Revisiting Javal's rule: a fresh and improved power vector approach according to age

PURPOSE

The scientific community has established Javal's rule as a model linking refractive (RA) and keratometric (KA) astigmatism since its appearance more than 100 years ago. The aim was to improve the accuracy of this relationship according to subject's age by applying the power vector analysis. Posterior corneal curvature has also been studied.

METHODS

The IOLMaster 700 optical biometer was used to measure the corneal thickness and the radius of curvature of the anterior and posterior corneal surfaces. Refractive error was determined by a non-cycloplegic subjective refraction process with trial lenses. Linear regression analyses were applied using J0 and J45 power vector components. An evaluation was carried out according to the subject's age resulting into eight regression relationships for each astigmatic vector component for each relationship.

RESULTS

A total of 2254 right eyes from 2254 healthy subjects were evaluated. A trend towards against-the-rule astigmatism (ATR) was found with aging, both for refractive astigmatism (RA) and keratometric astigmatism (KA), with 95.2% of subjects under 20 years old having with-the-rule (WTR) KA, and only 22.8% above 79 years old. The following regression equations were found between RA and KA: [Formula: see text] = 0.73 × [Formula: see text] - 0.18 (R = 0.78) and [Formula: see text] = 0.70 × [Formula: see text] + 0.04 (R = 0.69) and between RA and total corneal astigmatism (TCA): [Formula: see text] = 0.73 × [Formula: see text] + 0.13 (R=0.78) and [Formula: see text] = 0.70 × [Formula: see text] - 0.06 (R = 0.68) for the whole sample, but with sensible differences among age groups, both in the slope and in the intercept.

CONCLUSION

Ignoring the age of the subject when using Javal's rule could lead to an error in the final cylinder calculation that would increase in high astigmatisms. Applying this new power vector approach based on subject's age could improve the accuracy of the astigmatism prediction.

Physics-driven universal twin-image removal network for digital in-line holographic microscopy

Digital in-line holographic microscopy (DIHM) enables efficient and cost-effective computational quantitative phase imaging with a large field of view, making it valuable for studying cell motility, migration, and bio-microfluidics. However, the quality of DIHM reconstructions is compromised by twin-image noise, posing a significant challenge. Conventional methods for mitigating this noise involve complex hardware setups or time-consuming algorithms with often limited effectiveness. In this work, we propose UTIRnet, a deep learning solution for fast, robust, and universally applicable twin-image suppression, trained exclusively on numerically generated datasets. The availability of open-source UTIRnet codes facilitates its implementation in various DIHM systems without the need for extensive experimental training data. Notably, our network ensures the consistency of reconstruction results with input holograms, imparting a physics-based foundation and enhancing reliability compared to conventional deep learning approaches. Experimental verification was conducted among others on live neural glial cell culture migration sensing, which is crucial for neurodegenerative disease research.

Comparison of Seven Healthy Lifestyle Scores Cardiometabolic Health: Age, Sex, and Lifestyle Interactions in the NutrIMDEA Web-Based Study

BACKGROUND

Global health status concerns both the assessment of wellbeing as well as the associated individualized determinants including quality of life and lifestyle factors. This study aimed to evaluate seven cardiometabolic health related scores and the influence, as well as interactions of lifestyle, heart-related and health-related quality of life (HRQoL) factors in order to inform the future implementation of precision public health (PPH).

METHODS

Data collected from 17,333 participants who were enrolled of the NutrIMDEA study. The data collection period was between May 2020 and November 2020 through an online survey. The baseline questionnaire collected information on socio-demographic data, cardiometabolic history, anthropometric variables and lifestyle aspects. Also, physical and mental component scores of SF12 Health Survey (PCS12/MCS12) were assessed as HRQoL features, which were applied to estimated seven scores (LS7, HLS, 20-years DRS %, FBS, CLI, WAI derived, LWB-I).

RESULTS

Most indices (except FBS, CLI, 20-years DRS % and WAI derived) showed that cardiometabolic outcomes and HRQoL measures were dependent on interactions by age and sex. The largest ponderal effect was found in PA total and Mediterranean Diet Score (MEDAS-14) interaction using LS7 as reference. However, using LWB-I as standard, the greatest effect was found in the quality-of-life feature MCS12. Noteworthy, LS7 showed good discrimination against PCS12, while LWB-I demonstrated excellent discrimination to MCS12.

CONCLUSIONS

A major finding was the interplay between MEDAS-14 and PA on the LS7 scale as well as major effects of lifestyle factors and MCS12/PCS12 among scores, which need to be accounted with precision when implementing cardiometabolic screenings with PPH purposes.

Subjective refraction using power vectors by updating a conventional phoropter with a Stokes lens for continuous astigmatic power generation

PURPOSE

To implement a pure power vector method for monocular subjective refraction using a regular phoropter with the only modification being the inclusion of a Stokes lens. The proposed methodology was tested with three different Stokes lenses, and the results were compared with conventional clinical refraction procedures.

METHODS

Power vector subjective refraction was performed by attaching a Stokes lens to the Risley prism holder. Stokes lenses allow for pure astigmatic compensation in the form of the J0 , J45 components while the spherical lenses in the phoropter allow determination of the spherical component in the form of M (spherical equivalent). The proposed routine is presented step-by-step using three Stokes lenses having different astigmatic powers.

RESULTS

Monocular subjective refraction was performed on 26 healthy subjects with a mean age of 44 ± 16 years, mean spherical equivalent of -0.56 D (range -5.50 to +2.38 D) and refractive astigmatism ≤1.50 D. No differences were found between the results obtained with the conventional technique versus the vector-based procedure for the spherical equivalent (p = 0.28) or astigmatic components (p = 0.34). In addition, visual acuity (VA) was equivalent through the refractions measured with the conventional and vector procedures (p = 0.12). Repeatability coefficients for J0 and J45 with the new vector methodology were <0.38 D.

CONCLUSIONS

The proposed routine could be helpful for cases where it is difficult to get a valid starting point for conventional refraction (e.g., irregular corneas and media opacities), for testing facilities with limited resources/equipment and/or for motivated clinicians who wish to know about alternative methods of refractive error determination.

Single capture bright field and off-axis digital holographic microscopy: publisher's note

This publisher's note contains corrections to Opt. Lett.48, 876 (2023)10.1364/OL.478674.

Vecto-keratometry: determination of anterior corneal astigmatism in manual keratometers using power vectors

BACKGROUND

A new keratometric routine that employs power vector management for manual keratometers is described. This study evaluates the agreement of the new proposed keratometric technique with the classical one.

RESEARCH DESIGN AND METHODS

The applicability of a new keratometric routine was verified using Helmholtz's and Javal's keratometers. Results were obtained by two different and well-trained examiners over two different samples, one including 65 and the other 74 eyes, respectively. Both conventional keratometry and the newly proposed routine (named vecto-keratometry) were used in each eye to obtain the results. The clinical agreement between the methods was evaluated using Bland-Altman and Passing-Bablok analysis.

RESULTS

For Helmholtz's keratometer, Bland-Altman plots showed good agreement between methods for both astigmatic components being J₀ = 0.04 ± 0.20 D and J₄₅ = -0.07 ± 0.17 D. For Javal's keratometer, Passing-Bablok regression test determined regression line for J₀ difference as y₀ = 1.03, confidence interval: [0.98, 1.10] and regression line for J₄₅ difference as y₄₅ = 0.97, confidence interval: [0.83, 1.12].

CONCLUSIONS

Vecto-keratometry provides accurate clinical results. It has been demonstrated that there are no significant differences between methods in any of the power vector astigmatic components; thus, both methods can be applied interchangeably.

Single-shot wavelength-multiplexed phase microscopy under Gabor regime in a regular microscope embodiment

Phase imaging microscopy under Gabor regime has been recently reported as an extremely simple, low cost and compact way to update a standard bright-field microscope with coherent sensing capabilities. By inserting coherent illumination in the microscope embodiment and producing a small defocus distance of the sample at the input plane, the digital sensor records an in-line Gabor hologram of the target sample, which is then numerically post-processed to finally achieve the sample's quantitative phase information. However, the retrieved phase distribution is affected by the two well-known drawbacks when dealing with Gabor's regime, that is, coherent noise and twin image disturbances. Here, we present a single-shot technique based on wavelength multiplexing for mitigating these two effects. A multi-illumination laser source (including 3 diode lasers) illuminates the sample and a color digital sensor (conventional RGB color camera) is used to record the wavelength-multiplexed Gabor hologram in a single exposure. The technique is completed by presenting a novel algorithm based on a modified Gerchberg-Saxton kernel to finally retrieve an enhanced quantitative phase image of the sample, enhanced in terms of coherent noise removal and twin image minimization. Experimental validations are performed in a regular Olympus BX-60 upright microscope using a 20X 0.46NA objective lens and considering static (resolution test targets) and dynamic (living spermatozoa) phase samples.

Single capture bright field and off-axis digital holographic microscopy

We report on a single capture approach for simultaneous incoherent bright field (BF) and laser-based quantitative phase imaging (QPI). Common-path digital holographic microscopy (DHM) is implemented in parallel with BF imaging within the optical path of a commercial optical microscope to achieve spatially multiplexed recording of white light images and digital off-axis holograms, which are subsequently numerically demultiplexed. The performance of the proposed multimodal concept is firstly determined by investigations on microspheres. Then, the application for label-free dual-mode QPI and BF imaging of living pancreatic tumor cells is demonstrated.

Fluholoscopy-Compact and Simple Platform Combining Fluorescence and Holographic Microscopy

The combination of different imaging modalities into single imaging platforms has a strong potential in biomedical sciences as it permits the analysis of complementary properties of the target sample. Here, we report on an extremely simple, cost-effective, and compact microscope platform for achieving simultaneous fluorescence and quantitative phase imaging modes with the capability of working in a single snapshot. It is based on the use of a single illumination wavelength to both excite the sample's fluorescence and provide coherent illumination for phase imaging. After passing the microscope layout, the two imaging paths are separated using a bandpass filter, and the two imaging modes are simultaneously obtained using two digital cameras. We first present calibration and analysis of both fluorescence and phase imaging modalities working independently and, later on, experimental validation for the proposed common-path dual-mode imaging platform considering static (resolution test targets, fluorescent micro-beads, and water-suspended lab-made cultures) as well as dynamic (flowing fluorescent beads, human sperm cells, and live specimens from lab-made cultures) samples.

Multi-Illumination Single-Holographic-Exposure Lensless Fresnel (MISHELF) Microscopy: Principles and Biomedical Applications

Lensless holographic microscopy (LHM) comes out as a promising label-free technique since it supplies high-quality imaging and adaptive magnification in a lens-free, compact and cost-effective way. Compact sizes and reduced prices of LHMs make them a perfect instrument for point-of-care diagnosis and increase their usability in limited-resource laboratories, remote areas, and poor countries. LHM can provide excellent intensity and phase imaging when the twin image is removed. In that sense, multi-illumination single-holographic-exposure lensless Fresnel (MISHELF) microscopy appears as a single-shot and phase-retrieved imaging technique employing multiple illumination/detection channels and a fast-iterative phase-retrieval algorithm. In this contribution, we review MISHELF microscopy through the description of the principles, the analysis of the performance, the presentation of the microscope prototypes and the inclusion of the main biomedical applications reported so far.

Hilbert phase microscopy based on pseudo thermal illumination in the Linnik configuration

Quantitative phase microscopy (QPM) is often based on recording an object-reference interference pattern and its further phase demodulation. We propose pseudo Hilbert phase microscopy (PHPM) where we combine pseudo thermal light source illumination and Hilbert spiral transform (HST) phase demodulation to achieve hybrid hardware-software-driven noise robustness and an increase in resolution of single-shot coherent QPM. Those advantageous features stem from physically altering the laser spatial coherence and numerically restoring spectrally overlapped object spatial frequencies. The capabilities of PHPM are demonstrated by analyzing calibrated phase targets and live HeLa cells in comparison with laser illumination and phase demodulation via temporal phase shifting (TPS) and Fourier transform (FT) techniques. The performed studies verified the unique ability of PHPM to combine single-shot imaging, noise minimization, and preservation of phase details.

Shadowfocimetry: adapting the holographic principle to a manual focimeter for visualization/marking of permanent engravings in progressive addition lenses

Focimeters, especially manual versions, are the most used ophthalmic devices for dioptric power measurement in optometric clinical care. In the particular case of progressive addition lenses (PALs), they are used to determine far/near vision correction powers, but the user/clinician needs to know at which part of the PAL the measurement must be taken. For this reason, PALs have permanent engravings acting as reference marks to define the far/near vision areas for every PAL design. However, for several reasons these engravings are often difficult to localize and identify, making an accurate dioptric power determination difficult. In this Letter, we present an adaptation of the Gabor holographic principle to a manual focimeter and describe the methodology for the correct localization, visualization, and marking process of the reference engravings in PALs. Experimental results considering different types of PALs are included and the main limitations of the technique are also discussed.

Astigmatic Stokes lens revisited

Stokes lenses are variable power astigmatic lenses comprising of, in its standard version, two pure cylindrical lenses of equal but contrary power that rotate in opposite directions. Here, we present an optical device with variable and continuous astigmatic power which is based on a modified Stokes lens where two sphero-cylindrical lenses (in the form of pure astigmatic lenses) are combined in the classical way but merged with another fixed pure astigmatic lens for improving the capabilities of the resulting optical device concerning the expansion of the astigmatic range without worsening the dioptric power step resolution. The performance of this device is theoretically analyzed in virtue of the power vectors formalism including a three-dimensional (3-D) representation of the generated dioptric power as a function of both the meridian and the rotation angle between the cylinder's axes. In addition, we have assembled a lab-made prototype of the proposed modified Stokes lens and validated its theoretical behavior by dioptric power measurements with an automatic focimeter. As conventional Stokes lenses, the applications of this new optical device range from astigmatism compensation in optical instruments to measurement of refractive error in subjective routines with the previously commented improved capabilities.

Design, Calibration, and Application of a Robust, Cost-Effective, and High-Resolution Lensless Holographic Microscope

Lensless holographic microscope (LHM) is an emerging very promising technology that provides high-quality imaging and analysis of biological samples without utilizing any lens for imaging. Due to its small size and reduced price, LHM can be a very useful tool for the point-of-care diagnosis of diseases, sperm assessment, or microfluidics, among others, not only employed in advanced laboratories but also in poor and/or remote areas. Recently, several LHMs have been reported in the literature. However, complete characterization of their optical parameters remains not much presented yet. Hence, we present a complete analysis of the performance of a compact, reduced cost, and high-resolution LHM. In particular, optical parameters such as lateral and axial resolutions, lateral magnification, and field of view are discussed into detail, comparing the experimental results with the expected theoretical values for different layout configurations. We use high-resolution amplitude and phase test targets and several microbeads to characterize the proposed microscope. This characterization is used to define a balanced and matched setup showing a good compromise between the involved parameters. Finally, such a microscope is utilized for visualization of static, as well as dynamic biosamples.

Optical module for single-shot quantitative phase imaging based on the transport of intensity equation with field of view multiplexing

We present a cost-effective, simple, and robust method that enables single-shot quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) using an add-on optical module that can be assembled into the exit port of any regular microscope. The module integrates a beamsplitter (BS) cube (placed in a non-conventional way) for duplicating the output image onto the digital sensor (field of view - FOV - multiplexing), a Stokes lens (SL) for astigmatism compensation (introduced by the BS cube), and an optical quality glass plate over one of the FOV halves for defocusing generation (needed for single-shot TIE algorithm). Altogether, the system provides two laterally separated intensity images that are simultaneously recorded and slightly defocused one to each other, thus enabling accurate QPI by conventional TIE-based algorithms in a single snapshot. The proposed optical module is first calibrated for defining the configuration providing best QPI performance and, second, experimentally validated by using different phase samples (static and dynamic ones). The proposed configuration might be integrated in a compact three-dimensional (3D) printed module and coupled to any conventional microscope for QPI of dynamic transparent samples.

Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy

We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by applying the golden selection search with parabolic interpolation, which is the gold standard for tackling single-variable optimization problems. The proposed approach is successfully applied to three diverse autofocusing cases, providing up to 136-fold speed-up.

Author Correction: Variational Hilbert Quantitative Phase Imaging

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Variational Hilbert Quantitative Phase Imaging

Utilizing the refractive index as the endogenous contrast agent to noninvasively study transparent cells is a working principle of emerging quantitative phase imaging (QPI). In this contribution, we propose the Variational Hilbert Quantitative Phase Imaging (VHQPI)-end-to-end purely computational add-on module able to improve performance of a QPI-unit without hardware modifications. The VHQPI, deploying unique merger of tailored variational image decomposition and enhanced Hilbert spiral transform, adaptively provides high quality map of sample-induced phase delay, accepting particularly wide range of input single-shot interferograms (from off-axis to quasi on-axis configurations). It especially promotes high space-bandwidth-product QPI configurations alleviating the spectral overlapping problem. The VHQPI is tailored to deal with cumbersome interference patterns related to detailed locally varying biological objects with possibly high dynamic range of phase and relatively low carrier. In post-processing, the slowly varying phase-term associated with the instrumental optical aberrations is eliminated upon variational analysis to further boost the phase-imaging capabilities. The VHQPI is thoroughly studied employing numerical simulations and successfully validated using static and dynamic cells phase-analysis. It compares favorably with other single-shot phase reconstruction techniques based on the Fourier and Hilbert-Huang transforms, both in terms of visual inspection and quantitative evaluation, potentially opening up new possibilities in QPI.

Characterization of a compact low-cost Stokes lens for astigmatism compensation in optical instruments

Variable power cross-cylinder lenses (or Stokes lenses) have been widely known in the literature for decades. In this paper, we describe how to build a low-cost Stokes lens and discuss its calibration and its application to two significant cases. The construction is in virtue of a phoropter's Risley prism mount for assembling a couple of equal but opposite sign cylindrical lenses (we have selected $\,\pm 1.50$±1.50 D). Thus, variable astigmatic power is achieved by relative rotation of the lenses in opposite directions, and the resulting astigmatic axis is defined by the global rotation of the device. Calibration measurements are performed using an automatic lensmeter (Topcon CL-300) and an aberrometer (Zeiss iProfiler plus) for low and high order, respectively, aberration characterization. The proposed device has been adapted to a manual Topcon LM-8 lensmeter and to a regular Olympus BX-60 upright microscope for experimental validation concerning astigmatism compensation in a digital microscope and astigmatism cancellation in ophthalmic lenses, respectively. The device can be easily adapted to any ophthalmic/optic instrument for the compensation and/or measurement of astigmatism up to a maximum range of $|3|$|3| D of astigmatism.

Single-shot slightly off-axis digital holographic microscopy with add-on module based on beamsplitter cube

Slightly off-axis digital holographic microscopy (SO-DHM) has recently emerged as a novel experimental arrangement for quantitative phase imaging (QPI). It offers improved capabilities in conventional on-axis and off-axis interferometric configurations. In this contribution, we report on a single-shot SO-DHM approach based on an add-on module adapted to the exit port of a regular microscope. The module employs a beamsplitter (BS) cube interferometer and includes, in addition, a Stokes lens (SL) for astigmatism compensation. Each recorded frame contains two fields of view (FOVs) of the sample, where each FOV is a hologram which is phase shifted by π rads with respect to the other. These two simultaneously recorded holograms are numerically processed, in order to retrieve complex amplitude distribution with enhanced quality. The tradeoff is done in the FOV which becomes penalized as a consequence of the simultaneous recording of the two holograms in a single snapshot. Experimental validation is presented for a wide variety of samples using a regular Olympus BX-60 upright microscope. The proposed approach provides an optimized use of the imaging system, in terms of the space-bandwidth product, in comparison with off-axis configuration; allows the analysis of fast-dynamic events, owing to its single-shot capability when compared with on-axis arrangement; and becomes easily implementable in conventional white-light microscopes for upgrading them into holographic microscopes for QPI.

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy (H2S2MIM) is presented as the implementation of a robust, fast, and accurate single-shot phase estimation algorithm with an extremely simple, low-cost, and highly stable way to convert a bright field microscope into a holographic one using partially coherent illumination. Altogether, H2S2MIM adds high-speed (video frame rate) quantitative phase imaging capability to a commercially available nonholographic microscope with improved phase reconstruction (coherence noise reduction). The technique has been validated using a 20×/0.46  NA objective in a regular Olympus BX-60 upright microscope for static, as well as dynamic, samples showing perfect agreement with the results retrieved from a temporal phase-shifting algorithm.

Effect of counting chamber depth on the accuracy of lensless microscopy for the assessment of boar sperm motility

Sperm motility is one of the most significant parameters in the prediction of male fertility. Until now, both motility analysis using an optical microscope and computer-aided sperm analysis (CASA-Mot) entailed the use of counting chambers with a depth to 20 µm. Chamber depth significantly affects the intrinsic sperm movement, leading to an artificial motility pattern. For the first time, laser microscopy offers the possibility of avoiding this interference with sperm movement. The aims of the present study were to determine the different motility patterns observed in chambers with depths of 10, 20 and 100 µm using a new holographic approach and to compare the results obtained in the 20-µm chamber with those of the laser and optical CASA-Mot systems. The ISAS®3D-Track results showed that values for curvilinear velocity (VCL), straight line velocity, wobble and beat cross frequency were higher for the 100-µm chambers than for the 10- and 20-µm chambers. Only VCL showed a positive correlation between chambers. In addition, Bayesian analysis confirmed that the kinematic parameters observed with the 100-µm chamber were significantly different to those obtained using chambers with depths of 10 and 20 µm. When an optical analyser CASA-Mot system was used, all kinematic parameters, except VCL, were higher with ISAS®3D-Track, but were not relevant after Bayesian analysis. Finally, almost three different three-dimensional motility patterns were recognised. In conclusion, the use of the ISAS®3D-Track allows for the analysis of the natural three-dimensional pattern of sperm movement.

Single-shot, dual-mode, water-immersion microscopy platform for biological applications

A single-shot water-immersion digital holographic microscope combined with broadband (white light) illumination mode is presented. This double imaging platform allows conventional incoherent visualization with phase holographic imaging of inspected samples. The holographic architecture is implemented at the image space (that is, after passing the microscope lens), thus reducing the sensitivity of the system to vibrations and/or thermal changes in comparison to regular interferometers. Because of the off-axis holographic recording principle, quantitative phase images of live biosamples can be recorded in a single camera snapshot at full-field geometry without any moving parts. And, the use of water-immersion imaging lenses maximizes the achievable resolution limit. This dual-mode microscope platform is first calibrated using microbeads, then applied to the characterization of fixed cells (neuroblastoma, breast cancer, and hippocampal neuronal cells) and, finally, validated for visualization of dynamic living cells (hippocampal neurons).

Superresolved spatially multiplexed interferometric microscopy

Superresolution capability by angular and time multiplexing is implemented onto a regular microscope. The technique, named superresolved spatially multiplexed interferometric microscopy (S2MIM), follows our previously reported SMIM technique [Opt. Express22, 14929 (2014)OPEXFF1094-408710.1364/OE.22.014929, J. Biomed. Opt.21, 106007 (2016)JBOPFO1083-366810.1117/1.JBO.21.10.106007] improved with superresolved imaging. All together, S2MIM updates a commercially available non-holographic microscope into a superresolved holographic one. Validation is presented for an Olympus BX-60 upright microscope with resolution test targets.

An alternative clinical routine for subjective refraction based on power vectors with trial frames

PURPOSE

Subjective refraction determines the final point of refractive error assessment in most clinical environments and its foundations have remained unchanged for decades. The purpose of this paper is to compare the results obtained when monocular subjective refraction is assessed in trial frames by a new clinical procedure based on a pure power vector interpretation with conventional clinical refraction procedures.

METHODS

An alternative clinical routine is described that uses power vector interpretation with implementation in trial frames. Refractive error is determined in terms of: (i) the spherical equivalent (M component), and (ii) a pair of Jackson Crossed Cylinder lenses oriented at 0°/90° (J₀ component) and 45°/135° (J₄₅ component) for determination of astigmatism. This vector subjective refraction result (VR) is compared separately for right and left eyes of 25 subjects (mean age, 35 ± 4 years) against conventional sphero-cylindrical subjective refraction (RX) using a phoropter. The VR procedure was applied with both conventional tumbling E optotypes (VR1) and modified optotypes with oblique orientation (VR2).

RESULTS

Bland-Altman plots and intra-class correlation coefficient showed good agreement between VR, and RX (with coefficient values above 0.82) and anova showed no significant differences in any of the power vector components between RX and VR. VR1 and VR2 procedure results were similar (p ≥ 0.77).

CONCLUSIONS

The proposed routine determines the three components of refractive error in power vector notation [M, J₀ , J₄₅ ], with a refraction time similar to the one used in conventional subjective procedures. The proposed routine could be helpful for inexperienced clinicians and for experienced clinicians in those cases where it is difficult to get a valid starting point for conventional RX (irregular corneas, media opacities, etc.) and for refractive situations/places with inadequate refractive facilities/equipment.

Spatially multiplexed interferometric microscopy with partially coherent illumination

We have recently reported on a simple, low cost, and highly stable way to convert a standard microscope into a holographic one [Opt. Express 22, 14929 (2014)]. The method, named spatially multiplexed interferometric microscopy (SMIM), proposes an off-axis holographic architecture implemented onto a regular (nonholographic) microscope with minimum modifications: the use of coherent illumination and a properly placed and selected one-dimensional diffraction grating. In this contribution, we report on the implementation of partially (temporally reduced) coherent illumination in SMIM as a way to improve quantitative phase imaging. The use of low coherence sources forces the application of phase shifting algorithm instead of off-axis holographic recording to recover the sample’s phase information but improves phase reconstruction due to coherence noise reduction. In addition, a less restrictive field of view limitation (1/2) is implemented in comparison with our previously reported scheme (1/3). The proposed modification is experimentally validated in a regular Olympus BX-60 upright microscope considering a wide range of samples (resolution test, microbeads, swine sperm cells, red blood cells, and prostate cancer cells).

Improved quantitative phase imaging in lensless microscopy by single-shot multi-wavelength illumination using a fast convergence algorithm

We report on a novel algorithm for high-resolution quantitative phase imaging in a new concept of lensless holographic microscope based on single-shot multi-wavelength illumination. This new microscope layout, reported by Noom et al. along the past year and named by us as MISHELF (initials incoming from Multi-Illumination Single-Holographic-Exposure Lensless Fresnel) microscopy, rises from the simultaneous illumination and recording of multiple diffraction patterns in the Fresnel domain. In combination with a novel and fast iterative phase retrieval algorithm, MISHELF microscopy is capable of high-resolution (micron range) phase-retrieved (twin image elimination) biological imaging of dynamic events. In this contribution, MISHELF microscopy is demonstrated through qualitative concept description, algorithm implementation, and experimental validation using both a synthetic object (resolution test target) and a biological sample (swine sperm sample) for the case of three (RGB) illumination wavelengths. The proposed method becomes in an alternative instrument improving the capabilities of existing lensless microscopes.

Step-along power vector method for astigmatic wavefront propagation

PURPOSE

To propose both a new algebraic solution and a graphical monitoring method for astigmatic wavefront propagation in the framework provided by power vectors.

METHODS

The generalised propagation equation describing the propagation of astigmatic wavefronts from one plane to another is adapted to the power vectors formalism using a novel algorithm based on a step-along method. The step-along procedure is directly applied to the tuple of power vectors [M, J0 , J45 ] representing an arbitrary astigmatic wavefront and it permits the calculation of the tuple of power vectors [M', J'0 , J'45 ] after a given propagation distance. This is achieved mathematically first by temporarily rotating the astigmatic wavefront so that one of the principal meridians is horizontal, then propagating the wavefront, and finally rotating the propagated wavefront back to its original orientation.

RESULTS

A transfer rule for power vectors representing astigmatic wavefronts is analytically obtained. The new algorithm provides an algebraic solution for the propagation of astigmatic wavefronts using power vectors in a homogeneous medium. In addition, the new step-along procedure allows 2D as well as 3D graphical monitoring of the astigmatic wavefront being referred to the X-Y conventional reference framework by virtue of the trajectories of the power vector coordinates. The proposed solution has been validated through several numerical examples.

CONCLUSIONS

A new step-along method for astigmatic wavefront propagation using power vectors has been presented and validated for classical as well as new numerical examples. The method provides algebraic calculation as well as graphical monitoring of the wavefront vergence during propagation.

Wavefront holoscopy: application of digital in-line holography for the inspection of engraved marks in progressive addition lenses

Progressive addition lenses (PALs) are engraved with permanent marks at standardized locations in order to guarantee correct centering and alignment throughout the manufacturing and mounting processes. Out of the production line, engraved marks provide useful information about the PAL as well as act as locator marks to re-ink again the removable marks. Even though those marks should be visible by simple visual inspection with the naked eye, engraving marks are often faint and weak, obscured by scratches, and partially occluded and difficult to recognize on tinted or antireflection-coated lenses. Here, we present an extremely simple optical device (named as wavefront holoscope) for visualization and characterization of permanent marks in PAL based on digital in-line holography. Essentially, a point source of coherent light illuminates the engraved mark placed just before a CCD camera that records a classical Gabor in-line hologram. The recorded hologram is then digitally processed to provide a set of high-contrast images of the engraved marks. Experimental results are presented showing the applicability of the proposed method as a new ophthalmic instrument for visualization and characterization of engraved marks in PALs.

Speckle-based configuration for simultaneous in vitro inspection of mechanical contractions of cardiac myocyte cells

An optical lensless configuration for a remote noncontact measuring of mechanical contractions of a vast number of cardiac myocytes is proposed. All the myocytes were taken from rats, and the measurements were done in an in vitro mode. The optical method is based on temporal analysis of secondary reflected speckle patterns generated in lensless microscope configuration. The processing involves analyzing the movement and the change in the statistics of the secondary speckle patterns that are created on top of the cell culture when it is illuminated by a spot of laser beam. The main advantage of the proposed system is the ability to measure many cells simultaneously (∼1000 cells) and to extract the statistical data of their movement at once. The presented experimental results also include investigation of the effect of isoproteranol on cell contraction process.

Lensless object scanning holography for two-dimensional mirror-like and diffuse reflective objects

Recently proposed lensless object scanning holography (LOSH) [Opt. Express 20, 9382 (2012)] is a fully lensless method capable of improving the image quality in digital Fourier holography applied to one-dimensional (1D) reflective objects and it involves a very simplified experimental setup. LOSH is based on the recording and digital postprocessing of a set of digital lensless Fourier transform holograms, which finally results in a synthetic image with improved resolution, field-of-view (FOV), signal-to-noise ratio (SNR), and depth of field. In this paper, LOSH is extended to the cases of two-dimensional (2D) mirror-like and 1D diffuse-based objects. For 2D mirror-like objects, the experimental results show an impressive image quality improvement over a factor of 3 in FOV, SNR, and resolution, as good as that obtained for the 1D case but in two dimensions. For 1D diffuse-based objects, in general the speckle affects the image resolution, which will not be only a function of the aperture size. In this case, increasing the aperture produces a decrease of the speckle size. Moreover, due to the overlapping of speckles between successive images, different types of digital processing can be applied to obtain the final synthetic image: fully incoherent, fully coherent, and partially coherent. The last, arising from the incoherent sum of several independent sets of coherently added images, provides the best improvement in the resolution. Experimental results for both types of objects are presented.

Lateral magnification matrix from the dioptric power matrix formalism in the paraxial case

BACKGROUND

Previous studies have highlighted that power matrices fully characterize the concept of dioptric power of any astigmatic surface. Thus, the basic equations in physiological optics can be generalized using the matrix formalism of the dioptric power. Among others, lateral magnification has also been interpreted as a matrix but mainly concerning magnification modification induced by spectacle correction of refractive error.

PURPOSE

To provide a fresh look into a novel paraxial formulation for the assessment of the lateral magnification using power matrices and in presence of astigmatism for thin and thick imaging systems in general.

METHODS

Linear optics provides the frame to generalize into a matrix the lateral magnification concept. Using the power matrix formalism, a lateral magnification matrix is derived in virtue of the dioptric power matrix and the object's reduced axial object distance for the paraxial case. In addition, two different degrees of approximation (thin lens and distant object approximations) are analyzed to further simplify the calculations.

RESULTS

A general formulation of the lateral magnification matrix is obtained and validated by numerical examples showing its applicability to different examples in geometrical and physiological optics. As particular case of interest, the degree of asymmetry of the lateral magnification matrix has been derived from the degree of asymmetry of the dioptric power matrix when dealing with obliquely crossed astigmatic thick lenses.

CONCLUSIONS

The new formulation is applicable under paraxial approximation and is useful for arbitrary thin and thick imaging systems in any media of homogeneous index of refraction (air and others) and including obliquely crossed astigmatic surfaces. The proposed formulation also yields in a novel interpretation of the lateral magnification matrix concept.

Superresolved common-path phase-shifting digital inline holographic microscopy using a spatial light modulator

Common-path phase-shifting lensless holographic microscopy has been recently proposed as a novel approach capable of high numerical aperture imaging in a lensless digital inline holographic microscopy layout [Opt. Lett.35, 3919 (2010)]. Here we present proof-of-concept validation for improving the resolution limit imposed by diffraction in such a setup. This is accomplished by shifting the phase lens displayed at the spatial light modulator, which moves the illumination point source to different off-axis positions. For each off-axis position, a set of inline phase-shifted holograms are recorded by the digital sensor and stored at the computer's memory for later digital postprocessing. As a consequence, each recording allows the recovery of different spatial frequency content of the object's diffracted wavefront meaning a superresolved image of the input object. Experimental results are reported validating the proposed method.

Superresolved and field-of-view extended digital holography with particle encoding

We present a new configuration for superresolution (SR) as well as for field-of-view (FOV) extension in a digital holography concept based on random movement of sparse metallic particles. In the SR configuration, the particles are in proximity to the recorded object, while in the FOV configuration, the particles are in proximity to the hologram plane. The particles' movement encodes the high spatial features in the plane of their movement. This high-resolution information can later be decoded by proper numerical postprocessing that either remedies the resolution limitations in the object plane (or the limited NA of the lens) or extends the FOV in the object plane.

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.

Resolution improvement by single-exposure superresolved interferometric microscopy with a monochrome sensor

Single-exposure superresolved interferometric microscopy (SESRIM) by RGB multiplexing has recently been proposed as a way to achieve one-dimensional superresolved imaging in digital holographic microscopy by a single-color CCD snapshot [Opt. Lett. 36, 885 (2011)]. Here we provide the mathematical basis for the operating principle of SESRIM, while we also present a different experimental configuration where the color CCD camera is replaced by a monochrome (B&W) CCD camera. To maintain the single-exposure working principle, the object field of view (FOV) is restricted and the holographic recording is based on image-plane wavelength-dispersion spatial multiplexing to separately record the three bandpass images. Moreover, a two-dimensional extension is presented by considering two options: time multiplexing and selective angular multiplexing. And as an additional implementation, the FOV restriction is eliminated by varying the angle between the three reference beams in the interferometric recording. Experimental results are reported for all of the above-mentioned cases.

Single-exposure two-dimensional superresolution in digital holography using a vertical cavity surface-emitting laser source array

We present a new implementation capable of producing two-dimensional (2D) superresolution (SR) imaging in a single exposure by aperture synthesis in digital lensless Fourier holography when using angular multiplexing provided by a vertical cavity surface-emitting laser source array. The system performs the recording in a single CCD snapshot of a multiplexed hologram coming from the incoherent addition of multiple subholograms, where each contains information about a different 2D spatial frequency band of the object's spectrum. Thus, a set of nonoverlapping bandpass images of the input object can be recovered by Fourier transformation (FT) of the multiplexed hologram. The SR is obtained by coherent addition of the information contained in each bandpass image while generating an enlarged synthetic aperture. Experimental results demonstrate improvement in resolution and image quality.

Single-exposure super-resolved interferometric microscopy by red-green-blue multiplexing

We present single-exposure super-resolved interferometric microscopy (SESRIM) as a novel approach capable of providing one-dimensional (1-D) super-resolution (SR) imaging in holographic microscopy using a single illumination shot. The single-exposure SR working principle is achieved by combining angular and wavelength multiplexing incoming from a set of tilted beams with different wavelengths where each wavelength is tuned with the red-green-blue (RGB) channels of a color CCD. Thus, the information included in each color channel is retrieved by holographic recording using a single-color CCD capture and by analyzing the RGB channels. Finally, 1-D SR imaging is obtained after the digital postprocessing stage yielding the generation of a synthetic aperture. Experimental results are reported validating the proposed SESRIM approach while an extension of the proposed approach to the two-dimensional case is considered.

Common-path phase-shifting lensless holographic microscopy

We present an approach capable of high-NA imaging in a lensless digital in-line holographic microscopy layout even outside the Gabor's regime. The method is based on spatial multiplexing at the sample plane, allowing a common-path interferometric architecture, where two interferometric beams are generated by a spatial light modulator (SLM) prior to illuminating the sample. The SLM allows phase-shifting interferometry by phase modulation of the SLM diffracted beam. After proper digital processing, the complex amplitude distribution of the diffracted object wavefront is recovered and numerically propagated to image the sample. Experimental results are reported that validate the proposed method.

Linear optics based nanoscopy

Classically, optical systems are considered to have a fundamental resolution limit due to wave nature of light. This article presents a novel method for observing sub-wavelength features in a conventional optical microscope using linear optics. The operation principle is based on a random and time varying flow of nanoparticles moving in proximity to the inspected sample. Those particles excite the evanescent waves and couple them into harmonic waves. The sub-wavelength features are encoded and later on digitally decoded by proper image processing of a sequence of images. The achievable final resolution limit corresponds to the size of the nanoparticles. Experimental proof of principle validation of the technique is reported.

Random angular coding for superresolved imaging

In this paper, we present a new approach capable of working under coherent and incoherent illumination for achieving superresolution by random coding of the object's angular information. By placing two static random masks in optically conjugate planes inside an aperture-limited imaging setup, one may obtain a transmitted image containing spatial resolution higher than the one obtained without the masks. As the most noticeable fact, the superresolution effect is obtained without imposing any restrictions either in the time domain or in the field-of-view domain but rather only in the dynamic range of the camera device. Experimental verifications for the proposed technique with incoherent illumination with a low numerical aperture (NA) lens are presented.

Superresolved digital in-line holographic microscopy for high-resolution lensless biological imaging

Digital in-line holographic microscopy (DIHM) is a modern approach capable of achieving micron-range lateral and depth resolutions in three-dimensional imaging. DIHM in combination with numerical imaging reconstruction uses an extremely simplified setup while retaining the advantages provided by holography with enhanced capabilities derived from algorithmic digital processing. We introduce superresolved DIHM incoming from time and angular multiplexing of the sample spatial frequency information and yielding in the generation of a synthetic aperture (SA). The SA expands the cutoff frequency of the imaging system, allowing submicron resolutions in both transversal and axial directions. The proposed approach can be applied when imaging essentially transparent (low-concentration dilutions) and static (slow dynamics) samples. Validation of the method for both a synthetic object (U.S. Air Force resolution test) to quantify the resolution improvement and a biological specimen (sperm cells biosample) are reported showing the generation of high synthetic numerical aperture values working without lenses.

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).

Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information

The resolving power of an imaging system in digital lensless Fourier holographic configuration is mainly limited by the numerical aperture of the experimental setup that is defined by both the restricted CCD size and the presence of a beam splitter cube in front of the CCD. We present a method capable of improving the resolution in such a system configuration based on synthetic aperture (SA) generation by using time-multiplexing tilted illumination onto the input object. Moreover, a priori knowledge about the imaged object allows customized SA shaping by the addition of elementary apertures only in the directions of interest. Experimental results are provided, showing agreement with theoretical predictions and demonstrating a resolution limit corresponding with a synthetic numerical aperture value of 0.45.

Superresolution imaging method using phase-shifting digital lensless Fourier holography

A method which is useful for obtaining superresolved imaging in a digital lensless Fourier holographic configuration is presented. By placing a diffraction grating between the input object and the CCD recording device, additional high-order spatial-frequency content of the object spectrum is directed towards the CCD. Unlike other similar methods, the recovery of the different band pass images is performed by inserting a reference beam in on-axis mode and using phase-shifting method. This strategy provides advantages concerning the usage of the whole frequency plane as imaging plane. Thus, the method is no longer limited by the zero order term and the twin image. Finally, the whole process results in a synthetic aperture generation that expands up the system cutoff frequency and yields a superresolution effect. Experimental results validate our concepts for a resolution improvement factor of 3.

Phase-shifting Gabor holography

We present a modified Gabor-like setup able to recover the complex amplitude distribution of the object wavefront from a set of inline recorded holograms. The proposed configuration is characterized by the insertion of a condenser lens and a spatial light modulator (SLM) into the classical Gabor configuration. The phase shift is introduced by the SLM that modulates the central spot (dc term) in an intermediate plane, without an additional reference beam. Experimental results validate the proposed method and produce superior results to the Gabor method.