Airy Disk Research Articles

Field scanner design for MUSTANG of the Green Bank Telescope

MUSTANG is a bolometer camera for the Green Bank Telescope (GBT) working at a frequency of 90 GHz. The detector has a field of view of 40 arcseconds. To cancel out random emission change from atmosphere and other sources, requires a fast scanning reflecting system with a few arcminute ranges. In this paper, the aberrations of an off-axis system are reviewed. The condition for an optimized system is provided. In an optimized system, as additional image transfer mirrors are introduced, new aberrations of the off-axis system may be reintroduced, resulting in a limited field of view. In this paper, different scanning mirror arrangements for the GBT system are analyzed through the ray tracing analysis. These include using the subreflector as the scanning mirror, chopping a flat mirror and transferring image with an ellipse mirror, and chopping a flat mirror and transferring image with a pair of face-to-face paraboloid mirrors. The system analysis shows that chopping a flat mirror and using a well aligned pair of paraboloids can generate the required field of view for the MUSTUNG detector system, while other systems all suffer from larger off-axis aberrations added by the system modification. The spot diagrams of the well aligned pair of paraboloids produced is only about one Airy disk size within a scanning angle of about 3 arcmin.

Near-diffraction-limited dark hollow beam generated by using a hybrid control way

We propose and demonstrate the generation of dark hollow beam with plane wavefront in the near field based on a hybrid control way by using dual phase only liquid crystal spatial light modulators (LC-SLMs). One phase only LC-SLM redistributes the intensity to the target distribution based on refractive beam shaping system and the other phase only LC-SLM adaptively compensates the wavefront of the output beam by using stochastic parallel gradient descent (SPGD) algorithm. Compared with conventional refractive beam shaping system, the hybrid control way can not only improve the far-field energy concentration of the output beam, but also can correct the phase distortion of the system. Influences of phase distortion on laser beam shaping are analyzed in detail. The theoretical and experimental results show that the near-diffraction-limited dark hollow beam can be successfully generated by using this hybrid control way. The power in the main lobe of the airy disk pattern area in the far field is 2.3 times larger than that without being adaptively compensated.

Deformable mirrors based on piezoelectric unimorph microactuator array for adaptive optics correction

This paper describes a piezoelectric deformable mirror (DM) for adaptive optics (AO) applications, with a 100 μm thick silicon mirror driven by 61 unimorph microactuators. Measurement results show that the stroke of the DM is ~ 7.4 μm at 100 V, and the resonance frequency is at 18 kHz. To demonstrate the correction capability of the DM, low-order Zernike modes up to 14th term were reproduced. Furthermore, a close-loop correction of laser beam in a 633 nm helium-neon laser system was performed. After system aberrations being compensated, a focal spot approximate to Airy disk was achieved.

Hybrid pupil filter design using Bessel series

We propose a simple method of designing pupil filters for transverse super-resolution. For this end we represent the amplitude Point Spread Function (PSF) as a series expansion, constructed from the Fourier transform of a basis of Bessel functions. With this representation we optimize the intensity PSF according to certain desired characteristics, such as a smaller disk diameter than the corresponding, clear aperture, Airy disk. It is proved that by using few basis functions, it is possible to design pupils with similar or better PSF characteristics than previously reported.

Fabrication and Precise Alignment of Electron Lenses in the Microcolumn Using the Laser Diffraction Pattern

The quality of electron lenses and precision of their alignment are very important factors that determine the resolution of the microcolumn. In this work, we have fabricated the quality electron lenses using the semiconductor processing technologies and checked their circular shapes by using the laser diffraction pattern. The observed diffraction pattern by naked eyes was the circular Airy disk and the measured eccentricity of the lens aperture was found to be less than 0.02. We have also made precise alignment of the electron lenses by illuminating the laser beam through the roughly aligned electron lenses and adjusting the electron lenses while monitoring the diffraction pattern formed by the diffracted laser light from the lens apertures. This new method can replace the conventional alignment method where the expensive equipment like the aligner or the STM is required. We have also found the misalignment limit by measuring the e-beam current that came out from the microcolumn.

Pattern matching for three-dimensional tracking of sub-micron fluorescent particles

A microscope objective of NA = 0.6 designed for air medium has been used to generate diffraction patterns of sub-micron fluorescent particles with various defocus distances through a thick cover glass with a mismatched refractive index. The diffraction pattern centers were located by a cross-correlation analysis between the central Airy disk of the diffraction pattern and a template with the standard Airy intensity distribution. The locating accuracy of the diffraction pattern centers was 0.02–0.04 µm (0.1–0.2 pixels). Cross-correlation analyses were also performed to match the measured particle diffraction pattern to a calculated intensity distribution with the Gibson and Lanni scalar diffraction model to determine the particle defocus distance. The matching results showed that, unlike the product cross-correlation function, the least-squares error function, which has been extensively used to recognize objects in images, could be used to match the intensity distributions with a simple weight function. The defocus distances of particles under a 1.1 mm thick cover glass with the defocus distances larger than about 13 µm could be determined at an accuracy better than 0.1 µm by intensity distribution matching.

联合变换相关器远红外变焦距光学系统设计

Based on optical correlation theory and technical parameters of the optical system,an infrared zoom optical system with long wavebands is designed.The infrared materials germanium and AMTIR1 are selected for 8~ 12 μm long wave imaging system,15 times with a large zoom ratio,CCD pixels size of 45 μm × 45 μm.According to the optimization design of IR zoom optical system,MTF value is above 0.6,RMS radius of each field spot diagram close to Airy disk,wavefront aberration less than 1/4 wavelength when the cut-off frequency is 11 lp/mm.The stability of the image plane is well,the result of this system meets the requirement of technical specification and improves the ability of joint transform correlator in target tracking and recognition.

Measurements of spatial coherence of partially coherent light with and without orbital angular momentum

We study the spatial coherence of a partially coherent beam before and after being transmitted through a spiral phase plate that changes the overall orbital angular momentum of the field. The two-point coherence function is measured and directly visualized on a CCD through interference in a Mach-Zehnder interferometer equipped with an image rotator. We show, in particular, how the coherence singularities associated with Airy rings are strongly affected by the spiral phase plate.

What Brown saw and you can too

A discussion of Robert Brown’s original observations of particles ejected by pollen of the plant Clarkia pulchella undergoing what is now called Brownian motion is given. We consider the nature of those particles and how he misinterpreted the Airy disk of the smallest particles to be universal organic building blocks. Relevant qualitative and quantitative investigations with a modern microscope and with a “homemade” single lens microscope similar to Brown’s are presented.

Modeling the sharp focus of a radially polarized laser mode using a conical and a binary microaxicon

Based on the radial finite-difference time domain method we numerically show that the illumination of a conical glass microaxicon of base radius 7 μm and height 6 μm (numerical aperture NA=0.6) by a radially polarized annular R-TEM01 laser mode of wavelength λ=1 μm produces, 20 nm apart from the cone apex, a sharp focus of transverse diameter FWHM=0.30λ and longitudinal (axial) width FWHMz=0.08λ. The focal spot area at half-maximum intensity is HMA=0.071λ2. For comparison the focus diameter reported here is 1.7 times smaller than the diameter of the minimal diffraction spot (Airy disk, NA=1) of FWHM=0.51λ, with its area being 2.87 times smaller than that of the Airy disk HMA=0.204λ2. Also it is smaller than the diameter of a focal spot formed by a lens with NA=0.6 in an immersion medium n=1.5, FWHM=0.51λ/n NA=0.55λ, smaller than the diffraction limit in the medium (n=1.5, NA=1) FWHM=0.51λ/n=0.33λ and smaller than the focusing limit for the Bessel beam (NA=1)FWHM=0.36λ.

Amplitude and Phase Measurements of Highly Focused Light in Optical Data Storage Systems

We propose a new measurement technique to investigate the highly focused light used in optical data storage systems named immersion high resolution interference microscopy (HRIM). This system allows three-dimensional (3D) measurements of the amplitude and phase of light fields in a static scheme. In contrast to scanning techniques, HRIM allows the nondestructive investigation penetrating through the optical disc. We investigated the focusing of light in high-definition digital versatile disc (HD DVD) systems. The experimental spot sizes agree well with the theory in intensity measurements. The measured phase distributions resemble the wavefront propagation of aberration-free converging light beams. The observed phase singularity positions near the focal plane demonstrate the super-resolution capability of such measurements and give access to details of the Airy pattern. Our results prove the applicability of studying highly focused beams in advanced optical systems and its use to clarify storage mechanisms for future generations of optical memories.

Capabilities of using white x-rays for the reconstruction of surface morphology from coherent reflectivity

We present a new method to reconstruct the surface profile of a sample from coherent reflectivity data of a white x-ray beam experiment. As an example the surface profile of a laterally confined silicon wafer has been reconstructed quantitatively from static speckle measurements using white coherent x-rays from a bending magnet in the energy range between 5 < E < 20 keV. As a consequence of using white radiation, speckles appear in addition to the Airy pattern caused by scattering at the entrance pinhole. Nevertheless, the surface profile of a triangularly shaped specimen was reconstructed considering sufficient oversampling between the beam-footprint and the effective sample width. For the profile reconstruction the Error-Reduction phase retrieval algorithm was modified by including the spectral illumination function and a Fresnel propagator term. The simultaneous use of different x-ray energies having different penetration depth provides information on the evolution of the surface profile from the near-surface towards the bulk. The limitations of present experiment can be overcome using white or pink radiation from a source with higher photon flux.

Subnanometre single-molecule localization, registration and distance measurements

Remarkable progress in optical microscopy has been made in the measurement of nanometre distances. If diffraction blurs the image of a point object into an Airy disk with a root-mean-squared (r.m.s.) size of s = 0.44lambda/2NA (approximately 90 nm for light with a wavelength of lambda = 600 nm and an objective lens with a numerical aperture of NA = 1.49), limiting the resolution of the far-field microscope in use to d = 2.4s approximately = 200 nm, additional knowledge about the specimen can be used to great advantage. For example, if the source is known to be two spatially resolved fluorescent molecules, the distance between them is given by the separation of the centres of the two fluorescence images. In high-resolution microwave and optical spectroscopy, there are numerous examples where the line centre is determined with a precision of less than 10(-6) of the linewidth. In contrast, in biological applications the brightest single fluorescent emitters can be detected with a signal-to-noise ratio of approximately 100, limiting the centroid localization precision to s(loc) > or = 1% (> or = 1 nm) of the r.m.s. size, s, of the microscope point spread function (PSF). Moreover, the error in co-localizing two or more single emitters is notably worse, remaining greater than 5-10% (5-10 nm) of the PSF size. Here we report a distance resolution of s(reg) = 0.50 nm (1sigma) and an absolute accuracy of s(distance) = 0.77 nm (1sigma) in a measurement of the separation between differently coloured fluorescent molecules using conventional far-field fluorescence imaging in physiological buffer conditions. The statistical uncertainty in the mean for an ensemble of identical single-molecule samples is limited only by the total number of collected photons, to s(loc) approximately 0.3 nm, which is approximately 3 x 10(-3) times the size of the optical PSF. Our method may also be used to improve the resolution of many subwavelength, far-field imaging methods such as those based on co-localization of molecules that are stochastically switched on in space. The improved resolution will allow the structure of large, multisubunit biological complexes in biologically relevant environments to be deciphered at the single-molecule level.

Effect of Airy disk on schlieren diffraction interferometer

Schlieren is among the oldest and widely used optical techniques for detection of change in refractive index in transparent media. Present work demonstrates the effect of the position of schlieren element in the Airy pattern on the schlieren interferogram. It has been shown that the amplitude of the diffracted wave, starting from schlieren element and serving as an inbuilt reference beam for the schlieren diffraction interferometer, becomes maximum when schlieren element diffracts light from the Airy disk. Effect of F-number of the optical system on schlieren pattern is also demonstrated via observations on the amplitude of diffracted light.

Soft X-ray holographic microscopy of chromosomes with high aspect ratio pinholes

We used digital in-line soft X-ray holography (DIXH) in the Gabor geometry to image human chromosomes. The divergent wave front was generated by diffraction of synchrotron radiation from a high aspect ratio pinhole. As under our experimental conditions the achievable resolution depends on the pinhole radius, high aspect ratio holes with diameters in the 100 nm range were prepared by focused ion beam (FIB) milling. The central maximum of the obtained Airy pattern was used to image chromosomes prepared from metaphase HeLa cells at experimental resolutions of 370 ± 40 nm with soft X-rays at 260 eV photon energy provided by the BESSY II synchrotron radiation facility.

Gaussian modulated Ai- and Bi-based solutions of the 2D PWE: a comparison

We present a comparison of the evolution features, in terms of the intensity moments up to the second order, of what are here referred to as Ai-Gauss and Bi-Gausswave functions, which originate from source functions consisting of Gaussian-like modulated Airy patterns (of the first and second kind). Both have already been considered in the literature, the former being in particular analysed in detail. A paraxial-optics oriented view of the cos-like Airy–Hardy integrals, which stand out as a generalization of the well-known Airy integral, is also developed.

Diffractive optical elements for pitchfork beam shaping

A set of laser beam shaping optics is designed by an iterative method using an adaptive additive algorithm to transform a Gaussian beam into a pitchfork beam. Two diffractive optical elements are designed based on Fresnel diffraction to reduce the amount of energy in the first-order diffraction ring and to increase the depth of focus for the optical system. These two beam properties are found to depend on the diameter of the desired beam and the Airy disk diameter. If the diameter of the desired beam is large, then the optical system yields better results in achieving the above-mentioned two beam properties. The performance of the diffractive optical elements is compared to a previous laser beam shaping system designed by the ray-tracing technique. A pinhole scanning power meter is used to measure the laser irradiance profile at the focal plane to verify the existence of the pitchfork beam. The irradiance profile measurement shows that diffractive optical elements allow better control for reducing the amount of energy in the diffraction side lobes.

Definition of unifying decoupling efficiency of different array antennas—Case study of dense focal plane array feed for parabolic reflector

This paper emphasizes the importance of recognizing the major role played by mutual coupling effects in array antennas, especially for dense arrays with element spacing within half a wavelength. For array operation in transmit mode, backward waves emanate both from element ports that are excited by forward waves, and from non-excited ports. This overall and excitation-dependent mismatch is herein characterized in terms of a decoupling efficiency. It is shown how this decoupling efficiency reduces to the well-known impedance mismatch factor for a conventional phase-steered array (all elements excited), and to the embedded element efficiency (only one element excited) used to characterize multiple input and multiple output (MIMO) arrays. Generally, this decoupling efficiency can be used to characterize the combined effect of mismatch and coupling for any excitation of an array, for instance, the Airy pattern excitation of focal plane array (FPA) feeds for reflectors, as showcased here. The abovementioned forms of decoupling efficiencies are evaluated and discussed for an example array of idealized rectangular apertures with special emphasis on the Airy excitation.

Design status of ITER visible/IR outer strike point view

For ITER visible/IR imaging of the outer strike point from the six upper ports currently assigned, we show an optical design that provides a 4 mm Airy disk at 5 μm wavelength at the farthest point in the field of view (much smaller in the visible), with as complete toroidal coverage of the vertical target as possible. Plasma and optical effects provide fundamental limits on the performance and design of the system. Some effects involve interactions of the surfaces with the plasma, such as plasma transport and deposition of material on the surfaces to be viewed, plasma damage to those surfaces, and molecular emission by the plasma at IR wavelengths. We discuss a detailed optical design including the endoscope concept, entrance aperture and collection head, relay optics, and camera specifications and performance. We assess integration times for capture of IR emission from surfaces and visible line emission predicted by boundary modeling.

Fabrication of a three-dimensional optical vortices phase mask for astronomy by means of electron-beam lithography

In this work, a novel three-dimensional (3D) fabrication process was used to create a series of particular phase masks for astronomical applications. These phase masks, also known as spiral phase plates (SPP), find their application in astronomy for optical vortex coronagraphy in the search of extra solar planets. The 3D profile was directly written on 2.7 mm thick polymethylmethacrylate (PMMA) slide by electron beam lithography (EBL). The effect of electron scattering on topography profile was investigated and the relationship among spatial distribution of electron beam irradiation, spot size and dosage level of irradiation were experimentally characterized. The quality of the fabricated profiles was evaluated using atomic force microscopy (AFM) technique. SPPs were then optically tested by injecting a Gaussian beam and an airy diffraction pattern obtained from a laser source comparing the optical vortices so far obtained with those drawn with numerical simulations.