Fourier ptychography (FP) is a recently developed phase retrieval approach, which simultaneously realizes image restoration with super-resolution and a large field of view. This approach is also a novel super-resolution optical imaging technique that can be efficiently applied to microscopy and macroscopy respectively. However, one limitation of FP is the long acquisition and reconstruction time due to the numerous low-resolution (LR) images that are needed. Especially when the LR image is acquired under large angle illumination (dark field imaging), the low illumination intensity leads to the long exposure time of the imaging sensors. The situation becomes more time-consuming when a new sample is imaged, and thus a larger number of images with different exposure time for each LR image should be tested to obtain the corresponding best exposure time. Losing low gray value pixels exists in the FP algorithm preprocessing, which ultimately leads to the loss of image information due to the weak local image intensity in the recovery result. With the development of optical integration and micro/nano fabrication technology, the circular lens is no longer necessary. On the contrary, the square lens can fill the entire aperture of the miniaturized imaging system (cuboid) and collect more light fields. This paper introduces the square aperture lens into the FP approach which is conducive to collecting the complete aperture light field for further miniaturized imaging devices. The introduced square lens is expected to improve the image intensity and resolution of the FP approach, reduce the data acquisition time, and be more in line with the optical integration development.

According to the Rayleigh criterion, the low resolution of the optical imaging system is caused by the lens aperture. The FP approach achieves super-resolution and large-field imaging by combining multiple LR images. Different from the FP microscopy, the macroscopic FP technique requires moving the imaging camera or using array imaging cameras to obtain a series of LR images of the object. Each LR image is obtained by locating the aperture on the spatial spectrum plane with different positions set in horizontal and vertical directions. After the LR image is acquired at the current position, the aperture is moved to the next position according to the required step size until the spatial spectrum is fully collected. To overcome the position offset of each LR image, the template matching method based on cross-correlation is applied for image registration. This paper studies the macroscopic FP imaging technology based on square aperture. Using the imaging sensor and its natural rectangular structure in the spatial Fourier domain is more effective to use the synthesis of square aperture to improve the imaging resolution and reduce the time consumption. The macroscopic FP technology based on circular aperture is also tested to make a better comparison. In the simulation, the ptychographical iterative engine (PIE) algorithm on the MATLAB platform is adopted to iteratively recover the phase to obtain a high-resolution image. In the experiment, a macroscopic FP optical setup is built. A square aperture, a lens, and a CCD are mounted on an optical bench as a comment imaging system. The system translated in the x-y direction to collect different spatial spectra and obtain a series of LR images. The PIE algorithm used in the simulation can recover the super-resolution image from the LR images.

When the circular aperture is used in the FP method, the image intensity is too weak as luminous flux lacks. The low gray value pixels would be missed during the FP algorithm preprocessing, which ultimately leads to image information loss due to the weak local image intensity in the recovery result. Compared to the circular aperture, the square aperture has a greater luminous flux and can obtain higher image intensity when collecting image information in the spatial spectrum plane. In theory, it is well known that when the side length of the square aperture is the same as the diameter of the circular aperture, the coherence transfer function of the former is greater than that of the circular aperture. This means that the square aperture can collect more spatial frequency information in the spatial spectrum domain for each LR image. The experimental results show that the square aperture still has a good contrast of 0.4 in the case of groups (4,1) in the USAF target (Fig. 6). The high luminous flux of the square aperture is utilized to reduce the dynamic range of the data set, therefore reducing the image acquisition time. The small dynamic range recovery results are shown in Fig. 8, and the image still has good contrast.

This study demonstrates the macroscopic FP technique based on square aperture. The macroscopic FP technique has a better performance by replacing the conventional circular aperture scanning on the spatial spectrum plane with a square aperture. The numerical simulation and experimental verification show that when the square side length and circular diameter are the same, the square aperture has the advantages of high luminous flux and wide optical transfer function compared with the circular aperture. The wider spectrum of each LR image can increase the overlapping information between two adjacent images. The increase in luminous flux can reduce the dynamic range of image acquisition, thereby reducing the image acquisition time. As a result, the FP technique with the square aperture can achieve higher imaging resolution, speed, and signal-to-noise ratio. With the development of optical integration and micro/nano optical fabrication, the fabrication and integration of square aperture lens will be more convenient and can make full use of the aperture of the optical integrated devices. Considering the imaging sensor and its natural rectangular structure both in spatial and Fourier domains, the square aperture is more matched than the circular aperture. Square aperture lenses are promising to be integrated into various imaging systems and will appear in future miniaturized optical devices.