Airy Disk Research Articles

Detection of binary companions below the diffraction limit with lucky imaging

Binary stars are invaluable tools that can be used to precisely measure the fundamental properties of stars, to test stellar models, and further our understanding of stellar evolution. Stellar binarity may also play an important role in the formation and evolution of exoplanetary systems. We provide a technique for resolving intermediate-separation binaries stars with medium-sized telescopes (i.e. diameter less than or equal to 2.5 metres) at wavelengths around 825 nm in the super-resolution range (i.e. below the limit defined by the Rayleigh criterion). We combined two well-known algorithms that have been applied to reduce the halo in lucky imaging observations: COvariancE of Lucky Images (COELI) and the Lucky Imaging Speckle Suppression Algorithm (LISSA). We reviewed the fundamentals of both algorithms and describe a new technique called Lucky Imaging Super resolution Technique (LIST), which is optimized for peak highlighting within the first ring of the Airy pattern. To validate the technique, we carried out several observing campaigns of well-known binary stars with the FastCam instrument (FC) on the 1.52 m Carlos S'anchez Telescope (TCS) and 2.56 m Nordic Optical Telescope (NOT), both located at the Observatorios de Canarias (OCAN). The projected angular separation between objects was resolved by applying LIST to FC data taken with TCS and NOT, with a result below 0.15 . It can go down to approximately 0.05 given the limitations of the detector plate scale. This is, to our knowledge, the first time that binary companions with such small angular separations have been detected using only lucky imaging at optical wavelengths. The average accuracy achieved for the angular separation measurement is $16 ± 2$ mas with NOT and is $20 ± 1$ mas with TCS. The average accuracy obtained for the position angle measurement is $9.5 ^o ± 0.3 ^o$ for NOT and $11 ^o ± 2 ^o$ for TCS. We also made an attempt to measure the relative brightnesses of the binary components, obtaining results that are compatible with literature measurements. Using this comparison, the Δm uncertainty obtained was 0.1 mag for NOT and 0.48 mag for TCS, although it should be noted that the measurements have been taken using slightly different filters. Lucky imaging, in combination with speckle suppression and a covariance analysis, can allow the resolution of multiple point sources below the diffraction limit of 2-m class telescopes. However, it should be noted that measurements in the super-resolution regime are less sensitive than those above the first Airy ring.

Spindle vibration induced optical performance deterioration and its trans-scale characterization for diamond turned large-aperture optics

In ultra-precision diamond turning of large-aperture optics, the spindle vibration (SV) would cause a deterioration of optical performance. To discuss this issue, the spindle vibration was first excited by a series of designed mass center errors for diamond turning of large-aperture optics. Then, a trans-scale characterization was developed to reveal its dynamic behaviors by combining a white light interferometer and laser interferometer. Next, the amplitude variations were quantitatively evaluated by surface texture parameters and the scale bandwidth was revealed through power spectrum density (PSD). Finally, the point spread function (PSF), encircled energy ratio (EER), and modulation transfer function (MTF) were analyzed and compared. The results indicated that, with the increased SV, Sq and Sz increased and Ssk and Sku showed a transition from skew to normal height distribution. PSD showed that spindle vibration mainly affected the large-scale components rather than the small-scale components. The shape of PSF changed from a standard ring to a dispersed half ring. At the 1 µm radius of the Airy disk, the EER decreased from 82.0% (no SV) to 27.5% (high SV). At the scale of 200mm−1, the MTF decreased from 0.84 (no SV) to 0.44 (high SV). The work provides a fundamental understanding of the evolutionary mechanism of spindle vibration induced optical performance deterioration.

Realization of Airy pattern acoustic bullets by depth of focus synthesis.

Energy concentration is a key parameter for the characterization of light or acoustic bullets. To the best of our knowledge, the highest encircled-energy ratio in the mainlobe reported is merely 25% for the solitary bullet waves and 30% for the nonsolitary bullet waves. This letter reports experimentally and theoretically on a new family of acoustic bullets, namely, Airy pattern ultrasonic bullets, realized by the depth of focus synthesis. The Airy pattern ultrasonic bullets, regarded as a beam with an ultra-long depth of focus, exhibit Airy pattern energy distribution and contain 83.8% of total energy in their mainlobe. In the depth of focus synthesis proposed, an ultra-long depth of focus could be longitudinally synthesized by successive acoustic foci by using an acoustic reflection cavity (ARC). In contrast to the well-known aperture synthesis which utilizes a platform motion to extend the aperture, the depth of focus synthesis employs multiple reflections in ARC to extend its physical dimensions. The Airy pattern ultrasonic bullets presented would be potentially useful in long-range ultrasound imaging, ultrasonic therapy, and acoustic wireless energy transmission.

Precise measurement of spatial coherence and axial brightness based on the Wigner function reconstruction in transmission electron microscopes with field emission guns and a thermionic emission gun.

The spatial coherence and the axial brightness of a cold field emission gun, a Schottky field emission gun and a $\mathrm{LaB}_6$ thermionic gun are precisely measured. By analyzing the Airy pattern from a selected area aperture, various parameters including the spatial coherence length are determined. Using the determined coherence length, the axial brightness of the field emission guns is estimated using the equation which we previously derived based on the discussion of the Wigner function of an electron beam. We also make some extensions in the method to be applicable to the measurements of the thermionic gun, which has anisotropic intensity distribution in most case unlike the field emission guns. Not conventional average brightness but the axial brightness measured for the three kinds of emitters are compared accurately and precisely without influenced by the measurement conditions.

Designing an imaging spectrometer with high resolution using manufacturable gradient-index (MGRIN) lenses with a linear distribution of refractive index.

In this work, an imaging spectrometer with a diffraction-limited resolution of 0.043nm is designed by using two manufacturable gradient-index (MGRIN) lenses with a linear refractive index distribution to suppress the aberrations. The MGRIN lenses are made from a combination of two separate base materials that their refractive indices are determined by the fractional composition of each base material at any point. The volume fraction of each base material in both lenses changes linearly from the front edge to the rear vertex of the lens. The input light to the spectrometer originates from a single-mode fiber with a core diameter of 9μm and a numerical aperture of 0.1. The parallel rays after passing through the collimator are diffracted by a diffraction grating with a number of grooves of 1200 g/mm. The criteria determining the quality of the image show that the aberrations of the image have been optimally controlled. Comparing the results of this design with some similar studies done by other researchers shows that the root-mean-square radius of the spot diagram and Airy disk radius are significantly smaller than those designs. In addition, the modulation transfer function diagram has a better fit with the diffraction limit curve. These results make our proposed spectrometer have a stronger resolution than those in previous studies.

Design of a Continuous-Zoom 2D/3D Microscope with High Zoom Ratio and Full Field of View

A four-group mechanically compensated continuous-zoom microscope is proposed and designed based on the theory of continuous zoom. The system addresses the limitations of traditional continuous-zoom microscopes, including a small zoom ratio, a short working distance, and the loss of details during 2D–3D switching. The system has a magnification of 0.6×~6.0× under two-dimensional observation, adapts to two-third-inch sensors, has a working distance of 130 mm, and adds a 360-degree rotatable beamsplitter for three-dimensional full-field-of-view observation. The magnification, numerical aperture, and sensor dimensions remain unchanged under both two-dimensional and three-dimensional observation. The design results demonstrate that the system is capable of achieving a high zoom ratio of 10× while maintaining a high level of imaging quality in both two-dimensional and three-dimensional modes. The MTF curves for each magnification are in close proximity to the diffraction limit, the spot diagrams are smaller than the airy disk range, and the zoom cam curves are smooth with no inflection points. Furthermore, the system negates the visual discrepancies and loss of detail that arise when switching observation modes due to alterations in system magnification and numerical aperture, thereby broadening the scope of applications for continuous-zoom microscopes.

Post-ensemble generation with Airy beams for spatial and spectral switching in incoherent imaging.

Spatial, temporal, and spectral resolutions and field-of-view are important characteristics of any imaging system. In most, if not all, it is impossible to change the above characteristics after recording a digital picture, video, or hologram. In recent years, there have been investigations on the possibilities to change the above characteristics post-recording. In this Letter, for the first time, to the best of our knowledge, we report novel recording and reconstruction methods built upon the principles of coded aperture imaging that allow changing the axial and spectral resolutions post-recording. We named this method-post-ensemble generation with Airy beams for spatial and spectral switching (PEGASASS). In PEGASASS, light from an object point is converted into Airy beams and recorded such that every recording has a unique Airy pattern. An ensemble of Airy patterns is constructed post-recording and the axial and spectral resolutions are tuned by controlling the chaos in the ensemble. The above tunability is achieved without adversely affecting the lateral resolution. Proof-of-concept experimental results of PEGASASS in 3D in both (x,y,z) and (x,y,λ) and 4D in (x,y,z,λ) are presented. We believe that PEGASASS has the potential to revolutionize the field of imaging and holography.

Semi-supervised correction model for turbulence-distorted images

Significant progress has been made in addressing turbulence distortion in recent years, but persistent challenges remain. Firstly, existing methods heavily rely on fully supervised optimization strategies and synthetic datasets, posing difficulties in effectively utilizing unlabeled real data for training. Secondly, most approaches construct networks in a straightforward manner, overlooking the representation model of phase distortion and point spread function (PSF) in spatial and channel dimensions. This oversight restricts the potential for distortion correction. To address these challenges, this paper proposes a semi-supervised atmospheric turbulence correction method based on the mean-teacher framework. Our approach imposes constraints on the unlabeled data of student networks using pseudo-labels generated by teacher networks, thereby enhancing the generalization ability by leveraging information from unlabeled data. Furthermore, we introduce to use no-reference image quality assessment criterion to select the most reliable pseudo-label for each unlabeled sample by predicting physical parameters that indicating the level of degradation. Additionally, we propose to combine sliding window-based self-attention with channel attention to facilitate local-global context interaction. This design is inspired by the representation of phase distortion and PSF, which can be characterized by coefficients and basis functions corresponding to the channel-wise representation of convolutional neural network features. Moreover, the base functions exhibit spatial correlation, akin to Zenike and Airy disks. Experimental results show that the proposed method surpasses state-of-the-art models.

From fairy rings to fairy chemicals: The story from nature phenomenon to commercial application

AbstractFairy rings are naturally occurring phenomena that are circular or curved clusters of mushrooms that appear in meadows, forests, and other places. In recent decades, significant progress has been made in deciphering fairy chemicals (FCs) involved in the intricate crosstalk between mushrooms and plants. FCs contain three chemical components: 2‐azahypoxanthine (AHX), 2‐aza‐8‐oxohypoxanthine (AOH), and imidazole‐4‐carboxamide (ICA). FCs can enhance the plant's resistance to environmental stresses such as cold, heat, and salt, and can increase crop yields; In addition, it can also have biological activities such as skin barrier improvement, anti‐ageing, and anti‐tumour. This review systematically integrated multiple facets of FCs, encompassing their discovery, the biochemical synthesis pathways giving rise to FCs, the derivatives and compounds originated from FCs, and their emerging applications in agriculture, beauty industry and medical sciences. Moreover, the review also addresses outstanding questions in FCs and future challenges related to plant growth regulators and other compounds, promising a practical and innovative future in agriculture.

Design of an Imaging Optical System for Large-Sized Stepped Shaft Diameter Detection

Addressing the prevalent issues of low accuracy, low efficiency, and poor image quality in online diameter measurement of large-sized stepped shafts, this study introduces a novel method based on a symmetrical dual-telecentric optical path utilizing dual CCDs, specifically designed for step shafts with diameters ranging from 600 mm to 800 mm. By developing and optimizing an imaging system grounded in the object-image dual-telecentric optical path principle and employing Zemax software for comprehensive analysis and optimization, this research achieves significant findings. The system’s Airy disk radius is calculated at 3.204 μm; the modulation transfer function (MTF) remains above 0.6 across various fields of view at a spatial cutoff frequency of 71.4 lp/mm, with smooth MTF curves; the field curvature is confined within 0.1 μm; and the distortion is maintained below 0.1%, fulfilling high-quality imaging requirements. Additionally, a tolerance analysis is conducted to ensure the system’s stability and reliability. Applied to an experimental setup for measuring the diameter of large-sized step shafts, the system demonstrates an improved measurement precision of 0.02 mm. This research offers a robust technical solution for the high-precision online measurement of large stepped shaft diameters, presenting significant practical implications for enhancing productivity and product quality.

Spectrum conversion and pattern preservation of Airy beams in fractional systems with a dynamical harmonic-oscillator potential

We investigate the dynamics of optical Airy beams in the one-dimensional fractional Schrödinger equation with a harmonic-oscillator (HO) potential subjected to modulation along the propagation distance. Deriving general solutions for propagating beams and particular solutions for Airy waves with/without chirp, we study analytically the spectrum conversion and pattern preservation for the chirp-free and chirped Airy beams in the fractional system including the HO potential with moiré-lattice, hyperbolic-secant, and delta-functional modulation formats. For the HO-moiré-lattice potential, it is found that the chirp-free Airy beam experiences multiple spectrum conversions between the Airy and Gaussian patterns in the momentum space, preserving the Airy pattern in the coordinate space. The chirp magnitude of the chirped Airy beam determines whether the spectrum conversion occurs in the momentum space, and the splitting and evolution direction of the beam in the coordinate space. For the HO-hyperbolic-secant potential, the chirp-free Airy beam undergoes spectrum conversion and tunneling, with the positions of the spectrum conversion and tunneling significantly depending on parameters of the hyperbolic-secant potential; however, the spectrum conversion and pattern preservation of the chirped Airy beam occurs only under a certain relation of the chirp and parameters of the potential. In the case of the HO-delta-functional potential, the chirp-free Airy beam experiences abrupt spectrum conversion and a two-step spectrum shift; however, for the chirped Airy beam, the spectrum conversion is affected by the relation between the chirp and height of the potential. Effects of the fractional Lévy index on the spectrum conversion and pattern preservation of the Airy beams under the action of the three modulation patterns considered here are also explored in detail.

Using a machine vision sensor for wavelength estimation by measuring an Airy disk, with didactic purposes

In this manuscript, it is presented a simple and automated educational resource with the aim of determining the wavelength of a laser source that uses the Airy disk generated by a circular aperture. It is known that there is a relationship between the diameter of the central disk and the distance between the circular aperture and the image plane. These two parameters are automatically measured by using a machine vision sensor and an ultrasonic distance sensor, respectively. This resource can be applied in graduate or undergraduate Physics and Engineering laboratories and classrooms for educational, demonstrative, or measuring purposes.

Intelligent Beam Optimization for Light-Sheet Fluorescence Microscopy through Deep Learning.

Light-sheet fluorescence microscopy (LSFM) provides the benefit of optical sectioning coupled with rapid acquisition times, enabling high-resolution 3-dimensional imaging of large tissue-cleared samples. Inherent to LSFM, the quality of the imaging heavily relies on the characteristics of the illumination beam, which only illuminates a thin section of the sample. Therefore, substantial efforts are dedicated to identifying slender, nondiffracting beam profiles that yield uniform and high-contrast images. An ongoing debate concerns the identification of optimal illumination beams for different samples: Gaussian, Bessel, Airy patterns, and/or others. However, comparisons among different beam profiles are challenging as their optimization objectives are often different. Given that our large imaging datasets (approximately 0.5 TB of images per sample) are already analyzed using deep learning models, we envisioned a different approach to the problem by designing an illumination beam tailored to boost the performance of the deep learning model. We hypothesized that integrating the physical LSFM illumination model (after passing it through a variable phase mask) into the training of a cell detection network would achieve this goal. Here, we report that joint optimization continuously updates the phase mask and results in improved image quality for better cell detection. The efficacy of our method is demonstrated through both simulations and experiments that reveal substantial enhancements in imaging quality compared to the traditional Gaussian light sheet. We discuss how designing microscopy systems through a computational approach provides novel insights for advancing optical design that relies on deep learning models for the analysis of imaging datasets.

Terahertz Imaging Using Nanorectifier-Based Detectors and Broadband Thermal Sources

Several terahertz imaging experiments have been conducted at room temperature using a self-switching diode (SSD) rectenna as a detector, and a broadband thermal source (at 610 °C) as a continuous-wave terahertz generator. Since the terahertz emission produced by the source is non-coherent with random polarizations and has a wide-ranging spectrum, the SSD-based rectenna employed in this work utilizes a planar spiral micro- antenna which has a circular polarization that able to effectively capture all incident radiation regardless of the angles. The antenna has been designed for a broadband frequency response in the range of 0.1-10 THz. This is to ensure the terahertz images produced are ascribed to the terahertz radiation collected by the antenna, but without eliminating the possibility of thermal effects at frequencies higher than the terahertz region. In order to further validate the results obtained, an Airy pattern experiment has been conducted. Based on this experiment, the effective frequency response of the SSD rectenna is estimated at 2.29 THz. The utilization of thermal source and micro-size rectenna in this work may pave the way to explore many opportunities in developing flexible, compact, and low-cost terahertz imaging systems without the use of expensive components (e.g., typically lasers are used as terahertz sources).

Ultrasonido pulmonar: patrón pulmonar en preeclampsia con criterios de gravedad

Objective: To evaluate the pulmonary ultrasonographic pattern in pregnant women with a diagnosis of preeclampsia with severity criteria admitted to the Maternal Fetal Medicine Service of the Maternidad Concepción Palacios Hospital in the period between February and September 2020. Methods: The study will be prospective, descriptive, correlational and cross sectional, where patients with a diagnosis of severe preeclampsia will be included and lung ultrasound will be performed with convex transducer using the 8 quadrant technique to evaluate the B lines pattern. The pattern will be correlated with risk factors for preeclampsia and with the development of complications. The association between the number of B-lines and the diagnosis of pulmonary edema will be evaluated. Results: A group of 55 patients with preeclampsia with severity criteria was studied, 56,4 % had an airy lung pattern and 43,6 % a wet pattern. The relationship between the number of B lines and the development of pulmonary edema was statistically significant (p = 0.000) with an average of B lines of 23,3 ± 5,0. All patients who developed acute lung edema were postpartum. Conclusions: the predominant pulmonary pattern was the aerated or A-line pattern. HELLP syndrome may condition the development of a wet pattern and an increased risk of acute lung edema during the puerperium. The number of B lines is directly correlated with an increased risk of developing acute lung edema.

Contributed Session II: In vivo imaging of immune cell activity in primate retina after photoreceptor ablation.

The non-human primate (NHP) is the gold standard animal model for preclinical development of gene and cell based therapies for vision restoration. However, the ocular immune response to these interventions remains poorly understood. We conducted a proof of concept study using offset aperture adaptive optics scanning light ophthalmoscopy (AOSLO) to visualize cellular-scale changes in the primate retina following photoreceptor (PR) ablation. Ultrafast 730nm laser exposure at 26.6 - 32.5 J/cm2 was used to create six lesions in four NHPs. Offset aperture images focused on retinal vascular layers were collected with an offset distance of ~10 Airy Disk Diameters from 15 minutes up to three hours after PR ablation. We observed putative immune cells in and around vessels supplying the lesioned areas. Consistent with previous findings in murine models, cells within vessels adhered to the inner wall, exhibited crawling behavior, and had a diameter ranging from ~9.3 - 11.5 µm. Additionally, we observed the emergence of cellular-scale structures above the PR layer that originated in the center of the lesion 15 minutes post-insult and gradually radiated outward. Vascular perfusion was maintained in these regions. Our data suggest that offset aperture imaging offers cellular-scale, label free, in vivo assessment of the retinal response to insult in NHPs and could be employed to advance our understanding of the ocular immune response provoked by disease and therapeutic interventions.

Cooled infrared coaxial four-mirror system design with a low F-number.

A low F-number and 100% cold stop efficiency are beneficial for improving the performance of optical systems and have a wide range of applications in various thermal imaging scenarios. The cooled infrared coaxial four-mirror system can meet these two requirements, improve system integration, and reduce adjustment costs and difficulties. However, the secondary obstruction caused by the central hole of the third mirror will generate potential stray light. A structure model is proposed in which the primary mirror and the quaternary mirror are processed on the same mirror blank. In this model, a method is given to calculate system parameters using the obstruction ratio and magnification of each mirror. To evaluate the performance of the method, two design examples with different F-numbers (1.4, 1.0) were constructed. The influence of initial structural constraints on the exit pupil position and secondary obstruction was analyzed based on the design objectives of the examples. The aberrations were optimized by targeting the spot. In the optimization process, the incident coordinates and directions of the restricted edge field rays in the tertiary mirror and the quaternary mirror were limited to achieve control of the obstruction caused by the holes in the center of the mirrors. In the results, the RMS spot radius of the two design examples is smaller than the Airy disk radius, and the axial beam wavefront deviation RMS values are 0.026λ and 0.024λ, respectively. Moreover, the obstruction caused by the central holes of the mirrors is controlled within the given field of view. The results show that the proposed model and method can be used to design a low F-number cooled infrared coaxial four-mirror system and have good application prospects.

Image scanning microscopy with a doughnut beam: signal strength and integrated intensity.

We discuss the effects of image scanning microscopy using doughnut beam illumination on the properties of signal strength and integrated intensity. Doughnut beam illumination can give better optical sectioning and background rejection than Airy disk illumination. The outer pixels of a detector array give a signal from defocused regions, so digital processing of these (e.g.,by simple subtraction) can further improve optical sectioning and background rejection from a single in-focus scan.

3D incoherent imaging using an ensemble of sparse self-rotating beams.

Interferenceless coded aperture correlation holography (I-COACH) is one of the simplest incoherent holography techniques. In I-COACH, the light from an object is modulated by a coded mask, and the resulting intensity distribution is recorded. The 3D image of the object is reconstructed by processing the object intensity distribution with the pre-recorded 3D point spread intensity distributions. The first version of I-COACH was implemented using a scattering phase mask, which makes its implementation challenging in light-sensitive experiments. The I-COACH technique gradually evolved with the advancement in the engineering of coded phase masks that retain randomness but improve the concentration of light in smaller areas in the image sensor. In this direction, I-COACH was demonstrated using weakly scattered intensity patterns, dot patterns and recently using accelerating Airy patterns, and the case with accelerating Airy patterns exhibited the highest SNR. In this study, we propose and demonstrate I-COACH with an ensemble of self-rotating beams. Unlike accelerating Airy beams, self-rotating beams exhibit a better energy concentration. In the case of self-rotating beams, the uniqueness of the intensity distributions with depth is attributed to the rotation of the intensity pattern as opposed to the shifts of the Airy patterns, making the intensity distribution stable along depths. A significant improvement in SNR was observed in optical experiments.

A mid-infrared laser microscope for the time-resolved study of light-induced protein conformational changes.

We have developed a confocal laser microscope operating in the mid-infrared range for the study of light-sensitive proteins, such as rhodopsins. The microscope features a co-aligned infrared and visible illumination path for the selective excitation and probing of proteins located in the IR focus only. An external-cavity tunable quantum cascade laser provides a wavelength tuning range (5.80-6.35 µm or 1570-1724cm-1) suitable for studying protein conformational changes as a function of time delay after visible light excitation with a pulsed LED. Using cryogen-free detectors, the relative changes in the infrared absorption of rhodopsin thin films around 10-4 have been observed with a time resolution down to 30ms. The measured full-width at half maximum of the Airy disk at λ = 6.08 µm in transmission mode with a confocal arrangement of apertures is 6.6 µm or 1.1λ. Dark-adapted sample replacement at the beginning of each photocycle is then enabled by exchanging the illuminated thin-film location with the microscope mapping stage synchronized to data acquisition and LED excitation and by averaging hundreds of time traces acquired in different nearby locations within a homogeneous film area. We demonstrate that this instrument provides crucial advantages for time-resolved IR studies of rhodopsin thin films with a slow photocycle. Time-resolved studies of inhomogeneous samples may also be possible with the presented instrument.