An accurate projector gamma correction method for ...

An accurate projector gamma correction method for phase-measuring profilometry based on direct optical power detection Miao LIU1, Shibin YIN1, Shourui YANG1, Zonghua ZHANG2 1. State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, P.R.China; 2. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, P.R.China

ABSTRACT Digital projector is frequently applied to generate fringe pattern in phase calculation-based three dimensional (3D) imaging systems. Digital projector often works with camera in this kind of systems so the intensity response of a projector should be linear in order to ensure the measurement precision especially in Phase-Measuring Profilometry (PMP). Some correction methods are often applied to cope with the non-linear intensity response of the digital projector. These methods usually rely on camera and gamma function is often applied to compensate the non-linear response so the correction performance is restricted by the dynamic range of camera. In addition, the gamma function is not suitable to compensate the nonmonotonicity intensity response. This paper propose a gamma correction method by the precisely detecting the optical energy instead of using a plate and camera. A photodiode with high dynamic range and linear response is used to directly capture the light optical from the digital projector. After obtaining the real gamma curve precisely by photodiode, a gray level look-up table (LUT) is generated to correct the image to be projected. Finally, this proposed method is verified experimentally. Key words: Digital projector, Fringe projection, Gamma correction, 3D imaging

1. Introduction In three dimensional (3D) imaging system based on Phase-Measuring Profilometry (PMP), sinusoidal fringe pattern is often generated by digital projector due to its high contrast and fast response. The gray level distribution of the fringe pattern is projected onto the surface of the target to be measured should be sinusoidal strictly in the direction of the phase shifting. Thus, the intensity response of a digital projector is supposed to be linear so that the intensity distribution on the projector’s image plane is equal to the pre-generated pattern. However, most of the digital projectors are designed for presentation or other applications to satisfy the response of human eyes so the gamma curve of the projector is not suitable for fringe pattern projection purpose. Therefore a pre-generated sinusoidal pattern will become non-sinusoidal after projected onto the image plane. As a conclusion, the nonlinear intensity response of the projector largely reduces the final accuracy of the entire PMP imaging system. In order to alleviate the corruption caused by non-linearity of the gamma curve, many gamma correction method is proposed to linearize the response of the digital projector. The real gamma curve is usually approximated by the gamma function, where γ is optimized to complete the correction. By trying different gamma values in the experiment system,

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the optimized value is selected which can achieve highest accuracy in some methods [1]. Other methods estimate the optimal gamma value by image analysis approaches such as Fourier spectrum analysis

[2]

and gray level measurement [3]. Instead

of correcting gamma curve directly, merging the gamma effect into the geometrical parameter calibration is considered in some approaches

[4] [5] .

In the above literature a white diffusion plate and a camera are usually applied to calibrate the

nonlinear intensity response of a digital projector. Due to the defect of the diffusion plate, reflectogram is not constant at different orientations and positions. Meanwhile, the camera’s dynamic range is too small to meet the requirement of a highcontrast projector. In this article, we propose a nonlinear correction method by the precisely detecting the optical energy instead of using a plate and camera. A photodiode whose dynamic range, linear and noise performance of the photodiode are far superior to the CCD or CMOS imaging devices is applied to detect the light optical from the projector. By means of recording the corresponding radiant power in terms of gray levels and analyzing the radiant power sequences, the accurate gamma curve of the digital projector can be obtained. To maximize the contrast performance of the digital projector, a gray level rearrangement method is proposed to process the optical energy sequence data. Finally a gray Look-up-table (LUT) is generated and then used to correct each pixel of the pre-projection image. When the corrected image is projected onto the image plane, the gray scale distribution of original image is detected by image sensor or other linear response photoelectric sensors.

2. Principle of operation The intensity response of the digital projector originally linear while the non-linear factors are added later to satisfy human eyes or other commercial application. The intensity response of the digital projector is well linearized before the non-linear gamma curves are generated for the projector's image pre-processing system. The corresponding "gray level - optical power" LUT is applied to actualize the non-linear gamma curve on the digital projector. Therefore, if we can measure this LUT precisely, the original linear response can be restored. In addition, the intensity response of digital projector is difficult to be accurately represented by gamma function. The real gamma curve of a projector generated by gamma function is effected by round-off errors or even a pre-designed nonmonotonicity response. To solve these problems, the non-linearity factors of the intensity response can be largely removed by introducing an inverse LUT named ‘optical power - gray level’ LUT, which process the original fringe pattern image before projecting. The proposed method includes two main procedure: 1.

Measurement of projector’s real gamma curve

2.

Correction LUT generation based on the real gamma curve

In step 1, optical power is directly detected by a photodiode and is converted into voltage signal with a linear amplification circuit. By detecting the optical power corresponding to projector’s all gray levels (0~255), a ‘gray level – optical power’ curve is acquired and stored in measurement sequence G. =[ ,

]


(1)

In equation 1, ‘I’ represents the gray level for the projector; ‘P’ represents the voltage value corresponding to the received optical power. [.]T means the transpose of the matrix. Compared with the CCD and CMOS imaging device, the dynamic range of a photodiode light detector can achieve 70dB or higher. The contrast of the commonly used digital projector is 350:1 (51dB approximately). Therefore, the resolution of the PD based system is high enough for the gamma curve measurement. In Step 2, LUT is generated from sequence G to linearize the gamma curve as well as remove the its monotonicity, where the detailed schematic diagram is shown in Fig.1

Search the sequence PT and find the max

Choose a final LUT index number i as the

& min optical power value

LUT input value

Use the index number i to determine the Use the max & min optical power value to

expectation optical power value from the

generate the expectation gamma curve

expectation gamma curve

(linear)

Find the closest value of the expectation Loop procedure to rearrange all the PT

optical power value in the sequence G

with the index IT together in order to approach the expectation gamma curve Use the I of closest value from G as the output of the final LUT

Figure 1. Procedure of generating correction LUT

Finally, the non-linear intensity response of the projector can be minimized by processing the image with the correction LUT before projecting.

3. Experiment and results 3.1

Experiment setup

In this chapter, the experiment is detailed and results are analyzed. Fig. 2a shows the hardware system to measure the projector’s gamma curve (computer is not shown in this figure). A photoelectric module is designed to detect the optical power from the projector. As shown in Fig. 2b, a photodiode (OSRAM SFH2701) is soldered on the front of the module. A two-stage amplification circuit (a transpedance amplifier and an inversion amplifier) shown in Fig. 2c was applied to convert the photo-current signal of the PD to voltage signal. The voltage signal is inverse proportional to optical power


due to the inversion amplifier. The projector to be corrected is controlled by a computer as a secondary monitor. The voltage signal corresponding to the optical power is collected by an analog data collection card which is also controlled by the computer.

Column of photodiodes Two stage amplifier

Photodiode (b) Photoelectric module

Projector

Analog signal cable

BENQ CP270 VGA cable Digital projector

PC (a)

(c)

Figure 2. Experiment system setup

A solid square pattern in Fig 2c is generated by computer, whose gray level is sequentially send to projector from 0 to 255. The voltage value standing for the optical power is recorded together with the corresponding gray level by computer. After all the voltage value is recorded, the matrix G is obtained and then the matrix is processed by the method mentioned in chapter 2. Finally, a gamma correction LUT is generated and applied to correct the solid square pattern to validate the corrected gamma curve of the projector. 3.2

Experiment result

Two projector’s gamma curve sequences were measured and processed to generate the corresponding correction LUTs. The corrected gamma curve is also measured and shown in Fig. 3a and Fig. 3c. The corrected gamma curve of 60 Hz projection system is measured and shown in Fig. 3a and Fig. 3c, which is non-monotonic and have some deviations. After generating the correction LUTs, the corrected gamma curves were also measured and the result is illustrated in Fig. 3b and Fig. 3d. The corrected gamma curves showed that the proposed method can acquire a linear gamma curve via 8-bits LUT and it did not lose the dynamic range of the projectors. After correction process, some projector’s gray levels corresponding to optical power were discarded. Therefore, there are some small deviation in Fig. 3b and Fig. 3d, which will not effect the linearity and monotonicity of the corrected gamma curves.


3.8 Voltage(optical power)

Voltage (optical power)

3.8 3.4 3 2.6

3.4 3 2.6 2.2

2.2 1

51

101 151 Gray level

201

1

251

51

(a)

201

251

201

251

(b) 3.7 Voltage (optical power)

3.7 Voltage (optical power)

101 151 Gray level

3.2 2.7 2.2 1.7 1.2

3.2 2.7 2.2 1.7 1.2

1

51

101

151

201

251

1

51

Gray level

101

151

Gray level

(c)

(d)

Figure 3. Measurement result of real gamma curve and corrected gamma curve Fig. 3a & Fig 3c: TI Lightcrafter in HDMI-in mode Fig. 3b & Fig 3d: BENQ CP270 in high dynamic mode

4. Conclusion In this paper, a gamma curve correction system for digital projector is built based on direct optical power detection in order to improve the precision of PMP approach. The real gamma curve of the digital projector can be measured precisely and separately by a photodiode. A gray level rearranging method is proposed to generate gamma correction LUT in order to alternative the method based on gamma function fitting. The preliminary experimental result shows the effectiveness and accuracy of the gamma correction method based on direct optical power detection. This method can deal with the nonsmooth and non-monotonic gamma curve effectively and does not lose the dynamic range of the projectors. In further research, the method based on direct optical power detection can be applied in optical performance evaluation of the digital projector. It can be used in the precision geometrical parameter calibration of the projection lens especially.


Acknowledgment The authors would like to thank the National Natural Science Foundation of China (under grant 61171048，61311130138), Program for New Century Excellent Talents in University (under grant NCET-11-0932), Specialized Research Fund for the Doctoral Program of Higher Education ("SRFDP") (under grant 20111317120002), Key Basic Research Project of Applied Basic Research Programs Supported by Hebei Province (under grant 15961701D), and Research Project for Highlevel Talents in Hebei University (under grant GCC2014049).

References [1] Vo, M., Wang, Z. Y., Pan, B. and Pan, T. Y., "Hyper-accurate flexible calibration technique for fringe-projection-based three-dimensional imaging," Opt. Express 15(20), 16926-16941 (2012). [2] Ma, S., Quan, C., Zhu, R., Chen, L., Li, B. and Tay, C. J., "A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry," Opt. Commun., 5(285), 533-538 (2012). [3] Zhang, S. and Yau, S. T., "Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector," Appl. Opt. 1(46), 36-43 (2007). [4] Zhang, X., Zhu, L. M. and Li, Y. F., "Generic gamma correction for accuracy enhancement in fringe-projection profilometry," J. Opt. Soc. Am. A. 6(29), 1047-1058 (2012). [5] Ma, S., Zhu, R., Quan, C., Chen, L., Tay, C. J. and Li, B., "Flexible structured-light-based three-dimensional profile reconstruction method considering lens projection-imaging distortion," Appl. Opt. 13(51), 2419-2428 (2012).
