The competition between resolution and the imaging field of view is a long-standing problem in traditional imaging systems — they can produce either an image of a small area with fine details or an image of a large area with coarse details. Fourier ptychography (FP) is an approach for tackling this intrinsic trade-off in imaging systems. It takes the challenge of high-throughput and high-resolution imaging from the domain of improving the physical limitations of optics to the domain of computation. It also enables post-measurement computational correction of optical aberrations. We present the basic concept of FP, compare it to related imaging modalities and then discuss experimental implementations, such as aperture-scanning FP, macroscopic camera-scanning FP, reflection mode, single-shot set-up, X-ray FP, speckle-scanning scheme and deep-learning-related implementations. Various applications of FP are discussed, including quantitative phase imaging in 2D and 3D, digital pathology, high-throughput cytometry, aberration metrology, long-range imaging and coherent X-ray nanoscopy. A collection of datasets and reconstruction codes is provided for readers interested in implementing FP themselves. Fourier ptychography is an imaging approach that addresses the intrinsic trade-off between resolution and field of view in optical systems and provides computational correction of optical aberrations. This Technical Review surveys its implementations and applications.

Concept, implementations and applications of Fourier ptychography

Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular diversity illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3 to 0.7 with a 4X0.1 NA objective due to the constraint of planar geometry with weak illumination brightness and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500 to 1000 nm, which cannot fulfill some needs of high-resolution biomedical imaging applications. Although it is possible to improve the resolution by using a higher magnification objective with larger NA instead of enlarging the illumination NA, the SBP is suppressed to some extent, making the FP technique less appealing, since the reduction of field-of-view (FOV) is much larger than the improvement of resolution in this FP platform. Herein, in this paper, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform with a hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95NA, attaining a 4X0.1 NA objective with the final effective imaging performance of 1.05NA at a half-pitch resolution of 244 nm with a wavelength of 465 nm across a wide FOV of 14.60 mm2, corresponding to an SBP of 245 megapixels. Our work provides an essential step of FP towards high-NA imaging applications without scarfing the FOV, making it more practical and appealing.

Subwavelength resolution Fourier ptychography with hemispherical digital condensers.

Quantitative phase microscopy (QPM), a technique combining phase imaging and microscopy, enables visualization of the 3D topography in reflective samples, as well as the inner structure or refractive index distribution of transparent and translucent samples. Similar to other imaging modalities, QPM is constrained by the conflict between numerical aperture (NA) and field of view (FOV): an imaging system with a low NA has to be employed to maintain a large FOV. This fact severely limits the resolution in QPM up to 0.82λ/NA, λ being the illumination wavelength. Consequently, finer structures of samples cannot be resolved by using modest NA objectives in QPM. Aimed to that, many approaches, such as oblique illumination, structured illumination, and speckle illumination (just to cite a few), have been proposed to improve the spatial resolution (or the space–bandwidth product) in phase microscopy by restricting other degrees of freedom (mostly time). This paper aims to provide an up-to-date review on the resolution enhancement approaches in QPM, discussing the pros and cons of each technique as well as the confusion on resolution definition claims on QPM and other coherent microscopy methods. Through this survey, we will review the most appealing and useful techniques for superresolution in coherent microscopy, working with and without lenses and with special attention to QPM. Note that, throughout this review, with the term “superresolution” we denote enhancing the resolution to surpass the limit imposed by diffraction and proportional to λ/NA, rather than the physics limit λ/(2n
	 med
	), with n
	 med
	 being the refractive index value of the immersion medium.

Resolution enhancement in quantitative phase microscopy

Surface topography measurement for metal additive manufacturing (AM) is a challenging task for contact and non-contact methods. In this paper, we present an experimental investigation of the use of coherence scanning interferometry (CSI) for measurement of AM surfaces. Our approach takes advantage of recent technical enhancements in CSI, including high dynamic range for light level and adjustable data acquisition rates for noise reduction. The investigation covers several typical metal AM surfaces made from different materials and AM processes. Recommendations for measurement optimisation balance three aspects: data coverage, measurement area and measurement time. This study also presents insight into areas of interest for future rigorous examination, such as measurement noise and further development of guidelines for the measurement of metal AM surfaces.

https://www.spiedigitallibrary.org/journals/optical-engineering/volume-56/issue-11/111714/Optimization-of-surface-measurement-for-metal-additive-manufacturing-using-coherence/10.1117/1.OE.56.11.111714.pdf

Optimization of surface measurement for metal additive manufacturing using coherence scanning interferometry

This review gathers together 15 special topics in modern interferometric metrology representing a sampling of historical, current and future developments. The selected topics cover a wide range of applications, including distance and displacement measurement, the testing of optical components, interference microscopy for surface structure analysis, form and dimensional measurements of industrial parts, and recent applications in semiconductor manufacturing and consumer electronics. Techniques range from laser Fizeau systems to dynamic ellipsometry using polarized heterodyne interferometry.

https://iopscience.iop.org/article/10.1088/1361-6633/ab092d/pdf

A review of selected topics in interferometric optical metrology

Although coherence scanning interferometry (CSI) is capable of measuring surface topography with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterize the performance of surface measuring instruments and offers considerable insight into the origins of these errors. Furthermore, from the measurement of a precision sphere, a process to calibrate and partially correct instruments has been proposed. This paper presents, for the first time, a critical look at the calibration and correction process. Computational techniques are used to investigate the effects of radius error and measurement noise introduced during the calibration process for the measurement of spherical and sinusoidal profiles. Care is taken to illustrate the residual tilt and curvature dependent errors in a manner that will allow users to estimate measurement uncertainty. It is shown that by calibrating the instrument correctly and using appropriate methods to extract phase from the resulting fringes (such as frequency domain analysis), CSI is capable of measuring the topography of surfaces with varying tilt with sub-nanometre accuracy.

On tilt and curvature dependent errors and the calibration of coherence scanning interferometry

Improved differential confocal microscopy is proposed to improve axial resolution and to enhance disturbance resistibility of confocal microscopy. The subtraction and sum values of the two defocusing detected signals are divided as the response function. Both ultrahigh signal-to-noise ratio (SNR) and wide range can be selectively obtained by controlling the defocusing amount of the two differential detectors more tightly with the reflectance disturbance resistibility. Since the detecting sensitivity of the proposed confocal microscopy is unrelated to the energy loss of the reflected beam, the multiplicative mode disturbance can be used to measure microstructures made of hybrid materials and overcome the power drift of a laser source during long scanning. In the case of ultrahigh SNR, the axial resolution reaches 1 nm when NA=0.75 and λ=632.8 nm.

Improved differential confocal microscopy with ultrahigh signal-to-noise ratio and reflectance disturbance resistibility

Fourier ptychographic microscopy is a computational microscopy technique to achieve wide-field and super-resolution complex imaging which has been developed in recent years. The method is based on illuminating the sample by a light source array, and then computationally integrating different images correspondent to each of the sources, in the Fourier domain. Knowledge of the exact relative position of the light sources and the sample is critical for the quality of the final recovered image. In this paper, we present an iterative approach towards correcting the position in the Fourier domain based on Newton's method. Also, an analysis is presented which shows the relation between the position error and the deterioration of the final recovery quality. The effectiveness of the presented method in improving the quality of the final recovered image is demonstrated using simulation and experimental results. Moreover, the method is shown to be more stable and robust to noises in comparison with the state-of-the-art algorithm.

Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy

The invention discloses a fluorescence response follow-up pinhole microscopic confocal measuring device and belongs to an optical micro measurement technology A collimating beam expander, a first beam splitter and a second beam splitter are configured on a direct light path of a pulse laser; an optical power meter is arranged on the reflecting light path of the first beam splitter; a focusing object lens and a three-dimensional micro displacement objective table are arranged on a reflecting light path of the second beam splitter; a long-focus cemented doublet lens and a dichroscope are arranged on a transmitting light path of the second beam splitter; a two-photon fluorescence excitation reflector is arranged on the transmitting light path of the second beam splitter; and a narrow-band filter, a collecting objective lens and a high-gain photoelectric detector are arranged on a reflecting light path of the dichroscope The device is provided with a pinhole which can adaptively adjust the degree of freedom, the problems of pinhole drift and scanning light spot drift in the measuring process are solved, and the device has the characteristics of high stray light suppression capacity, sensitive response and high accuracy

Fluorescence response follow-up pinhole microscopic confocal measuring device

The three-dimensional (3D) precision measurement of subsurface defects (SSDs) remains a long-term, critical, and urgent challenge in advanced manufacturing technology. In this study, we present a 3D dark-field confocal microscopy technique with complementary illumination and detection apertures to detect the SSD in ultraprecise optical components, which are widely employed at laser fusion facilities. Under an annular illumination generated using a pair of axicons, the specular reflected beam from the surface can be blocked by a diaphragm placed in the detection path, while the scattered beam from the SSD can be effectively collected by the detector. Both surface topography and subsurface defects distribution can be measured simultaneously by this method. We constructed a dark-field confocal microscope that could readily detect the SSD 60 µm beneath the surface in neodymium glass. Furthermore, the 3D volume distributions of the SSD were also reconstructed.

Wang Yuhang

Papers

On tilt and curvature dependent errors and the calibration of coherence scanning interferometry

Improved differential confocal microscopy with ultrahigh signal-to-noise ratio and reflectance disturbance resistibility

Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy

Fluorescence response follow-up pinhole microscopic confocal measuring device

3D dark-field confocal microscopy for subsurface defects detection.