Solving inverse scattering problems in biological samples by quantitative phase imaging

Quantitative phase imaging (QPI), a method that precisely recovers the wavefront of an electromagnetic field scattered by a transparent, weakly scattering object, is a rapidly growing field of study. By solving the inverse scattering problem, the structure of the scattering object can be reconstructed from QPI data. In the past decade, 3D optical tomographic reconstruction methods based on QPI techniques to solve inverse scattering problems have made significant progress. In this review, we highlight a number of these advances and developments. In particular, we cover in depth Fourier transform light scattering (FTLS), optical diffraction tomography (ODT), and white‐light diffraction tomography (WDT).

     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination

We developed an off-axis quantitative phase microscopy that works for a light source with an extremely short spatial coherence length in order to reduce the diffraction noise and enhance the spatial resolution. A dynamic speckle wave whose coherence length is 440 nm was used as an illumination source. To implement an off-axis interferometry for a source of low spatial coherence, a diffraction grating was inserted in the reference beam path. In doing so, an oblique illumination was generated without rotation of the wavefront, which leads to a full-field and single-shot phase recording with improved phase sensitivity of more than a factor of 10 in comparison with coherent illumination. The spatial resolution, both laterally and axially, and the depth selectivity are significantly enhanced due to the wide angular spectrum of the speckle wave. We applied our method to image the dynamics of small intracellular particles in live biological cells. With enhanced phase sensitivity and speed, the proposed method will serve as a useful tool to study the dynamics of biological specimens.     

Full-field measurement of the phase retardation for birefringent elements by using common path heterodyne interferometry

A collimated heterodyne light passes through the tested material and an analyzer, full-field interference signals are taken by a fast CMOS camera. The series of interference intensities recorded at any pixel are the sampling points of a sinusoidal signal. From those points, the associated argument of that pixel can be derived by a least-square sine fitting algorithm on IEEE 1241 Standards. Subtracting the average argument of the reference signal, the phase retardation of that pixel can be obtained. The phase retardations of other pixels can be obtained similarly. Its validity is demonstrated.     

Testing micro devices with fringe projection and white-light interferometry

Optical sensors are very suitable for the analysis of microscopic structures and micro devices. We compare two very promising methods: the white-light interferometry and the fringe projection technique for the application to this task. The fringe projection is very useful for fast measurement of objects with vertical dimensions of some μm. White-light interferometry is especially useful for highly resolved 3-D measurements. Furthermore, we present a new technique, the scanning fringe projection (SFP), which enables absolute 3-D measurements with one single grating period.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

基于相位相关的亚像素配准技术及其在电子稳像中的应用

介绍一种基于相位相关的图像配准方法,并将该方法应用于序列图像的运动检测,通过运动补偿,实现了序列图像的稳定输出。采用相位相关配准方法对序列图像进行亚像素精度配准,运用基于最小二乘的曲面拟合法,估计当前图像相对参考图像的亚像素级的平移量。在补偿图像运动时,为保证亚像素级的补偿精度,采用平滑算法,避免在图像补偿时出现马赛克现象。最后,对样本图像进行了亚像素级位移配准和图像补偿对比实验。实验结果表明,提出的方法可以检测到0．01pixel的运动量,最大配准误差为0．008pixel;采用亚像素级运动量补偿图像,最大误差〈0．5。     

Subsurface imaging by dual-medium quantitative phase measurement

Quantitative phase imaging by itself allows for direct surface imaging of the transparent homogeneous sample, but it is very difficult or impossible for the inhomogeneous sample by itself due to the surface morphology and subsurface information are coupled. We hereby propose a simple method which obtains quantitative phase data and the physical thickness of sample by dual-medium quantitative phase measurement (DMQ) to extract subsurface sample information without the need of any exogenous dyes and any scan process. By using simulation technology, the feasibility of this method is demonstrated with subsurface imaging of a two-sphere model and a simulated monocyte.     

Digital phase shift holographic interferometry and its application in the experimental flow study

The application of digital phase shift holographic interferometry to flow-visualization and flow temperature measurement of a 2D thermal flow field was experimentally investigated. An improved recording system for two reference beam phase shift holographic interferometry is set up for this experiment, and details of this experimental technique are described. The phase distribution obtained by this technique presents an excellent picture of flow visualization. From this phase image, temperature distribution of the 2D thermal flow field is also calculated and compared with some measured values obtained using thermocouple probes.     

移相干涉测量术及其应用

为了对移相式数字干涉仪在光学元件测量中的应用有全面了解，介绍了移相干涉术的基本原理。结合激光数字波面干涉仪，阐述移相干涉术的四步重叠平均算法、压电晶体移相器(PZT)的结构、3 PZT的组合方法、移相器的标定误差和非线性误差的校正方法、波面相位解包的自适应种子算法、波面相位的评价指标等内容。结合移相数字波面干涉仪，叙述了移相干涉测量技术在普通光学元件、红外光学元件、大口径光学元件、非球面光学元件等测量中的应用并指出了应用过程中的注意事项。最后明确指出光干涉技术正沿着高相位分辨率、高空间分辨率、宽波段和瞬态高速测量的方向发展，并将会在瞬态波前测量、微机械的微结构动态分析等方面有着越来越广泛的应用。     

飞秒钛宝石放大激光脉冲的载波包络相位测量与控制

通过对重复频率为1 kHz的放大飞秒激光脉冲的光谱干涉实验,结合傅里叶变换进行了载波包络相位漂移的实验研究.在此基础上利用锁相环反馈控制技术实现了对载波包络相位的精密锁定,锁定后的激光脉冲稳态相位均方根误差小于80mrad,锁定时间超过3h.同时在理论上分析了光谱干涉测量放大激光脉冲载波包络相位的原理,给出了光谱干涉信号与载波包络相位的关系. 关键词： 飞秒钛宝石放大器 载波包络相位 光谱干涉 超连续     

High-resolution quantitative phase microscopic imaging in deep UV with phase retrieval

High-resolution three-dimensional (3D) microscopic imaging requires the use of short wavelengths. Quantitative 3D imaging techniques, such as digital holographic microscopy, require interference between the object beam and a known reference background for the extraction of phase information. At shorter wavelengths, due to short coherence lengths, it may be difficult to implement a two-beam off-axis setup. Thus, a single-beam technique, which provides complete phase information, may be better suited for short wavelengths. This Letter describes the development of a quantitative microscopy technique at 193 nm using multiple intensity samplings and phase retrieval.     

New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor

White-light phase shifting interferometry (WLPSI) is frequently used for the precision measurement of 3D patterns in various fields. Phase error is one of the most dominant errors in WLPSI, and it is mainly generated by the scanner positioning error and mechanical vibrations. In this paper, phase error detection method by image analysis is proposed, and the numerical correction method for minimizing the phase error is also proposed. The image reconstruction method (IRM), iterative IRM (IIRM) as pre-processors, partial IRM (PIRM), least squares method (LSM) as a main processor, and surface compensation method (SCM) as a post-processor were developed for correcting phase errors. The five methods are implemented and simulated, and the pros and cons of each method are explained.Mirau type interferometry and the phase error generator using a PZT stage were used, and the measurements by WLPSI were done under various vibration conditions. The captured images were analyzed by the five correction methods, and the results were compared. Phase error was effectively minimized by the correction methods, and repeatability of 0.2 nm was obtained in the case of the specimen of 500 nm in height. Repeatability of 10 nm was obtained by conventional WLPSI algorithms for the same specimen.     

Real-time quantitative phase imaging with a spatial phase-shifting algorithm

This Letter reports on the use of a spatial phase-shifting algorithm in a fast, straightforward method of real-time quantitative phase imaging. The computation time for phase extraction is five times faster than a Fourier transform and twice as fast as a Hilbert transform. The fact that the phase extraction from an interferogram of 512 × 512 pixels takes less than 8.93 ms with a typical desktop computer suggests the proposed method can be readily applied to high-speed dynamic quantitative phase imaging. The proposed method of quantitative phase imaging is effective and sufficiently general for application to the dynamic phenomena of biological samples.     

Broadly tunable UV-blue picosecond pulsed laser and its application for biological imaging

We have achieved a rapid and random wavelength tuned picosecond pulsed laser and a widely tunable UV-blue picosecond pulsed laser by using the intracavity second harmonic generation of the laser. The tuning range was from 384 to 434 nm with picosecond pulse oscillation. In addition, we demonstrated biological imaging using a fluorescent protein excited by the widely tunable UV-blue picosecond pulsed laser. We found that the laser is suitable for biological imaging using the fluorescent protein as an excitation light source without damages.     

Modulation analysis in spatial phase shifting electronic speckle pattern interferometry and application for automated data selection on biological specimens

In electronic speckle pattern interferometry (ESPI), for a fast and objective analysis of measurement data which occur with a high repetition rate, an automated data processing is of particular advantage. For this reason, investigations were carried out to determine if the modulation of speckle interferograms can be applied as a quality parameter for the selection of suitable interferogram data for further evaluation e.g. phase unwrapping when spatial phase shifting (SPS) is performed. Six methods for determining the modulation of speckle interferograms are characterised and compared. The applicability of the speckle interferogram modulation as a parameter for mask generation in the unwrapping process of the phase difference is demonstrated by the evaluation of measurement data obtained from experiments with a spatial phase shifting endoscopic ESPI system on a technical surface and on a human gastrectomy specimen.     

The neutron spin phase imaging technique applied to dia- and paramagnetic samples

We report on a novel application of the Neutron Spin Phase Imaging technique, by performing polarised neutron radiography on dia- and paramagnetic samples. In order to achieve the necessary sensitivity we employed a 2.5 T Ramsey apparatus which was used in a previous experiment to measure the spin-dependent neutron scattering length of the deuteron. First successful results on aluminium, lead, titanium and heavy water (D₂O) samples are presented. They are in good quantitative agreement with expected values deduced from susceptibility measurements.     

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.     

Label-free second-harmonic phase imaging of biological specimen by digital holographic microscopy

We have previously developed a new way for nonscanning second-harmonic generation (SHG) microscopy [Opt. Lett. 34, 2450 (2009)]. Based on digital holography, this technique captures, in single-shot hologram acquisition, both the amplitude and the phase of a coherent SHG radiation, which makes possible second harmonic phase microscopy. In this work, we present holographic SHG phase microscopy of a label-free biological tissue and discuss its added value to SHG microscopy.