The deflectometry provides an optical testing method with ultra-high dynamic range. In this paper, a microscopic testing method based on deflectometric technique is proposed to quantitatively evaluate the microstructures according to the wavefront aberration. To achieve the real-time and accurate wavefront testing for microstructure evaluation, a colorcoded phase-shifting fringe pattern is applied to illuminate the test object. It avoids the sequential projection of multistep phase-shifting fringes in traditional deflectometry, enabling the transient wavefront testing. The feasibility of the proposed transient microscopic testing method is demonstrated by the experiment. The proposed method enables accurate and transient testing of microstructures with high dynamic range, minimizing the environmental disturbance.
The deflectometry enables high-precision wavefront measurement with large dynamic range. Traditional multi-step phase-shifting fringe-illumination deflectometric methods involve at least three sinusoidal phase-shifting fringe patterns and require a sequential projection, making it not feasible for the instantaneous measurement. In this paper, a colorcoded method with frequency-carrier patterns is proposed to achieve the instantaneous wavefront measurement based on deflectometry. With the color extraction from different channels, composite patterns in x and y directions can be well separated with a single shot. Then, the phase-shifting patterns encoded in different frequencies can be demodulated with the designed filters, by which the local wavefront slopes can be obtained simultaneously to reconstruct the wavefront under test. Both the numerical simulation and experiments are performed to validate the feasibility of proposed method. The proposed method provides a feasible way for the real-time and instantaneous measurement with large dynamic range based on deflectometry.
The fiber point-diffraction interferometer provides a feasible method for the measurement of three-dimensional absolute displacement, in which the fiber point-diffraction sources generating coherent spherical reference waves are required to be parallel placed in the testing probe. However, the misalignment in the actual probe could introduce significant error in the displacement measurement result, and it also places high requirement on the adjustment of testing probe. A method based on phase difference in the axial displacement is proposed to calibrate the probe misalignment, and the numerical simulation is carried out to demonstrate the feasibility of the proposed method. The proposed method lowers the requirement on the processing of testing probe.
The deflectometry based on reverse-Hartmann-test configuration provides a feasible way for wavefront testing. Objects with complex surfaces place a high requirement on the wavefront testing accuracy, in which the systematic parameter is the key issue. In this paper, the effect of systematic parameters of the testing system such as the geometrical error and the approximation of systematic geometrical parameters are discussed in detail and a calibration method is proposed. Numerical simulation is carried out to demonstrate the feasibility of the proposed calibration method, for the transmitted wavefront with RMS 3.1220 μm, the testing optimization result of residual error with RMS value better than 20 nm is achieved.
In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, ray tracing of the modeled testing system is performed to reconstruct the test surface error. Careful calibration of system geometry is required to achieve high testing accuracy. To realize the high-precision surface testing with reverse Hartmann test, a computer-aided geometrical error calibration method is proposed. The aberrations corresponding to various geometrical errors are studied. With the aberration weights for various geometrical errors, the computer-aided optimization of system geometry with iterative ray tracing is carried out to calibration the geometrical error, and the accuracy in the order of subnanometer is achieved.
The testing technique with high dynamic range is required to meet the measurement of refractive wavefront with large distortion from test refractive surface. A general deflectometric method based on reverse Hartmann test is proposed to test refractive surfaces. Ray tracing of the modeled testing system is performed to reconstruct the refractive wavefront from test surface, in which computer-aided optimization of system geometry is performed to calibrate the geometrical error. For the refractive wavefront error with RMS 255 μm, the testing precision better than 0.5 μm is achieved.
The submicron-aperture fiber point-diffraction interferometer (SFPDI) can be applied to realize the measurement of
three-dimensional absolute displacement within large range, in which the performance of point-diffraction wavefront and
numerical iterative algorithm for displacement reconstruction determines the achievable measurement accuracy,
reliability and efficiency of the system. A method based on fast searching particle swarm optimization (FS-PSO)
algorithm is proposed to realize the rapid measurement of three-dimensional absolute displacement. Based on the SFPDI
with two submicron-aperture fiber pairs, FS-PSO method and the corresponding model of the SFPDI, the measurement
accuracy, reliability and efficiency of the SFPDI system are significantly improved, making it more feasible for practical
application. The effect of point-diffraction wavefront error on the measurement is analyzed. The error of pointdiffraction
wavefront obtained in the experiment is in the order of 1×10-4λ (the wavelength λ is 532 nm), and the
corresponding displacement measurement error is smaller than 0.03 μm. Both the numerical simulation and comparison
experiments have been carried out to demonstrate the accuracy and feasibility of the proposed SFPDI system, high
measurement accuracy in the order of 0.1 μm, convergence rate (~90.0%) and efficiency have been realized with the
proposed method, providing a feasible way to measure three-dimensional absolute displacement in the case of no guide
A measurement method with calotte cube was proposed to realize the high-precision calibration of size error in industrial computer tomography (CT) system. Using the traceability of calotte cube, the measurement of the repeatability error, probing error and length measurement error of industrial CT system was carried out to increase the acceptance of CT as a metrological method. The main error factors, including the material absorption, projection number and integration time and so on, had been studied in detail. Experimental results show that the proposed measurement method provides a feasible way to measure the size error of industrial CT system. Compared with the measurement results with invar 27- sphere gauge, a high accuracy in the order of microns is realized with the proposed method based on calotte cube. Differing from the invar 27-sphere gauge method, the material particularity of calotte cube (material of metallic titanium) could introduce beam hardening effect, the study on the influence of material absorption and structural specificity on the measurement, which provides significant reference for the measurement of metallic samples, is necessary.
To overcome the accuracy limitation due to the machining error of standard parts in measurement system, a threedimensional
coordinate measurement method with subwavelength-aperture-fiber point diffraction interferometer (PDI) is
proposed, in which the high-precision measurement standard is obtained from the ideal point-diffracted spherical
wavefront instead of standard components. On the basis of the phase distribution demodulated from point-diffraction
interference field, high-precision three-dimensional coordinate measurement is realized with numerical iteration
optimization algorithm. The subwavelength-aperture fiber is used as point-diffraction source to get precise and highenergy
spherical wavefront within high aperture angle range, by which the conflict between diffraction wave angle and
energy in traditional PDI can be avoided. Besides, a double-iterative method based on Levenbery-Marquardt algorithm is
proposed to realize precise reconstruct three-dimensional coordinate. The analysis shows that the proposed method can
reach the measurement precision better than microns within a 200×200×300 (in unit of mm) working volume. This
measurement method does not rely on the initial iteration value in numerical coordinate reconstruction, and also has high
measurement precision, large measuring range, fast processing speed and preferable anti-noise ability. It is of great
practicality for measurement of three-dimensional coordinate and calibration of measurement system.