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.

Bessel beams with controllable output angles and uniform intensity distribution along the propagation direction have critical applications in many fields. This paper introduces a novel method to generate high uniformity, high signal-to-noise ratio, and angle-controllable Bessel beams by combining a Fresnel zone plate (FZP) with an axicon. An apodizing phase axicon with an ideally fitted profile is used, with a Gaussian beam as the light source. The fitting profile is then optimized through a genetic algorithm (GA) and an unconstrained nonlinear optimization algorithm (UNMA). The combination of the optimized apodizing phase axicon and FZP achieves the uniform distribution of axial intensity and the control of Bessel beam angle by changing the center of FZP. The results demonstrate the effectiveness of this method, showing that it can achieve arbitrary angle control within the range of 4.0742°, with a resolution of 0.0008° and a uniformity of 94.66%. Furthermore, this method can be extended to multiple Bessel beams, enabling the angle control of various Bessel beams.

In order to accurately measure the phase modulation capability of the spatial light modulator (SLM) and improve its performance in optical applications, a multi-region phase response calibration scheme of SLM based on the Shack–Hartmann wavefront sensor (SHWS) is proposed. This scheme addresses the nonlinear sampling issue of the liquid crystals in different sampling areas on the SLM. By loading and shifting dual sine phase patterns, continuous variations of grayscale values in the same region on the SLM screen were achieved, with the corresponding wavefront data recorded by the SHWS after each grayscale change. Matrix calculations were performed in MATLAB to obtain the corresponding phase modulation curve. Subsequently, the multi-zone phase modulation characteristics of the SLM were measured. Following the nonlinear calibration of phase modulation in each zone of the SLM, the intrinsic wavefront distortion (WFD) of the SLM was measured using the SHWS in conjunction with the calibration results and compensated for. The compensated WFD of the SLM is reduced from 0.7976λ to 0.3415λ (λ=632.8nm), and in the verification experiment, the focused spots’ quality was greatly improved with the calibrated SLM. The experimental results proved the availability of the multi-region phase response calibration scheme. Compared to conventional methods, this approach demonstrates simplicity, real-time performance, and robustness.