## 4 Laboratory Test Results and Analysis  
To validate the accuracy and reliability of the testing methodology proposed in this paper, the MTF test experiment was designed for a laboratory CMOS camera, and an experimental verification platform was constructed. This platform comprises an integrating sphere light source, a slanted-edge target, an optical lens, a CMOS camera, a three-dimensional rotary platform, and an image acquisition device. The integrating sphere provides uniform illumination for the slanted-edge target. The light signal, after traversing the optical lens, is captured by the CMOS camera and subsequently converted into a grayscale image through signal acquisition and processing. This image represents the target as captured by the camera's imaging system and is depicted in Figure 16, showcasing the test equipment. The MTF of the optical system under test is computed from the slanted-edge target image using the proposed method. The resulting transfer function values are then employed to evaluate the accuracy and stability of the focal plane position and the MTF values obtained through this test method. The experimental setup included an integrating sphere source, a slanted-edge target, an optical lens, a CMOS camera, a 3D rotation platform, and an image acquisition device, all mounted on an optical vibration isolation platform. The 3D rotation platform was meticulously aligned to ensure the optical path was coaxial, enabling the CMOS camera to fully capture the slanted-edge target image. We maintained a precise 7\({}^{\circ}\) angle between the slanted-edge target and the detector. Additionally, the 3D rotation platform facilitated image acquisition at 0.1 mm intervals within a 1 mm depth range beyond the camera's focal length, capturing 20 frames at each position (see Figure 17a). Using the slanted-edge method outlined in this paper, we calculated the MTF values at various positions. These  
Figure 16: MTF laboratory test system. values were then used to construct through-focus MTF curves, as depicted in Figure 17b. The accuracy of our proposed algorithms was validated against reference MTFs derived from three-bar target images in a controlled laboratory environment. The curve displayed in the figure closely aligns with the through-focus curve derived using the three-bar method. This congruence provides experimental evidence that the slanted-edge method introduced in this paper is a viable approach for calculating the MTF. Subsequently, we altered the angle between the CMOS camera and the slanted-edge target. The 3D rotary stage was adjusted incrementally, starting from 1\({}^{\circ}\). Slanted-edge target images were captured at every 0.5\({}^{\circ}\) increment, collecting 20 frames at each angle, up to a maximum of 45\({}^{\circ}\), as illustrated in Figure 18. This procedure resulted in the acquisition of a total of 1760 slanted-edge target images. To mitigate the effects of air disturbance, the 20 frames obtained at each angle were aggregated and averaged, producing a representative slanted-edge image for each angle. We then computed the MTF values at the Nyquist frequency for the 88 distinct sets of slanted-edge images, facilitating the assessment and analysis of the impact of the slanted-edge angle on the accuracy of the slanted-edge method. Figure 19 presents the results, illustrating that the trend of MTF values at the Nyquist frequency for various slanted-edge images, as measured in the laboratory, aligns with the simulated results. This alignment corroborates the efficacy of the optimal OSR-based adaptive modeling algorithm introduced in our study. Notably, the MTF relative error remains within 1.5% for slanted-edge angles ranging from 6\({}^{\circ}\) to 12\({}^{\circ}\). The stability is particularly pronounced at a 7\({}^{\circ}\) slanted-edge angle, suggesting that the slanted-edge algorithm demonstrates optimal stability within this angle range. Additionally, this finding affirms the reliability and precision of the constraints specified in the slanted-edge method proposed in this paper.