# 'Blind spot' in atomic force microscopy discovered

*Image: Atomically-resolved image of two noble gas monolayers, measured using frequency-modulation AFM, [Huber/University of Regensburg].*

Researchers have discovered a ‘blind spot’ in atomic force microscopy, claiming that measurement accuracy depends on which force laws are in effect.

As Professor John Sader, from the University of Melbourne’s School of Mathematics and Statistics, and developer of the 'Calibration Method of Sader' for AFM cantilever calibration, highlights, force laws that reside in the newly discovered `blind spot’ can lead to incorrect results.

Publishing results in

*Nature Nanotechnology*, the researchers have developed mathematical methods to identify the interatomic force laws that evade dynamic measurement, and can avoid this blind spot to safeguard atomic force measurements from inaccurate results.To enable precise measurements at the atomic scale, the AFM cantilever is oscillated at the natural resonant frequency, slightly away from the surface, with the actual force experienced by the tip recovered from this measured frequency.

Sader and colleagues have shown that this dynamic measurement blurs the atomic scale force, removing information that can make recovery of the actual force problematic, in effect, creating a ‘blind spot’.

“The recovered force may look nothing like the true force,” says Sader. “It is remarkable that this issue is completely absent for some atomic force laws, while for others it creates a real problem."

“Dynamic force measurements effectively look at the atomic force through a blurred lens," he adds. "A mathematical algorithm is then needed to convert this to an actual force.”

**Algorithm development**

In 2003, Sader and a colleague developed such an algorithm - the Sader-Jarvis method - that is used widely to recover the atomic scale force from this blurred frequency measurement.

“There had been no hint that this blurring could be an issue since the dynamic AFM technique was invented in 1992," says Sader. "Many independent researchers have explored it and shown that all standard force laws give highly robust results.”

“Then, last year, collaborators and co-authors of this study from the University of Regensburg saw an anomaly for the first time in their measurements and conveyed it to me. I was surprised to see this anomaly and keen to identify the cause,” he explains.

The researchers found that mathematical features of the frequency measurements had effectively hidden this problem in plain sight.

“The issue is mathematically subtle,” highlights Sader. “Force laws that belong to [the mathematical transform] 'Laplace space' are fine. It’s the ones that aren’t part of this space that cause the problem, and there are many of those in nature.”

After scrutinising the details of this subtlety, Sader and colleagues formulated a mathematical theory and method that identifies when the blurring issue arises in a real measurement, allowing the AFM practitioner to avoid it.

“I like to think of our discovery as giving practitioners the ability to see a ‘pot hole’ in the road ahead, and thus avoid it with no damage," he says. "Previously, this pot hole had gone unnoticed and drivers were sometimes steering straight into it.”

According to the researcher, the next step is to understand how to remove this these issues entirely.

“Our work also highlights the importance of mathematicians and experimentalists working together to solve an important technological problem," he adds. "Without both skills sets, this problem would not have been identified and solved. It had gone unnoticed for more than 25 years.”

Professor Sader said this new understanding may provide insight into the operation of other dynamic AFM force measurements by identifying a previously unexplored feature.

Research is published in

*Nature Nanotechnology.*