Researchers at the National Institute of Standards and Technology (NIST) have devised a calibration method that enables conventional microscopes to accurately measure the positions of points of light on a sample in all three dimensions. To develop their approach, the researchers took a problem that affects nearly all optical microscopes — lens aberrations — and used the effects of aberrations to allow precise and accurate tracking of single emitters in 3D throughout an ultrawide and deep field. The researchers used intrinsic astigmatism and defocus, among other aberrations, to localize multiple emitters in 3D on an imaging substrate and on a complex microsystem, extending their concept to measurements of motion in six degrees of freedom. The calibration method relies on analysis of images of fluorescent particles that the researchers deposited on flat silicon wafers for calibration of their microscope. When the researchers analyzed images of these particles, they found that, due to lens aberrations, the images appeared lopsided and the shapes and positions of the particles appeared to change when the microscope moved up and down by specific increments along the vertical axis — that is, along the third dimension. The researchers further found that the lens aberrations could produce large distortions in images even if the microscope moved just a few micrometers in the lateral plane or a few tens of nanometers in the vertical plane. “The analysis enabled the researchers to model exactly how the lens aberrations altered the appearance and apparent location of the fluorescent particles with changes in the vertical position,” the researchers stated in their paper. Calibrating the changing appearance and apparent location of a particle to its vertical position allowed the team to successfully use the microscope to measure particle positions in all three dimensions. Images of fluorescent particles that, top to bottom, are above, at, and below the vertical position of the best focus of a microscope (left). Calibrating the effects of lens aberrations on the apparent shape and position of the particle images enables accurate measurement of the position in all three spatial dimensions using an ordinary optical microscope. Tracking and combining information from many fluorescent particles on a tiny rotating gear tests the results of the new calibration method and elucidates the motion of a complex microsystem in all three dimensions (right). Courtesy of NIST. To test their method, the researchers used their microscope to image a constellation of fluorescent particles deposited randomly on a microscopic silicon gear that rotated in three dimensions. The researchers showed that their model accurately corrected for the lens aberrations, enabling the microscope to provide full three-dimensional information about the position of the particles. The researchers extended their position measurements to capture the entire range of motion of the gear and complete the extraction of spatial information from the system. These additional measurements highlighted the consequences of nanoscale gaps between microsystem parts, which varied due to imperfections in the fabrication of the system. NIST researchers showed that nanoscale gaps between parts not only can degrade the precision of the intentional rotation, but also can cause unintentional wobbling, rocking, and flexing of the gear — all of which can limit performance and reliability. In terms of its precision, the calibration method was demonstrated to achieve axial precision of 25 nm and axial range of 10 µm, and lateral precision of 1 nm and lateral range of 250 µm, at a frequency of nearly 100 Hz. These values were true even for the slight aberrations that may remain in a modern microscope after corrections have been made through optical engineering. In addition to enabling ordinary microscopes to measure in 3D, the calibration method developed at NIST enables microscopes to more accurately and precisely locate the positions of objects. It provides the ability to measure motion in six degrees of freedom with an ordinary optical microscope and simple localization analysis, with accuracy and precision. The NIST team’s approach also does not require the microscope to be reengineered. The researchers said their study highlights the challenge of aberration effects in localization microscopy and redefines this challenge as an opportunity for accurate, precise, complete localization. “Counterintuitively, lens aberrations limit accuracy in two dimensions and enable accuracy in three dimensions,” researcher Samuel Stavis said. “In this way, our study changes the perspective of the dimensionality of optical microscope images, and reveals the potential of ordinary microscopes to make extraordinary measurements.” The information provided by lens aberrations complements the less accessible methods that microscopists currently use to make measurements in 3D, Stavis said. The NIST method has the potential to broaden the availability of 3D measurements. Researcher Craig Copeland said that microscopy laboratories could easily implement the new method. Aside from the fluorescent particles or a similar standard, which already exist or are emerging, no extra equipment is needed. “The user just needs a standard sample to measure their effects and a calibration to use the resulting data,” Stavis said. The research was published in Nature Communications (www.doi.org/10.1038/s41467-021-23419-y). The open access journal article includes demonstration software to guide researchers in how to apply the calibration.