Traditional imaging captures only light intensity and position information visible to the human eye, leaving out other details. Polarization imaging extends this by revealing spatial polarization characteristics alongside traditional data, enriching information acquisition with higher resolution, wider field of view, and reduced environmental sensitivity in optical imaging. Grating, a crucial optical element known for diffraction and the Talbot effect, holds promising applications across various fields. In the spectral domain, analyzing grating systems provides intuitive insights: distinct frequency components convey unique information, with higher frequencies offering finer object details. By changing parameters like grating frequency, imaging environment, and light source, changes in spectral components enrich the original data, enhancing high-frequency detail, and image resolution. Against this backdrop, we design a polarization system for a grating illuminated by partially coherent light. Given the static nature of the target object, a time-division polarization imaging system is employed to explore object-image relationships, analyze them in the spectral domain, and monitor changes in spectral components crucial for enhancing imaging resolution and target detection.

We investigate a polarization system for a grating illuminated by partially coherent light based on unified polarization theory. A physical model is built for the relationship between partially coherent light-illuminated gratings and polarization systems. The model is simulated to derive theoretical outcomes followed by the design and construction of an experimental platform. Experimental data is gathered, processed, and compared with theoretical results to validate conclusions. A simplified optical path diagram and mathematical model for the partially coherent light-illuminated grating polarization system are devised. By employing unified polarization and coherence theories, we introduce generalized Stokes parameters, extending the mutual intensity relationship of the object and image from a scalar system to a polarization vector system. This approach establishes the spatial and spectral domain relationships between object and image in this system. The mathematical model of the object-image relationship for the partially coherent light-illuminated grating polarization system is simulated using MATLAB. Based on the transfer cross coefficient within the established relationship, we simulate models for apparent transfer functions of first and second harmonic components. In addition, spatial domain models of object-image for partially coherent light-illuminated sinusoidal amplitude grating polarization system are simulated to obtain one-dimensional Stokes intensity distribution diagrams under three different coherence conditions. Simulation results demonstrate that spatial domain Stokes intensity distribution correlates with grating intrinsic frequency and coherence. Experimental studies are conducted using a time-division polarization imaging system on a partially coherent light-illuminated grating polarization system. Experimental schemes are designed, utilizing a sinusoidal amplitude grating with a line density of 50 line/mm, and an experimental platform is established. We analyze and process experimental data using MATLAB software.

Under various coherence conditions, we obtain curve graphs of apparent transfer functions for the first and second harmonic components. These graphs clearly illustrate that under nearly incoherent light sources, the apparent transfer function exhibits linear changes. As coherence increases, deviations from linear relationships become more pronounced for both first and second harmonic components. Spatial domain simulation results are present under different coherence conditions alongside several sets of spectral domain simulation results. Results indicate that with higher normalized intrinsic grating frequencies, higher-order spectral components diminish, influenced also by coherence (Figs. 2-3).

Leveraging coherent polarization unified theory, we establish a mathematical model for a partially coherent light-illuminated grating polarization system. Simulation results for apparent transfer functions of first and second harmonics show linear variation under incoherent light, i.e., when s=0, increased coherence leads to deviations from linearity. Spatial domain object-image models for partially coherent light-illuminated sinusoidal amplitude grating polarization system indicate that spatial domain Stokes intensity distributions correlate with grating intrinsic frequency and coherence. Spectral-domain object-image relationships demonstrate that as grating intrinsic frequency T(fx0)=0.8, and parameter s change from 1.0 to 0.5 while coherence increases, the first harmonic disappears. Experimental verification using a 50 line/mm sinusoidal amplitude grating confirms that as grating intrinsic frequency T(fx0)=0.8, and parameter s value decreases from 1.0 to 0.5, only zero-frequency components remain, aligning experimental results closely with theoretical expectations