Revolutionizing microscopy: 25 years of computational imaging breakthroughs

In 1999, then-graduate student Jianwei "John" Miao and his colleagues at the State University of New York, Stony Brook, demonstrated that a computational algorithm, combined with patterns of scattered photons, could reveal miniscule details previously impossible to capture with conventional microscopes.

Building on an established method for determining atomic structures called X-ray crystallography, they expanded its application to structures that lack the uniform, repeating patterns found in crystals. The algorithm reconstructs images from diffraction patterns - the arrangement of electromagnetic beams after they are bent and scattered as they pass through samples. This technique diverges from traditional microscopy by combining diffraction and computation to effectively replace the objective lens.

If you imagine microscopes as computer hardware, Miao's approach is the "killer app" that unlocks their full potential. Over the past 25 years, scientists have integrated this approach into different types of microscopes, driving the field of computational microscopy to achieve unparalleled resolution and precision, and to capture the broadest fields of view yet on samples under investigation. These advances have led to brand-new insights into the structure and behavior of catalysts, superconductors, computer chips and next-generation batteries and materials.

Miao, a professor of physics and astronomy in the UCLA College, has authored the first comprehensive review of computational microscopy. Published in Nature - a top journal that rarely features such single-author reviews - his article highlights innovative developments in the field, showcases multidisciplinary applications and outlines future directions.

For him, the quest to uncover fundamental knowledge through advances in microscopy reflects the philosophy of one of his favorite thinkers, the 17th-century Dutch philosopher Baruch Spinoza.

"Spinoza found ultimate happiness in discovering truth in nature," said Miao, who is a member of the California NanoSystems Institute at UCLA. "That philosophy is always on my mind. Each of us has only one life to live, and I am committed to seeking truth and addressing profound scientific problems."

In most forms of microscopy - whether using visible light, X-rays, electrons or other types of radiation - the waves in the beam interact as they pass through a sample. These waves can interfere out-of-phase, canceling each other out, or in-phase, amplifying their intensity.

The key to computational microscopy lies in unlocking phase information, which provides a far richer representation of a sample than intensity measurements alone. However, phase cannot be measured directly. Miao's method broke new ground by extracting phase information from diffraction patterns with an iterative computational algorithm. This algorithm alternates hundreds to thousands of times between analyzing a sample and analyzing the waves used to probe it.

His review article focuses on two closely related computational microscopy methods: coherent diffractive imaging, or CDI, and ptychography (with a silent "p" at the front).

CDI uses a highly synchronized coherent beam to analyze a single diffraction pattern, enabling it to capture events occurring in millionths of a billionth of a second. Building on the foundation of CDI, modern ptychography was introduced in 2007, utilizing an iterative computational algorithm to reconstruct images from multiple overlapping diffraction measurements. Although slower than CDI, ptychography produces minute detail across a larger field of view and can correct for imperfections in the beam.

Beyond detailing advancements in the techniques themselves, the review highlights new frontiers opened by computational microscopy, with applications spanning a wide range of scientific disciplines.

Researchers have used CDI and ptychography to reveal intricate biological structures, capture magnetic and quantum phenomena on ultrafast timescales and conduct three-dimensional, nondestructive inspections of cutting-edge microchips. These techniques also enable real-time observation of future-generation batteries as they charge. In his own research, Miao adapted this algorithmic approach for advanced electron microscopes without examining diffraction to achieve a breakthrough: the first three-dimensional atomic mapping of amorphous materials, which lack the orderly, repeating structures typical of crystals.

Miao expects that the expanding reach and versatility of computational microscopy will lead to significantly more breakthroughs. He and other researchers are investigating how artificial intelligence can accelerate the extraction of phase information from diffraction patterns, aiming to provide scientists real-time views of the phenomena they study. Miao also expects

computational microscopy advancing to determine the three-dimensional atomic structures of high-tech materials, including elements such as carbon, nitrogen and oxygen, which have traditionally been difficult to image at the single-atom level.

"Physics, chemistry, materials science, nanoscience, geology, applied mathematics, engineering, life sciences - every field stands to benefit," Miao said. "The future is cross-disciplinary. Nature itself doesn't separate scientific disciplines; the best way to truth is to follow nature."

In the review, Miao acknowledges support from the National Science Foundation - including from STROBE, an NSF Science and Technology Center for which he serves as deputy director - the Department of Energy, the Air Force Office of Scientific Research and the U.S. Army Research Office.

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