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Weak measurement is a novel technique for parameter estimation with higher precision. In this paper we develop a general theory for the parameter estimation based on weak measurement technique with arbitrary postselection. The previous weak value amplification model and the joint weak measurement model are two special cases in our theory. Applying the developed theory, the time-delay estimation is investigated in both theory and experiment. Experimental results shows that when the time-delay is ultra small, the joint weak measurement scheme outperforms the weak value amplification scheme, and is robust against not only the misalignment errors but also the wavelength-dependence of the optical components. These results are consistent with the theoretical predictions that has not been verified by any experiment before.

High-precision temperature measurements could guarantee temperature difference control accuracy in research and industrial production. To flexibly achieve high precision and large operating temperature range is a crucial problem for temperature measurements. Here, we demonstrate a method for a high-precision temperature measurement based on a weak measurement done using nematic liquid crystals (NLCs). By performing an analysis in the frequency domain, the temperature variation of NLCs is measured using a Sagnac interferometer with appropriate preselection and postselection. In order to obtain a large operating temperature range, there is a relatively large time delay that resulted from NLCs, and an operational principle is deduced explicitly by Jones matrices. In the proposed method, the precision of 3 × 10−6 °C could be achieved by a currently available spectrometer and the operating temperature range can be modulated by the thickness of NLCs. Moreover, the temperature sensitivity of 13.5 nm/°C could be realized for NLCs with 100 μm thickness, which exhibits at least three orders of magnitude larger than the value for other frequency domain analyses.

Axisymmetric standing waves occur across a wide range of free surface flows. When these waves reach a critical height (steepness), wave breaking and jet formation occur. For travelling surface gravity waves, wave breaking is generally considered to limit wave height and reversible wave motion. In the ocean, the behaviour of directionally spread waves lies between the limits of purely travelling (two dimensions) and axisymmetric (three dimensions). Hence, understanding wave breaking and jet formation on axisymmetric surface gravity waves is an important step in understanding extreme and breaking waves in the ocean. We examine an example of axisymmetric wave breaking and jet formation colloquially known as the ‘spike wave’, created in the FloWave circular wave tank at the University of Edinburgh, UK. We generate this spike wave with maximum crest amplitudes of 0.15–6.0 m (0.024–0.98 when made non-dimensional by characteristic radius), with wave breaking occurring for crest amplitudes greater than 1.0 m (0.16 non-dimensionalised). Unlike two-dimensional travelling waves, wave breaking does not limit maximum crest amplitude, and our measurements approximately follow the jet height scaling proposed by Ghabache et al. (J. Fluid Mech., vol. 761, 2014, pp. 206–219) for cavity collapse. The spike wave is predominantly created by linear dispersive focusing. A trough forms, then collapses producing a jet, which is sensitive to the trough's shape. The evolution of the jets that form in our experiments is predicted well by the hyperbolic jet model proposed by Longuet–Higgins (J. Fluid Mech., vol. 127, 1983, pp. 103–121), previously applied to jets forming on bubbles.