Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm

We propose an iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution. The new technique requires an aperture that is scanned to two or more positions over the object wave function. A simple implementation of the method is modeled and demonstrated, showing how the algorithm uses overlapping data in real space to resolve ambiguities in the solution. The technique opens up the possibility of practical transmission lensless microscopy at subatomic resolution using electrons, x rays, or nuclear particles.     

从电子显微镜的象面和衍射面强度复原相位的计算实例

高分辨率电子显微学中相位复原问题是一个重要问题。本文的计算表明,对于振幅为常数或线性函数,相位为抛物型、正弦型或指数型的波函数,可以采用Gerchberg-Saxton迭代算法从已知的象面和衍射面上的强度分布来唯一地和精确地复原真实的相位。我们编制了计算机程序,对于给定的象面波函数,采用离散的快速傅里叶算法,可以计算其衍射面的波函数。输入数值在-π,+π间的初始相位后,按照G-S迭代算法,利用本程序可以复原相位。文中详细给出了若干个计算实例。所得的相位迭代解对于1弧度的初始相位扰动是稳定的。 关键词：     

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.     

Hard X ray holographic diffraction imaging

We determine the absolute electron density of a lithographically grown nanostructure with 25 nm resolution by combining hard x-ray Fourier transform holography with iterative phase retrieval methods. While holography immediately reveals an unambiguous image of the object, we deploy in addition iterative phase retrieval algorithms for pushing the resolution close to the diffraction limit. The use of hard (8 keV) x rays eliminates practically all constraints on sample environment and enables a destruction-free investigation of relatively thick or buried samples, making holographic diffraction imaging a very attractive tool for materials science. We note that the technique is ideally suited for subpicosecond imaging that will become possible with the emerging hard x-ray free-electron lasers.     

Phase diversity imaging through atmospheric turbulence

A method of phase diversity imaging is applied to reconstruct an overly extended object from stellar speckle images. The reconstruction algorithm is based on the iterative blind deconvolution method and the Gerchberg-Saxon phase retrieval procedure. Computer simulations for reconstructing solar granulations are conducted. The simulation results exhibit the effectiveness of the phase diversity method for high-resolution solar imaging.     

On-line beam diagnostics based on single-shot beam splitting phase retrieval

We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through a weakly scattering phase plate with a known structure; the exiting beams propagate along their original direction and form an array of diffraction patterns on the detector plane. By applying the intensity of diffraction patterns into an iterative algorithm and calculating between the grating plane, weakly scattering plane, and detector plane, the complex field of the incident beam can be reconstructed rapidly; the feasibility of this method is verified experimentally with wavelengths of 1053 and 632.8 nm.     

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.     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

Digital holography from shadowgraphic phase estimates

We show experimentally that the recently proposed iterative shadowgraphic method can be applied to in-line digital holography, provided a suitable regularization step is introduced. We show that the method correctly solves the "twin-image" problem using just two samples of the intensity field scattered by a phase object. Field retrieval accuracy is significantly improved when compared to a reconstruction obtained with the defocusing variation algorithms.     

Evolving FROGS: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms

We present a new technique based on genetic algorithms for retrieving the electric field and the phase of ultrashort pulses from frequency-resolved optical gating (FROG) traces. We have successfully applied a very basic genetic algorithm to the two most common beam geometries: polarization gate and second-harmonic generation (SHG). In the case of SHG FROG, the genetic algorithm returns a lower error than the standard iterative composite algorithm.     

Integrated diffractive optical mode converter for fiber-to-waveguide coupling

An integrated diffractive optical mode converter, which can be integrated into planar lightwave circuits (PLCs), consisting of a diffractive optical element (DOE) and a slab waveguide is presented for fiber-to-waveguide coupling. The DOE is designed using iterative phase retrieval algorithm. In the iterative algorithm, we introduce a new modification of far-field amplitude constraint to provide very high mode conversion quality. Compared with previously published mode converters, the scheme is more universal because it is applicable for any waveguide structure. In simulation, coupling losses lower than 0.12 dB have been reached for all the discussed waveguides. The converter is shown to be polarization-insensitive and applicable in multi-wavelength PLCs. And the tolerance on axis misalignment has been investigated.     

Effective optical parameters of thin-film and bulk metamaterials ofmetallodielectric nanosandwiches

We report on the effective optical response of single- and multilayer periodic structures of metallodielectric nanosandwiches on the basis of rigorous, full-electrodynamic calculations by the extended layer-multiple-scattering method. It is shown that the complex photonic band structure and the reflection coefficient of the infinite and semi-infinite crystal, respectively, provide reliable bulk effective parameters, which can be used as a reference in order to resolve ambiguities and problems in the determination of these parameters for finite slabs by the S-matrix retrieval procedure. Our results show that the structures under consideration exhibit strong artificial optical magnetism and thin films consisting of a few layers already behave like the bulk metamaterial.     

X-ray diffraction microscopy of magnetic structures

We report the first proof-of-principle experiment of iterative phase retrieval from magnetic x-ray diffraction. By using the resonant x-ray excitation process and coherent x-ray scattering, we show that linearly polarized soft x rays can be used to image both the amplitude and the phase of magnetic domain structures. We recovered the magnetic structure of an amorphous terbium-cobalt thin film with a spatial resolution of about 75 nm at the Co L3 edge at 778 eV. In comparison with soft x-ray microscopy images recorded with Fresnel zone plate optics at better than 25 nm spatial resolution, we find qualitative agreement in the observed magnetic structure.     

Experimental verification of coherent diffractive imaging by a direct phase retrieval method with an aperture-array filter

Recently, we have proposed a coherent diffractive imaging using a noniterative phase retrieval method with the filter of an aperture array. The first (to our knowledge) experimental demonstration of this coherent imaging is presented here, in which a complex-valued object illuminated by a diode laser is reconstructed from the isolated diffraction intensities of the object's wave field, transmitted through an array filter of square apertures by using the phase retrieval method. This imaging method requires only a single measurement of the diffraction intensity and does not need a tight object's support constraint utilized in iterative phase retrieval algorithms or a reference wave used in holographic techniques.     

Mode content analysis from intensity measurements in a few cross sections of oversized waveguides

A method of mode content analysis in oversized waveguides basing on intensity measurements in a few cross sections is suggested. The method is based on iterative synthesis of phase fronts of the radiation measured in a few cross sections of an oversized waveguide. The phase reconstruction makes it possible to calculate field distribution as well as the mode content at any place of the waveguide. The method was tested in experiments with circular and rectangular waveguides with impedance corrugation of the walls [8].     

Mode content analysis from intensity measurements in a few cross sections of oversized waveguides

A method of mode content analysis in oversized waveguides basing on intensity measurements in a few cross sections is suggested. The method is based on iterative synthesis of phase fronts of the radiation measured in a few cross sections of an oversized waveguide. The phase reconstruction makes it possible to calculate field distribution as well as the mode content at any place of the waveguide. The method was tested in experiments with circular and rectangular waveguides with impedance corrugation of the walls [8].     

硬x射线同轴相衬成像的相位恢复

基于角谱的概念，分析了硬x射线同轴相衬成像过程，在传统相位恢复算法GS算法的基础上 ，提出了基于角谱传播的相位恢复算法——迭代角谱法（IASA），并利用数值法模拟研究了 相衬成像和相位恢复过程，从理论上验证了这一相位恢复算法. 关键词： 相位恢复 相位衬度 角谱 硬x射线     

Hard-x-ray lensless imaging of extended objects

We demonstrate a hard-x-ray microscope that does not use a lens and is not limited to a small field of view or an object of finite size. The method does not suffer any of the physical constraints, convergence problems, or defocus ambiguities that often arise in conventional phase-retrieval diffractive imaging techniques. Calculation times are about a thousand times shorter than in current iterative algorithms. We need no a priori knowledge about the object, which can be a transmission function with both modulus and phase components. The technique has revolutionary implications for x-ray imaging of all classes of specimen.     

A new method for information retrieval in two-dimensional grating-based X-ray phase contrast imaging

Grating-based X-ray phase contrast imaging has been demonstrated to be an extremely powerful phase-sensitive imaging technique.By using two-dimensional(2D) gratings,the observable contrast is extended to two refraction directions.Recently,we have developed a novel reverse-projection(RP) method,which is capable of retrieving the object information efficiently with one-dimensional(1D) grating-based phase contrast imaging.In this contribution,we present its extension to the 2D grating-based X-ray phase contrast imaging,named the two-dimensional reverseprojection(2D-RP) method,for information retrieval.The method takes into account the nonlinear contributions of two refraction directions and allows the retrieval of the absorption,the horizontal and the vertical refraction images.The obtained information can be used for the reconstruction of the three-dimensional phase gradient field,and for an improved phase map retrieval and reconstruction.Numerical experiments are carried out,and the results confirm the validity of the 2D-RP method.     

Phase-coded aperture for optical imaging

For the optical spectrum region, we describe a novel phase-coded aperture imaging system that can be used in a computational imaging camera. The optical design includes a phase-only screen followed by a detector array. A specific diffraction pattern forms at the detector array when the wavefront from a point source object passes through the phase screen. Since diffraction effects cannot be ignored in the optical regime, an iterative phase retrieval method is used to calculate the phase coded screen. Correlation type processing can be applied for the image recovery. Computer simulation results are presented to illustrate the excellent imaging performance of this camera.