Vibration hinders the application of phase-shifting interferometry (PSI) to on-machine test and large-aperture mirror measurement. The investigation of PSI fringe disturbed by vibration indicates that, besides tilt-shifting error, inter- and intra-frame contrast variation is significant. The contrast variation is another dominant error source in phase retrieval of PSI. An inter- and intra-frame contrast compensation method is proposed here to retrieve wavefront phase from interferograms subjected to vibration. The method constructs algebraic equations with interferogram data and solves equations using iterative procedures. Experiments validate its effectiveness and manifest its capability to suppress vibration-induced error over a large frequency region. To enhance the calculation efficiency, a spatial subsampling strategy is proposed. Practical testing shows that subsampling reduces calculation time exponentially and preserves retrieval accuracy and spatial resolution. The proposed method, of which the unique ability is compensating the tilt-shifting error and fringe blur caused by vibration, predicates an effective and low-cost solution for PSI applied in vibration.

This paper proposes a new method for the measurement of spherical coordinates by using capacitive sensors as a non-contact probe solution of measurement of aspheric surfaces. The measurement of the average effect of the capacitive probe and the influence of capacitive probe tilting were studied with respect to an eccentric spherical surface. Based on the tested characteristic curve of the average effect of the sphere and probe, it was found that nonlinear and linear compensation resulted in high measurement accuracy. The capacitance probe was found to be trying to fulfill a need for performing nm-level precision measurement of aspheric electromagnetic surfaces.

Error compensation technology is used for improving accuracy and reducing costs. Dynamic error compensation techniques of coordinate measuring machine (CMM) are still under study; the major problem is a lack of suitable models, which would be able to correctly and simply relate the dynamic errors with the structural and operational parameters. To avoid the complexity of local dynamic deformation measurement and modeling, a comprehensive calibration method is employed. Experimental research reveals specific qualities of dynamic Abbe errors; the results exceed the scope of ISO 10360-2 calibration method, showing the ISO 10360-2 dynamic error evaluation deficiencies. For calibrating the dynamic Abbe errors, the differential measurement method is presented based on the measurements of the internal and external dimensions. Referring probe tip radius correction, the dynamic Abbe errors compensation method is proposed for CMM end-users and is easy to use.

We introduce a high-precision self-adaptive phase-calibration method for performing wavelength-tuning interferometry. Our method is insensitive to the nonlinearity of the phase shifter, even under random control. Intensity errors derived from laser voltage changes can be restrained by adopting this approach. Furthermore, this method can effectively overcome the influences from the background and modulation intensities in the interferogram, regardless of the phase structure. Numerical simulations and experiments are implemented to verify the validity of this high-precision calibration method.

A multi-repeated photolithography method for manufacturing an incremental linear scale using projection lithography is presented. The method is based on the average homogenization effect that periodically superposes the light intensity of different locations of pitches in the mask to make a consistent energy distribution at a specific wavelength, from which the accuracy of a linear scale can be improved precisely using the average pitch with different step distances. The method’s theoretical error is within 0.01 µm for a periodic mask with a 2-µm sine-wave error. The intensity error models in the focal plane include the rectangular grating error on the mask, static positioning error, and lithography lens focal plane alignment error, which affect pitch uniformity less than in the common linear scale projection lithography splicing process. It was analyzed and confirmed that increasing the repeat exposure number of a single stripe could improve accuracy, as could adjusting the exposure spacing to achieve a set proportion of black and white stripes. According to the experimental results, the effectiveness of the multi-repeated photolithography method is confirmed to easily realize a pitch accuracy of 43 nm in any 10 locations of 1 m, and the whole length accuracy of the linear scale is less than 1 µm/m.