Quantitative phase retrieval in X‐ray Zernike phase contrast microscopy

In recent years, increasing attention has been devoted to X‐ray phase contrast imaging, since it can provide high‐contrast images by using phase variations. Among the different existing techniques, Zernike phase contrast microscopy is one of the most popular phase‐sensitive techniques for investigating the fine structure of the sample at high spatial resolution. In X‐ray Zernike phase contrast microscopy, the image contrast is indeed a mixture of absorption and phase contrast. Therefore, this technique just provides qualitative information on the object, which makes the interpretation of the image difficult. In this contribution, an approach is proposed for quantitative phase retrieval in X‐ray Zernike phase contrast microscopy. By shifting the phase of the direct light by π/2 and 3π/2, two images of the same object are measured successively. The phase information of the object can then be quantitatively retrieved by a proper combination of the measured images. Numerical experiments were carried out and the results confirmed the feasibility of the proposed method. It is expected that the proposed method will find widespread applications in biology, materials science and so on.     

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

A multiple-image encryption method is proposed that is based on row scanning compressive ghost imaging, (t, n) threshold secret sharing, and phase retrieval in the Fresnel domain. In the encryption process, after wavelet transform and Arnold transform of the target image, the ciphertext matrix can be first detected using a bucket detector. Based on a (t, n) threshold secret sharing algorithm, the measurement key used in the row scanning compressive ghost imaging can be decomposed and shared into two pairs of sub-keys, which are then reconstructed using two phase-only mask (POM) keys with fixed pixel values, placed in the input plane and transform plane 2 of the phase retrieval scheme, respectively; and the other POM key in the transform plane 1 can be generated and updated by the iterative encoding of each plaintext image. In each iteration, the target image acts as the input amplitude constraint in the input plane. During decryption, each plaintext image possessing all the correct keys can be successfully decrypted by measurement key regeneration, compression algorithm reconstruction, inverse wavelet transformation, and Fresnel transformation. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.     

近场X射线位相衬度成像及位相恢复算法

理论分析了X射线衍射位相成像和近场位相恢复算法。定义了一个最佳成像距离，给出了基于最佳成像距离和特征空间频率的衍射场光强分布新的表达形式。基于模拟位相物体给出了数值模拟结果。由此得出了探测距离和多色辐照对相衬图像和位相恢复结果的影响。本文给出的结果将对同轴x射线相衬成像实验具有一定的指导作用。     

Image encryption using fractional Mellin transform,structured phase filters,and phase retrieval

An image encryption scheme has been presented by using two structured phase masks in the fractional Mellin transform (FrMT) plane of a system, employing a phase retrieval technique. Since FrMT is a non-linear integral transform, its use enhances the system security. We also add further security features by carrying out spatial filtering in the frequency domain by using a combination of two phase masks: a toroidal zone plate (TZP) and a radial Hilbert mask (RHM). These masks together increase the key space making the system more secure. The phase key used in decryption has been obtained by applying an iterative phase retrieval algorithm based on the fractional Fourier transform. The algorithm uses amplitude constraints of secret target image and the ciphertext (encrypted image) obtained from multiplication of fractional Mellin transformed arbitrary input image and the two phase masks (TZP and RHM). The proposed encryption scheme has been validated for a few grayscale images, by numerical simulations. The efficacy of the scheme has been evaluated by computing mean-squared-error (MSE) between the secret target image and the decrypted image. The sensitivity analysis of the decryption process to variations in various encryption parameters has also been carried out.     

Full field deformation measurement of centimeter sized objects using optical phase retrieval

Most papers in the field of optical phase retrieval either consider only the intensity (or amplitude) profile of the object under inspection (or scatterer location in the X-ray version), or a uniform tilt/rotation of the object beam. However, phase retrieval is able to recover the phase profile of the object (beam) as well, which theoretically makes the observable interference of phase retrieved object waves possible. In this paper we demonstrate this principle experimentally on centimeter sized deformable reflective objects (as large as 40 mm by 40 mm) and corresponding simulations are also presented. When the CCD camera is moved along the optical axis in the Fresnel region, the interference fringes of the displacement field have low contrast. On the other hand, when an imaging setup is built, and the camera moves near the image plane, high fringe contrast can be obtained. These fringes however suffer from some phase error. In our work the iterative modulus projection algorithm was used as a simply implementable phase retrieval method.     

高阶光学强度相干成像的相位恢复方法改进

为了提高强度相干方法对空间目标的成像质量,避免复杂的相位估计过程及其引入的额外误差,对高阶强度相干的相位恢复方法进行了改进.在对高阶强度相干相位测量信噪比定量讨论的基础上,选择三阶强度相干方法对远场目标测量过程进行仿真,针对相位解算过程中频谱模值传递噪声放大等问题,根据相位估计与相位测量结合的思路,提出了相位闭合正则项改进算法.通过室内强度相干成像实验,比较改进算法与最速下降法、先验信息迭代方法对相同测量结果的图像恢复效果.实验结果表明,改进算法得到的图像误差值低于原有方法,较为有效地提高了成像质量.     

An improved phase retrieval algorithm for optical aspheric surface measurement

In order to overcome the measurement and calculation difficulty for aspheric surface with phase retrieval technology, an improved phase retrieval algorithm was proposed. Due to significant departure from sphere surface, reflected light from different part of the aspheric surface under test will overlap in some areas in the collected images by CCD with general phase retrieval measurement setup, which will lead to the failure to recover the surface phase. The proposed algorithm will only use those areas without light overlapping in each image in the iteration process and employ several defocused images to recover the whole surface. This algorithm can improve the measurement range for aspheric surface with phase retrieval technology. The experimental system was established and a 180 mm diameter, f/1.6 parabolic mirror and a 180 mm effective diameter, f/1.33 hyperboloid mirror were tested by the proposed method. The experimental results show that the retrieved surface errors are in good consistent with that obtained by interferometer, which confirms the validity of the proposed algorithm.     

位相恢复法与X射线激光等离子体密度诊断

 详细介绍了XUV波段Gabor全息及位相恢复法去除Gabor全息孪生像的全部过程,分析了X射线激光Gabor全息术对等离子体和实验条件的要求,编程对全息图的制作、反演以及位相恢复法的全过程进行了模拟,并对三个模型进行了计算比较。     

A review of iterative phase retrieval for measurement and encryption

Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed.     

Iterative phase retrieval without support

An iterative phase retrieval method for nonperiodic objects has been developed from the charge-flipping algorithm proposed in crystallography. A combination of the hybrid input-output (HIO) algorithm and the flipping algorithm has greatly improved performance. In this combined algorithm the flipping algorithm serves to find the support (object boundary) dynamically, and the HIO part improves convergence and moves the algorithm out of local minima. It starts with a single intensity measurement in the Fourier domain and does not require a priori knowledge of the support in the image domain. This method is suitable for general image recovery from oversampled diffuse elastic x-ray and electron-diffraction intensities. The relationship between this algorithm and the output-output algorithm is elucidated.     

Infrared super-resolution imaging based on compressed sensing

The theoretical basis of traditional infrared super-resolution imaging method is Nyquist sampling theorem. The reconstruction premise is that the relative positions of the infrared objects in the low-resolution image sequences should keep fixed and the image restoration means is the inverse operation of ill-posed issues without fixed rules. The super-resolution reconstruction ability of the infrared image, algorithm’s application area and stability of reconstruction algorithm are limited. To this end, we proposed super-resolution reconstruction method based on compressed sensing in this paper. In the method, we selected Toeplitz matrix as the measurement matrix and realized it by phase mask method. We researched complementary matching pursuit algorithm and selected it as the recovery algorithm. In order to adapt to the moving target and decrease imaging time, we take use of area infrared focal plane array to acquire multiple measurements at one time. Theoretically, the method breaks though Nyquist sampling theorem and can greatly improve the spatial resolution of the infrared image. The last image contrast and experiment data indicate that our method is effective in improving resolution of infrared images and is superior than some traditional super-resolution imaging method. The compressed sensing super-resolution method is expected to have a wide application prospect.     

Image watermarking by using phase retrieval algorithm in gyrator transform domain

We propose an image watermarking scheme based on the phase retrieval algorithm in gyrator domain. The watermark is converted into a noise-like image by Arnold transform. The scrambled image is regarded as the amplitude of gyrator spectrum. The Gerchberg-Saxton algorithm is employed to obtain the unknown phase function in gyrator pair, in which the host image is the amplitude of input function. The phase information and the parameters of the two transforms serve as the key of watermarking algorithm. The numerical simulation has demonstrated the performance of the proposed algorithm.     

Asymmetric multiple-image hiding using phase retrieval technique based on amplitude- and phase-truncation in fractional Fourier domain

We propose a multiple-image hiding scheme based on the amplitude- and phase-truncation approach, and phase retrieval iterative algorithm in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys. Multiple input images multiplied with random phase masks are independently fractional Fourier transformed with different orders. The individual keys and common keys are generated by using phase and amplitude truncation of fractional spectrum. After using two fractional Fourier transform, the resultant encrypted image is hided in a host image with phase retrieval iterative algorithm. Using the correct universal keys, individual keys, and fractional orders, one can recover the original image successfully. Computer simulation results with four gray-scale images support the proposed method. To measure the validity of the scheme, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and generation of decryption keys are complicated and should be realized using computer. For decryption, an optoelectronic setup has been suggested.     

Full‐field X‐ray reflection microscopy of epitaxial thin‐films

Novel X‐ray imaging of structural domains in a ferroelectric epitaxial thin film using diffraction contrast is presented. The full‐field hard X‐ray microscope uses the surface scattering signal, in a reflectivity or diffraction experiment, to spatially resolve the local structure with 70 nm lateral spatial resolution and sub‐nanometer height sensitivity. Sub‐second X‐ray exposures can be used to acquire a 14 µm × 14 µm image with an effective pixel size of 20 nm on the sample. The optical configuration and various engineering considerations that are necessary to achieve optimal imaging resolution and contrast in this type of microscopy are discussed.     

Feasibility study of propagation‐based phase‐contrast X‐ray lung imaging on the Imaging and Medical beamline at the Australian Synchrotron

Propagation‐based phase‐contrast X‐ray imaging (PB‐PCXI) using synchrotron radiation has achieved high‐resolution imaging of the lungs of small animals both in real time and in vivo. Current studies are applying such imaging techniques to lung disease models to aid in diagnosis and treatment development. At the Australian Synchrotron, the Imaging and Medical beamline (IMBL) is well equipped for PB‐PCXI, combining high flux and coherence with a beam size sufficient to image large animals, such as sheep, due to a wiggler source and source‐to‐sample distances of over 137 m. This study aimed to measure the capabilities of PB‐PCXI on IMBL for imaging small animal lungs to study lung disease. The feasibility of combining this technique with computed tomography for three‐dimensional imaging and X‐ray velocimetry for studies of airflow and non‐invasive lung function testing was also investigated. Detailed analysis of the role of the effective source size and sample‐to‐detector distance on lung image contrast was undertaken as well as phase retrieval for sample volume analysis. Results showed that PB‐PCXI of lung phantoms and mouse lungs produced high‐contrast images, with successful computed tomography and velocimetry also being carried out, suggesting that live animal lung imaging will also be feasible at the IMBL.     

Simulation study of phase retrieval for hard X-ray in-line phase contrast imaging

X-ray phase contrast imaging (XPCI) is a novel method that exploits the phase shift for the incident X-ray to form an image. For light elements such as carbon, hydrogen and oxygen, the phase-shift term can be up to 1000 times greater than the absorption term in the hard X-ray energy region. So XPCI has attracted much attention in recent years. Various methods for XPCI have been proposed and demonstrated on synchrotron devices and other X-ray sources[1―13], particularly the in-line metho…     

Retrieval of the atomic displacements in the crystal from the coherent X‐ray diffraction pattern

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)‐space image reconstructed from the strained crystal's coherent X‐ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first‐ and second‐order spatial displacement derivatives improves convergence of the iterative phase‐retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.     

Performance analysis of quantitative phase retrieval method in Zernike phase contrast X-ray microscopy

Since the invention of Zernike phase contrast method in 1930,it has been widely used in optical microscopy and more recently in X-ray microscopy.Considering the image contrast is a mixture of absorption and phase information,we recently have proposed and demonstrated a method for quantitative phase retrieval in Zernike phase contrast X-ray microscopy.In this contribution,we analyze the performance of this method at different photon energies.Intensity images of PMMA samples are simulated at 2.5 keV and 6.2 keV,respectively,and phase retrieval is performed using the proposed method.The results demonstrate that the proposed phase retrieval method is applicable over a wide energy range.For weakly absorbing features,the optimal photon energy is 2.5 keV,from the point of view of image contrast and accuracy of phase retrieval.On the other hand,in the case of strong absorption objects,a higher photon energy is preferred to reduce the error of phase retrieval.These results can be used as guidelines to perform quantitative phase retrieval in Zernike phase contrast X-ray microscopy with the proposed method.     

A method for calibrating the position error of phase retrieval with transverse translation diversity in optical wavefront measurement

We present a method for calibrating the position error of phase retrieval with transverse translation diversity in optical wavefront in situation where the position error sharply influences algorithm precision. This method involves testifying that the essence of the position error in phase retrieval is the translation in frequency domain and the minimum of iterative error against position error reaches when there is no position error. Then the least square method is used for fitting the relationship between the iterative error and the assumed position error in polynomial function. The computer simulations used to prove the validity of this method are described. The results indicated that this method can calibrate the position error to approximately 1/500 mm which nearly has no influence on the phase retrieval.     

免分析光栅一次曝光相位衬度成像方法

X射线光栅微分相位衬度成像技术可以观察到常规吸收衬度成像难以分辨的弱吸收物质的精细结构信息,因而在医学、材料学等研究领域具有巨大的应用前景.但传统的X射线光栅微分相位衬度成像技术由于采用分析光栅作为空间滤波器,需要采用相位步进法扫描分析光栅来获得样品的多张投影图像才能够分离出样品的吸收、折射和散射信息,因此存在样品曝光时间长、辐射剂量高以及X射线光通量利用率低等问题,限制了其在各个学科领域的应用研究.为克服上述问题,本文提出一种基于免分析光栅相位衬度成像系统的一次曝光样品信息提取算法.该算法只需要利用一块相位光栅,进而采用高分辨探测器进行样品投影数据的一次采集即可提取样品的吸收、折射和散射信息.理论和模拟研究结果表明:与传统相位步进法相比,该算法具有样品信息提取精度高,且不受光栅的自成像周期需为探测器像素尺寸的整数倍条件的限制.此外,该算法还能够有效地减少对生物样品的辐射损伤,因此在生物医学成像等研究领域中具有广泛的应用前景.