Phase microscopy of technical and biological samples through random phase modulation with a diffuser

Accelerated phase retrieval using adaptive support and statistical fringe processing of phase estimates

A technique for accelerated multiple-plane phase retrieval is demonstrated by creating adaptive support through the statistical analysis of phase estimates. Its technical advantage arises from, what we believe to be, the first time use of both phase estimates and a statistical metric, enabling the fast generation of noise-robust support masks. This results in a fourfold improvement in convergence speed when compared to the conventional multiple-plane method. Evaluating data fitting performance with fewer intensity recordings showed that using four or more recordings resulted in accurate fitting, three recordings caused overfitting, and two recordings led to underfitting for the test object waves used. In principle, the adaptive support strategy based on the statistical analysis of phase estimates may be applied to other iterative phase retrieval methods.

Lensless microscopy by multiplane recordings: sub-micrometer, diffraction-limited, wide field-of-view imaging

Lensless microscopy is attractive because lenses are often large, heavy and expensive. We report diffraction-limited, sub-micrometer resolution in a lensless imaging system that does not need a reference wave and imposes few restrictions on the density of the sample. We use measurements of the intensity of light scattered by the sample at multiple heights above the sample and a modified Gerchberg-Saxton algorithm to reconstruct the phase of the optical field. We introduce a pixel-splitting algorithm that increases resolution beyond the size of the sensor pixels, and implement high-dynamic-range measurements. The resolution depends on the numerical aperture of the first measurement height only, while the field of view is limited by the last measurement height only. As a result, resolution and field of view can be controlled independently. The pixel-splitting algorithm also allows imaging with light of low spatial coherence, and we show that such low coherence is beneficial for a larger field of view. Using illumination from three LEDs, we produce full-color images of biological samples. Finally, we provide a detailed analysis of the limiting factors of this lensless microscopy system. The good performance demonstrated here can allow lensless systems to replace conventional microscope objectives in some situations.

Lensless phase imaging microscopy using multiple intensity diffraction patterns obtained under coherent and partially coherent illumination

In this paper, we show how high-resolution phase imaging is obtained from multiple intensity diffraction patterns. The results of the experiments carried out with different microscopic phase and amplitude samples illuminated with coherent and partially coherent light are presented. A comparison with experimental results obtained by digital holographic microscopy is given, and advantages/disadvantages of the techniques are discussed.

Phase retrieval using bidirectional interference

In this paper we describe a phase retrieval algorithm using constraints given by diffraction patterns and phase difference obtained from bidirectional interference. Wave propagation and linear phase ramps are used to connect the recordings. At least three patterns are recorded and processed (two diffraction patterns and one interference pattern). The quality of the results can be improved when recording and processing more patterns. The method works well with non-sparse samples and short (few millimeter) recording distances. Simulations, comparisons with other methods, and experimental validations are presented.

Wavefront reconstruction of a non-coaxial diffraction model in a lens system

To reconstruct a wavefront in a non-coaxial lens system, we propose a diffraction model using the Fresnel integral. Inclination angle is the newly included parameter in the mathematical formula describing beam propagation. It is determined through two ways in this paper, which are correlation operation and optical flow method. Furthermore, the multi-image phase retrieval is incorporated to reconstruct the complex optical field of sample from an overdetermined dataset. The combination is much closer to the actual situation and thus more practical. The proposed diffraction model is validated by numerical analysis and experiment. The work will further benefit the application of multi-image phase retrieval, such as in biomedical imaging and optical metrology.

Coherent laser phase retrieval in the presence of measurement imperfections and incoherent light

Phase retrieval is a powerful numerical method that can be used to determine the wavefront of laser beams based only on intensity measurements, without the use of expensive, low-resolution specialized wavefront sensors such as Shack-Hartmann sensors. However, phase retrieval techniques generally suffer from poor convergence and fidelity when the input measurements contain electronic or optical noise and/or an incoherent intensity contribution overlapped with the otherwise spatially coherent laser beam. Here, we present an implementation of a modified version of the standard multiple-plane Gerchberg-Saxton algorithm and demonstrate that it is highly successful at extracting the intensity profile and wavefront of the spatially coherent part of the light from various lasers, including tapered laser diodes, at a very high fidelity despite the presence of incoherent light and noise.

Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint

We proposed two noise-robust iterative methods for phase retrieval and diffractive imaging based on the Pauta criterion and the smoothness constraint. The work is to address the noise issue plaguing the application of iterative phase retrieval algorithms in coherent diffraction imaging. It is demonstrated by numerical analysis and experimental results that our proposed algorithms have higher retrieval accuracy and faster convergence speed at a high shot noise level. Moreover, they are proved to hold the superiority to cope with other kinds of noises. Due to the inconvenience of conventional iteration indicators in experiments, a more reliable retrieval metric is put forward and verified its effectiveness. It should be noted that the proposed methods focus on exploiting the longitudinal diversity. It is anticipated that our work can further expand the application of iterative multi-image phase retrieval methods.

Spatial-light-modulator-based adaptive optical system for the use of multiple phase retrieval methods

We propose an adaptive optical setup using a spatial light modulator (SLM), which is suitable to perform different phase retrieval methods with varying optical features and without mechanical movement. By this approach, it is possible to test many different phase retrieval methods and their parameters (optical and algorithmic) using one stable setup and without hardware adaption. We show exemplary results for the well-known transport of intensity equation (TIE) method and a new iterative adaptive phase retrieval method, where the object phase is canceled by an inverse phase written into part of the SLM. The measurement results are compared to white light interferometric measurements.

Point spread function estimation from projected speckle illumination

The resolution of an imaging apparatus is ideally limited by the diffraction properties of the light passing through the system aperture, but in many practical cases, inhomogeneities in the light propagating medium or imperfections in the optics degrade the image resolution. Here we introduce a powerful and practical new approach for estimating the point spread function (PSF) of an imaging system on the basis of PSF Estimation from Projected Speckle Illumination (PEPSI). PEPSI uses the fact that the speckles' phase randomness cancels the effects of the aberrations in the illumination path, thereby providing an objective pattern for measuring the deformation of the imaging path. Using this approach, both wide-field-of-view and local-PSF estimation can be obtained by calibration-free, single-speckle-pattern projection. Finally, we demonstrate the feasibility of using PEPSI estimates for resolution improvement in iterative maximum likelihood deconvolution.

Exploring neural cell dynamics with digital holographic microscopy

In this review, we summarize how the new concept of digital optics applied to the field of holographic microscopy has allowed the development of a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM) technique at the nanoscale particularly suitable for cell imaging. Particular emphasis is placed on the original biological information provided by the quantitative phase signal. We present the most relevant DH-QPM applications in the field of cell biology, including automated cell counts, recognition, classification, three-dimensional tracking, discrimination between physiological and pathophysiological states, and the study of cell membrane fluctuations at the nanoscale. In the last part, original results show how DH-QPM can address two important issues in the field of neurobiology, namely, multiple-site optical recording of neuronal activity and noninvasive visualization of dendritic spine dynamics resulting from a full digital holographic microscopy tomographic approach.

Optical encryption using multiple intensity samplings in the axial domain

Image encryption with optical means has attracted attention due to its inherent multidimensionality and degrees of freedom, including phase, amplitude, polarization, and wavelength. In this paper, we propose an optical encoding system based on multiple intensity samplings of the complex-amplitude wavefront with axial translation of the image sensor. The optical encoding system is developed based on a single optical path, where multiple diffraction patterns, i.e., ciphertexts, are sequentially recorded through the axial translation of a CCD camera. During image decryption, an iterative phase retrieval algorithm is proposed for extracting the plaintext from ciphertexts. The results demonstrate that the proposed phase retrieval algorithm possesses a rapid convergence rate during image decryption, and high security can be achieved in the proposed optical cryptosystem. In addition, other advantages of the proposed method, such as high robustness against ciphertext contaminations, are also analyzed.

Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications

A cellular-level study of the pathophysiology is crucial for understanding the mechanisms behind human diseases. Recent advances in quantitative phase imaging (QPI) techniques show promises for the cellular-level understanding of the pathophysiology of diseases. To provide important insight on how the QPI techniques potentially improve the study of cell pathophysiology, here we present the principles of QPI and highlight some of the recent applications of QPI ranging from cell homeostasis to infectious diseases and cancer.

Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging

Fresnel Incoherent Correlation Holography (FINCH) enables holograms to be recorded from incoherent light with just a digital camera and spatial light modulator. We previously described its application to general three dimensional incoherent imaging and specifically to fluorescence microscopy, wherein one complex hologram contains the three dimensional information in the field of view, obviating the need for scanning or serial sectioning. We have now further analyzed FINCH in view of linear system theory and in comparison to conventional coherent and incoherent two dimensional imaging systems. We demonstrate, theoretically and experimentally, improved resolution by FINCH, when compared to conventional imaging.

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.

Quantitative cell imaging using single beam phase retrieval method

Quantitative three-dimensional imaging of cells can provide important information about their morphology as well as their dynamics, which will be useful in studying their behavior under various conditions. There are several microscopic techniques to image unstained, semi-transparent specimens, by converting the phase information into intensity information. But most of the quantitative phase contrast imaging techniques is realized either by using interference of the object wavefront with a known reference beam or using phase shifting interferometry. A two-beam interferometric method is challenging to implement especially with low coherent sources and it also requires a fine adjustment of beams to achieve high contrast fringes. In this letter, the development of a single beam phase retrieval microscopy technique for quantitative phase contrast imaging of cells using multiple intensity samplings of a volume speckle field in the axial direction is described. Single beam illumination with multiple intensity samplings provides fast convergence and a unique solution of the object wavefront. Three-dimensional thickness profiles of different cells such as red blood cells and onion skin cells were reconstructed using this technique with an axial resolution of the order of several nanometers.

Single-plane multiple speckle pattern phase retrieval using a deformable mirror

A design for a single-plane multiple speckle pattern phase retrieval technique using a deformable mirror (DM) is analyzed within the formalism of complex ABCD-matrices, facilitating its use in conjunction with dynamic wavefronts. The variable focal length DM positioned at a Fourier plane of a lens comprises the adaptive optical (AO) system that replaces the time-consuming axial displacements in the conventional free-space multiple plane setup. Compared with a spatial light modulator, a DM has a smooth continuous surface which avoids pixelation, pixel cross-talk and non-planarity issues. The calculated distances for the proposed AO-system are evaluated experimentally using the conventional free-space phase retrieval setup. Two distance ranges are investigated depending on whether the measurement planes satisfy the Nyquist detector sampling condition or not. It is shown numerically and experimentally that speckle patterns measured at the non-Nyquist range still yield good reconstructions. A DM with a surface height of 25 microns and an aperture diameter of 5.2 mm may be used to reconstruct spherical phase patterns with 50-micron fringe spacing.