Long focal lenses, which are a crucial optical element, are utilized extensively in high-power laser devices, including National Inertial Fusion and Shenguang (SG) laser devices in China. Thousands of large-aperture spherical and aspherical lenses have been employed in these expansive laser systems. These lenses have apertures larger than 400 mm×400 mm and focal lengths exceeding 10 m. They are primarily utilized in spatial filters to filter high-frequency components within the Fourier spectrum. This process facilitates image transmission and enhances the beam quality of the system, thereby augmenting its output power. The accurate measurement of the focal lengths of these lenses and the precise positioning of the focus directly affect the installation of the laser system and its spatial filtering effect. As the quality of high-power laser device beams improves and their load-capacity requirements increase, the demand for transmission using long-focal-length lenses increases. Consequently, the focal length and transmission wavefront distribution of long-focus lenses must be regulated strictly. These two parameters are pivotal indicators and indispensable for achieving optimal performance. Currently, the focal length and the two transmission wavefront indices of long-focus lenses are measured independently. This process presents challenges such as difficulty in accurately determining the focal length and high demands on the measurement system during parameter evaluation.

This study introduces a comprehensive measurement method for large-aperture, long-focal-length lenses based on phase recovery. The proposed method integrates a combined lens-measurement technique, thus significantly reducing the length of the optical path required for measurement, as compared with the ptychographic iterative engine (PIE) phase-measurement technology. This integration enhances the resistance of the system to environmental interference. The proposed method enhances the focusing precision of lenses with extended focal lengths by reconstructing the wavefront distribution of the examined lens. Subsequently, it infers the light-intensity distribution at various distances to determine the focus position. Using a digital benchmark, the wavefront error is derived from the deviation of the lens wavefront under measurement. Subsequently, this error is compared with respect to the standard spherical wavefront. By incorporating background cursor calibration, the optical component requirements of the system are reduced significantly.

In this study, we develop a reversible measurement device for lenses with long focal lengths, as illustrated in Fig. 2. Subsequently, the feasibility of this method is validated using a lens with a focal length of 16 m. Two sets of diffraction spots are obtained meticulously in a double-exposure format. Subsequently, an intricate amplitude reconstruction is performed using the ePIE algorithm. The morphology of the light-spot distribution on any plane proximal to the focal plane is successfully determined. As shown in Fig. 5, the relative error of the PV value between the measured wavefront error of the reference lens and the interferometer measurement is 2.6%. This indicates the favorable precision of the PIE wavefront measurement. We comprehensively analyze the effects of individual positional and phase-measurement errors associated with the PIE on both focal-length and wavefront measurements. The findings indicate that the positional error predominantly affects the focal length, with the error transfer coefficient of the moving distance exhibiting the greatest magnitude. The most significant effect of the PIE measurement error is reflected in the wavefront measurement, as shown in Table 1. In the future, we plan to enhance the precision of our measurements based on the findings from our error analysis.

This study introduces a comprehensive measurement method for large-aperture, long-focal-length lenses based on phase recovery. This method allows for the simultaneous measurement of multiple parameters, including the focal length and wavefront, thereby eliminating the requirement for multiple measuring devices. The viability of the proposed method is substantiated by its application using a lens with a focal length of 16 m. This approach effectively addresses the challenges associated with focus determination and the stringent requirements for measurement systems involving long-focal-length lenses. Additionally, it offers several advantages, including a straightforward and flexible measurement process, minimal space requirements, and robust resistance to environmental interference.