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Cite this article: Yang Yongying, Ling Tong, Cao Pin, Jiang Jiabin. Wavefront sensing technology and applications based on Quadriwave Lateral Shearing Interferometry (Invited) [J]. Infrared and Laser Engineering, 2024, 53(9): 20240331. DOI: 10.3788/IRLA20240331shu

Wavefront Sensing Technology and Applications Based on Quadriwave Lateral Shearing Interferometry (Invited)

Yongying Yang 1,4* $, T o n gL in g$ 2,3,4* $, P in C a o$ 4 $, J iabin J ian g$ 4

(1. College of Optical Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China;

2. School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Singapore 639798, Singapore;

3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore; 4. Hangzhou Zernike Optoelectronic Technology Co., Ltd., Hangzhou, Zhejiang 310027, China)

Fund Projects:

National Natural Science Foundation of China (11275172, 6187517); National Academic Monograph Publishing Fund Project; NTU Start-up Grant (SUG); NRF Fellowship Grant (NRF-NRFF14-2022-0005)

Corresponding Authors:

Yongying Yang, female, Professor, Ph.D., primarily engaged in research on precision interferometric metrology, particularly common-path multiwave lateral shearing interferometry.

Tong Ling, male, Assistant Professor, Ph.D., primarily engaged in research on precision interferometric imaging techniques for biomedical imaging.

Abstract

The advancement of high technology places increasingly stringent demands on precision interferometric imaging. In modern optics and biomedical fields, label-free imaging techniques are driving the development of quantitative phase microscopy by enabling 3D in situ observation and analysis of live cells without relying on traditional dyes or fluorescent markers.In the realm of optical testing technology, there's an urgent need for on-site, real-time applications of interferometric systems. For instance, transient detection and analysis of laser wavefronts, high-speed flow field detection, adaptive optics detection and control, and high-precision optical system aberration analysis all critically require a compact, environmentally robust, and transient imaging interferometric system. Addressing these demands, this paper comprehensively introduces the principles, development history, wavefront reconstruction methods, and wide-ranging applications of Quadriwave Lateral Shearing Interferometry for phase imaging.The Quadriwave Lateral Shearing Interferometry system can achieve transient phase imaging by acquiring four sheared wavefronts in two orthogonal shearing directions within a single interferogram. This is enabled by a novel Four-wave Interferometric Sensor (FIS4), composed of a randomly encoded grating and a phase chessboard.The FIS4 interferometric sensor, with its unique advantages such as compactness, robustness, high temporal resolution, and compatibility with existing microscopic systems, demonstrates broad application prospects in numerous fields, including biomedicine, optical metrology, and material characterization. The development of this technology not only provides new research tools for related fields but also opens up new possibilities for interdisciplinary innovation and discovery

Introduction

The demand for label-free imaging techniques continues to grow in modern optics and biomedical fields. These techniques don't rely on traditional dyes or fluorescent markers, allowing for in situ observation and analysis without interfering with the sample's natural state. Among these, Quantitative Phase Microscopy (QPM) has garnered significant attention in research and clinical diagnostics due to its ability to provide additional information about transparent biological samples, such as their volume and dry mass [1–4]. QPM's greatest advantage lies in its ability to significantly enhance the contrast of microscopic images without any dyes or fluorescent labels, making it particularly suitable for long-term tracking of dynamic processes in live cells.

QPM techniques can be categorized into different branches based on their implementation, including Fourier Ptychographic Microscopy, the Transport of Intensity Equation, Diffraction Phase Microscopy, and Digital Holographic Microscopy (see Table 1). Fourier Ptychographic Microscopy (FPM) is a method that reconstructs images by analyzing the phase and amplitude information of the scattered wavefield from a sample [5–8]. This technique uses a ptychographic iterative engine that processes the sample's diffraction patterns with complex algorithms to generate high-contrast, artifact-free images. However, a major drawback of this method is its low temporal efficiency, requiring the acquisition of a large number of ptychographic diffraction patterns and lengthy post-processing, which limits its use in real-time applications. The Transport of Intensity Equation (TIE) technique recovers the wavefront phase changes of a sample by analyzing image differences at various focal planes and can be directly applied to conventional bright-field microscopes [1, 9]. By introducing partially coherent light sources [10], such as light-emitting diodes, and using electrically tunable lenses [11], the image acquisition rate and signal-to-noise ratio of TIE technology have significantly improved, leading to more accurate and faster reconstruction of phase images.

The Transport of Intensity Equation (TIE) technique recovers a sample's wavefront phase changes by analyzing image differences at various focal planes and can be directly applied to conventional bright-field microscopes [1, 9]. By introducing partially coherent light sources [10], such as light-emitting diodes, and using electrically tunable lenses [11], the image acquisition rate and signal-to-noise ratio of TIE technology have significantly improved, leading to more accurate and faster reconstruction of phase images.

Principles of Quadriwave Lateral Shearing Interferometry Phase Imaging and Wavefront Reconstruction Methods

As shown in Figure 1, the principle of Quadriwave Lateral Shearing Interferometry phase imaging is as follows: when an input wavefront passes through a two-dimensional diffraction grating, the wavefront is replicated into four tilted wavefronts propagating in slightly different directions, with each wavefront retaining the phase distribution information of the original wavefront. Due to the tilt angles between the four wavefronts, the interferogram generated on the camera sensor appears as a grid-like dot pattern. When the input wavefront deviates from a plane wave, the positions of these bright spots will also be distorted compared to a regular dot pattern.Wavefront replication can be achieved using gratings, shearing mirrors, or other beamsplitting elements. Compared to other methods, the grating method offers easier control over deflection precision. Based on the grating's ability to diffract four wavefronts differently, Quadriwave Lateral Shearing Interferometry includes Crossgrating Lateral Shearing Interferometer (CGLSI) [19-20], Quadriwave Lateral Shearing Interferometry based on the modified Hartmann mask technique (MHM) [21-23], and Quadriwave Lateral Shearing Interferometry based on a randomly encoded hybrid grating [16-18].

A Crossgrating Lateral Shearing Interferometer (CGLSI) uses a conventional two-dimensional amplitude grating to generate different diffraction orders [19]. The grating consists of a periodic array of square apertures, typically with pitches ranging from a few to tens of micrometers. When an input wavefront illuminates the grating, the grating diffracts light into multiple orders, including the $\pm 1$ orders in both x and y directions. For unwanted diffraction orders, such as the zero order and higher-order components, a CGLSI requires an additional order-selection window placed at the Fourier focal plane of the lens [20]. This window only allows the $\pm 1$ orders to pass while blocking other orders. However, the need for an order-selection window increases system complexity and limits the flexibility of grating parameters and the magnification of the optical system under test.

The modified Hartmann mask technique combines a two-dimensional amplitude grating with a phase chessboard to reduce unwanted diffraction orders [22–23]. The phase chessboard consists of periodically arranged square cells with a $π$ phase shift, with a period twice that of the amplitude grating. This chessboard-like phase modulation can eliminate zero-order diffraction. Furthermore, by optimizing the duty cycle of the amplitude grating to 2/3 (i.e., the aperture size is 2/3 of the grating pitch), the modified Hartmann mask technique can also suppress $\pm 3$ order diffraction components. By eliminating the zero order and adjacent $\pm 3$ order components, the modified Hartmann mask technique significantly improves the contrast of the interferogram and removes the need for an order-selection window in the system, making the system more compact and flexible.

Since an ideal sinusoidal transmittance distribution would only produce the desired $\pm 1$ diffraction orders, the randomly encoded hybrid grating further improves the grating design by approximating an ideal sinusoidal transmittance distribution [17]. A randomly encoded hybrid grating is formed by superimposing a two-dimensional binary amplitude grating and a phase chessboard similar to the modified Hartmann mask technique. However, instead of a periodic amplitude grating, the randomly encoded hybrid grating employs a pseudo-random encoding scheme to approximate the ideal sinusoidal transmittance distribution. The amplitude grating consists of numerous tiny pixels, typically 1–2 $μ$ m in size, with each pixel randomly set to 0 (blocking) or 1 (passing) according to an ideal sinusoidal transmittance distribution [18]. This design breaks the periodic structure of the amplitude grating, minimizing artifacts and unwanted diffraction orders caused by periodic structures. Consequently, it can produce high-contrast Quadriwave Lateral Shearing Interferometry interferograms, enhancing the accuracy and robustness of the phase retrieval process, and enabling high-quality wavefront reconstruction with the same grating in optical systems with different parameters.After obtaining the Quadriwave Lateral Shearing Interferometry interferogram, the original wavefront distribution under test needs to be reconstructed computationally. Its phase retrieval process primarily involves two steps. As shown in Figure 2, first, by performing a Fourier transform on the interferogram generated by the interference of the four tilted wavefronts, the $+ 1$ orders in orthogonal directions (x and y) are extracted. Based on this, an inverse Fourier transform is performed, and algorithms such as Goldstein, quality map, or differential unwrapping [16] are used for phase unwrapping to obtain the sheared wavefronts in both x and y directions. To recover the original wavefront from the unwrapped sheared wavefronts, a differential Zernike polynomial fitting method [24] or Fourier transform-based algorithms [25–26] can be used. Differential Zernike polynomial fitting can effectively suppress random noise but filters out high-frequency information, while Fourier transform methods can preserve high-frequency information. For small shear amounts, the original wavefront can be reconstructed in the Fourier frequency domain by approximating the sheared wavefront as partial derivatives; for large shear amounts, the original wavefront can be reconstructed using a least-squares based method.

1.1

Wavefront Reconstruction Algorithm Based on Differential Zernike Polynomial Fitting

The original wavefront function $W (x, y)$ can be expressed as the following N-term Zernike polynomial:

In polar coordinates, represented by the radial coordinate $ρ$ and the azimuthal angle $θ$ , the Zernike polynomials can be written in the following form:

1.2

Wavefront Reconstruction Algorithm Based on Differential Fourier Transform

1.3

Fourier Transform Phase Reconstruction Algorithm for Large Shear Rates

Applications of Quadriwave Lateral Shearing Interferometry Wavefront Sensing

Quadriwave Lateral Shearing Interferometry has become a powerful and versatile tool due to its unique advantages, such as compactness, robustness, high temporal resolution, and compatibility with existing microscopic systems, offering broad application potential in both scientific research and industrial fields. Initially used for traditional optical workshop inspections, including optical component testing, laser beam assessment, and adaptive optics, its applications later expanded to include biomedical imaging, nanoparticle localization, characterization of metasurfaces, and temperature gradients.The compact design of Quadriwave Lateral Shearing Interferometry makes it easy to integrate with existing microscopic systems, while its robustness is demonstrated by its ability to maintain precise interference sensitivity even in high-vibration environments. Furthermore, Quadriwave Lateral Shearing Interferometry enables single-shot measurements, allowing for the capture of rapid dynamic processes.In the field of biomedical research, Quadriwave Lateral Shearing Interferometry has been used for label-free, high-resolution, real-time imaging of various live cells, such as COS-7 [14], HT1080 cells [27], RPE cells [28], CHO cells [15], HEK cells, and neurons [29]. Additionally, Quadriwave Lateral Shearing Interferometry has been applied to phase retardation imaging, providing strong contrast to visualize anisotropic tissues and subcellular structures [27], such as collagen fibers [30] and the cytoskeleton [15].This technology has also been extended to phase imaging in the X-ray [31], mid-wavelength infrared (MWIR), and long-wavelength infrared (LWIR) regions [32], further demonstrating its potential in cross-disciplinary applications. Moreover, Quadriwave Lateral Shearing Interferometry wavefront sensing technology has been widely applied in recent research for the characterization of metasurfaces [33] and two-dimensional materials [34], showcasing its numerous uses and potential value in optical and materials science.

2.1

Optical Component Measurement and Comparison

The research team at Zhejiang University provided a detailed introduction to the application of Quadriwave Lateral Shearing Interferometry in optical component measurement in 2015 [18]. In their experiment, they used a Quadriwave Lateral Shearing Interferometry system based on a randomly encoded hybrid grating to test two different cemented doublets and compared the results with those obtained from a ZYGO GPI interferometer.As shown in Figure 3, for a doublet with a 50mm focal length, using an REHG (Randomly Encoded Hybrid Grating) with a shear ratio of 0.066, they obtained a peak-to-valley (PV) aberration of 2.80λ and a root mean square (RMS) aberration of 0.731λ. In comparison, the ZYGO GPI interferometer measured the same doublet with a PV aberration of 2.84λ and an RMS aberration of 0.699λ.The second doublet tested had a 90mm focal length and exhibited smaller aberrations. To improve detection sensitivity, the authors increased the shear ratio to 0.119. Using the Quadriwave Lateral Shearing Interferometry system based on a randomly encoded hybrid grating, they obtained a PV aberration of 0.152λ and an RMS aberration of 0.035λ. The ZYGO GPI interferometer measured the same doublet with a PV aberration of 0.147λ and an RMS aberration of 0.033λ.

Experimental results show that the aberration measurements obtained using the Quadriwave Lateral Shearing Interferometry system are very close to those from the ZYGO GPI interferometer. This validates the accuracy and reliability of Quadriwave Lateral Shearing Interferometry based on randomly encoded hybrid gratings for optical component testing.Given that the Four-wave Interferometric Sensor (FIS4), hereafter referred to as the FIS4 interferometric sensor, utilizes the latest randomly encoded digital grating technology to form a common-path interferometric system through its inherent Quadriwave Lateral Shearing Interferometry, it holds broad application prospects. To facilitate its wider domestic application in defense and national economic sectors and to aid in understanding its principle, the most intuitive understanding of this interferometric sensor can be as the Four-wave Interferometric Sensor (FIS4).Because the system performs self-interference, it requires no reference mirror, boasts a compact structure, and exhibits strong resistance to external environmental interference. It can achieve high-precision and stable detection of the wavefront under test without demanding experimental conditions such as vibration isolation or constant temperature. By leveraging shear differential interference, the system offers a large dynamic range and broader applications. The FIS4 interferometric sensor is equipped with a 5-megapixel camera and features digital image processing software for high-precision FIS4 wavefront reconstruction. Depending on the application, it can output rich data images of the measured wavefront or precision component surface topography, including PV (peak-to-valley) values, RMS (root mean square) values, contour maps, and 3D plots.

Here are examples of the most common future applications for the FIS4 interferometric sensor: 3D live cell imaging in biology, resolved 3D localization, white light profilometry detection using Quadriwave Lateral Shearing Interferometry, laser wavefront and high-speed flow field detection, and applications in adaptive optics systems.

2.2

Live Cell Imaging

One of the most prominent applications of Quadriwave Lateral Shearing Interferometry phase imaging is live cell imaging. It offers label-free, high-resolution, wide-field, real-time imaging [16] with quantitative phase information. By capturing the phase differences caused by variations in refractive index among the culture medium, cytoplasm, and various organelles, Quadriwave Lateral Shearing Interferometry enables non-invasive observation of cellular structures and dynamics without exogenous labels, thereby eliminating the issues of photobleaching and phototoxicity associated with fluorescence microscopy.Research from the authors and other teams indicates that Quadriwave Lateral Shearing Interferometry can reveal subcellular structures like vesicles, folds, and lamellipodia [14–15, 27–28], demonstrating sensitivity to nanometer-scale optical path differences [16]. Furthermore, the compatibility of Quadriwave Lateral Shearing Interferometry phase imaging with standard inverted microscopes and its real-time imaging capability make it a powerful tool for monitoring cellular processes and dynamics, including red blood cell membrane fluctuations [16] and RPE cell movement [28].

Figure 4 shows a newly designed 3D live cell microscope utilizing Quadriwave Lateral Shearing Interferometry phase imaging, with the FIS4 interferometric sensor as its core component. Figure 4(a) shows the C-type upright and inverted alloy stage 3D live cell microscope in inverted mode (defined by the traditional microscope objective below); Figure 4(b) shows the microscope imaging optical path; Figure 4(c) shows the microscope in upright mode.The microscope's imaging optical path is simple and clear: visible light enters the culture dish through the illumination system, passes through live cells in the culture medium, and then enters the objective lens and imaging lens before being directed into a dual-camera imaging system composed of an observation camera and the FIS4 interferometric sensor. Different cameras can output 2D images of the sample, while the FIS4 interferometric sensor can output 3D images of the sample.The C-type upright and inverted alloy stage live cell microscope can perform precise alignment and detection of cells using an XYZ motorized stage. The C-type upright and inverted alloy stage has a smaller and more compact external dimension than traditional microscopes, making it easy to carry and operate.The difference between the inverted mode (Figure 4(a)) and the upright mode (Figure 4(c)) is that in the inverted mode, the objective is located at the bottom, and its optical path is similar to that of a traditional inverted microscope. When measuring very small cell or bacterial scales, if a large numerical aperture oil immersion objective is used, the C-type upright and inverted alloy stage live cell microscope can be rotated 180°. In this case, the oil immersion objective is in the upper part, and the immersion oil is injected onto the coverslip, avoiding the drawback of inverted microscopes being unable to use oil immersion objectives.

图5为利用FIS4干涉传感器研发的3D活体细胞显微镜观察的红细胞动态。

Since the microscope offers label-free 3D imaging of live cells, it can monitor the morphology of live cells throughout the culture process at various stages. This enables research into cell morphology, size, and activity characteristics. Figure 6 shows the state changes of ESC live cells during autophagy at different times, imaged at 20x magnification. The dashed circles in the contour maps highlight the changes in cell morphology at 0, 4, and 8 hours.The cellular objects acquired by the microscope are label-free and do not damage internal cell structures, thus allowing for long-term 3D imaging of live cells. The 3D cell images deciphered from the system's interferograms possess the characteristic of quantitative phase calculation. These 3D images and contour maps can be used to study various parameters during live cell culture, such as cell count, size, volume, and dry mass.

2.3

Super-resolution 3D Localization

Quadriwave Lateral Shearing Interferometry phase imaging has found novel applications in super-resolution microscopy and thermal imaging.In super-resolution imaging, researchers have leveraged the phase changes associated with axial defocus in Quadriwave Lateral Shearing Interferometry phase imaging (Figure 7) to achieve three-dimensional nanoscale localization of gold nanoparticles [35]. This method enabled nanoscale drift compensation in Direct Stochastic Optical Reconstruction Microscopy (dSTORM) imaging of CHO cells, leading to a lateral resolution of 1 nm for filamentous actin and a localization precision of 0.7 nm

\times

0.7 nm

\times

0.7 nm.In thermal imaging, Quadriwave Lateral Shearing Interferometry phase imaging can be used to observe changes in the refractive index of a medium related to temperature variations. Researchers successfully characterized the thermal distribution of gold nanoparticle arrays under laser beam illumination, demonstrating rapid, label-free thermal imaging with diffraction-limited resolution [36]. These applications underscore the potential of Quadriwave Lateral Shearing Interferometry phase imaging in advancing nanoscale microscopy and material characterization techniques.

Quadriwave Lateral Shearing Interferometry phase imaging has found novel applications in super-resolution microscopy and thermal imaging.In super-resolution imaging, researchers have leveraged the phase changes associated with axial defocus in Quadriwave Lateral Shearing Interferometry phase imaging (Figure 7) to achieve three-dimensional nanoscale localization of gold nanoparticles [35]. This method enabled nanoscale drift compensation in Direct Stochastic Optical Reconstruction Microscopy (dSTORM) imaging of CHO cells, leading to a lateral resolution of 1 nm for filamentous actin and a localization precision of 0.7 nm

\times

0.7 nm

\times

0.7 nm.In thermal imaging, Quadriwave Lateral Shearing Interferometry phase imaging can be used to observe changes in the refractive index of a medium related to temperature variations. Researchers successfully characterized the thermal distribution of gold nanoparticle arrays under laser beam illumination, demonstrating rapid, label-free thermal imaging with diffraction-limited resolution [36]. These applications underscore the potential of Quadriwave Lateral Shearing Interferometry phase imaging in advancing nanoscale microscopy and material characterization techniques.

2.4

Detection of White Light Profiles Using 4-Wave LateralShearing Interferometry

The FIS4 interferometer sensor, utilizing Quadri-Wave Lateral Shearing Interferometry, can be used not only for transmission microscopy of living cells but also, by employing the reflection imaging principle, for microscopic profile detection, which is the FIS4 white light profiling technique. Figure 8(a) shows a schematic diagram of the optical path of a white light profilometer based on 4-Wave LateralShearing Interferometry. LED white light passes through the illumination system and beam splitter, enters the objective lens, and then illuminates the surface of the precision component. The reflected light, carrying microscopic information about the surface under test, passes through the beam splitter and enters a dual-camera imaging system composed of an observation camera and the FIS4 interferometer sensor. Different cameras can output 2D images of the sample under test, while the FIS4 interferometer sensor can output 3D images of the sample. Figure 8(b) shows the portable FIS4 white light profilometer. The system is equipped with XYZ three-dimensional translation and adjustment mechanisms, as well as pitch and yaw adjustment mechanisms, to achieve alignment between the target and the device's detection optical axis. It can also be placed on a tripod to achieve arbitrary orientation adjustment and detection for different inspection targets (such as large-aperture optical components and large-aperture optical windows). The system is self-interfering, requires no reference mirror, has a compact structure, and strong resistance to external environmental interference. It can achieve high-precision and stable detection of the wavefront under test without stringent experimental conditions such as vibration isolation and constant temperature, making it particularly suitable for surface microscopic topography measurement and detection in workshop and outdoor environments.

A microscopy system can detect various microscopic features on optical component surfaces, such as the width and depth of scratch-like defects and surface roughness. Using a dual-camera imaging system, the 2D camera's wide field of view allows for rapid identification of surface microscopic feature information, while the digital wavefront interferometric sensor enables 3D depth detection of scratches.

Figure 9(a) presents a localized contour map and a 3D image of a protruding circular ring on a sample surface, as detected by the FIS4 white light profilometer. Figure 9(b) shows the detection of a standard etched line on a fused silica plate, fabricated using electron beam exposure and ion etching. Microscopic depth detection of this etched line provides contour and 3D images of the standard surface line. As seen in Figure 9(b), the peak-to-valley (PV) depth of the standard etched line on the fused silica plate is approximately 258 nm, which aligns with the depth calibrated by a step profiler at around 250 nm.

Figure 10(a) shows the contour map and surface roughness of an optical component surface detected by the FIS4 white light profilometer, revealing a surface roughness of approximately 4.7 nm. Figure 10(b) displays the contour map and microscopic morphology of a gauge block surface, with a detected peak-to-valley (PV) value of approximately 27 nm.This demonstrates that the reflective white light profilometer, built using the FIS4 interferometer sensor, can perform real-time, online measurements of the microscopic morphology and profiles of precision surfaces. Furthermore, due to the stability of its common-path interference, it's suitable for on-site and field inspections.

2.5

Laser Wavefront and High-Speed Flow Field Detection

Laser wave-front metrology is a technique used to measure the quality of a laser wavefront, providing phase information of the laser. It is widely applicable in optical system design and manufacturing, laser design and manufacturing, optical imaging, and microscopy. wave-front metrology sensors can be used to evaluate and test the performance of optical components and systems, design and optimize lasers, and measure and improve imaging quality and resolution. In some large scientific installations, such as laser inertial confinement fusion devices, the quality and shape of the laser beam significantly impact fusion efficiency and stability. The primary goal of wave-front metrology is to ensure that the laser beam generates uniform and concentrated heat on the target, which requires the use of high-precision and high-resolution wavefront sensors, as well as precise wavefront reconstruction algorithms. Therefore, wave-front metrology technology needs to meet requirements for high precision, high resolution, and so on.In summary, the FIS4 Quadriwave interferometer sensor, with its on-site vibration resistance, real-time capability, and high sampling resolution, is highly suitable for wave-front metrology. Figure 11 shows a schematic diagram of the optical path for the FIS4 used in laser wave-front metrology and analysis. The laser beam, after passing through a collimating and beam expansion system, enters the optical system under test. The wavefront carrying information from the tested system then passes through a beam compression system and enters the FIS4 interferometer sensor.Figure 12 shows the FIS4 used for laser wave-front metrology. Figure 12(a) presents the results of large-aperture wave-front metrology for a 351 nm wavelength, 100 mm aperture laser beam. Figure 12(b) shows the large-aperture wave-front metrology results for a 1053 nm near-infrared wavelength, 100 mm aperture laser beam. From Figure 12, it can be seen that for a 100 mm aperture, 351 nm wavelength laser beam, the PV value is approximately 96 nm, and for the 1053 nm near-infrared wavelength laser beam, the PV value is approximately 88 nm.

To verify the reliability of the FIS4 interferometer sensor in laser wave-front metrology, a fused silica annular step calibration plate, as shown in Figure 13(a), was specifically fabricated. This calibration plate was then measured using a step profiler, yielding a height H of approximately 123 nm.Using the optical path depicted in Figure 11, the calibration plate was placed in a parallel light path. A Helium-Neon laser beam was then used to measure the wavefront, resulting in a PV value of approximately 63 nm. Given that the refractive index of fused silica in the Helium-Neon laser wavelength band is about 1.4570, the optical path difference (OPD) due to the step height H in air can be calculated as approximately 56 nm. The deviation is only a few nanometers, which clearly demonstrates the accuracy of the FIS4 Quadriwave interferometer sensor for laser wave-front metrology.

Furthermore, in the field of aero-optical effect research within high-temperature plasma flow environments, these environments pose extreme challenges for optical measurement techniques. In such settings, high-temperature plasma can cause significant optical distortions, known as aero-optical effects. These effects primarily arise from temperature, pressure, and density gradients within the plasma flow field, leading to wave-front distortions that impact the accuracy of optical measurements. When light rays pass through a high-speed flow field, aero-optical effects can cause target image jitter, blurring, displacement, and energy attenuation. The essence of this phenomenon is the distortion of the light wave wave-front due to flow field disturbances. Therefore, theoretical research and experimental verification of the variation patterns in high-speed flow fields are crucial aspects of aero-optical effect studies.The FIS4 Quadriwave interferometer sensor is an excellent choice for this, as it provides a compact and stable detection optical path. Figure 14 illustrates a schematic of the optical layout for an FIS4 interferometer sensor used in a wind tunnel's high-speed flow field. The Z-axis represents the optical axis direction, and the wind tunnel flow direction is along the X-axis. The test laser beam passes through the wind tunnel window, enters the beam compression system and imaging system, and then proceeds into the FIS4 interferometer sensor to acquire transient flow field information of the high-speed flow.

2.6

Adaptive Optics System Applications

Adaptive Optics (AO) is a technology that compensates for wavefront errors in optical systems in real time. Its core principle involves dynamically adjusting components within the optical system (such as deformable mirrors or liquid crystal spatial light modulators) to alter the shape of the input light's wavefront, thereby enhancing the imaging quality or beam quality of the optical system.AO systems find widespread applications across various fields, including astronomical observation, laser communication, medical imaging, and precision manufacturing. For instance, in astronomical observation, the Earth's atmosphere introduces wavefront aberrations to light propagation, degrading the quality of starlight as it enters telescopes. An AO system can compensate for these wavefront aberrations in real time, improving the observation quality of the telescope. In medical imaging, such as ophthalmic imaging (e.g., Optical Coherence Tomography (OCT)) and biological microscopy, light scattering and refraction within biological tissues lead to wavefront aberrations that affect imaging quality. AO systems can compensate for these aberrations in real time, enhancing imaging resolution and contrast. Furthermore, AO systems are extensively applied in fields like laser weaponry, optical inspection, and optical metrology.Figure 15 illustrates an example optical path for the application of the FIS4 interferometer sensor within an AO system. The light source, which can be visible light or a laser depending on the specific requirement, passes through a beam expansion system and enters a spatial light modulator (or deformable mirror). After reflection, the light then enters the FIS4 interferometer sensor. The sensor acquires wavefront information and feeds this information back to the spatial light modulator. The spatial light modulator makes real-time adjustments, and finally, the ideal wavefront state is projected through an imaging lens into an observation camera, thereby completing the closed-loop control.

Based on the optical path described above, experiments were conducted to demonstrate the application of the FIS4 interferometer sensor combined with a spatial light modulator in an AO system.Figure 16(a) shows a wavefront with a PV of 0.49 μm generated by the spatial light modulator, while Figure 16(b) displays the corresponding result detected by the FIS4 interferometer sensor, showing a PV of 0.498 μm.Figure 17(a) illustrates a coma aberration with an input wavefront PV of 0.98 μm from the spatial light modulator. Figure 17(b) presents the detected coma aberration with a PV of 0.966 μm using the FIS4 interferometer sensor.Finally, Figure 18(a) depicts a spherical aberration with an input wavefront PV of 2.46 μm, which is the inverse of a spherical aberration correction function generated by the spatial light modulator. Figure 18(b) shows the detected spherical aberration with a PV of 2.434 μm, acquired by the FIS4 interferometer sensor.Multiple experiments confirmed that the closed-loop system, comprising the FIS4 interferometer sensor and the spatial light modulator, can effectively realize adaptive optics system applications.

in conclusion

This document comprehensively introduces the principle, development history, wavefront reconstruction methods, and broad applications of Quadriwave Lateral Shearing Interferometry for phase imaging, particularly focusing on its FIS4 interferometer sensor. By comparing different grating designs, such as cross-grating lateral shearing interferometers, modified Hartmann mask technique, and random encoded hybrid gratings, the advantages of random encoded hybrid gratings in eliminating unwanted diffraction orders and improving interferogram quality are highlighted. Furthermore, the two crucial steps of wavefront reconstruction—sheared wavefront extraction and various algorithms for recovering the original wavefront from the sheared wavefront—are elaborated in detail. Finally, the extensive applications of Quadriwave Lateral Shearing Interferometry for phase imaging in fields such as optical component measurement, live cell imaging, super-resolution 3D localization, and thermal imaging are discussed, showcasing its potential as a cross-disciplinary, versatile tool.

The FIS4 interferometer sensor, utilizing Quadriwave Lateral Shearing Interferometry for phase imaging, demonstrates broad application prospects in numerous fields including biomedicine, optical metrology, and material characterization, owing to its unique advantages such as compactness, robustness, high temporal resolution, and compatibility with existing microscopy systems. With continuous improvements in design and optimization of wavefront reconstruction algorithms, Quadriwave Lateral Shearing Interferometry for phase imaging is expected to achieve higher measurement precision and imaging quality in the future, further expanding its application range. Its excellent anti-vibration performance and online detection capability also hold significant potential for wavefront detection in lithography objectives. The development of this technology not only provides new research tools for relevant fields but also opens up new possibilities for interdisciplinary innovation and discovery.

References

"Infrared and Laser Engineering" Journal [Invited Article]: Wavefront Sensing Technology and Applications Based on Quadriwave Lateral Shearing Interferometry

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"Infrared and Laser Engineering" Journal [Invited Article]: Wavefront Sensing Technology and Applications Based on Quadriwave Lateral Shearing Interferometry

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