Wavefront Aberration Measurement Research Articles

Image system analysis of human eye wave-front aberration on the basis of HSS

Hartmann–Shack sensor (HSS) has been used in objective measurement of human eye wave-front aberration, but the research on the effects of sampling point size on the accuracy of the result has not been reported. In this paper, point spread function (PSF) of the whole system mathematical model was obtained via measuring the optical imaging system structure of human eye wave-front aberration measurement. The impact of Airy spot size on the accuracy of system was analyzed. Statistics study show that the geometry of Airy spot size of the ideal light source sent from eye retina formed on the surface of HSS is far smaller than the size of the HSS sample point image used in the experiment. Therefore, the effect of Airy spot on the precision of the system can be ignored. This study theoretically and experimentally justifies the reliability and accuracy of human eye wave-front aberration measurement based on HSS.

Focusing characteristics of a 4 \u03c0parabolic mirror light-matter interface

BackgroundFocusing with a 4 π parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror’s fabrication process and might introduce errors that reduce the focusing quality.MethodsTo determine these errors, we experimentally examine the focusing properties of a 4 π parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single 174Yb + ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap.ResultsWe demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface.ConclusionOur findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4 π parabolic mirror.

Design and fabrication of a passive droplet dispenser for portable high resolution imaging system

Moldless lens manufacturing techniques using standard droplet dispensing technology often require precise control over pressure to initiate fluid flow and control droplet formation. We have determined a series of interfacial fluid parameters optimised using standard 3D printed tools to extract, dispense and capture a single silicone droplet that is then cured to obtain high quality lenses. The dispensing process relies on the recapitulation of liquid dripping action (Rayleigh-Plateau instability) and the capturing method uses the interplay of gravitational force, capillary forces and liquid pinning to control the droplet shape. The key advantage of the passive lens fabrication approach is rapid scale-up using 3D printing by avoiding complex dispensing tools. We characterise the quality of the lenses fabricated using the passive approach by measuring wavefront aberration and high resolution imaging. The fabricated lenses are then integrated into a portable imaging system; a wearable thimble imaging device with a detachable camera housing, that is constructed for field imaging. This paper provides the full exposition of steps, from lens fabrication to imaging platform, necessary to construct a standalone high resolution imaging system. The simplicity of our methodology can be implemented using a regular desktop 3D printer and commercially available digital imaging systems.

Wavefront measurement of plastic lenses for mobile-phone applications

Abstract In camera lenses for mobile-phone applications, all lens elements have been designed with aspheric surfaces because of the requirements in minimal total track length of the lenses. Due to the diffraction-limited optics design with precision assembly procedures, element inspection and lens performance measurement have become cumbersome in the production of mobile-phone cameras. Recently, wavefront measurements based on Shack-Hartmann sensors have been successfully implemented on injection-molded plastic lens with aspheric surfaces. However, the applications of wavefront measurement on small-sized plastic lenses have yet to be studied both theoretically and experimentally. In this paper, both an in-house-built and a commercial wavefront measurement system configured on two optics structures have been investigated with measurement of wavefront aberrations on two lens elements from a mobile-phone camera. First, the wet-cell method has been employed for verifications of aberrations due to residual birefringence in an injection-molded lens. Then, two lens elements of a mobile-phone camera with large positive and negative power have been measured with aberrations expressed in Zernike polynomial to illustrate the effectiveness in wavefront measurement for troubleshooting defects in optical performance.

Wavefront aberration measurement method for a hyper-NA lithographic projection lens based on principal component analysis of an aerial image.

A wavefront aberration measurement method for a hyper-NA lithographic projection lens by use of an aerial image based on principal component analysis is proposed. Aerial images of the hyper-NA lithographic projection lens are expressed accurately by using polarized light and a vector imaging model, as well as by considering the polarization properties. As a result, the wavefront aberrations of the hyper-NA lithographic projection lens are measured accurately. The lithographic simulator PROLITH is used to validate the accuracies of the wavefront aberration measurement and analyze the impact of the polarization rotation of illumination on the accuracy of the wavefront aberration measurement, as well as the degree of polarized light and the sample interval of aerial images. The result shows that the proposed method can retrieve 33 terms of Zernike coefficients (Z5-Z37) with a maximum error of less than 0.00085λ.

Measurements of Pupillary Diameter and Wavefront Aberrations in Pregnant Women.

Purpose. To show whether pregnancy affects the measurements of pupillary diameter and wavefront (WF) aberrations. Methods. This was a case-control study including 34 healthy pregnant women in the third trimester and age-matched 34 nonpregnant women. Only women who had no ocular abnormalities and no refractive error were included. We measured photopic and mesopic pupil diameter and WF aberrations at the third trimester and at the second postpartum month. Measurements of the right eyes were used in this study. The differences between groups were analysed by paired t-test and t-test. Results. Pregnant women's mean photopic pupil size in the third trimester was significantly higher than in postpartum period and in control group (3.74 ± 0.77, 3.45 ± 0.53, and 3.49 ± 0.15 mm, p < 0.05, resp.). Mesopic pupil size in the third trimester was also higher than in postpartum period and in control group (6.77 ± 0.52, 6.42 ± 0.55, and 6.38 ± 0.21 mm, p < 0.05, resp.). RMS-3 and RMS-5 values were higher in pregnancy but these differences were not statistically significant. Conclusion. Pregnancy increased photopic and mesopic pupil size significantly but did not increase wavefront aberrations notably. Increased pupil size may be due to increased sympathetic activity during pregnancy. And this activity can be noninvasively determined by measuring pupil size.

基于光学相干层析成像的视网膜图像自动分层方法

Ptychography, a phase retrieval technology based on scanning coherent diffractive imaging, shows such advantages as simple experimental setup and strong anti-noise ability. Ptychography is used in the field of wavefront metrology for projection lens. The formulas of optical field propagation, the conditions of discretion, and the experimental configurations are analyzed in detail for projection lenses with different numerical apertures. Numerical simulations and experimental results show that to achieve reasonable convergence and measurement accuracy, the transmittance of the object should be set between 45% and 80%. Increasing the complexity of the object pattern and adding registration process of probe and object into the iterative algorithm can also improve the convergence speed and the recovery accuracy. The wavefront aberration measurement accuracy can reach 10~(-3)lambda or less. It is feasible to use ptychography in wavefront aberration measurement for extreme ultraviolet lithographic projection lenses.

大数值孔径物镜的波像差测量及其特殊问题

大数值孔径物镜的波像差测量及其特殊问题

Speckle based X-ray wavefront sensing with nanoradian angular sensitivity

X-ray wavefront sensing techniques play an important role in both in situ metrology of X-ray optics and X-ray phase contrast imaging. In this letter, we report an approach to measure wavefront aberrations simply using abrasive paper. The wavefront phase change induced by the sample under test was extracted from the speckle displacement by applying a cross-correlation algorithm to two series of speckle images collected using two one-dimensional scans, whilst scanning the abrasive paper in a transverse direction to the incident X-ray beam. The angular sensitivity of the proposed method is shown to be around 2 nanoradians. The potential of the proposed technique for characterizing X-ray optics and the study of biomedical specimens is demonstrated by imaging representative samples.

Simulation of the Through-Focus Modulation Transfer Functions According to the Change of Spherical Aberration in Pseudophakic Eyes

To evaluate the effects of spherical aberration (SA) correction on optical quality in pseudophakic eyes, we simulated the optical quality of the human eye by computation of the modulation transfer function (MTF). We reviewed the medical records of patients who underwent cataract surgery in Asan Medical Center, retrospectively. A Zywave aberrometer was used to measure optical aberrations at 1-12 postoperative months in patients with AR40e intraocular lens implants. The MTF was calculated for a 5 mm pupil from measured wavefront aberrations. The area under the MTF curve (aMTF) was analyzed and the maximal aMTF was calculated while changing the SA ( $-0.2{\sim}+0.2{\mu}m$ ) and the defocus (-2.0 ~ +2.0 D). Sixty-four eyes in 51 patients were examined. The maximal aMTF was $6.61{\pm}2.16$ at a defocus of $-0.25{\pm}0.66D$ with innate SA, and $7.64{\pm}2.63$ at a defocus of $0.08{\pm}0.53D$ when the SA was 0 (full correction of SA). With full SA correction, the aMTF increased in 47 eyes (73.4%; Group 1) and decreased in 17 eyes (26.6%; Group 2). There were statistically significant differences in Z(3, -1) (vertical coma; P = 0.01) and Z(4, 4) (tetrafoil; P = 0.04) between the groups. The maximal aMTF was obtained at an SA of $+0.01{\mu}m$ in Group 1 and an SA of $+0.13{\mu}m$ in Group 2. Optical quality can be improved by full correction of SA in most pseudophakic eyes. However, residual SA might provide benefits in eyes with significant radially asymmetric aberrations.

Comparison of corneal power, astigmatism, and wavefront aberration measurements obtained by a point-source color light-emitting diode–based topographer, a Placido-disk topographer, and a combined Placido and dual Scheimpflug device

To evaluate and compare the performance of a point-source color light-emitting diode (LED)-based topographer (color-LED) in measuring anterior corneal power and aberrations with that of a Placido-disk topographer and a combined Placido and dual Scheimpflug device. Cullen Eye Institute, Baylor College of Medicine, Houston, Texas USA. Retrospective observational case series. Normal eyes and post-refractive-surgery eyes were consecutively measured using color-LED, Placido, and dual-Scheimpflug devices. The main outcome measures were anterior corneal power, astigmatism, and higher-order aberrations (HOAs) (6.0 mm pupil), which were compared using the t test. There were no statistically significant differences in corneal power measurements in normal and post-refractive surgery eyes and in astigmatism magnitude in post-refractive surgery eyes between the color-LED device and Placido or dual Scheimpflug devices (all P > .05). In normal eyes, there were no statistically significant differences in 3rd-order coma and 4th-order spherical aberration between the color-LED and Placido devices and in HOA root mean square, 3rd-order coma, 3rd-order trefoil, 4th-order spherical aberration, and 4th-order secondary astigmatism between the color-LED and dual Scheimpflug devices (all P > .05). In post-refractive surgery eyes, the color-LED device agreed with the Placido and dual-Scheimpflug devices regarding 3rd-order coma and 4th-order spherical aberration (all P > .05). In normal and post-refractive surgery eyes, all 3 devices were comparable with respect to corneal power. The agreement in corneal aberrations varied. Drs. Wang, Koch, and Weikert are consultants to Ziemer Ophthalmic Systems AG. Dr. Koch is a consultant to Abbott Medical Optics, Inc., Alcon Surgical, Inc., and i-Optics Corp.

Parity decomposition theory of full wavefront aberration measurement using the intensity differences of aerial images in microlithography.

The theory of full wavefront aberration measurements is developed using the intensity differences of aerial images, which are the projected images of one-dimensional measurement patterns consisting of single- or multibars. The key concept is the parity decomposition about the optical axis for two optical components: illumination pupil and wavefront aberration. An additional mathematical treatment, which is a perturbative approach with regard to aberration, is applied to the partially coherent imaging formula. The intensity difference of the two peaks has terms that are linear to the odd and even aberration with rigorously canceled squared aberration terms. The full wavefront aberration measurement is realized from simultaneous linear equations about the intensity difference. The validity of this approach is numerically confirmed under practical lithography conditions.

Distribution of corneal and ocular spherical aberrations in eyes with cataract in the Taiwanese population

PurposeTo investigate the distribution of corneal and ocular spherical aberrations (SAs) in eyes with cataract in the Taiwanese population. MethodsCorneal and ocular SAs were measured in the central 6-mm optical zone using wavefront aberrometry. Axial length (AL) and keratometry (K) were also evaluated in each eye. ResultsA total of 413 eyes in 234 patients were analyzed. The mean age of the patients was 66.8 ± 10.64 years. The mean AL and K values were 24.32 mm and 44.08 D, respectively. The mean corneal SA was 0.307 ± 0.135 μm and ocular SA was −0.042 ± 0.487 μm. Ocular and corneal SAs were significantly correlated (r2 = 0.04, p < 0.001). Corneal and ocular SAs were not significantly correlated with K (p = 0.096 and p = 0.634, respectively), but were significantly correlated with AL (p < 0.001). Multilinear regression showed that corneal SAs and age were the dependent variables that predicted ocular SAs (r2 = 0.143, F = 13.65, p < 0.01), especially in patients who were aged > 50 years, for whom a strongly significant positive correlation was found (r2 = 0.102, F = 11.10, p < 0.001). ConclusionCorneal and ocular SAs varied among cataract patients and correlated with AL. After 50 years of age, ocular SAs increased significantly because of an increase in internal (lenticular) SAs. Corneal SAs in Taiwanese patients were larger than those in Japanese patients and similar to those in Chinese and Malaysian populations. Preoperative measurement of wavefront aberrations is necessary to select which aspherical intraocular lenses are most suitable for achieving better postoperative visual quality.

Extremely high-power CO2 laser beam correction.

This paper presents the results of high-power CO2 laser-aberration correction and jitter stabilization. A bimorph deformable mirror and two tip-tilt piezo correctors were used as executive elements. Two types of wavefront sensors, one Hartmann to measure higher-order aberrations (defocus, astigmatism etc.) based on an uncooled microbolometer long-wave infrared camera and the other a tip-tilt one based on the technology of obliquely sputtered, thin chromium films on Si substrates, were applied to measure wavefront aberrations. We discuss both positive and negative attributes of suggested wavefront sensors. The adaptive system is allowed to reduce aberrations of incoming laser radiation by seven times peak-to-valley and to stabilize the jitter of incoming beams up to 25 μrad at a speed of 100 Hz. The adaptive system frequency range for high-order aberration correction was 50 Hz.

A limitation of Hartmann-Shack system in measuring wavefront aberrations for patients received laser refractive surgery.

PurposeTo explore the relationship between ablation parameters of myopic laser surgery and measurement area of wavefront aberration (WA) with Hartmann-Shack wavefront sensor.Methods58 subjects undergone myopic laser surgeries and 74 uncorrected myopic subjects were enrolled in this experiment. The laser ablation parameters were obtained from surgical records, which included spherical error (Rx), depth, and optical zone (OZ) of ablation. The measured area of WA was tested by the WASCA, and the real pupil size was tested by Pentacam. The corneal eccentricity (E value) and curvature was also measured with the Pentacam. All the measurements were performed under mydriatic condition.ResultsFor uncorrected myopic eyes, the measured area of WA was similar with the real pupil size. But for the corrected eyes, the measured area of WA was smaller than the real pupil size with a mean difference of 0.66 ± 0.54 mm for moderate myopia (t = 6.45, p < 0.0001) and 1.76 ± 0.55 mm for high myopia (t = 18.92, p < 0.0001), but not for mild myopia. The Rx (t = -3.20, p = 0.0017), OZ (t = 64.4, p < 0.0001) and postoperative corneal E value (t = 2.52, p = 0.017) were the independent factors of measured area of WA. Measured area of WA = -0.81*Rx + 1.13*OZ + 0.49*postoperative corneal E value (r2 = 0.997).ConclusionsThe WASCA has a limitation in measuring wavefront aberration over the whole pupil area when it’s used for patients received myopic laser surgery. The measured area is smaller than the real pupil size and depends linearly on ablation depth, optical zone and corneal eccentricity.

Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations

Eye models are valuable tools that can help delineate the role of anatomical parameters on visual performance and guide the design of advanced ophthalmic instrumentation. We propose an optically accurate wide-field schematic eye that reproduces the complete aberration profile of the human eye across a wide visual field. The optical performance of the schematic eye is based on experimentally measured wavefront aberrations taken with a four mm pupil for the central 80° of the horizontal meridian (101 eyes) and 50° of the vertical meridian (10 eyes). Across the entire field of view, our model shows excellent agreement with the measured data both comprehensively and for low-order and high-order aberrations. In comparison to previous eye models, our schematic eye excels at reproducing the aberrations of the retinal periphery. Also unlike previous models, tilt and decentering of the gradient refractive index crystalline lens, which arose naturally through the optimization process, permits our model to mimic the asymmetries of real human eyes while remaining both anatomically and optically correct. Finally, we outline a robust reverse building eye modeling technique that is capable of predicting trends beyond those defined explicitly in the optimization routine. Our proposed model may aid in the design of wide-field imaging instrumentation, including optical coherence tomography, scanning laser ophthalmoscopy, fluorescence imaging, and fundus photography, and it has the potential to provide further insights in the study and understanding of the peripheral optics of the human eye.

Aberration compensation of holographic particle images using digital holographic microscopy

Characterisation of small and large-scale vortices in turbulent flows demands a system with high spatial resolution. The measurement of high spatial resolution, three-dimensional vector displacements in fluid mechanics using holography, is usually hampered by aberration. Aberration poses some problems in particle image identification due to low fidelity of real image reconstruction. Phase mismatch between the recording and the reconstruction waves was identified as the main source of aberration in this study. This paper demonstrates how aberration compensation can be achieved by cross-correlating the complex amplitude of an aberrated reconstructed object with the phase conjugate of a known reference object in the plane of the hologram (frequency space). Results favourably show significant increase in Strehl ratio and suppression of background noise that are more pronounced for particle images of 10 and 5 microns. It is clear from the work conducted that wavefront aberration measurement and compensation of holographic microscopic objects are now possible with the use of a variant digital holographic microscope.

Ronchi剪切干涉光刻投影物镜波像差检测技术研究

Ronchi剪切干涉光刻投影物镜波像差检测技术研究

Polychromatic refractive error from monochromatic wavefront aberrometry.

To determine if measurement of monochromatic wavefront aberrations in near-infrared light can accurately and precisely predict subjective refractive error for polychromatic light. Our approach requires knowledge of the monochromatic wavelength-in-focus (WiF) when polychromatic light is well focused, for which new empirical measurements are reported. With accommodation paralyzed, subjective refractive error was measured as a function of wavelength using a Badal optometer by optimally focusing a letter chart illuminated with monochromatic or white light (color temperature, 4575 K). Wavelength-in-focus was determined by interpolation as that wavelength for which monochromatic refractive error matches white light refractive error. The population-based mean value of WiF, used in conjunction with the Indiana Eye model of chromatic aberration, corrected for monochromatic (842 nm) estimates of refractive error obtained from wavefront aberration measurements, predicts the absolute refractive error of individual eye for polychromatic light for comparison with empirical measurements. Average WiF for eight subjects was 569 nm (SE = 3.6 nm) for a 3-mm pupil and 575 nm (SE = 3.0 nm) for an 8-mm pupil. For small (3 mm) pupils, the mean (±SD) error in predicting refractive error for white light was 0.20 (±0.05) diopters (D) (range, +0.70 to -0.46 D), and for large (>8 mm) pupils, the mean (±SD) prediction error was 0.004 (±0.12) D (range, +0.56 to -0.52 D). The population mean of prediction errors was statistically not different from zero for large pupils but was slightly hyperopic for small pupils. Subjective refractive error for white light can be accurately and precisely predicted objectively from monochromatic wavefront aberrations obtained for near-infrared light, but intersubject variability limits accuracy for individual subjects.

Tunable microlens actuated via a thermoelectrically driven liquid heat engine

We have developed a thermally actuated liquid microlens. An embedded thermoelectric element is used to actuate the liquid based heat engine. A closed-loop system is harnessed to drive and stabilize the temperature of the heat engine. Direct contact between the thermoelectric device and the water results in greatly improved, sub-second thermal rise time (0.8 s). The water based heat engine reacts to the variation in the temperature via expansion and contraction. In turn, the shape of a pinned water-oil meniscus at a lens aperture is deformed in response to the net volume change in the water, creating a tunable microlens. A method to fabricate microfluidic devices with relatively high thickness (250–750 μm) and large length-to-depth aspect ratio (280:1) was developed and used in the process. After fabrication and thermal calibration, optical characteristic of the microlens was assessed. Back focal length of the microlens was shown to vary continuously from −19.6 mm to −6.5 mm as the temperature increased from 5 °C to 35 °C. A thin film air was further introduced to insulate the heat engine from the substrate to protect the microlens area from the temperature fluctuation of the heat engine, thus preventing the change of the refractive indices and thermally induced aberrations. Wavefront aberration measurement was conducted. Surface profile of the microlens was mapped and found to have a conical shape. Both 3-dimensional and 1-dimensional thermal models for the device structure were developed and thermal simulation of the device was performed.