PI-FPM: pupil initialization for Fourier ptychographic microscopy directly from measurement data

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput. Moreover, the underlying theoretical mechanism as well as optimum illumination scheme for high-accuracy phase imaging in FPM remains unclear. Herein, we report a high-speed FPM technique based on programmable annular illuminations (AIFPM). The optical-transfer-function (OTF) analysis of FPM reveals that the low-frequency phase information can only be correctly recovered if the LEDs are precisely located at the edge of the objective numerical aperture (NA) in the frequency space. By using only 4 low-resolution images corresponding to 4 tilted illuminations matching a 10×, 0.4 NA objective, we present the high-speed imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm (effective NA = 0.8) across a wide field-of-view (FOV) of 1.77 mm2, corresponding to a space–bandwidth–time product of 411 megapixels per second. Our work reveals an important capability of FPM towards high-speed high-throughput imaging of in vitro live cells, achieving video-rate QPI performance across a wide range of scales, both spatial and temporal.

Color Fourier ptychographic microscopy (FPM), particularly for high-throughput applications like digital pathology, is fundamentally limited by the trade-off between acquisition speed (sampling density) and reconstruction fidelity. To address this, we propose a novel, to the best of our knowledge, physics-guided deep learning framework for high-fidelity color FPM reconstruction under low-frequency spectrum acquisition. The core of our approach is the deep integration of the FPM physical model into a generative diffusion model, which effectively guides the model to extrapolate high-frequency spectral information beyond the captured synthetic aperture. This hybrid physical-generative approach enables robust image reconstruction from significantly reduced acquisition data, achieving high-quality results using illumination restricted to the bright-field region of the objective lens. Both simulations and experiments demonstrate that our method significantly outperforms existing traditional and deep learning-based approaches in recovering fine structural details while suppressing artifacts, without compromising computational efficiency. This physics-guided deep learning paradigm provides a novel strategy for high-speed, high-fidelity computational microscopy with significant potential for clinical translation.

Fourier ptychographic microscopy (FPM) is a computational imaging technique developed in recent years. The validity of the final reconstruction results is closely related to many systematic errors, among which the pupil aberration is a key one. Although the traditional FPM can recover the pupil function in the iterative process, it increases the dependence on data redundancy invisibly, and cannot satisfy the high-speed and low redundancy FPM reconstruction with few images. In this paper, a pupil function recovering method based on annular illumination is proposed, which only uses a small number of LEDs matching the NAobj for illumination. In addition, the Zernike polynomial is used to constrain the freedom degree of aberration, to ensure that the object and pupil can be recovered correctly with fewer data. The simulation results show that the proposed method can recover and correct the pupil function within 6 annular bright-field images, which greatly reduces the requirement of data redundancy and provides the possibility for high-speed aberration recovery based on FPM.

Structural imaging using light microscopy is a cornerstone of histology and cytology. However, the utility of the optical microscope for diagnostic imaging is limited by the fundamental tradeoff between the field of view and spatial resolution and a reliance on exogenous dyes to generate sufficient image contrast. Fourier Ptychographic Microscopy (FPM) is a complex imaging modality with the potential to overcome these limitations by recovering high-resolution images of sample amplitude and phase from a set of low-resolution raw images captured under inclined illumination. In this article we explore the application of FPM to clinical imaging using a simple, low-cost FPM system and simulated and experimental data to explore the influence of both image acquisition parameters and hardware configuration on image quality and imaging throughput. The practical performance of the method is investigated by imaging peripheral blood films and histological tissue sections. We find that, at the cost of increased computational complexity, FPM increases the information capture capacity of the optical microscope significantly, allowing label-free examination and quantification of features such as tissue and cell morphology over large sample areas.

Fourier ptychographic microscopy is a computational microscopy technique to achieve wide-field and super-resolution complex imaging which has been developed in recent years. The method is based on illuminating the sample by a light source array, and then computationally integrating different images correspondent to each of the sources, in the Fourier domain. Knowledge of the exact relative position of the light sources and the sample is critical for the quality of the final recovered image. In this paper, we present an iterative approach towards correcting the position in the Fourier domain based on Newton's method. Also, an analysis is presented which shows the relation between the position error and the deterioration of the final recovery quality. The effectiveness of the presented method in improving the quality of the final recovered image is demonstrated using simulation and experimental results. Moreover, the method is shown to be more stable and robust to noises in comparison with the state-of-the-art algorithm.

A physical lens is limited in its ability to capture an image that is both high- resolution and wide-field due to aberrations even with a sophisticated lens design. This thesis explores computational methods that expand on the recently developed Fourier ptychographic microscopy (FPM) to overcome the physical limitations. New algorithms and imaging methods extend the computational aberration correction to more general imaging modalities including fluorescence microscopy and incoherent bright-field imaging so as to allow even a crude lens to perform like an ideal lens. This paradigm shift from the lens design to computational algorithms democratizes high-resolution imaging by making it easier to use and less complicated to build.

This study aimed to compare ocular wavefront aberrations for pupil diameters of 4 mm and 6 mm, and contrast sensitivity, in eyes with AcrySof IQ and AcrySof Natural intraocular lenses (IOLs). Sixty eyes of 60 patients were enrolled in this prospective randomized study. After phacoemulsification the eyes received either AcrySof IQ SN60WF or AcrySof Natural SN60AT IOLs. One month after surgery, all patients underwent complete ophthalmological examination including corneal topography, wavefront analysis for pupil diameters of 4 mm and 6 mm, and contrast sensitivity measurements with the CSV 1000E instrument under photopic and mesopic conditions with and without glare. There was no statistically significant difference between groups in age, sex or other preoperative ocular characteristics (p > 0.05). Patients with AcrySof IQ IOLs had higher contrast sensitivity at 6 c.p.d. under photopic conditions, at 6 c.p.d. and 18 c.p.d. under mesopic conditions, and at 6 c.p.d., 12 c.p.d. and 18 c.p.d. under mesopic conditions with glare (p < 0.05). Corneal spherical aberration was 0.273 ± 0.074 μm in the AcrySof Natural group and 0.294 ± 0.086 μm in the AcrySof IQ group (p = 0489). Ocular spherical aberration was 0.362 ± 0.141 μm and 0.069 ± 0.043 μm (p < 0.001) for 6-mm diameter pupils and 0.143 ± 0.091 μm and 0.017 ± 0.016 μm (p < 0.001) for 4-mm diameter pupils, with AcrySof Natural and AcrySof IQ IOLs, respectively. There were no significant differences in other higher-order aberrations between the groups (p > 0.05). Aspherical AcrySof IQ IOLs significantly reduced spherical aberration for pupil diameters of both 4 mm and 6 mm and also improved contrast sensitivity more than spherical AcrySof Natural IOLs, especially in mesopic conditions.

To determine the median spherical aberration (SA) of the cataractous population, how it relates to biometry, and the theoretical effect of different intraocular lens (IOL) platforms. A retrospective chart review of patients undergoing cataract surgery evaluation with a high quality Pentacam (Oculus Optikgeräte GmbH) were included. Age, gender, Q-value, mean total SA, higher order aberration root mean square wavefront error, and equivalent keratometry were collected from the Holladay report and axial length and anterior chamber depth (ACD) from the IOLMaster 700 (Carl Zeiss Meditec AG). Data from 1,725 eyes of 999 patients were collected. SA had a median of 0.37 µm (95% confidence interval: 0.36 to 0.38. Age (r = .136, P < .001), Q-factor (r = .743, P < .001), and higher order aberration root mean square wavefront error (r = .307, P < .001) were positively correlated with SA. Average equivalent keratometry (r = -.310, P < .001) was negatively correlated with SA. Axial length (r = -0.037, P = .120) and ACD (r = .004, P = .856) had no association with SA. Up to 1,499 (86.9%) theoretically had SA moved closer to zero with IOLs that had negative SA. Up to 102 (5.9%) had SA theoretically worsened. SA is not normally distributed, suggesting that there may be no "average" SA that IOLs should aim to correct. Patients might benefit from tailoring IOL choice to individual SA. Without access to SA data, eyes with steeper average keratometry or younger patients may have less SA, which could influence IOL choice. [J Refract Surg. 2023;39(2):89-94.].

BackgroundThe rabbit is one of the most common animal models used for preclinical safety evaluation of new cataract surgery and laser vision‐correction technologies in ophthalmic research; however, the distributions of wavefront aberrations in rabbit eyes are unknown. The purpose of this study was to investigate the similarities and differences of wavefront aberrations between rabbit and human eyes.MethodsMonochromatic wavefront aberrations of left and right eyes of 12 rabbits and 12 human subjects with normal vision were measured by a commercial aberrometer (WaveScan Wavefront System, Abbott Medical Optics Inc, California, USA). Comparison of wavefront aberrations in rabbit and human eyes is based on a 6.0-mm pupil.ResultsThe rabbit eyes have an average spherical refraction of 1.51 ± 0.83-D and a cylindrical refraction of ‐1.03 ± 0.63-D. The average spherical refractive error of the human eyes used in this study was ‐2.03 ± 2.59-D with a cylindrical refraction of ‐1.27 ± 1.01-D. The average wavefront error root‐mean‐square (RMS) from higher‐order aberrations is 0.34 μm in rabbits (6.0-mm pupil), which is higher compared to the wavefront error RMS value of human eyes (0.26 μm). The largest higher‐order aberration in rabbit eyes is vertical coma (Z7, 0.19 ± 0.16 μm), whereas the largest higher‐order aberration in human eyes is spherical aberration (Z12, 0.07 ± 0.13 μm). Wavefront error RMS, vertical coma and some higher‐order aberrations are significantly correlated between the right and left rabbit eye.ConclusionCompared to wavefront aberrations in the human eye measured in this study, the rabbit eye has less refractive error but larger higher‐order aberrations both in wavefront error RMS and some higher‐order aberration terms. Similar to human eyes, wavefront error and some higher‐order aberrations are significantly correlated between the right and left rabbit eye.

The quality of the reference wave front in point diffraction interferometer (PDI) is mainly determined by pinhole diameter, pinhole edge roughness and so on. The edge roughness of an actually electric beam etched pinhole is determined by least square fitting method. The Gaussian noise with zero means and σ root mean square (RMS) is added to a perfect pinhole to model the edge roughness pinhole. Based on Rayleigh-Sommegeld diffraction formula, the quality of the far field wave front diffracted by a rough edge pinhole is analyzed in detail. Pinhole edge roughness mainly causes trefoil and coma aberrations in diffracted wave front. For pinholes with diameters from 400 nm to 1000 nm, when the edge roughness σ are 0 nm, 15 nm and 30 nm, the RMS deviation of the diffracted wave fronts are in the order of 10 -8 λ, 10 -4 λ and 10 -3 λ, respectively. The results show that pinhole edge roughness has a significance infection on wave front errors, while it has little to do with the intensity distribution in the diffracted wave front. The edge roughness of the reality pinhole used in PDI is 2.37 nm, and the wave front errors of the wave front diffracted from this pinhole can reach 0.08 nm RMS.

Context.One of the key limitations of the direct imaging of exoplanets at small angular separations are quasi-static speckles that originate from evolving non-common path aberrations (NCPA) in the optical train downstream of the instrument’s main wavefront sensor split-off.Aims.In this article we show that the vector-Apodizing Phase Plate (vAPP) coronagraph can be designed such that the coronagraphic point spread functions (PSFs) can act as wavefront sensors to measure and correct the (quasi-)static aberrations without dedicated wavefront sensing holograms or modulation by the deformable mirror. The absolute wavefront retrieval is performed with a non-linear algorithm.Methods.The focal-plane wavefront sensing (FPWFS) performance of the vAPP and the algorithm are evaluated via numerical simulations to test various photon and read noise levels, the sensitivity to the 100 lowest Zernike modes, and the maximum wavefront error (WFE) that can be accurately estimated in one iteration. We apply these methods to the vAPP within SCExAO, first with the internal source and subsequently on-sky.Results.In idealized simulations we show that for 107photons the root mean square (rms) WFE can be reduced to ∼λ/1000, which is 1 nm rms in the context of the SCExAO system. We find that the maximum WFE that can be corrected in one iteration is ∼λ/8 rms or ∼200 nm rms (SCExAO). Furthermore, we demonstrate the SCExAO vAPP capabilities by measuring and controlling the 30 lowest Zernike modes with the internal source and on-sky. On-sky, we report a raw contrast improvement of a factor ∼2 between 2 and 4λ/Dafter five iterations of closed-loop correction. When artificially introducing 150 nm rms WFE, the algorithm corrects it within five iterations of closed-loop operation.Conclusions.FPWFS with the vAPP coronagraphic PSFs is a powerful technique since it integrates coronagraphy and wavefront sensing, eliminating the need for additional probes and thus resulting in a 100% science duty cycle and maximum throughput for the target.

Customized aspheric intraocular lenses calculated with real ray tracing

To analyze ocular wavefront error and corneal asphericity (Q) in patients treated with aspheric profile photorefractive keratectomy (PRK) compared with patients having conventional PRK to correct myopia and myopic astigmatism and to evaluate the effect of postoperative corneal shape on visual performance. Eye Clinic, University G. d'Annunzio, Chieti-Pescara, Italy. Fifty eyes were treated with aspheric profile PRK using the MEL 80 flying-spot excimer laser, and 24 eyes were treated with standard PRK using the MEL 70 flying-spot excimer laser. Postoperative wavefront error increased in both groups. Six months after surgery, there was a smaller increase in root mean square (RMS) of total higher-order aberrations and spherical aberration (59% and 106%, respectively) in the aspheric profile PRK group than in the conventional PRK group (94% and 136%, respectively) (P<.01). The aspheric profile PRK group showed more prolate corneal asphericities (mean Q of 0.15 +/- 0.26) than the conventional group (mean Q of 0.45 +/- 0.26) (P<.001), with increasing oblateness for higher attempted corrections. A higher percentage of patients with better low-contrast uncorrected visual acuity and best corrected visual acuity was observed in the aspheric PRK group than in the conventional PRK group (P<.05). Aspheric profile and conventional PRK were safe and efficient for the correction of myopia and myopic astigmatism. Moreover, aspheric profile PRK induced a smaller increment of total wavefront error, was related to a smaller increase in spherical aberration, and better maintained the physiology of the corneal surface than conventional treatment.

Focusing and imaging optics can be characterized by evaluating the wavefront error of the focused beam. We have bean developing a ptychographic phase retrieval method using a visible laser to measure the wavefront error. In this study, the measurement accuracy of the method is increased by improving both the phase retrieval algorithm and the experimental setup. The system is applied to the characterization of an ellipsoidal mirror used for the focusing of soft X-rays. The posture of the mirror can be measured with a resolution of 1.4 μrad. The wavefront error originating from the surface profile error can be detected with an accuracy of 0.01λ (root mean square).

To evaluate visual performance and wavefront error after multifocal intraocular lens (MIOL) implant with or without capsular tension ring (CTR). Sixty eyes of 60 candidates for phacoemulsification and MIOL implantation were included in the study and were randomly divided into 2 groups. Thirty eyes (group 1) were implanted with the AcrySof ReSTOR® SN60D3 MIOL and Corneal® ACPI 11 CTR and 30 eyes (group 2) received the same MIOL with no CTR. Twenty days and at 360 days after surgery, the uncorrected and corrected distance visual acuity at high and low contrast were not significantly different between the 2 groups. The root mean square (RMS) of ocular and internal wavefront error was significantly different in the 2 groups early after surgery and did not modify significantly over the 1-year follow-up period. The RMS of total and internal high-order aberrations and ocular and internal trefoil and coma aberrations were significantly lower in group 1 compared to group 2 (p<0.05). Ocular, corneal, internal modulation transfer function at high and low spatial frequencies and ocular, corneal, internal Strehl ratio were not significantly different between the groups. The IOL decentration and tilt were higher in group 1 compared to group 2. ReSTOR MIOL was effective in improving visual performance and provided a good quality of vision due to a significant reduction of high-order spherical aberration. The implant of CTR additionally reduced the ocular wavefront error related to a reduction of third-order aberration related to better IOL position.