Prompt Description
Draw a diagram of an optical experimental design. The following is an introduction: To reproduce the dominant dynamic instrumental polarization effect caused by the relative rotation of the mirror group in the horizontal telescope, a simplified desktop simulation experimental system is built in this chapter. The experimental optical path consists of three parts in the direction of beam propagation: a Polarization State Generator (PSG), a relatively rotating mirror group, and a Polarization State Analyzer (PSA). The PSG unit is composed of a light source and a polarizer, and is used to generate four standard incident polarization states: horizontal linear polarization (0L), +45° linear polarization (45L), left-handed circular polarization (LCP), and right-handed circular polarization (RCP). The relatively rotating mirror group in the middle of the optical path includes two reflectors (M1 and M2) installed on optical lifting stages. In the experiment, the relative rotation between the mirror groups is simulated by controlling the rotation of M2, which is the physical origin of the dynamic IP generated by the horizontal telescope. Finally, the outgoing beam enters the PSA unit, is modulated by the analyzer, and the light intensity is detected by the camera, and then the Stokes vector of the system is calculated.
Related Illustrations
![The specific implementation process of PCA model training in PSF data processing is as follows:
1. **Data Matrix Construction:** Flatten the standardized PSF images into vectors to form a data matrix \(X_{\text{scaled}} \in \mathbb{R}^{N \times D}\).
2. **Singular Value Decomposition (SVD):** The implementation in the library uses SVD optimization instead of directly calculating the eigenvalue decomposition of the covariance matrix. Perform SVD decomposition on the flattened image matrix \(X_{\text{scaled}}\): \(X_{\text{scaled}} = U \Sigma V^\top\). Here, the column vectors of the right singular vector \(V \in \mathbb{R}^{D \times D}\) are the principal component directions, and the square of the singular value \(\sigma_k^2\) is proportional to the eigenvalue \(\lambda_k\).
3. **Principal Component Selection:** Sort the principal components according to the eigenvalue size and select the top \(K\) principal components. These principal components constitute the projection matrix \(V_K = [v_1, v_2, ..., v_K] \in \mathbb{R}^{D \times K}\), where \(v_1\) corresponds to the direction of maximum variance, \(v_2\) to the next, and so on.
4. **Dimensionality Reduction and Coefficient Extraction:** Project the centered data into a low-dimensional space: \(Z = X_{\text{centered}} V_K \in \mathbb{R}^{N \times K}\), where each row of \(Z\) is the coefficient (also called 'score') of the corresponding PSF in the principal component space.
Draw a schematic diagram of this process, requiring no shading or watermarks, and a color style that meets the requirements of SCI journal papers.](/_next/image?url=https%3A%2F%2Fpub-8c0ddfa5c0454d40822bc9944fe6f303.r2.dev%2Fai-drawings%2FVSt6TNY52kYACNod5QcmZwP8nP4PfcsA%2F284075ba-a796-4c71-9eeb-4dbea1d89ee4%2Fa852e641-9a39-4397-90cd-d4d710834d23.png&w=3840&q=75)