Twin-stagnation-free phase retrieval with vortex phase illumination.

The recovery of a complex-valued exit wavefront from its Fourier transform magnitude is challenging due to the stagnation problems associated with iterative phase retrieval algorithms. Among the various stagnation artifacts, the twin-image stagnation is the most difficult to address. The upright object and its inverted and complex-conjugated twin correspond to the identical Fourier magnitude data and hence appear simultaneously in the iterative solution. We show that the twin stagnation problem can be eliminated completely if a coherent beam with charge-1 vortex phase is used for illumination. Unlike the usual plane wave illumination case, a charge-1 vortex illumination intentionally introduces an isolated zero near the zero spatial frequency region, where maximal energy in the Fourier space is usually concentrated for most natural objects. The early iterations of iterative phase retrieval algorithms are observed to develop a clockwise or anti-clockwise vortex in the vicinity of this isolated zero. Once the Fourier transform of the solution latches onto a specific vortex profile in the neighborhood of this intentionally introduced intensity zero in early iterations, the solution quickly adjusts to the corresponding twin (upright or inverted) and further iterations are not observed to bring the other twin into the reconstruction. Our simulation studies with the well-known hybrid input-output (HIO) algorithm show that the solution always converges to one of the twins within a few hundred iterations when vortex phase illumination is used. Using a clockwise or anti-clockwise vortex phase as an initial guess is also seen to deterministically lead to a solution consisting of the corresponding twin. The resultant solution still has some faint residual artifacts that can be addressed via the recently introduced complexity guidance methodology. There is an additional vortex phase in the final solution that can simply be subtracted out to obtain the original test object. The near guaranteed convergence to a twin-stagnation-free solution with vortex illumination as described here is potentially valuable for deploying practical imaging systems that work based on the iterative phase retrieval algorithms.

Radiologists' Rating for Comparative Qualitative Assessment of Intravoxel Incoherent Motion Using Novel Analysis Methods.

OBJECTIVE: The objective was to assess qualitative interpretability and quantitative precision and reproducibility of intravoxel incoherent motion ( IVIM) parametric images evaluated using novel IVIM analysis methods for diagnostic accuracy. METHODS: Intravoxel incoherent motion datasets of 55 patients (male/female = 41:14; age = 17.8 ± 5.5 years) with histopathology-proven osteosarcoma were analyzed. Intravoxel incoherent motion parameters-diffusion coefficient ( D ), perfusion fraction ( f ), and perfusion coefficient ( D* )-were estimated using 5 IVIM analysis methods-(i) biexponential (BE) model, (ii) BE-segmented fitting 2-parameter (BESeg-2), (iii) BE-segmented fitting 1-parameter (BESeg-1), (iv) BE model with total variation penalty function (BE + TV), and (v) BE model with Huber penalty function (BE + HPF). Qualitative scoring in a 5-point Likert scale (uninterpretable: 1; poor: 2; fair: 3; good: 4; excellent: 5) was performed by 2 radiologists for 4 criteria: (a) tumor shape and margin, (b) morphologic correlation, (c) noise suppression, and (d) overall interpretability. Interobserver agreement was evaluated using Spearman rank-order correlation ( rs ). Precision and reproducibility were evaluated using within-subject coefficient of variation (wCV) and between-subject coefficient of variation (bCV). RESULTS: BE + TV and BE + HPF produced significantly ( P < 10 -3 ) higher qualitative scores for D (fair-good [3.3-3.8]) than BE (poor [2.3]) and for D* (poor-fair [2.2-2.7]) and f (fair-good [3.2-3.8]) than BE, BESeg-2, and BESeg-1 ( D* : uninterpretable-poor [1.3-1.9] and f : poor-fair [1.5-3]). Interobserver agreement for qualitative scoring was rs = 0.48-0.59, P < 0.009. BE + TV and BE + HPF showed significantly ( P < 0.05) improved reproducibility in estimating D (wCV: 24%-31%, bCV: 21%-31% improvement) than the BE method and D* (wCV: 4%-19%, bCV: 5%-19% improvement) and f (wCV: 25%-49%, bCV: 25%-47% improvement) than BE, BESeg-2, and BESeg-1 methods. CONCLUSIONS: BE + TV and BE + HPF demonstrated qualitatively and quantitatively improved IVIM parameter estimation and may be considered for clinical use further.

Carrier-frequency estimation for digital holograms of phase objects.

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel's criterion [J. Opt. Soc. Am.57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.

Determining the transfer function of a reconstructive spectrometer using measurements at two wavelengths.

The transfer function is the characteristic function of the dispersive element of a reconstructive spectrometer. It maps the transmitted spatial intensity profile to the incident spectral intensity profile of an input. Typically, a widely tunable and narrowband source is required to determine the transfer function across the entire operating wavelength range, which increases the developmental cost of these reconstructive spectrometers. In this Letter, we utilize the parabolic dispersion relation of a planar one-dimensional photonic crystal cavity, which acts as the dispersive element, to determine the entire transfer function of the spectrometer using measurements made at only two wavelengths. Using this approach, we demonstrate reliable reconstruction of input spectra in simulations, even in the presence of noise. The experimentally reconstructed spectra also follow the spectra measured using a commercial spectrometer.

Fluorescence by self-assembly: autofluorescent peptide vesicles and fibers.

A series of oxidized cysteinyl peptides ([P-Cys-X-OMe]2; P = Boc or H; X = Trp or Glu) showed vesicular and fibrillar assemblies. The anatomy of the self-assembled vesicles from the water-soluble cystine peptide [Cys-Trp-OMe]2 (1a) has been investigated by using various fluorescent probes such as ammonium 8-anilinonaphthalene-1-sulfonate, Nile Red and pyrene. The morphological characterization was carried out by fluorescence lifetime imaging microscopy (FLIM) and super resolution-structured illumination microscopy (SR-SIM) utilizing the autofluorescence of the vesicles stemming from the self-assembly. The self-assembled structures are also observed in solution as evident from the quantitative phase images obtained using a dual-mode digital holographic microscope (DHM) system. Present investigations show that the self-assembly is enthalpy- and entropy-driven in the aqueous medium. Based on the CD spectral studies, we proposed that 1a organizes into vesicles through the sequestration of indole units. We observed that the solutions of dipeptides 1a-b exhibit autofluorescence in the blue region upon excitation at a wavelength >350 nm. Detailed spectroscopic studies on the peptides lacking tryptophan 2a-b unequivocally showed that the autofluorescence stems exclusively from peptide aggregation. Our experimental results with appropriate controls revealed that the clustering of carbonyl chromophores is central to autofluorescence. Autofluorescence was also used to probe the vesicle formation without using any external fluorescent probe. To the best of our knowledge, this is the first report on autofluorescent vesicles formed by the spontaneous association of dipeptides. We also found that the vesicles formed by 1a can act as a host for guests like C60. The biocompatibility and biodegradability of these peptides along with the autofluorescent nature and guest binding ability of peptide-based vesicles offer numerous applications in the biomedical area.

Single-shot extended field of view imaging using point spread function engineering.

We present a single-shot computational imaging system employing pupil phase engineering to extend the field of view (FOV) beyond the physical sensor limit. Our approach uses a point spread function in the form of a multiple-point impulse response (MPIR). Unlike the traditional point-to-point imaging model used by most traditional optical imaging systems, the proposed MPIR model can collect information from within and outside the sensor boundary. The detected raw image despite being scrambled can be decoded via a sparse optimization algorithm to get extended FOV imaging performance. We provide a thorough analysis of MPIR design regarding the number of impulses and their spatial extent. Increasing the number of impulses in MPIR of a given spatial extent leads to better information gathering within the detector region; however, it also reduces contrast in the raw data. Therefore, a trade-off between increasing the information and keeping adequate contrast in the detected data is necessary to achieve high-quality reconstruction. We first illustrate this trade-off with a simulation study and present experimental results on a suitably designed extended FOV imaging system. We demonstrate reconstructed images with a 4× gain in pixels over the native detection area without loss of spatial resolution. The proposed system design considerations are generic and can be applied to various imaging systems for extended FOV performance.

3D reconstruction of unstained weakly scattering cells from a single defocused hologram.

We investigate the problem of 3D complex field reconstruction corresponding to unstained red blood cells (RBCs) with a single defocused off-axis digital hologram. The main challenge in this problem is the localization of cells to the correct axial range. While investigating the volume recovery problem for a continuous phase object like the RBC, we observe an interesting feature of the backpropagated field that it does not show a clear focusing effect. Therefore, sparsity enforcement within the iterative optimization framework using a single hologram data frame cannot effectively restrict the reconstruction to the true object volume. For phase objects, it is known that the amplitude contrast of the backpropagated object field at the focus plane is minimum. We use this information available in the recovered object field in the hologram plane to device depth-dependent weights that are proportional to the inverse of amplitude contrast. This weight function is employed in the iterative steps of the optimization algorithm to assist the object volume localization. The overall reconstruction process is performed using the mean gradient descent (MGD) framework. Experimental illustrations of 3D volume reconstruction of the healthy as well as malaria-infected RBCs are presented. A test sample of polystyrene microsphere bead is also used to validate the axial localization capability of the proposed iterative technique. The proposed methodology is simple to implement experimentally and provides an approximate tomographic solution, which is axially restricted and consistent with the object field data.

Non-invasive intravoxel incoherent motion MRI in prediction of histopathological response to neoadjuvant chemotherapy and survival outcome in osteosarcoma at the time of diagnosis.

BACKGROUND: Early prediction of response to neoadjuvant chemotherapy (NACT) is important to aid personalized treatment in osteosarcoma. Diffusion-weighted Intravoxel Incoherent Motion (IVIM) MRI was used to evaluate the predictive value for response to NACT and survival outcome in osteosarcoma. METHODS: Total fifty-five patients with biopsy-proven osteosarcoma were recruited prospectively, among them 35 patients were further analysed. Patients underwent 3 cycles of NACT (Cisplatin + Doxorubicin) followed by surgery and response adapted adjuvant chemotherapy. Treatment outcomes were histopathological response to NACT (good-response ≥ 50% necrosis and poor-response < 50% necrosis) and survival outcome (event-free survival (EFS) and overall survival (OS)). IVIM MRI was acquired at 1.5T at baseline (t0), after 1-cycle (t1) and after 3-cycles (t2) of NACT. Quantitative IVIM parameters (D, D*, f & D*.f) were estimated using advanced state-of-the-art spatial penalty based IVIM analysis method bi-exponential model with total-variation penalty function (BETV) at 3 time-points and histogram analysis was performed. RESULTS: Good-responders: Poor-responders ratio was 13 (37%):22 (63%). EFS and OS were 31% and 69% with 16.27 and 25.9 months of median duration respectively. For predicting poor-response to NACT, IVIM parameters showed AUC = 0.87, Sensitivity = 86%, Specificity = 77% at t0, and AUC = 0.96, Sensitivity = 86%, Specificity = 100% at t1. Multivariate Cox regression analysis showed smaller tumour volume (HR = 1.002, p = 0.001) higher ADC-25th-percentile (HR = 0.047, p = 0.005) & D-Mean (HR = 0.1, p = 0.023) and lower D*-Mean (HR = 1.052, p = 0.039) were independent predictors of longer EFS (log-rank p-values: 0.054, 0.0034, 0.0017, 0.0019 respectively) and non-metastatic disease (HR = 4.33, p < 10-3), smaller tumour-volume (HR = 1.001, p = 0.042), lower D*-Mean (HR = 1.045, p = 0.056) and higher D*.f-skewness (HR = 0.544, p = 0.048) were independent predictors of longer OS (log-rank p-values: < 10-3, 0.07, < 10-3, 0.019 respectively). CONCLUSION: IVIM parameters obtained with a 1.5T scanner along with novel BETV method and their histogram analysis indicating tumour heterogeneity were informative in characterizing NACT response and survival outcome in osteosarcoma.

IVIM-DKI for differentiation between prostate cancer and benign prostatic hyperplasia: comparison of 1.5 T vs. 3 T MRI.

OBJECTIVE: To implement an advanced spatial penalty-based reconstruction to constrain the intravoxel incoherent motion (IVIM)-diffusion kurtosis imaging (DKI) model and investigate whether it provides a suitable alternative at 1.5 T to the traditional IVIM-DKI model at 3 T for clinical characterization of prostate cancer (PCa) and benign prostatic hyperplasia (BPH). MATERIALS AND METHODS: Thirty-two patients with biopsy-proven PCa were recruited for MRI examination (n = 16 scanned at 1.5 T, n = 16 scanned at 3 T). Diffusion-weighted imaging (DWI) with 13 b values (b = 0 to 2000 s/mm2 up to 3 averages, 1.5 T: TR = 5.774 s, TE = 81 ms and 3 T: TR = 4.899 s, TE = 100 ms), T2-weighted, and T1-weighted imaging were used on the 1.5 T and 3 T MRI scanner, respectively. The IVIM-DKI signal was modeled using the traditional IVIM-DKI model and a novel model in which the total variation (TV) penalty function was combined with the traditional model to optimize non-physiological variations. Paired and unpaired t-tests were used to compare intra-scanner and scanner group differences in IVIM-DKI parameters obtained using the novel and the traditional models. Analysis of variance with post hoc test and receiver operating characteristic (ROC) curve analysis were used to assess the ability of parameters obtained using the novel model (at 1.5 T) and the traditional model (at 3 T) to characterize prostate lesions. RESULTS: IVIM-DKI modeled using novel model with TV spatial penalty function at 1.5 T, produced parameter maps with 50-78% lower coefficient of variation (CV) than traditional model at 3 T. Novel model estimated higher D with lower D*, f and k values at both field strengths compared to traditional model. For scanner differences, the novel model at 1.5 T estimated lower D* and f values as compared to traditional model at 3 T. At 1.5 T, D and f values were significantly lower with k values significantly higher in tumor than BPH and healthy tissue. D (AUC: 0.98), f (AUC: 0.82), and k (AUC: 0.91) parameters estimated using novel model showed high diagnostic performance in cancer lesion detection at 1.5 T. DISCUSSION: In comparison with the IVIM-DKI model at 3 T, IVIM-DKI signal modeled with the TV penalty function at 1.5 T showed lower estimation errors. The proposed novel model can be utilized for improved detection of prostate lesions.

Roadmap on digital holography [Invited].

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

Texture analysis for chemotherapy response evaluation in osteosarcoma using MR imaging.

The efficacy of MRI-based statistical texture analysis (TA) in predicting chemotherapy response among patients with osteosarcoma was assessed. Forty patients (male: female = 31:9; age = 17.2 ± 5.7 years) with biopsy-proven osteosarcoma were analyzed in this prospective study. Patients were scheduled for three cycles of neoadjuvant chemotherapy (NACT) and diffusion-weighted MRI acquisition at three time points: at baseline (t0), after the first NACT (t1) and after the third NACT (t2) using a 1.5 T scanner. Eight patients (nonsurvivors) died during NACT while 34 patients (survivors) completed the NACT regimen followed by surgery. Histopathological evaluation was performed in the resected tumor to assess NACT response (responder [≤50% viable tumor] and nonresponder [>50% viable tumor]) and revealed nonresponder: responder = 20:12. Apparent diffusion coefficient (ADC) and intravoxel incoherent motion (IVIM) parameters, diffusion coefficient (D), perfusion coefficient (D*) and perfusion fraction (f) were evaluated. A total of 25 textural features were evaluated on ADC, D, D* and f parametric maps and structural T1-weighted (T1W) and T2-weighted (T2W) images in the entire tumor volume using 3D TA methods gray-level cooccurrence matrix (GLCM), neighborhood gray-tone-difference matrix (NGTDM) and run-length matrix (RLM). Receiver-operating-characteristic curve analysis was performed on the selected textural feature set to assess the role of TA features (a) as marker(s) of tumor aggressiveness leading to mortality at baseline and (b) in predicting the NACT response among survivors in the course of treatment. Findings showed that the NGTDM features coarseness, busyness and strength quantifying tumor heterogeneity in D, D* and f maps and T1W and T2W images were useful markers of tumor aggressiveness in identifying the nonsurvivor group (area-under-the-curve [AUC] = 0.82-0.88) at baseline. The GLCM features contrast and correlation, NGTDM features contrast and complexity and RLM feature short-run-low-gray-level-emphasis quantifying homogeneity/terogeneity in tumor were effective markers for predicting chemotherapeutic response using D (AUC = 0.80), D* (AUC = 0.80) and T2W (AUC = 0.70) at t0, and D* (AUC = 0.80) and f (AUC = 0.70) at t1. 3D statistical TA features might be useful as imaging-based markers for characterizing tumor aggressiveness and predicting chemotherapeutic response in patients with osteosarcoma.

Complexity-guided Fourier phase retrieval from noisy data.

Reconstruction of a stable and good quality solution from noisy single-shot Fourier intensity data is a challenging problem for phase retrieval algorithms. We examine behavior of the solution provided by the hybrid input-output (HIO) algorithm for noisy data, from the perspective of the complexity guidance methodology that was introduced by us in an earlier paper [J. Opt. Soc. Am. A36, 202 (2019)JOAOD60740-323210.1364/JOSAA.36.000202]. We find that for noisy data, the complexity of the solution outside the support keeps increasing as the HIO iterations progress. Based on this observation, a strategy for controlling the solution complexity within and outside the support during the HIO iterations is proposed and tested. In particular, we actively track and control the growth of complexity of the solution outside the support region with iterations. This in turn provides us with guidance regarding the level to which the complexity of the solution within the support region needs to be adjusted, such that the total solution complexity is equal to that estimated from raw Fourier intensity data. In our studies, Poisson noise with mean photon counts per pixel in the Fourier intensity data ranges over four orders of magnitude. We observe that the performance of the proposed strategy is noise robust in the sense that with increasing noise, the quality of the phase solution degrades gradually. For higher noise levels, the solution loses textural details while retaining the main object features. Our numerical experiments show that the proposed strategy can uniformly handle pure phase objects, mixed amplitude-phase objects, and the case of dc blocked Fourier intensity data. The results may find a number of applications where single-shot Fourier phase retrieval is critical to the success of corresponding applications.

Regularization-parameter-free optimization approach for image deconvolution.

Image deconvolution is often modeled as an optimization problem for a cost function involving two or more terms that represent the data fidelity and the image domain constraints (or penalties). While a number of choices for modeling the cost function and implementing the optimization algorithms exist, selection of the regularization parameter in the cost function usually involves empirical tuning, which is a tedious process. Any optimization framework provides a family of solutions, depending on the numerical value of the regularization parameter. The end-user has to perform the task of tuning the regularization parameter based on visual inspection of the recovered solutions and then use the suitable image for further applications. In this work, we present an image deconvolution framework using the methodology of mean gradient descent (MGD), which does not involve any regularization parameter. The aim of our approach is instead to arrive at a solution point where the different costs balance each other. This is achieved by progressing the solution in the direction that bisects the steepest descent directions corresponding to the two cost terms in each iteration. The methodology is illustrated with numerical simulations as well as with experimental image records from a bright-field microscope system and shows uniform deconvolution performance for data with different noise levels. MGD offers an efficient and user-friendly method that may be employed for a variety of image deconvolution tools. The MGD approach as discussed here may find applications in the context of more general optimization problems as well.

Mean gradient descent: an optimization approach for single-shot interferogram analysis.

Complex object wave recovery from a single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of the cross term, but this method suffers from poor resolution. To obtain full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this method is not used widely due to several tedious and difficult tasks such as empirical tuning of free parameters. We introduce a new optimization approach, mean gradient descent (MGD), for single-shot interferogram analysis that is simple to implement. MGD does not have any free parameters whose empirical tuning is critical to the object wave recovery. The MGD iteration does not try to achieve minimization of a cost function but instead aims to reach a solution point where the data consistency and the constraint terms balance each other. This is achieved by iteratively progressing the solution in the direction that bisects the descent directions associated with the error and constraint terms. Numerical illustrations are shown for recovery of a step phase object from its corresponding off-axis as well as on-axis interferograms simulated with multiple noise levels. Our results show full pixel resolution as evident from the recovery of the phase step and excellent rms phase accuracy relative to the ground truth phase map. The concept of MGD as presented here can potentially find applications to a wider class of optimization problems.

Phase retrieval with complexity guidance.

Iterative phase retrieval methods based on the Gerchberg-Saxton (GS) or Fienup algorithm typically show stagnation artifacts even after a large number of iterations. We introduce a complexity parameter ζ that can be computed directly from the Fourier magnitude data and provides a measure of fluctuations in the desired phase retrieval solution. It is observed that when initiated with a constant or a uniformly random phase map, the complexity of the Fienup solution containing stagnation artifacts stabilizes at a numerical value that is higher than ζ. We propose a modified Fienup algorithm that uses a controlled sparsity-enhancing step such that in every iteration the complexity of the resulting guess solution is explicitly made close to ζ. This approach, which we refer to as complexity-guided phase retrieval, is seen to provide an artifact-free phase retrieval solution within a few hundred iterations. Numerical illustrations are provided for both amplitude as well as phase objects with and without Poisson noise introduced in the Fourier intensity data. The complexity-guidance concept may potentially be combined with a variety of phase retrieval algorithms and can enable several practical applications.

Propagation of converging polarization singular beams through atmospheric turbulence.

We report investigations on propagation of converging vector beams containing C-point and V-point polarization singularities through atmospheric turbulence. The C-point singularity is generated by superposition of the l=0 and l=1 orbital angular momentum (OAM) states, whereas the V-point singularity is generated by a superposition of the l=-1 and l=1 OAM states in orthogonal polarizations. The propagation of these beams through extended atmosphere is modeled by placing random phase screens along a 2 km propagation path. The random phase screens were generated using the FFT method with von Karman spectrum and Cn2=10-14 m-2/3. The quality of intensity profile of the focused vector beams after propagation through turbulence is assessed using the instantaneous signal-to-noise ratio and the on-axis scintillation index measurements. Our simulation results show that although both the C-point and V-point beams perform better than their scalar OAM components, C-point beams are seen to maintain much better beam intensity profile compared to the V-point beams. This observation is explained in terms of the OAM diversity of the individual polarization states and the correlation of their associated speckle patterns. The results presented here are important for engineering laser beams that can maintain a robust intensity profile on propagation through long-range atmospheric turbulence.

Effect of combination and number of b values in IVIM analysis with post-processing methodology: simulation and clinical study.

OBJECTIVE: To investigate the effect of number and combination of b values used on the accuracy of estimated Intravoxel Incoherent Motion (IVIM) parameters using simulation and clinical data. MATERIALS AND METHODS: Simulations with seven combinations of b values were performed for 4, 6, 8, and 13 numbers of b values with six different values of D, D*, and f parameters. Two methodologies were implemented for IVIM analysis: standard biexponential model (BE) and biexponential model with total variation penalty function (BE + TV). Clinical data set of six patients with prostate cancer was retrospectively analyzed using 4, 8, and 13 b values. RESULTS: BE + TV method showed lesser error and lower variability in simulation and clinical data, respectively. 8 and 13 b values showed good agreement in the values of parameters estimated with high correlation coefficient (ρ = 0.83-0.93). Clinical data showed high spurious noise with lower b values [4 b values leading to high coefficient of variation (CV); however, substantially, lower CV was observed with 8 and 13 b values]. DISCUSSION: BE model with TV penalty function is robust to combination of b values used for IVIM analysis. Combination of 8 b values provided a reasonably good accuracy in IVIM parameters.

Angular lens.

We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it separates out OAM modes in a manner analogous to how a converging lens separates out transverse wave-vector modes at the focal plane. We also simulate the proposed angular lens using a spatial light modulator and experimentally demonstrate its working. Our work can have important implications for OAM-based classical and quantum communication applications.

Accurate estimation of the illumination pattern's orientation and wavelength in sinusoidal structured illumination microscopy.

Structured illumination microscopy is able to improve the spatial resolution of wide-field fluorescence imaging by applying sinusoidal stripe pattern illumination to the sample. The corresponding computational image reconstruction requires precise knowledge of the pattern's parameters, which are its phase (ϕ) and wave vector (p). Here, a computationally inexpensive method for estimation of p from the raw data is proposed and illustrated with simulations. The method estimates p through a selective discrete Fourier transform at tunable subpixel precision. This results in an accurate p estimation for all the illumination patterns and subsequently improves the superresolution image recovery by a factor of 10 around sharp edges as compared to an integer pixel approach. The technique as presented here is of major interest to the large variety of custom-build systems that are used. The feasibility of the presented method is proven in comparison with published data.

Robust laser beam engineering using polarization and angular momentum diversity.

We describe a laser beam engineered to carry l = 0 and l = 1 orbital angular momentum (OAM) states in orthogonal polarizations. It is observed that on collinear transmission through a random phase screen, the far field diffraction intensity patterns for the individual polarization states are complementary with significant negative correlation. As a result the combined intensity profile for the beam remains robust against time varying phase fluctuations. In our simulation and experiment the SNR for the central lobe of the combined far-field diffraction pattern defined as mean divided by the standard deviation of intensity values shows significant improvement over that for individual polarizations. The concept of polarization and OAM diversity as demonstrated here can be considered valuable for robust laser beam engineering without the requirement of any active real-time correction methods.