Phase aberration compensation of digital holographic microscopy based on least squares surface fitting

Digital holographic microscopy allows the numerical reconstruction of the complex wavefront of samples, especially biological samples such as living cells. In digital holographic microscopy, a microscope objective is introduced to improve the transverse resolution of the sample; however a phase aberration in the object wavefront is also brought along, which will affect the phase distribution of the reconstructed image. We propose here a numerical method to compensate for the phase aberration of thin transparent objects with a single hologram. The least squares surface fitting with points number less than the matrix of the original hologram is performed on the unwrapped phase distribution to remove the unwanted wavefront curvature. The proposed method is demonstrated with the samples of the cicada wings and epidermal cells of garlic, and the experimental results are consistent with that of the double exposure method.     

Physical spherical phase compensation in reflection digital holographic microscopy

Reflection configured digital holographic microscopy (DHM) can perform accurate optical topography measurements of reflecting objects, such as MEMs, MOEMs, and semiconductor wafer. It can provide non-destructive quantitative measurements of surface roughness and geometric pattern characterization with nanometric axial resolution in real-time. However, the measurement results may be affected by an additional phase curvature introduced by the microscope objective (MO) used in DHM. It needs to be removed either by numerical compensation or by physical compensation.We present a method of physical spherical phase compensation for reflection DHM in the Michelson configuration. In the object arm, collimated light is used for illumination. Due to the use of the MO, the object wavefront may have a spherical phase curvature. In the reference arm, a lens and mirror combination is used to generate a spherical recording reference wave in order to physically compensate the spherical phase curvature of the object wavefront. By controlling the position of the mirror and the sample stage, the compensation process has been demonstrated. The relative positions of the test specimen and the reference mirror must be fixed for the physical spherical phase to be totally compensated. A numerical plane reference wave is preferred for the numerical reconstruction of the phase introduced by the test specimen. Experimental results on wafer pattern recognition are also given.     

Phase reconstruction in lensless digital in-line holographic microscopy

The phase reconstruction in a digital in-line holographic microscopy is compared using two numerical reconstruction methods. The first method uses one Fourier transform and second one uses three Fourier transforms. It is shown that the latter method gives improved object phase reconstruction as compared to the former.     

Error evaluation for Zernike polynomials fitting based phase compensation of digital holographic microscopy

Combining the experimental research with the simulation calculation, the error evaluation for Zernike polynomials fitting (ZPF) based phase compensation of digital holographic microscopy (DHM) is performed. The obtained results show that the reconstructed phase with high precision can be obtained by ZPF phase compensation algorithm. Moreover, the phase error for ZPF based phase compensation algorithm increases with both the variation of object height and object transverse area, the larger variation of object height, the larger of phase error, and the larger of object transverse area, the faster increase of RMS phase error. To decrease the error of ZPF phase compensation algorithm, it is required to ensure one of the variations of object height and object transverse area to be a small value. Importantly, the proposed method supplies a useful tool for the error evaluation of phase compensation algorithm.     

Disturbance-free digital holographic microscopy via a micro-phase-step approach

This work proposes a cost-effective, simple, micro-phase-step (MPS) method for suppressing the zero-order diffraction and conjugate-image interferences that are caused during digital holographic microscopic image reconstruction. The proposed MPS method replaces the conventional phase modulation approach; it uses a rotatable cover glass that enables smooth modification of the incidence angle and the optical path of the reference beam. This setup allows the phase step to be accurately estimated by shifting the reference wave phase more freely close to π/2, at which the background noise can be suppressed more effectively. In the proposed MPS method, the optimal conditions for suppressing conjugate-image interference are identified using a relatively moderate intensity distribution and suppression of noise in the numerically reconstructed object wave-field. In addition, the proposed method mitigates the effect of disturbances that are caused by environmental factors, such as minor vibrations and small changes in temperature and humidity. Importantly, only two holograms are required to satisfy the objective of image reconstruction. The results in this work reveal that even with intentional interference caused by minor vibrations, conjugate-image interference can still be suppressed by determining the phase deviation between the two original holograms.     

Complex-amplitude-based phase unwrapping method for digital holographic microscopy

A complex-amplitude-based phase unwrapping approach for digital holographic microscopy is proposed in this paper. A quality map is derived directly from the reconstructed complex amplitude distribution of object wave to evaluate noise influence and phase reliability in the wrapped phase image. Quality-guided phase unwrapping algorithm is then implemented with the quality map to retrieve continuous phase profile. Unwrapping errors caused by unreliable phase data are successfully suppressed. The effectiveness of this method is demonstrated with simulation and experimental results.     

Study on the simplified phase-shifting digital holographic microscopy

In this paper, a new simplified technique for effectively eliminating the zero order and the conjugate virtual image in digital holographic microcopy, which makes use of two-step phase-shifting method of just recording two holograms and an intensity image of object wave, is proposed. Meanwhile, combined with the principle of making full use of spatial bandwidth of the CCD sensor by in-line lens-less Fourier holographic recording geometry, the theory and experimental methods to increase the resolution of the reconstructed image in digital holography by using phase-shifting technique are detailedly analyzed. At end, the validity and availability of this technique has been demonstrated through the off-axis and in-line Fourier transform recording geometry. The study provides some theoretical and experimental guidance for the design and operation of a digital holographic microscopy system.     

Reconstruction algorithms applied to in-line Gabor digital holographic microscopy

This paper investigates the application of Fresnel based numerical algorithms for the reconstruction of Gabor in-line holograms. We focus on the two most widely used Fresnel approximation algorithms, the direct method and the angular spectrum method. Both algorithms involve calculating a Fresnel integral, but they accomplish it in fundamentally different ways. The algorithms perform differently for different physical parameters such as distance, CCD pixel size, and so on. We investigate the constraints for the algorithms when applied to in-line Gabor digital holographic microscopy. We show why the algorithms fail in some instances and how to alter them in order to obtain useful images of the microscopic specimen. We verify the altered algorithms using an optically captured digital hologram.     

Internal inspection of semi-transparent objects by digital holographic micro-tomography

The combined use of digital holographic microscopy and computer tomography, here named digital holographic micro-tomography, is used to examine the interior of transparent channels. The proposed method is used to identify internal obstacles inside of transparent troughs having slightly different refractive index. The method is based in the acquisition of a set of digital holograms of the specimen whereas it is axially rotated from 0° to 180°. The phase differences retrieved from the obtained holograms are the inputs to a computerised axial tomography procedure. The technique has been numerically modelled in order to find the optimal tomographic conditions and also to realise the minimum difference of refractive index the method could detect. The obtained results show the feasibility of the proposed method for the non-destructive evaluation of transparent micro-objects.     

基于涡旋光照明的暗场数字全息显微方法研究

提出了一种基于涡旋光照明的暗场数字全息显微方法. 从理论上阐述了涡旋光环形照明原理和暗场数字全息显微原理, 分析了涡旋光的准无衍射特性对成像的影响; 搭建了相应的数字全息显微成像系统, 采用690 nm的聚苯乙烯小球作为实验样品; 最后通过对小球明暗场下数字全息显微再现像的分析对比, 证明该方法可以有效地提高数字全息系统的分辨率, 同时增强了再现像的对比度. 关键词： 全息 暗场数字全息显微 涡旋光 分辨率     

Rough surface characterization using off-axis digital holographic microscopy compensated with self-hologram rotation

In this paper, an off-axis digital holographic microscopy compensated with self-hologram rotation is presented. The process is implemented via subtracting the unwrapped phase maps of the off-axis parabolic hologram and its rotation 180° to eliminate the tilt induced by the angle between the spherical object wave O and the plane reference wave R. Merit of the proposed method is that it can be done without prior knowledge of physical parameters and hence can reconstruct a parabolic hologram of 1024 × 768 pixels within tens of milliseconds since it doesn't require a digital reference wave. The method is applied to characterize rough gold bumps and the obtained results were compared with those extracted from the conventional reconstruction method. The comparison showed that the proposed method can characterize rough surfaces with excellent contrast and in real-time. Merit of the proposed method is that it can be used for monitoring smaller biological cells and micro-fluidic devices.     

High resolution digital holographic microscopy for the study of aggregated natural cellulose nanowhisker fibers

In this paper, digital holographic (DH) microscopy demonstrates its ability to perform a full characterization of nanofibers. The high resolution and magnification of the presented method to study the nanofibers are tested using standard MIL-STD-150A 1951 USAF resolution test target. In this investigation, aggregated natural cellulose nanowhisker fibers are positioned in the front of the microscopic objective using a 3D translation stage in the object arm of DH setup. The recorded off-axis holograms are refocused using the angular spectrum method. The reconstructed complex field is used to calculate optical phase and intensity distributions of the object at different reconstruction depths. A simple algorithm is used to define the focused image with suitable accuracy. The dimensions and orientation of the fibers can be evaluated from the optical field at different depths. Then, the shape and textures along the aggregated natural cellulose nanowhisker fiber can be presented in a 3D space.     

数字全息显微像平面相位畸变的自动补偿研究

对离轴数字全息显微相位畸变的自动补偿进行了理论和实验研究。首先对由CCD记录的数字全息图采用平均梯度自聚焦方法确定最佳再现距离,然后将修正的虚拟参考光作用于切趾滤波后的全息图进行数字再现,经像平面相位自动补偿后得到无畸变的物体相位分布。该方法仅需记录一幅离轴数字全息图就可以自动快速地重建物体的真实相位信息。     

Common-path phase-shifting digital holographic microscopy: A way to quantitative phase imaging and superresolution

We present an experimental setup useful for complex amplitude evaluation and phase image quantification of three-dimensional (3-D) samples in digital holographic microscopy (DHM). It is based on a common-path interferometric configuration performed by dividing the input plane in two contiguous regions and by placing a translation grating near to the Fourier plane. Then, complex amplitude distribution of the sample under test is recovered with phase-shifting standard method obtained by moving the grating using a linear motion stage. Some experimental results of an USAF resolution test are presented for different numerical aperture (NA) microscope lenses. In a second part, the proposed setup is tested under superresolution purposes. Based on the object’s spectrum shift produced by off-axis illumination, we use time multiplexing to generate a synthetic aperture enlargement that improves the final image resolution. Experimental results for the case of a biosample (human red blood cells) and a commercial low NA microscope lens validates the suggested superresolution approach.     

Characterisation of light emitting diodes (LEDs) for application in digital holographic microscopy for inspection of micro and nanostructured surfaces

Partial coherent light sources open up prospects for phase noise reduction in digital holographically reconstructed phase distributions by suppressing multiple reflections in the experimental setup. Thus, light emitting diodes (LEDs) are investigated for application in digital holographic microscopy. First, the spectral properties and the resulting coherence length of an LED are characterised. In addition, an analysis of dispersion effects and their influence on the hologram formation is carried out. The coherence length of LEDs in the range of a few micrometers restricts the maximum interference fringe number in off-axis holography for spatial phase shifting. Thus, the application of temporal phase-shifting-based digital holographic reconstruction techniques is compared to spatial phase-shifting-based methods. It is demonstrated that LEDs are applicable for digital holographic microscopy in connection with both spatial and temporal phase-shifting-based techniques for reduction of noise in comparison to a laser-light-based experimental setup.     

数字显微全息中记录参数对颗粒测量影响的数值模拟

数字显微全息技术由于具有三维、非接触和实时测量微小空间内流场的能力, 已引起了国内外学者的广泛关注. 利用数字显微全息方法测量微通道流场时, 记录距离、颗粒尺寸、颗粒浓度、入射光波长、CCD分辨率等参数会对颗粒重建结果产生重要影响. 为了评估颗粒浓度和样本空间深度对重建结果的影响, 本文开展了数值模拟研究. 采用基于洛伦兹-米散射理论的程序产生不同浓度的颗粒全息图, 用小波变换重建算法对其进行重建. 结果表明: 在样本空间深度为24 μm 时, 颗粒浓度n_s在3.44×10⁵ mm^-3–13.77×10⁵ mm^-3 范围内时, 颗粒重建率E_p随着颗粒浓度n_s 的增大而迅速减小, 在13.77×10⁵ mm^-3–55.08×10⁵ mm^-3范围内时, 颗粒重建率E_p 随颗粒浓度n_s增大而缓慢减少. 在颗粒浓度n_s (13.77×10⁵ mm^-3) 保持不变时, 颗粒重建率E_p与样本空间深度满足单调递减的线性关系. 当阴影密度不变时, 重建率的变化呈现一定的规律性:当深度L较小时, 样本空间深度对颗粒重建的影响要比颗粒浓度的影响大; 当深度L较大时, 颗粒浓度对颗粒重建的影响较大. 关键词： 数字显微全息 颗粒浓度 粒径误差 位置误差     

Advances in digital holographic micro-PTV for analyzing microscale flows

The accurate three-dimensional (3D) velocity field measurement technique has been receiving large attention in the study of microfluidics. DHM-PTV technique was developed by combining the digital holographic microscopy and particle tracking velocimetry technique. DHM-PTV is an ideal method for measuring three-component-three-dimensional (3C-3D) velocity field in a microscale flow with a fairly good spatial resolution. The advances in the DHM-PTV technique enable the measurement of various microscale flows, such as transport of red blood cells in a microtube and 3D flows in microfluidic devices. DHM-PTV is also applied in studying the motile behavior of swimming microorganisms. DHM-PTV would play an important role in ascertaining the undiscovered basic physics in various microscale and biofluid flow phenomena. In the current study, the basic principle of the DHM-PTV technique and its typical applications to microscale flows are introduced and discussed.     

Accuracy improvement in digital holographic microtomography by multiple numerical reconstructions

In this paper, we describe a method to improve the accuracy in digital holographic microtomography (DHMT) for measurement of thick samples. Two key factors impairing the accuracy, the deficiency of depth of focus and the rotational error, are considered and addressed simultaneously. The hologram is propagated to a series of distances by multiple numerical reconstructions so as to extend the depth of focus. The correction of the rotational error, implemented by numerical refocusing and image realigning, is merged into the computational process. The method is validated by tomographic results of a four-core optical fiber and a large mode optical crystal fiber. A sample as thick as 258 μm is accurately reconstructed and the quantitative three-dimensional distribution of refractive index is demonstrated.     

Dynamic measurement by digital holographic interferometry based on complex phasor method

In this paper, complex phasor (CP) method is employed in digital holographic interferometry. Unlike commonly used digital phase subtraction (DPS), the proposed technique processes a CP instead of phase. It is shown that the results obtained by directly filtering the phase produce large errors. It is demonstrated that the phase is not a signal but rather a property of a signal. In addition, the results obtained by the CP method are also compared with those obtained by conventional sine/cosine transformation method.     

An experimental investigation of three-dimensional particle aggregation using digital holographic microscopy

The tendency of particles to aggregate depends on particle-particle and particle-fluid interactions. These interactions can be characterized but it requires accurate 3D measurements of particle distributions. We introduce the application of an off-axis digital holographic microscopy for measuring distributions of dense micrometer (2 μm) particles in a liquid solution. We demonstrate that digital holographic microscopy is capable of recording the instantaneous 3D position of particles in a flow volume. A new reconstruction method that aids identification of particle images was used in this work. About 62% of the expected number of particles within the interrogated flow volume was detected. Based on the 3D position of individual particles, the tendency of particle to aggregate is investigated. Results show that relatively few particles (around 5–10 of a cohort of 1500) were aggregates. This number did not change significantly with time.