The temperature compensation effect of FBG sensors is crucial to their measuring accuracy. In the design of a FBG sensor, two FBGs are often adopted to subject positive and negative strains through two packaging methods including all grating pasting and two-end pasting after grating pretension. Temperature compensation of the FBG sensor is often realized by using the difference of the wavelength shift of the two FBGs as the sensing signal. In current reports, temperature compensation is performed based on the assumption that the wavelength shifts of the two FBGs are the same. However, the difference of the wavelength shift is also influenced by the packaging methods and the temperature changing environment. This work presents an experimental study on the temperature compensation effect of two pair different packaged FBGs under abrupt temperature changing environment. For each packaging method, two FBGs with same parameters are pasted on the upper and lower surfaces of an equal-strength cantilever and assembled in a shell to serve as a FBG sensor. Boiling water and ice-water mixture are used to pour on the shell to form abrupt temperature changing, whereas an adjustable thermostat provides slowly temperature changing environment. Experimental results shows that the temperature compensation effects for the two different packaging method are same(within 21pm) when slowly temperature changing slowly, however, the compensation effects are significantly degraded during abrupt temperature increasing (58 pm and 48 pm for all grating pasting and two-end pasting, respectively). The results can provide a scientific reference for the design of FBG sensors.
Wafer surface defect detection plays an important role in product yield improvement. Particles are the main source in the majority of defects on wafer. We calculate and analyze the scattering field around the particles on the un-patterned wafer surface by light scattering method. A model was built to calculate an isolated particle based on Mie theory firstly, and another model was built to calculate particle scattering field on a smooth wafer surface based on Bidirectional Reflectance Distribution Function (BRDF). We simulated the scattering field with different parameters set: incidence angle, polarization state and scattering angle channel. The results verify the feasibility of our method to calculate the scattering field.
A three-dimensional profile measurement method based on digital photoelastic fringe analysis technology is proposed in this paper. According to the actual stress field of a disc under appropriate load, the photoelastic fringe patterns are generated. These patterns are illuminated on the reference plane and objects through a projector, which are regarded as the structured-light pattern sequence. Then a series of images including normal images and deformed fringe images are captured. These images contain two significant photoelastic parameters, isoclinic parameter and isochromatic parameter, which could be evaluated by the phase shifting method. Therefore, phase differences can be calculated by photoelastic isochromatic parameter after phase unwrapping. Depth information is carried in the phase differences and virtual 3D profile equal to real objects could be reconstructed. Experiments demonstrate that this method is robust and suitable for measuring objects with regular and general shape.
In engineering practice, especially in the structural health monitoring (SHM) of civil engineering, the deformation of concrete is usually small, so a strain sensor don’t need a large measuring range but a high sensitivity. This work presents the structural design, measuring and sensitization principle, and full test of an embedded FBG strain sensor for SHM of reinforced concrete. Two capillary steel tubes protected by a stainless steel tube and embedded with each end fiber of a FBG have been proposed, which possesses the capacity of strain sensitization and adjustment. Experimental results show that sensor provides a sensitivity of 4.2 pm/με in measurement range of ±300με, which is 3.5 times than the bare FBG with center wavelength of 1550 nm. Test results also demonstrate that the sensor possesses good repeatability and creep resistance, which is promising for applications in civil engineering.
Hypernumerical aperture and polarized illumination are the key technologies of resolution enhancement of lithography. When the numerical aperture reaches 0.85 and above, especially in the immersion lithography, polarization effect must be taken into consideration. The performance of the projection lens needs to be characterized by rigorous polarization aberration. The vector polarization imaging system that is suitable for hypernumerical aperture is established, and the distortion effects introduced by polarization aberration are analyzed. Orientation Zernike polynomials-based method and Pauli–Zernike polynomials-based method are adopted to parameterize the polarization aberration represented by Jones pupil. Critical dimension error, placement error, and normal int. log slope index are introduced as the index to value imaging distortion. The proposed method and analysis conclusion would provide meaningful guidance for projection lens design of lithographic tools.
For lithographic tools, the forward model of imaging system is repeated many times in the inverse optimization algorithm of optical proximity correction (OPC). Fast and accurate imaging simulation is highly desirable as one of the most critical components in the forward modeling simulations. We have focused on investigating the physical properties of optical imaging in lithography and introduced the method of separation of variables in Mathematical Physics as the fundamental theory to deal with a wide range of process variables. We proposed a rigorous methodology from first principles to speed up image simulations. The proposed imaging formula can be rearranged by two parts, one with only variables, while the remaining part independent with the variables. Simulations for a variety of different process variables confirmed that the proposed method yields a superior quality of image with an accuracy of 10-3 and superior performance of speed. Therefore, the proposed method provides a novel theory and practical means for OPC and other resolution enhancement technologies (RETs) in optical lithography.
The NA of immersion lithography has reached 1.35, in which case polarization effect must be taken into account. The performance of the projection lens should be characterized by polarization aberration. We proposed a polarization aberration measurement theory and method, using the binary grating structure as the mask pattern, with intensity distribution signal as the measuring signal. Pauli Zernike polynomials are adopted to characterizing the polarization aberration, and a linear relationship between intensity signal and Pauli Zernike coefficients was derived. Simulation results show that using the proposed method, the polarization aberration can be reconstructed with relative error of refactoring to 10-2.
Information of lens aberration of lithographic tools is important as it directly affects the intensity distribution in the image plane. Zernike polynomials are commonly used for a mathematical description of lens aberrations. Due to the advantage of lower cost and easier implementation of tools, image based measurement techniques have been widely used. Lithographic tools are typically partially coherent systems that can be described by a bilinear model, which entails time consuming calculations and does not lend a simple and intuitive relationship between lens aberrations and the resulted images. Previous methods for retrieving lens aberrations in such partially coherent systems involve through-focus image measurements and time-consuming iterative algorithms. In this work, we propose a method for aberration measurement in lithographic tools, which only requires measuring two images of intensity distribution. Two linear formulations are derived in matrix forms that directly relate the measured images to the unknown Zernike coefficients. Consequently, an efficient non-iterative solution is obtained.