Marechal Criterion Research Articles

Direct wavefront sensing with a plenoptic sensor based on deep learning.

Traditional plenoptic wavefront sensors (PWS) suffer from the obvious step change of the slope response which leads to the poor performance of phase retrieval. In this paper, a neural network model combining the transformer architecture with the U-Net model is utilized to restore wavefront directly from the plenoptic image of PWS. The simulation results show that the averaged root mean square error (RMSE) of residual wavefront is less than 1/14λ (Marechal criterion), proving the proposed method successfully breaks through the non-linear problem existed in PWS wavefront sensing. In addition, our model performs better than the recently developed deep learning models and traditional modal approach. Furthermore, the robustness of our model to turbulence strength and signal level is also tested, proving the good generalizability of our model. To the best of our knowledge, it is the first time to perform direct wavefront detection with a deep-learning-based method in PWS-based applications and achieve the state-of-the-art performance.

In-vivo digital wavefront sensing using swept source OCT.

Sub-aperture based digital adaptive optics is demonstrated in a fiber based point scanning optical coherence tomography system using a 1060 nm swept source laser. To detect optical aberrations in-vivo, a small lateral field of view of ~[Formula: see text] is scanned on the sample at a high volume rate of 17 Hz (~1.3 kHz B-scan rate) to avoid any significant lateral and axial motion of the sample, and is used as a "guide star" for the sub-aperture based DAO. The proof of principle is demonstrated using a micro-beads phantom sample, wherein a significant root mean square wavefront error (RMS WFE) of 1.48 waves (> 1[Formula: see text]) is detected. In-vivo aberration measurement with a RMS WFE of 0.33 waves, which is ~5 times higher than the Marechal's criterion of [Formula: see text] waves for the diffraction limited performance, is shown for a human retinal OCT. Attempt has been made to validate the experimental results with the conventional Shack-Hartmann wavefront sensor within reasonable limitations.

Rapid mesoscale multiphoton microscopy of human skin.

We present a multiphoton microscope designed for mesoscale imaging of human skin. The system is based on two-photon excited fluorescence and second-harmonic generation, and images areas of ~0.8x0.8 mm2 at speeds of 0.8 fps (800x800 pixels; 12 frame averages) for high signal-to-noise ratio, with lateral and axial resolutions of 0.5µm and 3.3µm, respectively. The main novelty of this instrument is the design of the scan head, which includes a fast galvanometric scanner, optimized relay optics, a beam expander and high NA objective lens. Computed aberrations in focus are below the Marechal criterion of 0.07λ rms for diffraction-limited performance. We demonstrate the practical utility of this microscope by ex-vivo imaging of wide areas in normal human skin.

Influence of aberrations in microholographic recording

The influence of various types of aberrations (spherical, coma, and astigmatic) of recording and read- out beams on the readout signal in a microholographic recording was investigated through a numerical simu- lation. The simulation conditions were that the wavelength of the laser was 405 nm and the numerical aperture of the objective lenses was 0.85. The tolerance of the root-mean-square (RMS) wavefront aberrations was defined as the aberration when the normalized signal level decreased to 0.8. Among the three types of aberrations, the influence of the spherical aberration was the most significant. When both the recording and readout beams were aberrated and the signs of the aberrations were in the worst case, the tolerance of the RMS wavefront aberra- tions was less than half of the Marechal's criterion. Moreover, when the RMS wavefront aberrations of the record- ing and readout beams were within the above tolerance, the bit intervals of 0.13 and 0.65 μm in the inplane and vertical directions, respectively, which correspond to the recording density of 91 bit∕μm 3 (recording capacity of 16 TB for a 120-mm-diameter optical disk having a 300-μm-thick recording layer), were shown to be feasible for confocal detection with an allowable signal-to-noise ratio. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.OE.54.11.117104)

Stabilized high-accuracy correction of ocular aberrations with liquid crystal on silicon spatial light modulator in adaptive optics retinal imaging system

We studied the long-term optical performance of an adaptive optics scanning laser ophthalmoscope that uses a liquid crystal on silicon spatial light modulator to correct ocular aberrations. The system achieved good compensation of aberrations while acquiring images of fine retinal structures, excepting during sudden eye movements. The residual wavefront aberrations collected over several minutes in several situations were statistically analyzed. The mean values of the root-mean-square residual wavefront errors were 23-30 nm, and for around 91-94% of the effective time the errors were below the Marechal criterion for diffraction limited imaging. The ability to axially shift the imaging plane to different retinal depths was also demonstrated.

PVr—a robust amplitude parameter for optical surface specification

Peak-to-valley departure (PV) is entrenched in optics design and manufacture as a characterization of an optical figure; modern interferometers commonly use 1k×1k detectors, the output of which may not be well represented by two points. PVr is a newly proposed robust amplitude parameter that combines the PV of a 36-term Zernike fit and the root mean square of the residual. This provides automatic filtering, is insensitive to system resolution, and relates directly to imaging performance via the Marechal criterion. Use of PVr in place of PV is recommended.

Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging

Conventional adaptive optics enables correction of high-order aberrations of the eye, but only for a single retinal point. When imaging extended regions of the retina, aberrations increase away from this point and degrade image quality. The zone over which aberrations do not change significantly is called the "isoplanatic patch." Literature concerning the human isoplanatic patch is incomplete. We determine foveal isoplanatic patch characteristics by performing Hartmann-Shack aberrometry in 1 deg increments in 8 directions on 7 human eyes. Using these measurements, we establish the correction quality required to yield at least 80% of the potential patch size for a given eye. Single-point correction systems (conventional adaptive optics) and multiple-point correction systems (multiconjugate adaptive optics) are simulated. Results are compared to a model eye. Using the Marechal criterion for 555-nm light, average isoplanatic patch diameter for our subjects is 0.80+/-0.10 deg. The required order of aberration correction depends on desired image quality over the patch. For the more realistically achievable criterion of 0.1 mum root mean square (rms) wavefront error over a 6.0-mm pupil, correction to at least sixth order is recommended for all adaptive optics systems. The most important aberrations to target for a multiconjugate correction are defocus, astigmatism, and coma.

Fabrication and optical evaluation of aspheric glass lenses for 3 megapixel zoom camera phone module

The purpose of this study is to develop aspheric glass lenses 4mm in diameter by compression molding. The lens is intended for use as an optical design of 3 megapixel and 2.5 magnifications zoom in a camera phone module. Because of the excellent optical performance of glass and aspheric element, which minimize optical aberrations, the adoption of optical designs using of aspheric glass lenses is rapidly increasing with the progress of precision image forming optics. We fabricated the mold using ultra-precision processing of tungsten carbide (WC). The aspheric glass lens was precisely molded and then its characteristics were evaluated. The mechanical and optical properties of the molded lens were investigated and it showed 90–95% transcription ratio and 0:0655λ root-mean-square optical path difference (OPD-rms), which corresponds to a 0.844 Strehl ratio. Based on the optical performance using the Marechal criterion, we supposed that the molded lens is suitable for the optical design. It also means our fabrication process is available.

Effect of Decentration of Wavefront-Corrected Intraocular Lenses on the Higher-Order Aberrations of the Eye

To evaluate the theoretical effect of decentration of aspherical intraocular lenses (IOLs) and wavefront-corrected IOLs up to the sixth order on higher-order aberrations (HOAs) (third through sixth order) of the eye. An aspherical IOL with HOAs of fourth-order spherical aberrations only (-0.287 microm with a 6-mm pupil) and a wavefront-corrected IOL with HOAs of equal magnitude and opposite from the corneal HOAs were created and laterally shifted up to 1 mm to simulate decentered IOLs. The residual HOAs for pupils of 3 to 6 mm were calculated by combining the HOAs from the cornea and the decentered IOL. Based on the residual HOAs, optical quality was rated by 3 criteria: the Marechal criterion, a diffraction-limited optical system with an aberration less than lambda/14; P(10), the lower 10th percentile of the corneal HOAs in this study group; and decreased HOA, residual ocular HOAs less than the corresponding corneal HOAs. Simulated implantation of the aspherical IOLs and wavefront-corrected IOLs was performed in 154 eyes of 94 patients aged 40 to 80 years. For a centered aspherical IOL and a 6-mm pupil, no eyes met the Marechal criterion, and the P(10) and decreased-HOA criteria were met by 46% and 93% of eyes, respectively. For a 6-mm pupil, the required centration was 0.47 mm to meet the decreased-HOA criterion in 50% of eyes. With a wavefront-corrected IOL and a 6-mm pupil, the centrations required to meet the criteria for 90% of eyes were 0.04 mm for the Marechal criterion, 0.36 mm for P(10), and 0.48 mm for the decreased-HOA criterion. Excellent centration is required to maximize the visual outcome of wavefront-corrected IOLs. With current surgical techniques, implantation of aspherical IOLs and wavefront-corrected IOLs will reduce total ocular HOAs below corneal HOAs in approximately 45% and 86% of eyes (6-mm pupil), respectively.

Relevance of Wavefront Aberrations of the Human Eye in Corneal Laser Surgery

Summary The classical optical errors of the human eye – myopia, hyperopia, and astigmatism – are known to reduce the visual performance of the patient eye and can be corrected by means of glasses, contact lenses, or corneal laser surgery. However, the optic of each individual eye includes also imaging errors of higher order (wavefront aberrations or optical aberrations) such as spherical aberration or coma like aberrations that can decrease the visual performance. In contrast to the classical optical errors, the wavefront aberrations of higher order can not be corrected by means of glasses or contact lenses. However, modern laser systems used in corneal laser surgery possess the potential to correct the optics of an individual eye for such higher order imaging errors. The correction of higher order aberrations improving imaging quality requires a precise knowledge of the relevance of such aberrations. Therefore, we performed a clinical trail to measure the higher order wavefront aberrations in a large population of 130 eyes that were scheduled for corneal laser surgery. The averaged human eye was found to be of good optical quality. On average all Zernike coefficient are statistically not significant different from zero, except the vertical coma and the spherical aberration for 5 and 7 mm pupil size. None of the individual eyes had ideal optical performance with an rms- wavefront error smaller than the Marechal criterion (diffraction limit). Fifty percent of the investigated eyes had significant optical aberrations at pupil sizes >3.2 mm. This critical pupil size represents the smallest pupil diameter at which diffraction limit is achieved. A statistical cluster analysis demonstrates a significant increase of the rms-wavefront errors in the eyes of patients over 40 years old. In conclusion, the averaged human eye has a rather good optical quality exceeding the Marechal criterion (diffraction limit) only by a factor of 2. However, none of the individual eyes achieved the optical quality of “averaged eye”. Thus, the human eye is in general designed to have an almost perfect optical performance, whereas the individual eye deviates significantly from this ideal imaging quality. Optical aberration become significant at a pupil individual size above >3.2 mm and as a consequence optical quality decreases drastically at larger pupil diameters as they occur under dimmed light conditions (mesopic vision). As the pupil diameter can be as large as 6 mm in diameter under such low light conditions, modern corneal laser surgery uses optical relevant treatment zones of 6.0mm or larger and, consequently, the corrections should include the higher order wavefront aberrations. Surgeons and patients should be aware that the corrections of the higher order aberrations are not stable over time because optical performance decreases also with age.

Statistical variation of aberration structure and image quality in a normal population of healthy eyes.

A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

Characterization of aplanatic hologram lenses for optical disk pick-ups

Imaging characteristics for holographic objective lenses application to optical disk pick-ups was analyzed by a comparison between flat and spherical aplanatic hologram lenses with the aid of the third order aberration theory and ray tracing method. The aplanatic hologram lens image field was 0.5 deg for NA=0.5 with focal length f=5 mm under the Marechal criterion. The results indicates that the aplanatic hologram lenses are feasible for optical disk applications.

Parabolic mirror optics for collimation of a crescent blue laser beam radiated from channel waveguide Čerenkov second-harmonic generation

Parabolic mirror optics to collimate the crescent-shaped blue laser beam that radiates from Čerenkov second-harmonic generation (SHG) in a channel waveguide configuration is proposed. Mirror collimation optics has a large tolerance to the variations of SHG element parameters, such as the laser source wavelength, as well as to mirror displacement. The anisotropy of a nonlinear crystal in which the waveguide is fabricated has been taken into account. The optimum mirror alignment to obtain a collimated blue laser beam is evaluated in terms of Marechal's criterion. The minimum wave-front aberration with beam intensity weighted is 0.054 λSH. The convergence of the collimated beam is less than 1.6 mrad, and, by using an objective lens, the collimated beam can be focused to a diameter of less than 1 µm, which is 1.27 times the diffraction-limited focusing point.

Aberrations and convergence characteristics of a concentric-circular focusing grating coupler: analysis

The convergence characteristics of the previously proposed concentric-circular focusing grating coupler (CFGC) are analyzed, and aberration functions for such typical errors as wavelength errors, effective index errors, grating pattern distortion, and CFGC eccentricity are derived for evaluation of their allowances. The analyzed results prove that the Strehl intensity deterioration caused by a wavelength error and an effective index offset can be minimized by optimization of the annular aperture of the CFGC. In the case of Marechal's criterion, a wavelength error of ±8.6% at the annular aperture of NA = 0.440-0.607 and an effective index error of ±20.4% at NA = 0.500-0.652 are permissible, and these values are ∼100 times greater than those that are seen in a conventional focusing grating coupler that has a rotationally asymmetrical structure with respect to its optical axis.

Intensity and resolution at the diffraction focus of optical systems with rotationally symmetric aberration functions: erratum

The intensities and resolutions at the diffraction focus of optical systems with rotationally symmetric minimum-variance aberration functions as well as functions with slight variations from this shape and a prescribed fixed maximum deviation value at the edge of the exit pupil are calculated for circular and annular exit pupils. The results for the intensity at the diffraction focus obtained either by numerical integration of the diffraction integral or by using the Marechal formula show that the maxima of these intensities are achieved for optical systems with wave aberration functions of minimum variance, thus verifying the Marechal criterion. The resolutions (first zeros of the intensities in the radial direction) at this diffraction focus are also presented.

Performance limits of acoustooptic light deflectors due to thermal effects

Transducer conversion losses as well as acoustic and optic attenuation in solidstate acoustooptic light deflectors are responsible for temperature and stress fields which lead to deformation, index fields and changes in acoustic wavelength. For users, these effects result in beam deflection, lensing, aberration and a deterioration in efficiency. The known Marechal criterion and a new criterion noted by the author set a limit of about one quarter wavelength to optic and acoustic wave aberrations. Maximum deflection efficiencies and light powers are determined as functions of the geometry, thermal boundary conditions, material constants and operating modes. A new thermal figure of meritM th 1 equalizes the differences of the acoustooptic figures of meritM 2. To corroborate the theoretical results, performance limits for typical operating modes have been measured. Some new deflector designs are proposed and experimentally verified on the basis of the theoretical results.