Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

Phase retrieval using spatially modulated illumination

In this Letter, we propose a method for retrieving the phase of a wavefront from the diffraction patterns recorded when the object is sequentially illuminated by spatially modulated light. For wavefronts having a smooth phase, the retrieval is achieved by using a deterministic method. When the phase has discontinuities, an iterative process is used for the retrieval and enhancement of the spatial resolution. Both the deterministic and iterative phase reconstructions are demonstrated by experiments.

Quantitative phase imaging using a deep UV LED source

We propose a method for high resolution phase imaging of biological and non-biological samples using an incoherent deep ultraviolet (DUV) LED source. The diffraction pattern of the object wave is recorded at different axial planes and the phase is retrieved by propagation of the angular spectrum. To maintain enough light intensity, we avoided using a pinhole or spectral filter for increasing the coherence of the DUV LED source. This makes the setup very simple and cost effective. The short wavelength (285 nm) of the DUV light, tuned to the absorption peak of the biological samples, allows simultaneously high resolution and high contrast images. The experimental results are presented to verify this principle.

Optical phase imaging using a synthetic aperture phase retrieval technique

Optical phase imaging enables visualization of transparent samples, numerical refocusing, and other computational processing. Typically phase is measured quantitatively using interferometric techniques such as digital holography. Researchers have demonstrated image enhancement by synthetic aperture imaging based on digital holography. In this work we introduce a novel imaging technique that implements synthetic aperture imaging using phase retrieval, a non-interferometric technique. Unlike digital holography, phase retrieval obviates the need for a reference arm and provides a more compact, less expensive, and more stable experimental setup. We call this technique synthetic aperture phase retrieval.

Laser beam complex amplitude measurement by phase diversity

The control of the optical quality of a laser beam requires a complex amplitude measurement able to deal with strong modulus variations and potentially highly perturbed wavefronts. The method proposed here consists in an extension of phase diversity to complex amplitude measurements that is effective for highly perturbed beams. Named camelot for Complex Amplitude MEasurement by a Likelihood Optimization Tool, it relies on the acquisition and processing of few images of the beam section taken along the optical path. The complex amplitude of the beam is retrieved from the images by the minimization of a Maximum a Posteriori error metric between the images and a model of the beam propagation. The analytical formalism of the method and its experimental validation are presented. The modulus of the beam is compared to a measurement of the beam profile, the phase of the beam is compared to a conventional phase diversity estimate. The precision of the experimental measurements is investigated by numerical simulations.

Phase retrieval with resolution enhancement by using structured illumination

In this Letter, we present referenceless phase retrieval methods with resolution enhancement. Structured illuminations with different orientations and phase shifts are generated by a spatial light modulator and are used to illuminate the specimen. The generated diffraction patterns are recorded by a CCD camera, and the phase of the wavefront is reconstructed from these patterns.

Field-portable pixel super-resolution colour microscope

Based on partially-coherent digital in-line holography, we report a field-portable microscope that can render lensfree colour images over a wide field-of-view of e.g., >20 mm(2). This computational holographic microscope weighs less than 145 grams with dimensions smaller than 17×6×5 cm, making it especially suitable for field settings and point-of-care use. In this lensfree imaging design, we merged a colorization algorithm with a source shifting based multi-height pixel super-resolution technique to mitigate 'rainbow' like colour artefacts that are typical in holographic imaging. This image processing scheme is based on transforming the colour components of an RGB image into YUV colour space, which separates colour information from brightness component of an image. The resolution of our super-resolution colour microscope was characterized using a USAF test chart to confirm sub-micron spatial resolution, even for reconstructions that employ multi-height phase recovery to handle dense and connected objects. To further demonstrate the performance of this colour microscope Papanicolaou (Pap) smears were also successfully imaged. This field-portable and wide-field computational colour microscope could be useful for tele-medicine applications in resource poor settings.

Investigation of composite materials using SLM-based phase retrieval

We present a robust method to inspect a typical composite material constructed of carbon fiber reinforced plastic (CFRP). It is based on optical surface contouring using the spatial light modulator (SLM)-based phase retrieval technique. The method utilizes multiple intensity observations of the wave field, diffracted by the investigated object, captured at different planes along the optical axis to recover the phase information across the object plane. The SLM-based system allows for the recording of the required consecutive intensity measurements in various propagation states across a common recording plane. This overcomes the mechanical shifting of a camera sensor required within the capturing process. In contrast to existing phase retrieval approaches, the measuring time is considerably reduced, since the switching time of the SLM is less than 50 ms. This enables nondestructive testing under thermal load. Experimental results are presented that demonstrate the approach can be used to assess structural properties of technical components made from CFRP.

Phase-retrieved pupil function and coherent transfer function in confocal microscopy

This work reports on the retrieval of the pupil function and coherent transfer function of a coherent reflection type confocal microscope from simulated measurements of the intensity point spread function. Two phase retrieval algorithms are presented in this vein, which incorporate the multiple pupil dependence of image formation in confocal microscopy. Verification of the algorithms follows by numerical simulations.

Wide-field computational color imaging using pixel super-resolved on-chip microscopy

Lens-free holographic on-chip imaging is an emerging approach that offers both wide field-of-view (FOV) and high spatial resolution in a cost-effective and compact design using source shifting based pixel super-resolution. However, color imaging has remained relatively immature for lens-free on-chip imaging, since a 'rainbow' like color artifact appears in reconstructed holographic images. To provide a solution for pixel super-resolved color imaging on a chip, here we introduce and compare the performances of two computational methods based on (1) YUV color space averaging, and (2) Dijkstra's shortest path, both of which eliminate color artifacts in reconstructed images, without compromising the spatial resolution or the wide FOV of lens-free on-chip microscopes. To demonstrate the potential of this lens-free color microscope we imaged stained Papanicolaou (Pap) smears over a wide FOV of ~14 mm(2) with sub-micron spatial resolution.

Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy

Pixel-size limitation of lensfree on-chip microscopy can be circumvented by utilizing pixel-super-resolution techniques to synthesize a smaller effective pixel, improving the resolution. Here we report that by using the two-dimensional pixel-function of an image sensor-array as an input to lensfree image reconstruction, pixel-super-resolution can improve the numerical aperture of the reconstructed image by ~3 fold compared to a raw lensfree image. This improvement was confirmed using two different sensor-arrays that significantly vary in their pixel-sizes, circuit architectures and digital/optical readout mechanisms, empirically pointing to roughly the same space-bandwidth improvement factor regardless of the sensor-array employed in our set-up. Furthermore, such a pixel-count increase also renders our on-chip microscope into a Giga-pixel imager, where an effective pixel count of ~1.6–2.5 billion can be obtained with different sensors. Finally, using an ultra-violet light-emitting-diode, this platform resolves 225 nm grating lines and can be useful for wide-field on-chip imaging of nano-scale objects, e.g., multi-walled-carbon-nanotubes.

Phase retrieval in 4f optical system: background compensation and sparse regularization of object with binary amplitude

Generally, wave field reconstructions obtained by phase-retrieval algorithms are noisy, blurred, and corrupted by various artifacts such as irregular waves, spots, etc. These distortions, arising due to many factors, such as nonidealities of the optical system (misalignment, focusing errors), dust on optical elements, reflections, and vibration, are hard to localize and specify. It is assumed that there is a cumulative disturbance called "background," which describes mentioned distortions in the coherent imaging system manifested at the sensor plane. Here we propose a novel iterative phase-retrieval algorithm compensating for these distortions in the optical system. An estimate of this background is obtained via special calibration experiments, and then it is used for the object reconstruction. The algorithm is based on the maximum likelihood approach targeting on the optimal object reconstruction from noisy data and imaging enhancement using a priori information on the object amplitude. In this work we demonstrate the compensation of the distortions of the optical trace for a complex-valued object with a binary amplitude. The developed algorithm results in state-of-the-art filtering, and sharp reconstruction imaging of the object amplitude can be achieved.

Lensless phase microscopy using phase retrieval with multiple illumination wavelengths

A phase retrieval method for microscopy using multiple illumination wavelengths is proposed. A fast algorithm suitable for calculations with high numerical aperture is used for the iterative retrieval of the object wavefront. The advantages and limitations of the technique are systematically analyzed and demonstrated by both simulation and experimental results.

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.

Surpassing digital holography limits by lensless object scanning holography

We present lensless object scanning holography (LOSH) as a fully lensless method, capable of improving image quality in reflective digital Fourier holography, by means of an extremely simplified experimental setup. LOSH is based on the recording and digital post-processing of a set of digital lensless holograms and results in a synthetic image with improved resolution, field of view (FOV), signal-to-noise ratio (SNR), and depth of field (DOF). The superresolution (SR) effect arises from the generation of a synthetic aperture (SA) based on the linear movement of the inspected object. The same scanning principle enlarges the object FOV. SNR enhancement is achieved by speckle suppression and coherent artifacts averaging due to the coherent addition of the multiple partially overlapping bandpass images. And DOF extension is performed by digital refocusing to different object's sections. Experimental results showing an impressive image quality improvement are reported for a one-dimensional reflective resolution test target.

Phase retrieval via spatial light modulator phase modulation in 4f optical setup: numerical inverse imaging with sparse regularization for phase and amplitude

The 4f optical setup is considered with a wave field modulation by a spatial light modulator located in the focal plane of the first lens. Phase as well as amplitude of the wave field are reconstructed from noisy multiple-intensity observations. The reconstruction is optimal due to a constrained maximum likelihood formulation of the problem. The proposed algorithm is iterative with decoupling of the inverse of the forward propagation of the wave field and the filtering of phase and amplitude. The sparse modeling of phase and amplitude enables the advanced high-accuracy filtering and sharp imaging of the complex-valued wave field. Artifacts typical for the conventional algorithms (wiggles, ringing, waves, etc.) and attributed to optical diffraction can be suppressed by the proposed algorithm.

Automated compensation of misalignment in phase retrieval based on a spatial light modulator

In this paper, the issue of misalignment in phase retrieval by means of optical linear filtering is discussed. The filtering setup is based on a 4f configuration with a spatial light modulator (SLM) as an active element, located in the Fourier domain. From the analysis, crucial parameters for the alignment procedure of the setup's optical axes and the center of the SLM are identified. Furthermore, a method to automatically as well as electronically compensate such effects by modifying the phase pattern displayed on the SLM is introduced. Experimental results are presented that validate the compensation approach.

Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm

A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.

Phase retrieval by pinhole scanning

We describe a method where phase and amplitude of a wavefront are obtained by processing a sequence of pattern produced by the interference between the light transmitted by a scanning pinhole (which is sequentially shifted) and a reference pinhole. Simulations and experimental results are presented.

Quantization analysis of speckle intensity measurements for phase retrieval

Speckle intensity measurements utilized for phase retrieval (PR) are sequentially taken with a digital camera, which introduces quantization error that diminishes the signal quality. Influences of quantization on the speckle intensity distribution and PR are investigated numerically and experimentally in the static wavefront sensing setup. Results show that 3 to 4 bits are adequate to represent the speckle intensities and yield acceptable reconstructions at relatively fast convergence rates. Computer memory requirements may be eased down by 2.4 times if a 4 bit instead of an 8 bit camera is used. This may facilitate rapid speckle data acquisition for dynamic wavefront sensing.

Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system

We present an experimental configuration for phase retrieval from a set of intensity measurements. The key component is a spatial light modulator located in the Fourier domain of an imaging system. It performs a linear filter operation that is associated to the process of propagation in the image plane. In contrast to the state of the art, no mechanical adjustment is required during the recording process, thus reducing the measurement time considerably. The method is experimentally demonstrated by investigating a wave field scattered by a diffuser, and the results are verified by comparing them to those obtained from standard interferometry.

Quantitative phase microscopy using defocusing by means of a spatial light modulator

A new method for recovery the quantitative phase information of microscopic samples is presented. It is based on a spatial light modulator (SLM) and digital image processing as key elements to extract the sample's phase distribution. By displaying a set of lenses with different focal power, the SLM produces a set of defocused images of the input sample at the CCD plane. Such recorded images are then numerically processed to retrieve phase information. This iterative process is based on the wave propagation equation and leads on a complex amplitude image containing information of both amplitude and phase distributions of the input sample diffracted wave front. The proposed configuration is a non-interferometric architecture (conventional transmission imaging mode) where no moving elements are included. Experimental results perfectly correlate with the results obtained by conventional digital holographic microscopy (DHM).

Complex pupil retrieval with undersampled data

The ability to retrieve the complex-valued, generalized pupil function of an imaging system from undersampled measurements of the defocused system point spread function (PSF) is examined through numerical simulations. The ability to do so degrades as the detector pixel pitch increases when using a fixed number of PSF measurements. Two strategies for obtaining better results with undersampled data are demonstrated using additional PSF measurements with (i) random shifts due to system pointing fluctuations and (ii) intermediate amounts of defocus.

Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval

Shape and deformation measurement of diffusely reflecting 3D objects are very important in many application areas, including quality control, nondestructive testing, and design. When rough objects are exposed to coherent beams, the scattered light produces speckle fields. A method to measure the shape and deformation of 3D objects from the sequential intensity measurements of volume speckle field and phase retrieval based on angular-spectrum propagation technique is described here. The shape of a convex spherical surface was measured directly from the calculated phase map, and micrometer-sized deformation induced on a metal sheet was obtained upon subtraction of the phase, corresponding to unloaded and loaded states. Results from computer simulations confirm the experiments.

Fast-convergent algorithm for speckle-based phase retrieval and a design for dynamic wavefront sensing

Wavefront reconstruction is carried out using sequentially recorded speckle patterns and an iterative phase retrieval method based on wave propagation. A novel fast-convergent algorithm that maintains the propagation distance in the iteration step equal to the distance between measurement planes is demonstrated. Employing the new algorithm, influences of the number of measurement planes, number of iterations, and uncertainties in the detector's transverse and axial positions on the rate of phase convergence are analyzed experimentally. A conceptual design for a dynamic wavefront sensor using arrays of beam splitters and detectors for parallel speckle recording is described.

Amplitude metrics for field retrieval with hard-edged and uniformly illuminated apertures

In field retrieval, the amplitude and phase of the generalized pupil function for an optical system are estimated from multiple defocused measurements of the system point-spread function. A baseline field reconstruction algorithm optimizing a data consistency metric is described. Additionally, two metrics specifically designed to incorporate a priori knowledge about pupil amplitude for hard-edged and uniformly illuminated aperture systems are given. Experimental results demonstrate the benefit of using these amplitude metrics in addition to the baseline metric.

Resolution-enhanced subpixel phase retrieval method

Phase retrieval is a wavefront sensing method that uses a series of intensity images to reconstruct the wavefront. The resolution of phase retrieval testing is limited mainly by the resolution of intensity images captured by CCD cameras. A subpixel phase retrieval method is presented to retrieve the wave field at subpixel resolution by using the information of a sequence of low-resolution images captured along the propagation direction. In this method, the sampling interval for the wave field under test is smaller than the CCD pixel size in phase reconstruction. The wave field is recovered at subpixel resolution by utilizing the energy conservation relationship between CCD pixels and their subpixels by the subpixel phase retrieval (SPR) algorithm. Numerical experiments have shown that more than a fourfold resolution enhancement can be achieved. The method has also been studied in some experiments under noisy and off-axis conditions. A mirror surface testing experiment was conducted to demonstrate the performance of SPR in the real world. The results of these experiments have shown the effectiveness and robustness of this method. SPR allows low-resolution images to be used to retrieve high-resolution wave fields and will be useful in testing wave fields from large objects.

Phase retrieval of complex optical fields by binary amplitude modulation

A method to retrieve the complex optical fields from the intensity information recorded in only one plane is discussed. The wavefront to be reconstructed is modulated by using a random binary amplitude mask. Wavefronts with a rather large phase depth can be accurately retrieved by using several masks in combination with iterative Fresnel algorithms and without any prior information. The influences of the contrast of the mask and the dynamic range of the detector on the accuracy of the phase retrieval are analyzed.

Efficient reconstruction of two-dimensional complex amplitudes utilizing the redundancy of the ambiguity function

In a previous paper [Opt. Commun.225, 19-30 (2003)] we presented a method to reconstruct two-dimensional complex amplitudes by using the ambiguity function of one-dimensional intensity scans, obtained from two optical setups involving cylindrical lenses. We demonstrate that the internal redundancy of the ambiguity function can be utilized to improve the efficiency of this method even further. We show that the phase reconstruction errors can be minimized with an appropriate algorithm, and we present experimental data that illustrate the efficient reconstruction of a two-dimensional phase element.

Wavefront sensing using speckles with fringe compensation

Wavefront sensing with numerical phase-error correction system is carried out using a random phase plate and phase retrieval using multiple intensity measurements of axially-displaced speckle patterns and the wave propagation equation. Various wavefronts with smooth curvatures incident on the developed phase plate (DPP) are examined: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious fringe pattern in the wavefront reconstructions due to a small tilt (Delta theta=0.212 degrees) in the plane illumination wave is detected and numerically corrected for. Fringe pattern of the illumination wave obtained for the setup without the phase object being investigated is used as reference fringe pattern. Fringe compensation yields wavefronts with the correct shape and numerical value based on the specifications of the setup. The numerical phase-error correction system described in this study can be extended to other types of phase errors such as those due to aberrations if optical elements are present in the setup or due to perturbations in the environment.

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.

Aperture synthesis in phase retrieval using a volume-speckle field

The resolution of the reconstructed wave by a phase-retrieval method using a volume-speckle field depends on the aperture defined by the size of the CCD array. The use of a larger aperture is introduced by measuring the speckle field at two different positions in the transverse plane and stitching the measurements together. Improvements in the quality of reconstructions are demonstrated experimentally and by computer simulations. Undesirable effects of camera tilt on the quality of reconstructions from synthetic aperture intensity measurements are experimentally observed and corrected.