Featured Application: The method can be used in such areas as optical wave reconstruction, three dimensional microscopic imaging, and interference measurement.Abstract: A convenient and powerful method is proposed and presented to find the unknown phase shifts in three-step generalized phase-shifting interferometry. A slight-tilt reference of 0.1 degrees is employed. As a result, the developed theory shows that the unknown phase shifts can be simply extracted by subtraction operations. Also, from the theory developed, the tilt angle of the tilt reference can also be calculated, which is important as it allows us to extract the object wave precisely. Numerical simulations and optical experiments were performed to demonstrate the validity and efficiency of the proposed method. The proposed slight-tilt reference allows the full and efficient use of the space-bandwidth product of the limited resolution of digital recording devices as compared to the situation in standard off-axis holography where typically several degrees for off-axis angle is employed.

The drift trajectory of a floe near the North Pole (87°N, 175°W) was observed during 8-19 August, 2010 based on the fourth Chinese National Arctic Research Expedition. The trajectory of the floe showed circular motions superimposed on straight drift. Each cycle had a period of about 12 h. The circular motion is inertial oscillation. The largest amplitude of inertial oscillation speed can reach 20 cm/ s. After removing the inertial oscillation, the floe drift direction is about 40°on average to the right of the observed 10-m wind which is much larger than previous reports on the angle between sea-ice velocity and the geostrophic wind, and floe drift moves with a speed of about 1.4 % of the observed 10-m wind speed throughout the whole observation period. A simple dynamic sea ice-ocean coupled model and a threedimensional sea ice-ocean coupled model are employed to simulate the floe drift. Both numerical models are with the widely used quadratic water-drag formulation, i.e., the stress is proportional to the square of the ice velocity relative to the ocean surface current. The inertial oscillation of the floe is successfully simulated by the simple passive drag model, while the floe drift amplitudes simulated from the threedimensional model are relatively small.

The direct-global-matrix coupled-mode model (DGMCM) for sound propagation in range-dependent waveguides was recently developed by Luo et al. [A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides, Sci. China G: Phys. Mech. Astron. 55 (2012) 572–588]. A brief review of the formulation and characteristics of this model is given. This paper extends this model to deal with realistic problems involving an inhomogeneous water column and a penetrable sloping bottom. To this end, the normal mode model KRAKEN is adopted to provide local modal solutions and their associated coupling matrices. As a result, the extended DGMCM model is capable of providing full two-way solutions to two-dimensional (2D) realistic problems with a depth- and range-dependent sound speed profile as well as a penetrable sloping bottom. To validate this model, it is first applied to a benchmark problem of sound propagation in a plane-parallel waveguide with a depth- and range-dependent sound speed profile, and then it is applied to a problem involving both an inhomogeneous water column and a sloping bottom. Comparisons with the analytical solution proposed by DeSanto and with the numerical model COUPLE are also provided, which show that the extended DGMCM model is accurate and efficient and hence can serve as a benchmark for realistic problems of sound propagation in an inhomogeneous waveguide.

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