High-accuracy wavefront measurement is crucial in lithography systems because the image quality of the projection lens directly influences lithography overlay and critical dimensions [1], [2]. Ronchi lateral shearing interferometry (LSI) offers significant potential for high-accuracy in-situ wavefront measurements due to its advantages of simple structure, common optical path, and reference-free interference, etc. [3], [4], [5]. Over the past few decades, various Ronchi LSI systems have been developed. Early implementations of Ronchi LSI faced limitations in effectively distinguishing shear directions [6]. To address this, modifications were introduced, involving the incorporation of a double-frequency crossed diffraction grating [7] and the utilization of two identical gratings for zonal aberrations [8]. Subsequently, a modified Ronchi LSI employing an extended incoherent quasi-monochromatic light source and two Ronchi gratings was proposed [9]. This refinement significantly augmented the throughput of the Ronchi LSI, rendering it well-suited for in-situ wavefront measurements of lithography projection lens [10], [11]. In the modified Ronchi LSI system of our interest, the gratings are precisely positioned at the object plane and image plane of the optical system under test. The object grating effectively modulates the extended source intensity distribution. Subsequently, the phase-shifting operation is executed by laterally translating the image grating. This procedure yields a series of interferograms, from which shear phases are extracted. These shear phases are then utilized in various wavefront fitting reconstruction algorithms to derive the optical system’s wavefront aberration [12].

The main challenge in Ronchi LSI lies in mitigating the influence of high diffraction orders on the interferogram [9]. Numerous studies have been conducted to address this concern. Initially, efforts were directed towards configuring the lateral shear distance to exceed the zeroth-order radius, thereby engendering a 2-beam interference pattern [5]. However, adopting a substantial lateral shear distance comes at the cost of compromised accuracy in wavefront reconstruction due to the inherent loss of information during shearing [13]. There are also methods that incorporate a double-window mask to suppress unwanted diffraction orders [14], [15], [16], at the cost of heightened mechanical intricacy. Moreover, the influence of high diffraction orders can be eliminated by introducing more phase shifts. Based on the classical 4-frame phase-shifting method [5], researchers proposed 8-frame, 10-frame, 13-frame, and (3N+1)-frame algorithms to eliminate the effects of the first ±5, ±9, ±15, and all multi-diffraction orders [17], [18], [19], respectively. Among the existing algorithms, the 8-frame, 10-frame, and 13-frame algorithms cannot completely negate the effects of all diffraction orders, resulting in relatively large root mean square error (RMSE) at a small shear ratio. Although the (3N+1)-frame algorithm offers high accuracy, it requires more phase shifts, especially for small shear ratio systems. In this algorithm, N can be calculated as N=(M+1)/2, where M is the maximum diffraction order in the overlapping area. To illustrate, in the case of a shear ratio set at 0.04, 37 frames of phase-shifted interferograms are required. The (3N+1)-frame algorithm was enhanced based on the Fourier transform, resulting in a 25% increase in measurement efficiency [20], however, the measurement process remains time-consuming. This temporal intricacy gives rise to added vibration errors and phase-shifting errors, thereby reducing the accuracy of the measurement [21] and is not suitable for measuring highly dynamic targets. Moreover, the above multi-frame algorithms require high accuracy of the phase shifter, leading to an escalation in measurement costs. Various effective 2-frame phase-shifting methods [22], [23], [24], [25], [26] have been proposed for conventional interferograms without high diffraction orders. However, due to the complexity of the Ronchi LSI interferogram, these methods cannot be applied. Therefore, there is a particular interest in the development of a rapid wavefront reconstruction method.

In this paper, we introduce a novel nonlinear cross-iteration optimization technique designed for high-precision wavefront reconstruction employing 2-frame phase-shifted interferograms. Our method achieves a high-precision wavefront reconstruction by utilizing only 2 frames of interferograms, thereby significantly reducing the measurement time, minimizing the noise inherent in the phase-shifting procedure, and is suitable for dynamic measurements. Notably, our method streamlines the reconstruction process by directly optimizing the Zernike coefficients, obviating the need for the customary Zernike polynomials fitting procedure after phase retrieval. Based on the cross-iteration optimization algorithm, the proposed method enables accurate wavefront reconstruction even in the presence of significant Gaussian noise and phase-shifting errors. Simulations and experiments demonstrate the high accuracy and robustness of the proposed method.

The remainder of this paper is organized as follows. Section 2 introduces the Ronchi LSI model and its interference field. Section 3 provides a detailed description of the nonlinear optimization method that combines a 2-frame phase-shifting algorithm. Section 4 verifies the accuracy and robustness of our proposed method through numerical simulations. Section 5 presents verified experiments. Section 6 discusses and concludes the paper.