Color-encoded single-shot computer-generated Moiré profilometry

A color-encoded single-shot computer-generated Moiré profilometry (CSCGMP) is proposed. Two sinusoidal gratings with a π phase difference are encoded in red and blue channels respectively to combine a composite color grating. While this composite color grating is projected onto the measured object, the corresponding color deformed pattern can be captured. So two deformed patterns with a π phase difference are separated from its red and blue components respectively. After normalization and subtraction, the AC component of both separated deformed patterns can be extracted. If this AC component respectively multiplied by the two AC components of fringe patterns of reference plane with a π/2 phase difference prepared and saved on the computer in advance, two computer-generated Moiré fringes just respectively standing for sine and cosine of phase which is modulated by the height of the object relative to the reference plane are figured out. So the 3D shape of the measured object can be reconstructed with normal computer-generated Moiré profilometry. Both simulation and experimental results show the feasibility and validity of the proposed method. It has potential in real-time 3D measurement due to its single-shot feature.

Computer-generated moiré profilometry based on fringe-superposition

A computer-generated moiré profilometry based on algebraic addition instead of algebraic multiplication is proposed. Firstly, the two AC components of the captured fringe patterns on the reference plane with $$\pi /2$$ π / 2 phase difference are retrieved and saved in advance. While measuring, two sinusoidal gratings with $$\pi$$ π phase difference are projected onto the measured object alternatively, and the corresponding deformed patterns are captured. Then the AC component of the captured deformed pattern can be separated exactly. When the positive and negative AC component of the captured deformed pattern are added to the two prestored AC components respectively, two moiré fringes only reflect sine and cosine of the object’s phase information can be successfully generated via a series of data processing procedures. Finally, the phase distribution of the measured object can be extracted by arctangent of the ratio of these two moiré fringes. Compared with computer-generated moiré profilometry based on algebraic multiplication, this proposed method can reduce the effect of high frequency noise and residual DC component on measurement and improve the measurement accuracy. While compared with $$\pi$$ π phase shifting FTP, this method can measure more complex objects with better measurement capability. Experimental results verify the feasibility and validity of the proposed method.

Research on Focal Length Measurement Scheme of Self-Collimating Optical Instrument Based on Double Grating

In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moiré fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moiré fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moiré image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.