Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3D surface profilometry

Nanoscale surface metrology with a liquid crystal-based phase-shifting angular shearing interferometer

In this Letter, a phase-shifting angular shearing interferometer has been proposed for the application in optical surface metrology (SM) by using a combination of a wedge-shaped liquid crystal (LC) cell and a polarization phase shifter. The demonstration of this angular shearing interferometer for step height measurement is accomplished with the help of a phase-shifting technique. Four phase-shifted interferograms produced by a geometrical phase shifter are subjected to a simplified Wiener deconvolution method, which resembles a simple analysis technique for shearing interferograms in comparison to alternative approaches. A simulation study has been conducted to validate the proposed technique. The experimental results show an accuracy of 5.56% for determining the step height, which also agrees with the results obtained by atomic force microscopy. Owing to the tunability of birefringence, the proposed LC-based angular shearing interferometry technique will be useful to control spatial resolution in optical metrology.

Accurate and flexible calibration method for a 3D microscopic structured light system with telecentric imaging and Scheimpflug projection

3D imaging and metrology of complex micro-structures is a critical task for precision manufacturing and inspection. In this paper, an accurate and flexible calibration method for 3D microscopic structured light system with telecentric imaging and Scheimpflug projector is proposed. Firstly, a fringe projection 3D microscopy (FP-3DM) system consisting of a telecentric camera and a Scheimpflug projector is developed, which can take full advantage of the depth of field (DOF) and increase the measurement depth range. Secondly, an accurate and flexible joint calibration method is proposed to calibrate the developed system, which utilizes the established pinhole imaging model and Scheimpflug distortion model to calibrate telecentric imaging, and fully considers the correction and error optimization of the Scheimpflug projection model. Meanwhile, the optimized local homography is calculated to obtain more accurate sub-pixel correspondence between the camera and the projector, and the perspective-n-point (PnP) method make the 3D coordinate estimation of the feature point more accurate. Finally, a prototype and a dedicated calibration program are developed to realize high-resolution and high-precision 3D imaging. The experimental results demonstrate that the re-projection error is less than 1µm, and the 3D repeated measurement error based on feature fitting is less than 4µm, within the calibrated volume of 10(H)mm × 50(W)mm × 40(D)mm.

State-of-the-art active optical techniques for three-dimensional surface metrology: a review [Invited]

This paper reviews recent developments of non-contact three-dimensional (3D) surface metrology using an active structured optical probe. We focus primarily on those active non-contact 3D surface measurement techniques that could be applicable to the manufacturing industry. We discuss principles of each technology, and its advantageous characteristics as well as limitations. Towards the end, we discuss our perspectives on the current technological challenges in designing and implementing these methods in practical applications.

Shape measurement with modified phase-shift lateral shearing interferometry illumination and radial basis function

Three-dimensional shapes of objects were evaluated with modified phase-shift lateral shearing interferometry illumination and radial basis function. A simple optical system was developed to create the fringe pattern based on the Murty interferometer. The phase shift was generated only by moving a plane-parallel plate along an in-plane parallel direction. A novel moving radial basis function method was presented to improve the quality of fringe patterns. And the proper calculation window size was given based on numerical simulation. Three-dimensional shapes of two kinds of objects were determined to verify the feasibility and effectiveness of the proposed method, and the reconstructed height distributions were in good accordance with the referenced data.

Generalized phase-shifting for three-wave shearing interferometry

A generalized phase-shifting method for three-wave shearing interferometry is proposed. The phase-shifting algorithm is derived by an optimal process based on least-squares fitting. With this generalized algorithm, the steps of phase-shifting can be reduced to five, which greatly simplifies the measurement and decreases the burden of computation. Both the numerical simulation and the optical experiment are carried out to demonstrate the adaptability of the method.

Flexible calibration method for microscopic structured light system using telecentric lens

This research presents a novel method to calibrate a microscopic structured light system using a camera with a telecentric lens. The pin-hole projector calibration follows the standard pin-hole camera calibration procedures. With the calibrated projector, the 3D coordinates of those feature points used for projector calibration are then estimated through iterative Levenberg-Marquardt optimization. Those 3D feature points are further used to calibrate the camera with a telecentric lens. We will describe the mathematical model of a telecentric lens, and demonstrate that the proposed calibration framework can achieve very high accuracy: approximately 10 μm with a volume of approximately 10(H) mm × 8(W) mm × 5(D) mm.

Fringe projection 3D microscopy with the general imaging model

Three-dimensional (3D) imaging and metrology of microstructures is a critical task for the design, fabrication, and inspection of microelements. Newly developed fringe projection 3D microscopy is presented in this paper. The system is configured according to camera-projector layout and long working distance lenses. The Scheimpflug principle is employed to make full use of the limited depth of field. For such a specific system, the general imaging model is introduced to reach a full 3D reconstruction. A dedicated calibration procedure is developed to realize quantitative 3D imaging. Experiments with a prototype demonstrate the accessibility of the proposed configuration, model, and calibration approach.

Phase-shifting lateral shearing interferometry using wedge-plate and interferometric grating

A simple and robust method for introducing a phase-shifting test procedure in a wedge-plate shearing interferometer is proposed. The output of the wedge-plate lateral shearing interferometer (LSI) is superposed onto a sinusoidal grating, forming a moiré pattern. The in-plane translation of grating perpendicular to the grating lines is used for introducing a known amount of phase shifts in the interferometer. Direct measurement of phase using a four-step phase-shifting method is undertaken. The applicability of this devised phase-shifting wedge-plate LSI has been successfully tested for setting the collimation position of optical beams. Good accuracy and precision are achieved.