There are two sampling models of digital hologram in digital holographic research. The complex mathematical operation is involved in these two models, thereby leading to different results frequently and inconvenient theoretical analysis and practical application. Based on the analysis of physical processes in recording digital hologram and the study on geometry structure of CCD detector, the two sampling models are simplified into the same mathematical expression in this paper. Through studying the simplified model with cosine series expansion of digital hologram and sampling theorem, it is shown that the model has clear physical meanings and can be used for application study conveniently. Using the simplified model, we study digital holographic recording system with optical system and exact wavefront reconstruction expression verified in experiment.

A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox–Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano–concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO₂ laser and high-quality laser beams can be expected.

Internet service platforms dynamically charge service prices to satisfy the time-varying service demand by leveraging both full- and part-time service providers. This study developed a dynamic pricing model for a monopolistic service platform under two pricing strategies: unified pricing and differentiated pricing. The model incorporates key factors such as demand fluctuations, initial demand constraints, and service quality. It proved the optimal dynamic pricing scheme aimed at maximizing the platform’s expected revenue and analyzed the equilibrium gap between the two strategies based on the optimal control theory. The results reveal the following: (a) The service quality elasticity coefficient, potential market, and demand fluctuation factor all positively affect the optimal service price under the two types of pricing strategies, whereas service quality has the opposite effect. (b) Regardless of pricing strategy, the initial service demand restriction negatively affects the optimal price of the platform. The gap between the optimal service prices under the two types of pricing strategies narrows as the potential service demand rises when customers are less sensitive to service price. (c) With initial demand restriction, the optimal service price rises over time as long as the service market satisfies specific conditions, but the expected revenue under the two types of pricing strategies evolves in significantly different trajectories. (d) The differentiated pricing strategy can help the platform improve revenue by setting a lower revenue-sharing ratio.