Axicon is an interesting optical element for its optical properties. This paper presents an approach to dynamically generated tunable axicons with a spatial light modulator (SLM). 256-level phase computer-generated holograms (CGHs) were loaded into the SLM to simulate the positive and negative axicons. The intensity distributions of beams passing through these axicons were analyzed with the principle of blazed grating and Fresnel diffraction; and the diffraction patterns were obtained theoretically in terms of zero-order Bessel beams and annular hollow beams, corresponding to the positive and negative axicons, respectively. Experimental results verified that the diffraction patterns have the same distribution as the real axicon. The types of the axicon and the axicon’s parameters can be easily altered through changing the CGHs.

The existing ultrasonic thickness measurement systems require high sampling frequencies for echo signal acquisition, leading to complex circuit designs and high costs. Moreover, extracting the characteristics of ultrasonic echo signals for accurate thickness measurement poses significant challenges. To address these issues, this paper proposes a method that utilizes conventional sampling frequencies to acquire high-frequency ultrasonic echo signals, overcoming the limitations of high-frequency data acquisition imposed by the Nyquist–Shannon sampling theorem. By employing an improved sampling reconstruction technique, the multi-cycle sampling signals are reconstructed and rearranged within a single cycle, effectively increasing the equivalent sampling frequency. Additionally, a combination of coarse estimation using fast Fourier transform (FFT) and precise phase extraction using the moving sine fitting algorithm is proposed for accurate thickness measurement, resolving the limitations of common thickness measurement methods such as peak detection, envelope detection, and Hilbert autocorrelation in terms of low measurement accuracy. Experimental results obtained from thickness measurements on 45 steel ultrasonic test blocks within the range of 3 mm to 20 mm indicate a measurement error of ±0.01 mm, while for thicknesses ranging from 1 mm to 50 mm, the measurement error is ±0.05 mm.

A new method of laser beam shaping with hybrid gratings is presented. The hybrid gratings consist of a blazed grating and a gradient binary grating. The blazed grating is used to separate the incident Gaussian beam into zero order and nonzero diffraction orders. A filter is used to block the nonzero order beams and obtain the zero orders with the desired shape. The gradient binary grating is used to improve the energy distribution of the inside area of the geometric shape. A phase hologram designed with the desired shape and hybrid gratings, is loaded on a phase-only spatial light modulation to achieve arbitrary geometric flattop shapes with high uniformity. Squared and hexagonal shaping experiments demonstrated that the presented method can convert a Gaussian beam into a flattop beam with steepness edge and high uniformity. Experimental results show that the beam non-uniformity is less than 0.037.