The comparisons between the preconditioned conjugate-gradient method and the Fourier transform method in lateral shearing interferometry

2019 ◽  
Author(s):  
Peiying Liang ◽  
Jianping Ding ◽  
Yangqing Zhu ◽  
Bangyun Xiong ◽  
Yuhua Wang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Transform Method ◽  
Shearing Interferometry ◽  
Lateral Shearing ◽  
The Fourier Transform ◽  
Lateral Shearing Interferometry

Study on Measurement of Thin Film Thickness with Lateral Shearing Interferometry

2013 ◽  
Vol 718-720 ◽  
pp. 848-852
Author(s):  
Jun Hong Su ◽  
Ying Shi ◽  
Jin Man Ge
Keyword(s):  
Film Thickness ◽  
Transform Method ◽  
Shearing Interferometry ◽  
Platform Process ◽  
Fast Fourier Transform Method ◽  
Lateral Shearing ◽  
Phase Unwrap ◽  
Technical Indicator ◽  
Lateral Shearing Interferometry ◽  
Shearing Interference

The film thickness is an important technical indicator of film devices, and its accuracy directly affects various performances of optical components. In fabrication process of film device, fast and accurate measurement of film thickness has positive significance on product quality control. In this paper, measure film thickness with lateral shearing interferometry. Collect interferograms through structured lateral shearing interference platform, process interferogram with Fast Fourier Transform method to extract phase, unwrap the wrapped phase to achieve phase value. Finally, calculate film thickness based on lateral shearing interference principle. The thickness of sample is 119.6800nm measured by this method, basically the same with the result 120.6036nm that measured by ZYGO interferometer. This experiment shows that lateral shearing interferometry not only suit to measurement of film thickness, but also abundant high-precision method of measuring film thickness, and has high practical value.

Magnetization vector imaging for borehole magnetic data based on magnitude magnetic anomaly

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. D429-D444 ◽  
Author(s):  
Shuang Liu ◽  
Xiangyun Hu ◽  
Tianyou Liu ◽  
Jie Feng ◽  
Wenli Gao ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Magnetization Vector ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Magnetization Direction ◽  
Magnetization Intensity

Remanent magnetization and self-demagnetization change the magnitude and direction of the magnetization vector, which complicates the interpretation of magnetic data. To deal with this problem, we evaluated a method for inverting the distributions of 2D magnetization vector or effective susceptibility using 3C borehole magnetic data. The basis for this method is the fact that 2D magnitude magnetic anomalies are not sensitive to the magnetization direction. We calculated magnitude anomalies from the measured borehole magnetic data in a spatial domain. The vector distributions of magnetization were inverted methodically in two steps. The distributions of magnetization magnitude were initially solved based on magnitude magnetic anomalies using the preconditioned conjugate gradient method. The preconditioner determined by the distances between the cells and the borehole observation points greatly improved the quality of the magnetization magnitude imaging. With the calculated magnetization magnitude, the distributions of magnetization direction were computed by fitting the component anomalies secondly using the conjugate gradient method. The two-step approach made full use of the amplitude and phase anomalies of the borehole magnetic data. We studied the influence of remanence and demagnetization based on the recovered magnetization intensity and direction distributions. Finally, we tested our method using synthetic and real data from scenarios that involved high susceptibility and complicated remanence, and all tests returned favorable results.

Sign in / Sign up

Export Citation Format

Share Document