient to take out the line defects distributed on screen due to optical crosstalk. In this report, we present a calibration method using a recursively converging algorithm that successfully transforms the unacceptable line-defected images into a uniform display image.

© 2009 Optical Society of America

## 1. Introduction

## 2. Line-scanning display system

### 2.1 Line-scanning optics and imaging device

^{th}and 1

^{st}diffraction orders.

^{th}order diffractive beams. In the central mirror part of the SOM device, a laser shines through the illumination lens system. When the OPD (optical path difference) between the bottom and top mirrors is an odd multiple of

*λ*/4, the beam is diffracted ±1 order and blocked by a Schlieren stop that is located in the Fourier plane of the projection lens. When the OPD is a multiple of λ/2, the bottom and top mirrors are like flat mirrors, and the 0

^{th}order coming through the projection lens is magnified to the screen. The magnified line image on the screen is progressively scanned by a vibrating mechanical mirror to complete the 2-D image.

_{x}N

_{y}and Al layers is actuated by a PZT (lead-zirconate-titanate) material force. When a voltage is applied to the PZT, horizontal shrinkage of the PZT material induces a vertical motion of the bridged ribbon as shown in Fig. 1(d). The gap-height is defined as the gap between the top mirror and the bottom reflector. The piezoelectric actuation of the individual grating micro-mirrors controls the gap-height to achieve the variable phase shift, providing diffractive light modulation of the irradiating laser. The light intensity change is expressed as follows:

*I*is the normalized light intensity of the

_{n}*n*-th pixel,

*s*is the

_{n}*n*-th pixel’s gap-height plus the displacement driven by the voltage, and

*λ*is the wavelength of the laser. The light propagation has double path when the light beam is reflected from bottom mirror. When

*s*is an even multiple of

_{n}*λ*/4, the 0

^{th}diffraction order intensity reaches its maximum value. When

*s*is odd multiple of λ/4, the 0

_{n}^{th}diffraction order intensity reaches its minimum value.

### 2.2 Driving electronics

8. J. Kang, J. Kim, S. Kim, J. Song, O. Kyong, Y. Lee, C. Park, K. Kwon, W. Choi, S. Yun, I. Yeo, K. Han, T. Kim, and S. Park, “10-bit Driver IC Using 3-bit DAC Embedded Operational Amplifier for Spatial Optical Modulator,” IEEE J. Solid-state Circuits **42**, 2913–2922 (2007).
[CrossRef]

## 3. Influence of line defects on display image quality

9. J. Dijon and A. Fournier, “6” Colour FED Demonstrator with High Peak Brightness,” in SID 2007, 1313–1316 (2007). [CrossRef]

## 4. Sources of defects in the image

10. M. Young, “Scratch-and-dig standard revisited,” Appl. Opt. **25**, 1922–1929 (1986).
[CrossRef] [PubMed]

11. J. A. Hoffnagle and C. M. Jefferson, “Beam shaping with a plano-aspheric lens pair,” Opt. Eng. **42**, 3090–3099 (2003).
[CrossRef]

12. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. **39**, 5488–5499 (2000).
[CrossRef]

13. H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. **40**, 1936–1943 (2001).
[CrossRef]

## 5. A recursively converging calibration algorithm

### 5.1 Single pixel sweeping method of calibration

### 5.2 Optical crosstalk

*E*is the reflected field,

*E*is the incident field amplitude,

_{o}*j*is the imaginary unit,

*k*is the wavenumber,

*h*is the fixed reference plane, and

*s*is the gap-height of the

_{n}*n*-th pixel. After diffraction on the SOM, the light beam is projected to a photo-detector by the objective lens. In the focal plane (Fourier plane), a Schlieren stop rejects all diffraction orders except the working diffractive order. All light that passes through the aperture is detected by a photodiode, and the maximum and minimum photodiode signals are used to find the actuation voltage for black and white images. To calculate the photodiode signal, one should calculate the Fourier spatial spectrum of the amplitude of the SOM-diffracted field, make the spatial spectrum truncation to take into account the beam truncation by Schlieren stop, and finally calculate the energy passing through the aperture. In this case (using a spatial Fourier filter), it is more convenient to calculate the photodiode signal by integration of the electromagnetic energy of the passed beam in the spatial Fourier plane using Parseval’s theorem. It is assumed that we use the 0

^{th}diffractive order for calibration and image projection, and the Schlieren stop has an aperture in the area of the 0

^{th}order spot of light. Only diffraction orders having light spots close to this area have a considerable effect on calibration. Therefore, only the 0

^{th}and ±1

^{st}diffractive orders will be taken into account below, and the higher diffraction orders will be ignored.

*F*(

*α*) is the diffracted field on the SOM in the spatial frequency domain,

*α*is the spatial frequency,

*F*(

_{n}*s*) is the n-th pixel field in the spatial frequency domain,

_{n},α*a*is field amplitude,

*N*is the number of pixels in the SOM,

_{pixel}*N*is the number of grating pairs in one pixel whose grating pair has a 1:1 land/groove widths ratio, and

_{ribbo}n*T*is the period of one grating pair (see Fig. 4(a) for the definition of

*T*). The last factor in Eq. (4) has two parts,

*cos*(

*ks*)

_{n}*cos*(

*αT/4*) and -sin(

*ks*)sin(

_{n}*αT/4*). The first part corresponds to the 0

^{th}diffractive order with a maximum at 0 spatial frequency and the second to the ±1

^{st}diffractive orders with amplitude maxima at ±

*k*

*λ/T*values of the spatial frequency. The field amplitude in the spatial Fourier plane is the sum of the field amplitudes of separate pixels, each one having its own phase and amplitude. Due to the effects of interference of fields from different pixels, one pixel’s signal shape should depend on the position of all other pixels. It is not difficult to see that the interference between far pixel fields would have a large number of fringes in the spatial Fourier domain (domain of integration), due to a factor

*ex*p[

*iα*(

*nN*)]. After integration of the energy over the spatial frequency interval corresponding to the aperture size, the interference effect between far pixels would be negligibly small due to averaging over a large number of fringes. Therefore, only close pixels influence the signal shape of a moving pixel because the interference of their fields with the actuated pixel’s field creates only a few fringes in the interval of integration. Therefore, integration over the aperture area in the Fourier plane would be sensitive to the fringe amplitudes and positions, which change with the actuation positions of the moving pixels. To find the degree of influence of optical crosstalk, we choose the case when all pixels are shifted a distance

_{ribbon}T-N_{pixel}N_{ribbon}T/2*s*from white level, and we find the shift

_{0}*Δs*of the actuated pixel signal curve at all of the pixel shift positions. For this specific case, Eq. (4) simplifies to the following formula:

^{th}diffractive order). In this case, the terms of Eq. (5) corresponding to the 0

^{th}diffractive order have even symmetry and those corresponding to the ±1

^{st}order have odd symmetry. Therefore, after integration in the Fourier plane for the detector signal calculation, the energy of the ±1

^{st}and 0

^{th}orders would be separated, meaning that the photodiode signal is the sum of the pure 0

^{th}order signal and residual ±1st order signal. Therefore, without undermining the accuracy of the crosstalk calculation, we can write the field of the photodiode signal as follows:

*I*and

_{0}*I*represent the constant background signal level due to contributions from the 0

_{1}^{th}and residual 1

^{st}diffractive orders from all pixels,

*NA*is the numerical aperture of the beam passed through the Schlieren stop (

*NA*=

*0.5*d/F*). The background signal terms

*I*and

_{0}*I*in Eq. (8) are constant during one pixel’s actuation and therefore give no contribution to the change in photodiode signal nor provide any contribution to the shift in grey scale level due to optical crosstalk. In Eq. (8), the

_{1}*I*and

_{2}*I*terms give contributions to the signal from the actuated pixel in the 0

_{4}^{th}and residual ±1

^{st}diffractive orders, respectively (signal of one pixel without background from other pixels). The

*2*(

*I*)

_{3}-I_{2}*cos*(

*ks*) term in Eq. (8) gives the photodiode signal due to the fringes caused by the interference between the actuated pixel’s 0

_{0}^{th}order fields and the 0t

^{h}order of the background fields. The -

*2I*(

_{4}sin*ks*) term gives the photodiode signal change due to the fringes caused by the interference between the actuated pixel’s residual ±1

_{0}^{st}order fields and the ±1

^{st}orders background field. After a simple transformation of Eq. (8), the optical signal can be written as follows

*C*,

_{0}*C*and

_{1}*φ*are constants depending only on

*s*(no dependence on

_{0}*s*). From Eq. (9) it follows that the photo-detector signal always has the same shape and period (as a function of the actuated pixel’s displacement); hence, cross talk just provides a signal curve shift at some constant value of the pixel displacement. Our numerical simulation has shown that in spite of the small amplitude of the residual ±1

^{st}order signals, the fringe signal in the ±1

^{st}orders provides a strong influence on the shift of the gray scale level arising from the optical crosstalk for the case of relatively large

*NA*(

*NA*/(

*λ/T*)>0.4, however in this case the shift is small). Therefore, the fringe signal in ±1

^{st }orders, contrary to other terms, has a sufficiently different (min and max curve position are shifted) dependence on the pixel displacement than the pure calibration 0

^{th}order signals.

*Δs*) is a periodical odd function of

*s*with a period of

_{0}*λ/2*.

*NA*/(

*λ/T*)=0.25 and

*NA*/(

*λ/T*)=0.5. From the curves in Fig. 5, it is clear that the level of crosstalk increases with a decrease in the number of grating pairs in one pixel and increases when the aperture size width (

*NA*) decreases. It is an expected result since a decrease in hole size decreases the integration area in the Fourier plane and therefore the degree of averaging over fringes. The decrease in the number of ribbons increases the fringe size in the Fourier plane. Since the area of integration in the Fourier plane is fixed, this also decreases the average number of fringes. As one can see from Fig. 5(b) for the SOM with one grating pair in one pixel, optical crosstalk can cause a large shift in the calibration curves with

*Δs*/(

*λ/4*)<=0.175. Therefore, a large error in the calibration system is introduced. For an SOM with two grating pairs in one pixel, the optical crosstalk is not so large however, it is still sufficient to induce visible image deterioration.

_{0}and only neighboring pixels are important, we should expect that our case provides close to the maximum crosstalk effect and the simulation data above provides close to the maximum value in calibration deterioration. From the data above, it follows that crosstalk could cause sufficient image deterioration, and a special scheme of calibration is needed to avoid problems with image quality enhancement.

### 5.3 A recursively converging calibration algorithm in line-scanning display

## 6. Experimental results and discussion

### 6.1 Experimental setup

### 6.2 Vertical line intensity profile

### 6.3 Calibrated projection image quality

## 7. Summary

## Acknowledgment

## References and links

1. | J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, “Overview and applications of Grating Light Valve |

2. | S. K. Yun, J. Song, T.-W. Lee, I. Yeo, Y. Choi, Y. Lee, S. An, K. Han, Y. Victor, H.-W. Park, C. Park, H. Kim, J. Yang, J. Cheong, S. Ryu, K. Oh, H. Yang, Y. Hong, S. Hong, S. Yoon, J. Jang, J. Kyoung, O. Lim, C. Kim, A. Lapchuk, S. Ihar, S. Lee, S. Kim, Y. Hwang, K. Woo, S. Shin, J. Kang, and D.-H. Park, “Spatial Optical Modulator (SOM): Samsung’s Light Modulator for the Next Generation Laser Display,” IMID/IDMC ’06 DIGEST (Proceeding of Society for Information Display - SID. August, 2006), 29-1, 551–555. |

3. | M. W. Kowarz, J. C. Brazas, and J. G. Phalen, “Conformal Grating Electromechanical system (GEMS) for High-Speed Digital Light Modulation,” IEEE, 15th Int. MEMS Conf. Digest, 568–573 (2002). |

4. | L. A. Yoder, “An Introduction to the Digital Light Processing Technology,” (Texas Instruments). http://dlp.com/tech/what.aspx. |

5. | B. T. Teipen and D. L. MacFarlane, “Liquid-crystal-display projector-based modulation transfer function measurements of charge-coupled-device video camera systems,” Appl. Opt. |

6. | S. Lee, M. Sullivan, C. Mao, and K. M. Johnson, “High-contrast, fast-switching liquid-crystal-on-silicon microdisplay with a frame buffer pixel array,” Opt. Lett. |

7. | R. W. Corrigan, D. T. Amm, P. A. Alioshin, B. Staker, D. A. LeHoty, K. P. Gross, and B. R. Lang, “Calibration of a Scanned Linear Grating Light Value |

8. | J. Kang, J. Kim, S. Kim, J. Song, O. Kyong, Y. Lee, C. Park, K. Kwon, W. Choi, S. Yun, I. Yeo, K. Han, T. Kim, and S. Park, “10-bit Driver IC Using 3-bit DAC Embedded Operational Amplifier for Spatial Optical Modulator,” IEEE J. Solid-state Circuits |

9. | J. Dijon and A. Fournier, “6” Colour FED Demonstrator with High Peak Brightness,” in SID 2007, 1313–1316 (2007). [CrossRef] |

10. | M. Young, “Scratch-and-dig standard revisited,” Appl. Opt. |

11. | J. A. Hoffnagle and C. M. Jefferson, “Beam shaping with a plano-aspheric lens pair,” Opt. Eng. |

12. | J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. |

13. | H. Lee and M. Yang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt. Eng. |

14. | J. W. Goodman, |

**OCIS Codes**

(100.2980) Image processing : Image enhancement

(120.1880) Instrumentation, measurement, and metrology : Detection

(120.2040) Instrumentation, measurement, and metrology : Displays

(350.4600) Other areas of optics : Optical engineering

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: October 31, 2008

Revised Manuscript: March 5, 2009

Manuscript Accepted: April 6, 2009

Published: September 1, 2009

**Citation**

Seungdo An, Jonghyeong Song, Anatoliy Lapchuk, Victor Yurlov, Seung-Won Ryu, Eungju Kim, and Sang Kyeong Yun, "Line-defect calibration for line-scanning
projection display," Opt. Express **17**, 16492-16504 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16492

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### References

- J. I. Trisnadi, C. B. Carlisle, and R. Monteverde, "Overview and applications of Grating Light ValveTM based optical write engines for high-speed digital imaging," Proc. SPIE 5348, 52-64 (2004). [CrossRef]
- S. K. Yun, J. Song, T.-W. Lee, I. Yeo, Y. Choi, Y. Lee, S. An, K. Han, Y. Victor, H.-W. Park, C. Park, H. Kim, J. Yang, J. Cheong, S. Ryu, K. Oh, H. Yang, Y. Hong, S. Hong, S. Yoon, J. Jang, J. Kyoung, O. Lim, C. Kim, A. Lapchuk, S. Ihar, S. Lee, S. Kim, Y. Hwang, K. Woo, S. Shin, J. Kang and D.-H. Park, "Spatial Optical Modulator (SOM): Samsung’s Light Modulator for the Next Generation Laser Display," IMID/IDMC '06 DIGEST (Proceeding of Society for Information Display - SID. August, 2006), 29-1, 551-555.</other>
- M. W. Kowarz, J. C. Brazas and J. G. Phalen, "Conformal Grating Electromechanical system (GEMS) for High-Speed Digital Light Modulation," IEEE, 15th Int. MEMS Conf. Digest, 568-573 (2002).
- L. A. Yoder, "An Introduction to the Digital Light Processing Technology," (Texas Instruments). http://dlp.com/tech/what.aspx.
- B. T. Teipen and D. L. MacFarlane, "Liquid-crystal-display projector-based modulation transfer function measurements of charge-coupled-device video camera systems," Appl. Opt. 39, 515-525 (2000). [CrossRef]
- S. Lee, M. Sullivan, C. Mao and K. M. Johnson, "High-contrast, fast-switching liquid-crystal-on-silicon microdisplay with a frame buffer pixel array," Opt. Lett. 29, 751-753 (2004). [CrossRef] [PubMed]
- R. W. Corrigan, D. T. Amm, P. A. Alioshin, B. Staker, D. A. LeHoty, K. P. Gross and B. R. Lang, "Calibration of a Scanned Linear Grating Light ValueTM Projection System," in SID 99 Digest (Society for Information Display, San Jose, Calif., 1999), 200-223 (1999).
- J. Kang, J. Kim, S. Kim, J. Song, O. Kyong, Y. Lee, C. Park, K. Kwon, W. Choi, S. Yun, I. Yeo, K. Han, T. Kim and S. Park, "10-bit Driver IC Using 3-bit DAC Embedded Operational Amplifier for Spatial Optical Modulator," IEEE J. Solid-state Circuits 42, 2913-2922 (2007). [CrossRef]
- J. Dijon and A. Fournier, "6" Colour FED Demonstrator with High Peak Brightness," in SID 2007, 1313-1316 (2007). [CrossRef]
- M. Young, "Scratch-and-dig standard revisited," Appl. Opt. 25, 1922-1929 (1986). [CrossRef] [PubMed]
- J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003). [CrossRef]
- J. A. Hoffnagle and C. M. Jefferson, "Design and performance of a refractive optical system that converts a Gaussian to a flattop beam," Appl. Opt. 39, 5488-5499 (2000). [CrossRef]
- Q3. H. Lee and M. Yang, "Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold," Opt. Eng. 40, 1936-1943 (2001). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 2005), Chap. 5.

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