ABSTRACT
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.
ABSTRACT
In conventional multiple-plane phase retrieval method, the wave propagations that proceed in the same ordered sequence could slow down convergence or lead to stagnation. In this Letter, a novel, to the best of our knowledge, algorithmic technique to accelerate phase retrieval using an unordered sequence of propagations is demonstrated experimentally. The main advantage of the technique is the significant increase in the change in amplitude, a key and essential element for a successful iterative phase retrieval. For N planes, the number of possible ways to implement the sequence of propagations is increased by a factor of N!(N-1)!, providing diversity for the change in the amplitude. Compared to the conventional algorithm, the technique performed 2 times faster and reduced the number of needed intensity patterns for the test object wave used. The technique may be adopted in the other multiple intensity-based phase retrieval methods.
ABSTRACT
In the single-plane phase retrieval method, the use of a fixed object support is not efficient and could lead to inaccurate reconstructions. While there have been adaptive support strategies for the single-plane method, numerical processing is slow because such strategies are based in the space domain. Here, an adaptive support strategy based in the Fourier domain in conjunction with the multiple-plane phase retrieval method is presented and demonstrated through simulations and experiments. Optimizations of Fourier filter size and mask threshold parameters result in 3× faster convergence compared to the conventional multiple-plane method for the test object waves used. The proposed strategy offers fast, automated determination of the object support and affords the use of fewer intensity patterns.
ABSTRACT
In the multiple-plane phase retrieval method, a tedious-to-fabricate phase diffuser plate is used to increase the axial intensity variation for a nonstagnating iterative reconstruction of a smooth object wavefront. Here we show that a spatial light modulator (SLM) can be used as an easily controllable diffuser for phase retrieval. The polarization modulation at the SLM facilitates independent formation of orthogonally polarized scattered and specularly reflected beams. Through an analyzer, the polarization states are filtered enabling beam interference, thereby efficiently encoding the phase information in the axially diverse speckle intensity measurements. The technique is described using wave propagation and Jones calculus, and demonstrated experimentally on technical and biological samples.
ABSTRACT
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.
ABSTRACT
This paper proposed an automated technique for vibration detection using statistical focus measure to evaluate interferogram contrast. An interferogram sequence from a Mach-Zehnder interferometer setup is recorded (frame rate: 24 fps) and the gray-level variance (GLVA) is plotted versus time. Occurrence of induced vibration in the setup causes a decrease in the interferogram contrast which, in turn, manifests as an evident rapid drop in the variance plot. The technique is demonstrated experimentally using periodic microvibrations (frequency range, ≤6 Hz) and aperiodic disturbances.
ABSTRACT
We demonstrate experimentally a technique for the numerical correction of an optical vortex with a unitary topological charge. A developed algorithm based on the axial behavior of a reconstructed wavefront is used in the detection of the optical vortex. Optimizations of the number of axial phase maps and the window size used in the algorithm yield the precise coordinates of the vortex eye. The obtained coordinates and vortex handedness are used in designing a proper filter, facilitating numerical correction of the vortex phase map. The developed algorithm can be applied to absolute phase and phase difference maps obtained through any reconstruction method.
ABSTRACT
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.
Subject(s)
Image Processing, Computer-Assisted/methods , Optics and Photonics , Algorithms , Artifacts , Computer Graphics , Computer Simulation , Equipment Design , Light , Models, StatisticalABSTRACT
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.
ABSTRACT
A technique for phase microscopy using a phase diffuser and a reconstruction algorithm is proposed. A magnified specimen wavefront is projected on the diffuser plane that modulates the wavefront into a speckle field. The speckle patterns at axially displaced planes are sampled and used in an iterative phase retrieval algorithm based on a wave-propagation equation. The technique offers a whole-field and high-resolution wavefront reconstruction of unstained microstructures. Phase maps of photoresist targets and human cheek cells are obtained to demonstrate the effectiveness of our method.
Subject(s)
Algorithms , Image Interpretation, Computer-Assisted/methods , Lenses , Microscopy, Phase-Contrast/instrumentation , Microscopy, Phase-Contrast/methods , Refractometry/instrumentation , Refractometry/methods , Computer-Aided Design , Equipment Design , Equipment Failure Analysis , Reproducibility of Results , Sensitivity and SpecificityABSTRACT
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.
ABSTRACT
What we believe to be a novel technique for wavefront aberration measurement using speckle patterns is presented. The aberration correction is done numerically. A tilted lens is illuminated with a partially developed speckle field, and the transmitted light intensity is sampled at axially displaced planes. The speckle intensity patterns are then sent to a phase-retrieval algorithm to reconstruct the complete wavefront. The nature of the wavefront aberration is determined through Zernike polynomials. Numerical correction of the perturbed wavefront is performed based on rms error and the Strehl ratio. Restoration of the wavefront from a phase object with high spatial frequency content shows the effectiveness of our method.
ABSTRACT
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.
ABSTRACT
Wavefronts incident on a random phase plate are reconstructed via phase retrieval utilizing axially displaced speckle intensity measurements and the wave propagation equation. Retrieved phases and phase subtraction facilitate the investigations of wavefronts from test objects before and after undergoing a small rotation or deformation without sign ambiguity. Angular displacement (Deltatheta) between incident planar wavefronts is determined from the light source vacuum wavelength (lambda) divided by the fringe spacing (Lambda). Fourier analysis of the wavefront phase difference yields a peak frequency that is inversely proportional to Lambda, and the sign gives the direction of rotation. Numerical simulations confirm the experimental results. In the experiments, the smallest Deltatheta measured is 0.031 degrees . The technique also permits deformation analysis of a reflecting test object under thermal loading. The technique offers simple, high resolution, noncontact, and whole field evaluation of three-dimensional objects before and after undergoing rotation or deformation.
Subject(s)
Computer-Aided Design , Equipment Failure Analysis , Models, Theoretical , Refractometry/instrumentation , Transducers , Computer Simulation , Equipment Design , Light , Refractometry/methods , Reproducibility of Results , Scattering, Radiation , Sensitivity and SpecificityABSTRACT
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.
ABSTRACT
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.
Subject(s)
Artifacts , Computer-Aided Design , Models, Theoretical , Optics and Photonics/instrumentation , Refractometry/instrumentation , Refractometry/methods , Transducers , Computer Simulation , Equipment Design , Equipment Failure AnalysisABSTRACT
A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.
ABSTRACT
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.
ABSTRACT
Multi-wavelength holography is demonstrated with a H(2) Raman shifter that is pumped with an elliptically-polarized pulsed 532 nm beam to produce temporally coherent, intense, polarized output lines. Digital holograms of two-dimensional colored objects are recorded using Raman output lines at 630.4 nm (S(05), Red), 532 nm (Rayleigh, Green) and 435.7 nm (aS(10), Blue). Object reconstruction is done numerically via the convolution method and colored object recognition is achieved by multi-channel correlation of the Red, Green, and Blue reconstructions of the reference and the target object.
ABSTRACT
The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.
