Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization.

Micro Fourier transform profilometry (µFTP) is a recently developed computational framework for high-speed dynamic 3D shape measurement of transient scenes based on fringe projection. It has been demonstrated that by using high-frame-rate fringe projection hardware, µFTP can achieve accurate, denser, unambiguous, and motion-artifact-free 3D reconstruction at a speed up to 10,000 Hz. µFTP utilizes a temporal phase unwrapping algorithm, so-called projection distance minimization (PDM), in which multiple wavelengths are used to solve the phase ambiguity optimally in the maximum-likelihood sense. However, it has been found that the choice of the wavelengths is essential to the unambiguous measurement range as well as the unwrapping reliability in the presence of noise. In this work, the relations between the wavelength combination and the noise resistance ability of PDM are analyzed and investigated in detail by analytical, emulational, and experimental means. This leads to a qualitative conclusion that the noise resistance ability of PDM is fundamentally determined by the value of each item in wavelength ratio: a smaller value of each item in wavelength ratio means better noise resistance ability in phase unwrapping. Our result provides a guideline for optimal wavelengths selection in order to improve the noise resistance ability of a practical fringe projection system. Simulations and experiments based on a microscopic fringe projection system are demonstrated to validate the correctness of our conclusion.

Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection.

Temporal phase unwrapping (TPU) is an essential algorithm in fringe projection profilometry (FPP), especially when measuring complex objects with discontinuities and isolated surfaces. Among others, the multi-frequency TPU has been proven to be the most reliable algorithm in the presence of noise. For a practical FPP system, in order to achieve an accurate, efficient, and reliable measurement, one needs to make wise choices about three key experimental parameters: the highest fringe frequency, the phase-shifting steps, and the fringe pattern sequence. However, there was very little research on how to optimize these parameters quantitatively, especially considering all three aspects from a theoretical and analytical perspective simultaneously. In this work, we propose a new scheme to determine simultaneously the optimal fringe frequency, phase-shifting steps and pattern sequence under multi-frequency TPU, robustly achieving high accuracy measurement by a minimum number of fringe frames. Firstly, noise models regarding phase-shifting algorithms as well as 3-D coordinates are established under a projector defocusing condition, which leads to the optimal highest fringe frequency for a FPP system. Then, a new concept termed frequency-to-frame ratio (FFR) that evaluates the magnitude of the contribution of each frame for TPU is defined, on which an optimal phase-shifting combination scheme is proposed. Finally, a judgment criterion is established, which can be used to judge whether the ratio between adjacent fringe frequencies is conducive to stably and efficiently unwrapping the phase. The proposed method provides a simple and effective theoretical framework to improve the accuracy, efficiency, and robustness of a practical FPP system in actual measurement conditions. The correctness of the derived models as well as the validity of the proposed schemes have been verified through extensive simulations and experiments. Based on a normal monocular 3-D FPP hardware system, our method enables high-precision unambiguous 3-D shape measurement with the highest fringe frequency up to 180 by using only 7 fringe patterns achieving a depth precision ∼ 38µm across a field of view of 400 × 300 × 400 mm.

Reversible shear thickening at low shear rates of electrorheological fluids under electric fields.

By shearing electrorheological (ER) fluids between two concentric cylinders, we show a reversible shear thickening of ER fluids above a low critical shear rate (<1 s(-1)) and a high critical electric field strength (>100 V/mm), which can be characterized by a critical apparent viscosity. Shear thickening and electrostatic particle interaction-induced interparticle friction forces are considered to play an important role in the origin of lateral shear resistance of ER fluids, while the applied electric field controls the extent of shear thickening. The electric-field-controlled reversible shear thickening has implications for high-performance electrorheological-magnetorheological fluid design, clutch fluids with high friction forces triggered by applying a local electric field, other field-responsive materials, and intelligent systems.

Transient response of an electrorheological fluid under square-wave electric field excitation.

The transient process of an electrorheological (ER) fluid based on zeolite and silicone oil sheared between two parallel plates to which a square-wave electric field is applied has been experimentally studied. The transient shear stress response to the strain or time is tested. The characteristic constants of time under different applied electric fields and shear rates have been determined. The response time is found to be proportional to shear rate with an exponent of about -0.75 in the tested shear rate range, which agrees with the theoretical predictions made by others. But it only shows a small dependence on the strength of the applied electric field. The results show that the transient process of ER fluids is related to the structure formation in the shearing. When the required shear strain is reached, the shear stress rises to a stable value under constant electric field. Although the electric field strength greatly affects the yield strength, it shows little effect on the stress response time. Also, experiments showed the electric field-induced shear stress decreased with an increase of shear rate.

Transient response of compressed electrorheological fluid.

Transient behaviors of a compressed electrorheological (ER) fluid based on zeolite and silicone oil have been experimentally investigated. The ER fluid is purely compressed between two parallel plates. Compressive speed and voltage amplitude effects on the transient process and randomly applied on/off voltages have been studied. Through normalizing compressive stress of the ER fluid, the characteristic compressive strain and the response time constant corresponding to the rise of compressive stress have been fitted with exponential equations. Results show that the rising time of the transient compressive stress is greatly affected by the compressive speed and the compressive strain position applying voltages, while the amplitude of the applied voltage has little effect on the rising time. The obtained transient compressive strain for the compressive stress to rise to its stable value is much smaller than that working in the transient process of ER fluids under shearing. The decay time and decay strain of compressive stress are much less than for stress rising. The half decay compressive strain is as small as 0.0003 in the experiment. Results show that the response time of compressed ER fluids is quick enough for the usual working conditions of squeezing ER dampers.