Enhanced deterministic phase retrieval using a partially developed speckle field

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.     

Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

Edge enhancement of phase objects through complex media by using transmission-matrix-based spiral phase contrast imaging

The wavefront shaping based technique has been introduced to detect the edges of amplitude objects through complex media, but the extraction of the boundary information of invisible phase objects through complex media has not been demonstrated yet. Here, we present a phase contrast imaging technique to overcome the scattering, aiming to achieve the edge detection of the phase object through the complex media. An operator based on the experimentally measured transmission matrix is obtained by numerically adding a spiral phase in the Fourier domain. With the inverse of the filtered transmission matrix, we can directly reconstruct the edge enhanced images for both amplitude object and phase object beyond scattering. Experimentally, both digital and real objects are imaged, and the results verify that isotropic edge detection can be achieved with our technique. Our work could benefit the detection of invisible phase objects through complex media.     

Wavefront sensing with random amplitude mask and phase retrieval

A light beam with an ideal wavefront that is transmitted or reflected from an object is modified by different characteristics of the object such as shape, refractive index, density, or temperature. Wavefront sensing therefore yields valuable information about the system or the changes happening to the system. A new method for wavefront sensing using a random amplitude mask and a phase retrieval method based on the Rayleigh-Sommerfeld wave propagation equation is described. The proposed method has many potential applications ranging from phase contrast imaging and measurement of lens aberration to shape measurement of three-dimensional objects.     

Dynamic behaviour of speckle cluster formation

In this work, we analyse the speckle cluster structure generated when a coherently illuminated diffuser is imaged by introducing a multiple aperture pupil mask in front of the lens plane. We demonstrate that the speckle cluster originates from the complex speckle modulation generated by multiple interferences among the wavefront passing through each aperture. The auto-correlation function of the intensity distribution when using a multiple aperture pupil arrangement is calculated. Besides, we demonstrate that the autocorrelation function and the intensity corresponding to a single scattering element of the input are coincident. This result allows interpretation of the dynamics behaviour of the speckle cluster formation by considering the result obtained by a single scattering element. Then, we determine the pupil mask geometrical parameters that control the cluster behaviour and therefore the condition for obtaining a highly repetitive cluster structure that we define as a 'regular cluster'. The theoretical simulations based on the random walk model are in agreement with the experimental results supporting the validity of our approach.     

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.     

Enhancing the phase profile and contrast of an interferogram by polarization recording in bacteriorhodopsin

Interferometry is a technique for reconstructing the profiles of phase objects. We present a novel interferometric setup for generating interferograms with doubled phase profile and enhanced contrast compared with the standard interferogram. The proposed system consists of a two-beam interferometer in which the reference and test waves are circularly polarized orthogonally to each other. They are superposed upon a bacteriorhodopsin film, creating a polarization grating that is distorted by the phase of the test object. This polarization pattern is read by a polarized He-Ne beam. We show analytically and experimentally that, when the zero diffraction order is removed, an interferogram with doubled phase profile and enhanced contrast is obtained.     

Adaptive phase distortion correction in strong speckle-modulation conditions

We introduce beam-quality metrics for adaptive wave-front control that permit estimation of the degree of laser beam energy concentration on a remotely located extended object based upon the backscattered wave intensity distribution at the receiver. A 37-control-channel adaptive optics system with phase correction of the output wave capable of operating in the presence of speckle-field-induced strong intensity modulation is presented. System operation is based on optimization of the speckle-field-based metric by the stochastic parallel gradient descent technique. Results demonstrate that adaptive wave-front correction using speckle-field-based beam-quality metrics can significantly improve laser beam concentration on extended objects.     

A study on spatially extended phase objects using speckle photography

We present an application of an improved speckle photography technique for spatially extended phase objects. A contour mapping of a thin lens displaying its phase variation is presented. A theoretical analysis is investigated followed by the experimental presentation. Reasonable interference fringes are obtained and compared with the fringes obtained for hot air. The phase information of the object is extracted using the point-by-point technique.     

Parallel wavefront optimization method for focusing light through random scattering media

A parallel wavefront optimization method is demonstrated experimentally to focus light through random scattering media. The simultaneous modulation of multiple phase elements, each at a unique frequency, enables a parallel determination of the optimal wavefront. Compared to a pixel-by-pixel measurement, the reported parallel method uses the target signal in a highly efficient way. With 441 phase elements, a high-quality focus was formed through a glass diffuser with a peak-to-background ratio of ～270. The accuracy and repeatability of the system were tested through experiments.     

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.     

Interferometric evaluation of angular displacements using phase retrieval

Phase retrieval is carried out using sequential intensity measurements of a volume speckle field and a wave propagation equation. Retrieved phases and phase subtraction facilitate the analysis of wavefronts before and after undergoing a small rotation. Angular displacement between incident planar wavefronts is determined from the unwrapped phase difference, phase diffuser aperture diameter, and the light source wavelength. Numerical simulations confirm the experimental results.     

A ferroelectric liquid crystal spatial light modulator encoded with orthogonal arrays and its optimized design for laser speckle reduction

In laser projectors, speckle reduction can be achieved by projecting a changing binary phase diffuser onto the screen. Here, we sequentially encoded a commercialized ferroelectric liquid crystal spatial light modulator (FLC-SLM) with the rows of a two-level orthogonal array of order sixty-four, thus obtaining a changing binary phase diffuser. With the help of this binary phase diffuser, the subjective speckle contrast ratio on the screen is reduced from C_b=0.71 to C_a=0.1. Based on the experimental results, a simplified transparent FLC-SLM design is first proposed. This newly designed FLC-SLM has two phase modulation depths and can be driven with the passive matrix addressing scheme. Therefore, the control electronics of the proposed FLC-SLM can be significantly simplified compared to the currently used one.     

Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane

In the present paper, we describe multiplexing in optical encryption of two-dimensional images, by using apertures and rotation of one of the constituent phase diffusers of a sandwich phase diffuser in the Fourier plane. The sandwich phase diffuser is made with two random constituent phase-diffusing surfaces sandwiched together. The apertures of different sizes and shapes are made with the help of ‘paint brush’ software. Simulation results are presented showing the effects of size, shape, and orientation of the apertures on the decrypted images obtained via multiplexing techniques. In addition to the results of using aperture systems in encryption and decryption, the results of rotation of one of the constituent phase diffusers in decryption are analyzed and used in multiplexing. Due to the use of aperture systems and the rotation of the constituent phase diffuser, the multiplexing capability of the system in encryption is enhanced along with the enhanced security due to using a sandwich diffuser. To evaluate the reliability of the technique, mean square error between the decrypted and the original image has been calculated.     

天文望远镜像差对斑点成像技术的影响

着重研究了采用斑点成像技术处理天文望远镜图像时,光学系统固定像差对图像恢复结果的影响。在详细研究各种恢复天文图像振幅和相位的理论和方法的基础上,建立了一个包括Labeyrie振幅恢复方法和KnoxThompson相位重构方法的恢复扩展目标的斑点成像处理模型,分析了光学系统固定像差对系统传递函数相位分布和目标相位重构的影响：天文目标通过大气成像,固定像差将会被淹没在大气湍流随机起伏中,像差对相位重构没有显著影响。处理图像结果表明,斑点成像技术能同时消除大气湍流和望远镜系统固定像差的影响,得到高分辨力的扩展目标图像。还提出了一种消除光学系统像差的方法。     

Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry

If a laser beam illuminates a continual deformation object surface, it will lead to a temporal speckle pattern on the observation plane. Recording this time-dependent speckle pattern the deformation of the surface of an object can be obtained. Two methods, scanning phase method (SPM) and time sequence phase method (TSPM), have been introduced for measuring the displacement caused by the deformation in temporal speckle pattern interferometry (TSPI). Their principle is that by capturing a series of speckle interference patterns related to the object deformations, the fluctuations in the intensity of the interference patterns can be obtained. Through scanning these fluctuations and estimating both the average intensity and modulation of the temporal speckle interference patterns, the phase maps for whole-field displacements are calculated. In this way one is capable of quantitatively measuring continual displacements simply using a conventional electronic speckle pattern interferometry (ESPI) system without phase shifting or a carrier. The elaboration on the new methods is given in this paper and experiments are performed to demonstrate their performance with a conventional ESPI system.     

Deterministic phase retrieval from diffracted intensities speckle fields

We present a model where the phase of a wave front is obtained by processing the intensity of speckle field pattern. By using the light propagation equation and knowing the intensity of the wavefront it is possible to build a system of linear equations which can be solved to give the wanted phase information. Simulations are presented and the convergence of the solution is discussed.     

Reconstructing spatial phase distributions and object images from speckle intensity patterns of the diffraction field

A method of reconstruction of the spatial phase distribution and the image of a scattering object from a recorded speckle pattern of the diffraction field has been developed and verified on test objects. The proposed method is based on an assumption that, for objects of a certain class, the phase difference between adjacent speckles in the far zone is equal to π. Digital records of Fourier speckle patterns and the corresponding digitally reconstructed images are presented.