## 4 Experimental Application  
To further substantiate the efficacy and applicability of the algorithm proposed in this paper, this section employs both the ZA and FA methods to reconstruct the collected information from a hybrid wavefront sensor via a null test experiment. The primary objective of this experiment is to ascertain whether the wavefront reconstruction algorithm can accurately recover the known wavefront shape from measured data, particularly under no aberration or ideal wavefront conditions.  
This experiment is based on the innovative four-hole amplitude-modulated wavefront sensor (FHAM-WS) [23] proposed by our research group, shown in Figure 9. Building upon the Shack-Hartmann sensor, this sensor modulates the incident wavefront by depositing a chrome layer on the front surface of the microlens array and incorporating four specifically arranged light-transmitting circular apertures within the chrome layer corresponding to each sub-aperture. Based on the far-field optical intensity distribution, the structure can simultaneously measure slope information and curvature information through scalar diffraction theory. This technology utilizes the collection of focal plane spot arrays for wavefront detection, and it has advantages such as a large dynamic range. It holds broad prospects for applications in areas such as high-order aberration measurement.  
The specific experimental procedure is as follows. As shown in Figure 10, a single-mode laser source with wavelength of 635 nm is used to generate an approximately ideal spherical wave, and the FHAM-WS, composed of a microlens array and CCD, is placed 1 m away from the light source, which can be considered as an ideal plane wave incident, and the light spot diagram is collected. In this case, the true value of the measurement result of FHAM-WS should be zero, and the closer the actual measurement result is to zero, the smaller the measurement error. Firstly, the slope and curvature extraction algorithm of our research group is used to obtain the complete slope and curvature information of each sub-aperture from the spot pattern. After obtaining the complete mixed data of slope and  
Figure 8: Comparison of the reconstruction error of each reconstruction algorithm for a signal-to-noise ratio (SNR) of 30: (**a**) PA and FA, (**b**) BA and FA, (**c**) ZA and FA.  
curvature, the extracted data are processed twice to obtain the slope and curvature data matrix, which is suitable for wavefront reconstruction. Finally, the measured wavefront is reconstructed by using the hybrid slope and curvature algorithm. The experiment reduces random errors by averaging multiple measurements. Focal plane spot arrays are collected every minute, and this process is repeated 10 times. The ideal wavefront slope and curvature information matrices extracted by the experimental setup are reconstructed using the ZA and FA.  
The reconstruction results of 10 groups of FHAM-WS measurements produced by the two algorithms are shown in Figure 11. In terms of reconstruction accuracy, the FA algorithm maintains consistency with established, mature algorithms. This is attributable to the simple structure of the reconstructed wavefront under null test conditions. As the complexity of the waveform increases, the precision advantages of the FA algorithm become progressively apparent. Regarding reconstruction time, the FA algorithm exhibits a significant advantage over existing hybrid slope-curvature algorithms. Moreover, the average reconstructed wavefront of the 10 repeated measurements produced using the FA algorithm is shown in Figure 11. It is evident that, under the experimental conditions, the proposed FA algorithm can accurately process slope and curvature information to reconstruct the test wavefront, thereby further validating the effectiveness of the algorithm.  
Figure 10: Experimental setup of the null test experiment using FHAM-WS.  
Figure 9: Schematic diagram of the null test experiment using FHAM-WS.