Prior to the advent of computational microscopy in 2013, microscopes were limited by their optical elements. Development of the technology focused on pushing the capabilities of these elements through continuous refinement to view smaller and smaller objects with greater clarity. Still, scientists had to decide between high resolution and a small field of view (FOV) on the one hand or low resolution and a large FOV on the other. In 2013, Caltech researchers developed Fourier ptychographic microscopy (FPM), a computational imaging technique that uses iterative reconstruction algorithms to acquire high-resolution images of samples while maintaining a large FOV. The method has been adopted in biomedical imaging, digital pathology, drug screening, and other applications to obtain accurate, label-free, high-throughput images The same lab has developed a method capable of outperforming the method in its ability to obtain images free of blurriness or distortion, even while taking fewer measurements. The technique is expected to enable further research advancements in its predecessor’s application fields. The new technique, called Angular Ptychographic Imaging with Closed-form method (APIC), uses only numerical aperture (NA)-matching and darkfield measurements. APIC acquires a closed-form, complex field solution without the need for iterative algorithms or human-designed convergence metrics. It provides exceptional robustness against aberrations and can retrieve complex aberrations without requiring additional hardware. A stained breast cancer sample was imaged using red, green, and blue LEDs. A new computational microscopy technique developed at Caltech, called APIC, was used to reconstruct the detailed color image shown on the right. The image shows even higher resolution than the image on the left, which was obtained using FPM, a widely-used microscopy technique. Courtesy of Caltech. Unlike FPM, which relies on iterative trial-and-error adjustments to attain the optimal image, APIC uses a linear equation to uncover the details of the aberrations introduced by the microscope’s optical system. Once the aberrations are known, the system can make the proper adjustments to deliver a clear image with a large FOV. “We arrive at a solution of the high-resolution complex field in a closed-form fashion, as we now have a deeper understanding in what a microscope captures, what we already know, and what we need to truly figure out, so we don't need any iteration,” researcher Ruizhi Cao said. “In this way, we can basically guarantee that we are seeing the true, final details of a sample.” FPM, in contrast, operates by collecting a series of low-resolution images under tilted illumination and applying a core iterative phase retrieval algorithm to reconstruct a sample’s high spatial frequency features and optical aberration. FPM increases the spatial bandwidth product of standard microscopy significantly, but its iterative reconstruction approach may not always result in a solution that is true to the original image. This is especially problematic for applications such as digital pathology, where even small errors in the image are unacceptable. APIC also allows researchers to gather clear images over a large FOV without needing to repeatedly refocus the microscope if, for example, the sample size varies slightly from one section to another. Computational microscopy techniques can require more than 100 low-resolution images to be pieced together to reach a large FOV. APIC can streamline this process, making it quicker and lowering the potential for human error. “We have proven that our method gives you an analytical solution and in a much more straightforward way,” researcher Cheng Shen said. “It is faster, more accurate, and leverages some deep insights about the optical system.” Professor Changhuei Yang, who led the research, said the development of APIC is vital to his lab’s efforts to optimize image data input for AI applications. “Recently, my lab showed that AI can outperform expert pathologists at predicting metastatic progression from simple histopathology slides from lung cancer patients,” he said. “That prediction ability is exquisitely dependent on obtaining uniformly in-focus and high-quality microscopy images, something that APIC is highly suited for.” The team demonstrated that APIC can extract large aberrations and synthesize large FOV and high-resolution images using low NA objectives. When APIC and FPM were put under the same aberration conditions, APIC provided correct reconstruction results in cases where FPM failed, and more than double the computation speed. The researchers believe that APIC represents an important step forward in the field of computational imaging by providing a framework to correct aberrations and improve resolution. “Those two capabilities can be potentially fruitful for a broader range of imaging systems,” Cao said. The research was published in Nature Communications (www.doi.org/10.1038/s41467-024-49126-y).