傅里叶叠层显微成像技术：高分辨率与深度扩展

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"傅里叶叠层显微成像技术是一种创新的光学成像方法，它结合了大孔径和高分辨率的特点，通过迭代合成不同照明条件下的低分辨率强度图像在傅里叶空间中的信息，从而实现宽视场、高分辨率的复杂样本图像。这种方法还能够校正像差，并通过数字手段将显微镜的景深扩展到其物理限制之外。" 傅里叶叠层显微成像（FPM）技术是基于光学成像原理的先进方法，其核心在于利用傅里叶变换的性质来提升成像质量。在传统的光学显微镜中，物镜的分辨率和视场通常受到衍射极限的约束，而FPM通过获取一系列不同照明角度的图像，然后在傅里叶域进行处理，实现了超越这些限制的可能性。在FPM技术中，每个低分辨率的图像对应于不同的照明模式，这些模式在傅里叶空间中形成互补的信息。通过对这些信息进行迭代拼接，可以重建出高分辨率的复数图像，即包含幅度和相位信息的完整图像。这使得FPM在保持大视场的同时，也能够获得细节丰富的图像。 FPM还引入了一种波前校正策略，这对于消除由于系统光学元件不完善或样品本身引起的像差至关重要。通过这种校正，FPM可以扩大显微镜的有效深度范围，使其具有不变的分辨率深度。例如，所构建的原型显微镜在632纳米波长下，分辨率达到了0.78微米，视场约为120平方毫米，且具有0.3毫米的深度焦点（在相同条件下测量）。为了验证FPM技术的有效性，研究人员拍摄了病理切片的吉咖像素彩色图像，这些结果显示FPM成功地实现了高通量、高分辨率的成像。这一成像过程的转变意味着，以前受限于系统光学元件性能的高通量、高分辨率显微问题，现在可以通过计算手段来解决，极大地拓展了显微镜的应用潜力。值得注意的是，成像平台的吞吐量往往受到空间带宽产品（Space-Bandwidth Product, SWBP）的限制，这是决定光学系统分辨率和视场的关键因素。FPM通过计算后处理的方式，有效地提升了SWBP，从而提高了系统的整体性能。傅里叶叠层显微成像技术是一种革命性的光学成像解决方案，它通过组合多个低分辨率图像并利用傅里叶变换，实现了高分辨率、大视场和深景深的成像效果，为生物医学研究、材料科学和其他领域的显微成像应用提供了新的可能性。

Wide-ﬁeld, high-resolution Fourier ptychographic

microscopy

Guoan Zheng

†

, Roarke Horstmeyer and Changhuei Yang

We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a

number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-ﬁeld, high-resolution

complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and

digitally extend a microscope’s depth of focus beyond the physical limitations of its optics. As a demonstration, we built a

microscope prototype with a resolution of 0.78 mm, a ﬁeld of view of ∼120 mm

and a resolution-invariant depth of focus

of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The

reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one

that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

he throughput of an imaging platform is fundamentally

limited by the space–bandwidth product (SBP)

of its

optical system, which is deﬁned as the number of degrees of

freedom it can extract from an optical signal. The SBP of a conven-

tional microscope platform is typically in megapixels, regardless of

the magniﬁcation factor or numerical aperture (NA) used. As a

reference point, a standard ×20 microscope objective (MPLN

×20, 0.4 NA, Olympus) has a resolution of 0.8 mm and a

1.1-mm-diameter ﬁeld of view (FOV), corresponding to an SBP of

7 megapixels. Increasing the SBP of a microscope is fundamen-

tally confounded by the scale-dependent geometric aberrations of

its optical elements

, resulting in a compromise between achievable

image resolution and FOV.

In microscopy, however, a large SBP is highly desirable for

biomedical applications such as digital pathology, haematology,

immunohistochemistry and neuroanatomy. The strong need in

biomedicine and neuroscience to digitally image large numbers of

histology slides for analysis has prompted the commercial develop-

ment of sophisticated mechanical scanning microscope systems and

lensless microscopy set-ups. Artiﬁcially increasing the SBP of an

imaging system by mechanical means is suboptimal, as it requires

precise control over actuation, optical alignment and motion track-

ing. Furthermore, a mechanical solution simply accepts the intrinsic

resolution limit and SBP of a conventional microscope’s optics,

neglecting the computationally addressable problem of resolution

enhancement. Lensless microscopy methods such as digital in-line

holography

2–4

and contact-imaging microscopy

5,6

offer unique

imaging capabilities, but also present certain drawbacks. For

example, digital in-line holography does not work well for contigu-

ous samples, and contact-imaging microscopy requires a sample to

be in close proximity to the sensor.

Here, we present a computational imaging method that is

capable of providing a scalable SBP for most existing microscopes

without involving mechanical scanning or phase measurements.

Although the method does require the acquisition of a plurality of

images, it does so non-mechanically and accomplishes its SBP

improvement using the plural data to overcome the physical limit-

ations of the system’s optics.

The imaging method we introduce and demonstrate, termed

Fourier ptychographic microscopy (FPM), shares its roots with

interferometric synthetic aperture microscopy

7–20

, ptychography

21–27

phase retrieval

28–31

, light-ﬁeld imaging

32–35

, structured illumina-

tion

and adaptive optics

. It works by iteratively stitching together

a number of low-resolution images in Fourier space to recover an

accurate high-resolution, high-SBP output image. Unlike systems

designed to increase the SBP of a single acquisition

, combining

time-sequential measurements for the same goal allows our set-up

to maintain a simple and compact form factor. The main design

strategy of FPM is similar to that of interferometric synthetic aper-

ture microscopy

7–20

: expanding the SBP in Fourier space via multi-

image fusion. However, because no measured phase information is

needed for FPM, our set-up eliminates the design challenges associ-

ated with interferometric detection schemes. Furthermore, the

image recovery procedure of FPM follows a strategy similar to pty-

chography (that is, scanning diffraction microscopy)

21–27

: iteratively

solving for a sample estimate that is consistent with many intensity

measurements. Unlike ptychography, however, FPM’s object

support constraints are imposed in the Fourier domain, offering

several unique advantages and opportunities.

By adding a simple light-emitting diode (LED) matrix illumina-

tion module and applying the FPM reconstruction algorithm, we

transform a conventional optical microscope into a high-resolution

(0.78 mm, 0.5 NA), wide-FOV (120 mm

) microscope with a ﬁnal

SBP of 1 gigapixel. Our joint optical–digital solution further

allows us to exploit adaptive optics-based wavefront correction strat-

egies to compensate for aberrations and expand the depth of focus

beyond conventional optical limits. Speciﬁcally, we use our FPM

procedure to extend a conventional microscope’s 80 mm depth of

focus to 0.3 mm, creating a platform with a large tolerance to

microscope slide placement errors. In the following, we will

brieﬂy outline the FPM operation and experimental set-up,

discuss how to apply the FPM digital wavefront correction tech-

nique, and demonstrate successful gigapixel imaging of a

pathology slide.

Principle of FPM

The data collection procedure of FPM is straightforward. A two-

dimensional sample is placed at the focal plane of a low-NA micro-

scope objective and a sequence of N images is collected, with the

sample successively illuminated by plane waves at N different

Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA;

†

Present address: Biomedical Engineering and Electrical

Engineering, University of Connecticut, Storrs, Connecticut, 06269, USA.

e-mail: gazheng@caltech.edu

ARTICLES

PUBLISHED ONLINE: 28 JULY 2013 | DOI: 10.1038/NPHOTON.2013.187

NATURE PHOTONICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephotonics 1

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