Precise phase demodulation of single carrier-frequency interferogram by pixel-level Lissajous figure and ellipse fitting

Fast and precise single-frame phase demodulation interferometry

To achieve real-time phase detection, this paper presents a fast and precise spatial carrier phase-shifting interferometry based on the dynamic mode decomposition strategy. The algorithm initially produces a series of phase-shifted sub-interferograms with the aid of a spatial carrier interferogram. Subsequently, the measured phases are derived with great accuracy from these sub-interferograms through the use of the dynamic mode decomposition strategy, an outstanding non-iterative algorithm. Numerical simulation and experimental comparison show that this method is an efficient and accurate single-frame phase demodulation algorithm. The paper also analyzes the performance of the proposed method based on influencing factors such as random noise level, carrier frequency size, and carrier frequency direction. The results indicate that this method is a fast and accurate phase solution method, offering another effective solution for dynamic real-time phase measurement.

Phase retrieval from single interferogram without carrier using Lissajous ellipse fitting technology

Phase extraction from single interferogram is of high significance and increasingly interest in optical metrology. In this contribute we propose an advanced Pixel-level Lissajous Ellipse Fitting (APLEF) method to extract the phase from single interferogram without carrier. At each pixel, a Lissajous figure is created by plotting N against D, where N and D are subtractions and additions of intensities of adjacent pixels in a small window. The so created Lissajous figure is already in phase quadrature because of the subtraction and addition process, and the Lissajous Figure is forced to be closed by taking the opposite values of N and D, i.e. -N and -D into account. The closed and in phase quadrature Lissajous Figure is the key point for APLEF to demodulate the single inteferogram without carrier in theoretically. The simulation shows its higher accuracy than existed SPT and Garbusi's method and the experiments finally corroborate its effectiveness.

Single-shot 4-step phase-shifting multispectral fringe projection profilometry

Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which has limited PSP to static or quasi-static imaging. In this paper, we introduce multispectral 4-step phase-shifting FPP that provides 3D imaging using a single acquisition. The method enables real-time profilometry applications. A single frame provides all four phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. The multispectral nature of the system ensures that light does not leak between the spectral bands, which is a common problem in simultaneous phase-shifting with color cameras. With the use of this new concept, custom composite patterns containing multiple patterns can be acquired with a single acquisition.

Snapshot 3D reconstruction of liquid surfaces

In contrast to static objects, liquid structures such as drops, blobs, as well as waves and ripples on water surfaces are challenging to image in 3D due to two main reasons: first, the transient nature of those phenomena requires snapshot imaging that is fast enough to freeze the motion of the liquid. Second, the transparency of liquids and the specular reflections from their surfaces induce complex image artefacts. In this article we present a novel imaging approach to reconstruct in 3D the surface of irregular liquid structures that only requires a single snapshot. The technique is named Fringe Projection - Laser Induced Fluorescence (FP-LIF) and uses a high concentration of fluorescent dye in the probed liquid. By exciting this dye with a fringe projection structured laser beam, fluorescence is generated primarily at the liquid surface and imaged at a backward angle. By analysing the deformation of the initial projected fringes using phase-demodulation image post-processing, the 3D coordinates of the liquid surface are deduced. In this article, the approach is first numerically tested by considering a simulated pending drop, in order to analyse its performance. Then, FP-LIF is applied for two experimental cases: a quasi-static pending drop as well as a transient liquid sheet. We demonstrate reconstruction RMS errors of 1.4% and 6.1% for the simulated and experimental cases respectively. The technique presented here demonstrates, for the first time, a fringe projection approach based on LIF detection to reconstruct liquid surfaces in 3D. FP-LIF is promising for the study of more complex liquid structures and is paving the way for high-speed 3D videography of liquid surfaces.

Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method

We propose a new concept of single-shot deflectometry for real-time measurement of three-dimensional surface profile using a single composite pattern. To retrieve an accurate phase from one-frame composite pattern, we adapt the Fourier Transform (FT) method and the spatial carrier-frequency phase-shifting (SCPS) technique to our proposed deflectometry. Based on Lissajous figure and ellipse fitting method, we also correct the phase extraction error in SCPS technique by reducing the effect of background and modulation variations. The proposed technique is verified by comparing our measurement results with phase-shifting deflectometry, and the maximum difference between two measurement results is less than 30 nm rms. We also test the robustness to vibration and the measurement capability for dynamic object.