MicroscopyEducation
Introduction to Fourier Ptychography: Part I Kevin C. Zhou,1
and Roarke Horstmeyer1
Tomas Aidukas,2 *
Lars Loetgering,3
1Department of Biomedical Engineering, Duke University, Durham, NC 2Swiss Light Source, Paul Scherrer Institut, Switzerland 3Leibniz Institute of Photonic Technology, Jena, Germany
*
roarke.w.horstmeyer@duke.edu
Abstract: Fourier ptychography is an emerging computational micros- copy technique that can generate gigapixel-scale images of biological samples. With only the addition of a low-cost LED array to a standard digital microscope and a reconstruction algorithm, Fourier ptychog- raphy overcomes the fundamental trade-off between a microscope’s resolution and field-of-view without any moving parts. This article is the first in a three-part series that aims to introduce the fundamentals of the technology to the broader microscopy community and beyond, using intuitive explanations.
Keywords: Fourier ptychography, Fourier transform, computational microscopy, space-bandwidth product, gigapixel microscopy
Introduction Most users of an optical microscope encounter a common
question when preparing to view a specimen—which objective lens will allow for best observation? A low-magnification objec- tive lens makes it possible to view a large area, albeit at poor resolution. Viewing a large area is helpful for rapidly identify- ing macroscopic areas of interest, such as clusters of important cells. However, higher resolution is oſten required to observe specific features, such as subcellular structures that indicate cell condition. To image at higher resolution and observe such fine features, one must “zoom in” using a high-magnification lens. Zooming in significantly limits the observable specimen area and thus the overall viewing context, which can oſten cause one to lose what they were searching for. Ideally, one would like an imaging system that simultaneously offers high resolution and a large field-of-view (FOV) (Figure 1). Te trade-off between viewing a larger sample area, versus
zooming in to observe finer specimen detail, is common to all microscopes—and all imaging systems in general. Within the modern digital optical microscope, the primary cause of this trade-off is not the size or pixel count of today’s digital image sensors. Tese can now reach into the hundreds of megapixels. Instead, it is typically caused by limits imposed by microscope objective lens design. All lenses have a finite “space-bandwidth product,” or number of optically resolved spots across a given FOV. Optical aberrations limit the ability to focus light to a tight spot across a large area, which in turn limits the ability to form sharp images without “zooming in,” especially in the peripheral regions of the FOV. Many high-end digital microscopes include an auto- mated X-Y translation stage to help address the trade-off
36 doi:10.1017/S1551929522000670
between resolution and FOV. After capturing multiple X-Y images during step-and-repeat scanning, large image com- posites are then digitally tiled together for subsequent obser- vation and analysis. There are several practical limitations to such scanning approaches, including lengthy acquisition times, setup complexity, cost, and stitching inaccuracies, to name a few. In 2013, a novel imaging method to address the large-area, high-resolution imaging problem was devel- oped, termed “Fourier ptychography” (with a silent “p”) [1,2]. Fourier ptychography uses programmable illumina- tion and computational reconstruction algorithms to create gigapixel-scale images that provide high-resolution imagery over a large area without requiring a mechanical stage or any moving parts. Over the past several years, Fourier ptychography has
grown into a mature method that now offers a variety of unique benefits [3,4]. It is now also being pursued in several commer- cial applications. Tis short article is the first in a three-part series that will aim to explain the basics of how Fourier pty- chography works to a non-specialist.
Basic Operation of Fourier Ptychography To understand the basic operation of Fourier ptychogra-
phy, let’s first consider the simplified microscope diagrammed in Figure 2a. Here, a small point-like source of light is placed at a large distance beneath the specimen of interest. In this diagram the specimen is a resolution target. Te simplified microscope above forms an image of the resolution target. Although the point-like source emits light in all directions as a spherical-like wave, the relatively small specimen located several centimeters away “sees” approximately a planar wave, or in other words a parallel set of light rays, reaching its bot- tom surface. Specimens one might be interested in examining under a
microscope contain features of various sizes, including some that approach the wavelength of light. When light interacts with such features, it diffracts or spreads in many directions— the smaller the feature, the larger the angle of diffraction. Tis interaction typically results in a large cone of diffracted light emerging from the specimen’s surface. To best understand the specimen, it would be ideal for the microscope objective lens to collect as much of this diffracted light as possible. In
www.microscopy-today.com • 2022 May Felix Wechsler,3
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