Spatial resolution is a key metric for evaluating the ability of an imaging system to resolve fine details and is a critical indicator of image quality. However, traditional imaging methods are constrained by the resolution limits of optical devices and the optical diffraction limit, often resulting in images that fail to meet high-resolution requirements. Consequently, a sustained effort has been conducted to overcome the diffraction limit in optical imaging. In the field of computational imaging, techniques such as compressed sensing, the design of specialized speckles, and subpixel sampling are commonly employed to achieve more stable and high-quality reconstructed images at low sampling rates. In this study, we proposed a computational ghost imaging resolution enhancement technique based on Zernike polynomial phase modulation. This method overcomes the resolution limits of traditional point scanning imaging systems. Our hope is that this research will inspire further studies aimed at overcoming the diffraction limits in computational imaging and that these concepts will be extended to a broader range of research in the field of imaging.

The basic structure of an imaging system was first designed, and a computational ghost imaging simulation was performed using LabVIEW. In the simulation, two methods of projecting masks, namely, point scanning and phase modulation based on the Zernike polynomial, were employed, and traditional (TGI) and orthogonalized (OGI) ghost imaging algorithms were used to reconstruct the edge image. The Zernike polynomial is a function used to describe the aberrations that occur in an optical system during imaging with lenses and other optical components. The masks generated based on the Zernike polynomial modulation form a set of non-orthogonal patterns, which necessitates that the corresponding OGI algorithm be used for image reconstruction. After the image was reconstructed, a quantitative analysis was conducted on the energy distribution of the masks and the quality of the reconstructed images to draw conclusions. Upon completion of the simulation, a physical imaging system was constructed based on the system design and simulation results. A computational ghost imaging experiment was conducted using point scanning and without applying any modulation to the spatial light modulator (SLM). The Zernike polynomial was then loaded onto the SLM to modulate the phase of the incident light, generating special mask patterns in the Fourier plane of the 4F system that were ultimately projected onto the object. A Siemens star and edge image were selected as the objects for image reconstruction to provide a more comprehensive comparison of the reconstruction quality. Finally, a quantitative analysis of the experimental results was performed to validate the conclusions of the simulation.

Figure 5 shows the modulation transfer function (MTF) of the simulation results based on the Zernike polynomial phase modulation and point scanning. The quality of the reconstructed images was evaluated using the area enclosed by the MTF curves, horizontal and vertical axes acted as indicators (Table 1). Results show that our method significantly outperforms traditional point-scanning imaging, and a potential correlation exists between the quality of the reconstructed images and the proportion of high-frequency light intensity in the corresponding masks. Specifically, a higher proportion of high-frequency light intensity in the mask directly corresponds to an enhancement of the resolution of the reconstructed image. In the experiments, image quality was compared in the same manner (Table 2). Experiments showed that our method consistently outperforms traditional point scanning imaging, successfully surpassing the resolution limits.

In this study, we proposed an image resolution enhancement method based on Zernike polynomial phase modulation. In the constructed computational ghost imaging system, the incident light was modulated using Zernike polynomials through a spatial light modulator (SLM) to generate special mask patterns in the far field. These mask patterns were projected onto an object, and the OGI algorithm was applied for image correlation to achieve image reconstruction. The resolution of the reconstructed image surpasses that of traditional point scanning results, achieving enhanced resolution at a reduced time cost. This method successfully overcomes the spatial resolution limits imposed by the SLM aperture in point scanning. In addition, a quantitative analysis of the relationship between the proportion of high-frequency light intensity in the mask patterns and the image resolution was conducted to explore the mechanism behind the resolution enhancement achieved by this system. The feasibility of this method for overcoming the resolution limits in computational imaging was also explored. In the future, experimentations with more Zernike polynomials to adjust the high-frequency light intensity proportion can be expected to further improve image resolution. In addition, because the peak intensity of the mask patterns irradiating an object is relatively low, this method can avoid sample damage, making it promising for applications in the field of microscopy to achieve super-resolution imaging.