Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

Angle measurement error and compensation for pitched rotation of circular grating

As circular grating is not vertical to the shaft,the angle measurement error of the circular grating is analyzed.Based on the moire fringe equations in pitched condition,the mathematic model of the angle measurement error is derived.The paper comes to the conclusion that the nonorthogonal angle between the circular grating and the shaft leads to the second harmonic error of the angle measurement,and the correctness of the result is proved by the experimental data.The method of the error compensation is presented,and the angle measurement accuracy of the circular grating is improved by the error compensation.

Angle measurement error and compensation for decentration rotation of circular gratings

As the geometric center of circular grating does not coincide with the rotation center,the angle measurement error of circular grating is analyzed. Based on the moire fringe equations in decentration condition,the mathematical model of angle measurement error is derived. It is concluded that the decentration between the centre of circular grating and the center of revolving shaft leads to the first-harmonic error of angle measurement. The correctness of the result is proved by experimental data. The method of error compensation is presented,and the angle measurement accuracy of the circular grating is effectively improved by the error compensation.

Plasmonic lithography with 100nm overlay accuracy

In this paper,we demonstrate an auto accurate alignment method to align mask-substrate in the prototype of plasmonic lithography(PL),which is essential for multilayer nanostructure fabrication with high resolution,low cost,high efficiency,and high throughput,such as circuit manufacturing and other applications.We obtained an alignment signal with sensitivity better than 20 nm by using the Moiréfringe image.However,only using the Moiréfringes cannot guarantee the alignment of the mask and the substrate because the Moiréfringe repeats itself when the mask and substrate are offset by a fixed displacement.To eliminate the ambiguity,boxes and the crosses alignment marks are designed beside the grating marks on the substrate and the mask,respectively.A two-step alignment scheme including coarse alignment and fine alignment is explored in the auto alignment system.In the stage of coarse alignment,the edge detection algorithm based on Canny operator is adopted to detect the edges image effectively.In the process of fine alignment,Fourier transform based on Moiréfringe image is obtained to improve the alignment accuracy.In addition,experimental results of overlay indicate that PL can obtain sub-100 nm alignment accuracy over an area of 1 cm^2 using the proposed two-step alignment scheme.Via the substrate-mask mismatch compensation,better stages and precise environment control,it is expected that much higher overlay accuracy is feasible.

Three-Dimensional Shape Measuring Method Based on Dual-Frequency Digital Moiré Fringe

A dual-frequency digital Moiré measurement method(DFDM) is proposed for the three-dimensional(3D) shape measurement of an object.The high-and low-frequency fringes are modulated separately along orthogonal direction using different carrier frequencies before being projected onto the measured object.After collecting and demodulating the composite fringe,the digital π phase shift is used to remove the DC component of the demodulated fringes,resulting in high-precision Moiré fringes for calculating the wrapped phase.The unwrapping of the high-frequency wrapped phase is guided by the low-frequency phase to further realistically reconstruct the surface of the measured object.When compared with existing single-shot digital Moiré profilometry,DFDM effectively removes the DC component of the fringe and calculates the phase more accurately.

A digital moiré fringe method for displacement sensors

In this study, a displacement measurement method based on digital moiré fringe is described and experimentally demonstrated. The method is formed by only one grating with a constant pitch. First, the magnified grating image is received by an imaging array and is sent to a computer. Then, the digital moiré fringes are generated by overlaying the grating image with its mirrored one. Finally, a specifically designed algorithm is used to obtain the fringes' phase difference before and after movement and calculate the displacement. This method has the effects of amplifying displacement and averaging the grating lines error, the same as the traditional moiré technique using two pieces of gratings. At the same time, the proposed system is much easier to assemble and the measurement resolution can be set more flexibly. One displacement measuring system based on this method was built up. Experiment results show that its measurement errors are less than 0.3 μm and less than 0.12 μm at the resolutions of 0.1 μm and 0.03 μm, respectively.