The dual wavelength interferometry in digital holography can eliminate 2π ambiguities with a large synthetic wavelength, but the measurement error tends to be amplified. In this paper, a new numerical algorithm is proposed to reduce the amplification error, and further expand the measurement range. The wrapped phase map associated with one wavelength is used to assist unwrapping the phase map associated with the other wavelength. Since these two phase maps correspond to the same step height, an exhaustive searching method is applied. The measurement error will not be amplified linearly with the synthetic wavelength, but controlled at the same level with the single wavelength interferometry. In consideration of the measurement errors such as the environmental vibration, instability of wavelength and so on, a tolerance is set to guarantee the stability of the solution. The performance and feasibility of the proposed algorithm is verified by the numerical demonstration.
In the phase measuring deflectometry, the phase error caused by the nonlinear intensity response, called the gamma distortion, can negatively affect the measurement quality of specular surfaces. Based on the generic exponential four-step phase-shifting fringe modal, this paper proposes a flexible and simple phase retrieval method to eliminate the phase errors without complex calibration or additional fringe patterns. The experimental results illustrate that the proposed method can accurately retrieve the phases from the distorted fringe patterns with the Gamma distortion, and the measurement precision can henceforth be improved.
Phase measuring deflectometry is a powerful in-situ measuring technique for complex specular surfaces. Its measuring accuracy depends on the quality of geometric calibration. An in-situ deflectometric measuring system is integrated into a single point diamond turning machine. An accurate self-calibration method is proposed to refine the positions of the camera and the screen. A world coordinate system is established by introducing a flat mirror without markers. The geometric positions are solved by minimizing the deviations of the traced screen pixels. The tracing deviations caused by the form errors behave differently with those caused by the position errors. Precise localization of the measured surface can be realized by error separation, so that detecting of feature points can be avoided. Experimental results demonstrate that the measurement error is below 300 nm.
Industrial robots have great potential for efficient and flexible polishing of large optical components, but the low positioning accuracy and control stability limits the polishing form quality. A model is established to describe the pressure distribution at the edge based on FEA analysis, and the effects of form deviation between the workpiece and the polishing pad is also investigated, thus TIFs can be calculated reliably. Polishing paths are planned to avoid sharp turning angles and fast movement, which can lead to unstable material removal. The dwell time is calculated via deconvolution with the space-variant TIFs. Experiments are conducted and the results show that the edge-roll error is significantly reduced and the polishing time is saved by 80%. Hence the robotic polisher can be comparable to the conventional polishing machines, which has a great significance for the ultra-precision optical manufacturing.