Edge-enhanced upconversion detection is a technique to enhance the geometric edges of a target and convert infrared (or terahertz, etc.) targets into the visible spectrum by nonlinear optics. Utilizing this technique for identifying and retrieving edge information within images can substantially mitigate computational burdens in image processing. This is of paramount significance in areas like machine vision, bio-imaging, and related disciplines. However, previous studies have predominantly focused on the "spiral phase contrast" resulting from nonlinear phase transfer and neglected the influence of nonlinear amplitude modulation on targets. The latter is determined by the pump amplitude distribution and the spatial overlap between the pumps and signals, both of which control the spatial spectrum distribution of upconversion images. We theoretically and experimentally investigate the effect of spatial-complex amplitude modulation of pumps on upconversion target based on edge-enhanced upconversion detection caused by amplitude bandpass filtering and spiral phase contrast, followed by analyzing quantum efficiency differences. Finally, based on research findings, we provide practical recommendations for multiple typical scenarios.

The principle of edge-enhanced upconversion detection (Fig. 1) allows for spatial filtering operations on the signal spatial spectrum by utilizing the spatial amplitude distribution and spiral phase of the pump via parametric nonlinear interactions. This process influences the outcomes of edge-enhanced upconversion detection, thus bringing an improved and more refined detection method. The nonlinear optics platform described by us is based on non-degenerate sum-frequency generation with type-0 phase matching (Fig. 2). Initially, the Laguerre-Gaussian (LG01) beam is employed as the pump beam, which has circular amplitude distribution and spiral phase similar to previous research. Subsequently, a hollow beam with the same spatial amplitude distribution is adopted as the pump beam, and only amplitude spatial filtering is applied to the signal. By comparing the differences between the imaging results and a reference, we can investigate the effect of the spiral phase on edge enhancement. Additionally, Gaussian and super-Gaussian vortex beams carrying spiral phase are employed as pump beam sources to examine how different spatial amplitude distributions of vortex beams affect both imaging results and quantum efficiency in an upconversion detection system.

Theoretical and experimental imaging results are compared and analyzed for the pump with four different spatial-complex amplitude distributions under two beam waist radii (Fig. 3). Specifically, when the LG01 beam is utilized as the pump beam, bandpass filtering, and spiral phase modulation are simultaneously applied to the target spatial spectrum, which leads to rounded edge distribution of the upconversion image. Additionally, an increase in the pump beam waist radius reduces the conversion of low-frequency components and sharper edges in the upconversion image. On the other hand, the hollow beam only applies amplitude bandpass filtering on the spatial spectrum of the target, enhancing regions with intensity gradients. In contrast, Gaussian vortex beams exhibit higher conversion efficiency for low-frequency components compared to high-frequency ones, thereby bringing smoother edge profiles for upconversion images. When the waist of the Gaussian vortex beam expands, due to the conversion of a greater proportion of high-frequency components, the low-pass filtering effect on the original image is diminished. Consequently, the contour width of the upconversion image becomes more pronounced. Lastly, super-Gaussian vortex beam has uniform spatial amplitude distribution that converts all spectral components equally, leading to nonlinear spiral phase contrast results close to linear ones.

The quantum efficiency corresponding to these four pump beams at identical peak amplitudes and two beam waist radii is obtained (Fig. 4). Since the spectral energy of the image is predominantly concentrated in the low-frequency range, the super-Gaussian vortex beam overlaps most extensively with the spatial spectrum of the signal image, which brings the highest nonlinear conversion efficiency. Importantly, under intense pumping, a pump light characterized by super-Gaussian amplitude can attain the theoretical quantum efficiency upper limit of 100%. The quantum efficiency of the Gaussian vortex beam is surpassed only by the super-Gaussian vortex beam. In contrast, the nonlinear conversion efficiency of the LG01 pump light is comparatively inferior.

The results indicate that the utilization of a circular beam with a spiral phase as the pump light can obtain an upconversion image with enhanced edge sharpness. This technique is particularly suitable for scenarios where precise extraction of the target edge is desired. Conversely, a hollow beam outperforms a circular beam with a spiral phase in preserving more image features. Super-Gaussian vortex beams exhibit the highest quantum efficiency and approach theoretical limits under intense pumping. As a result, when efficient conversion of weak signals is necessary, the utilization of super-Gaussian vortex beam is recommended. On the other hand, the Gaussian vortex beams can be employed to smooth the target edge. It is important to note that Gaussian and super-Gaussian vortex beams are not spatial eigenmodes, whose transverse structures are propagation variants. Thus, imaging should be conducted on the pump light carrying the spiral phase to the signal image spectrum plane and then achieve superior enhancement of the upconversion target edge.