Diffraction-limited Optical System Research Articles

Analytical Model of Point Spread Function under Defocused Degradation in Diffraction-Limited Systems: Confluent Hypergeometric Function

Analytical Model of Point Spread Function under Defocused Degradation in Diffraction-Limited Systems: Confluent Hypergeometric Function

A generalized expression for accelerating beamlet decomposition simulations

Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of algorithms has been developed that employs hybrid propagation physics to compute the propagation of an elementary beamlet along geometric ray paths. These “beamlet decomposition” algorithms include the well-known Gaussian beamlet decomposition (GBD) algorithm, of which several variants have been created. To increase the computational efficiency of the GBD algorithm, we derive an alternative expression of the technique that utilizes the analytical propagation of beamlets to tilted planes. We then use this accelerated algorithm to conduct a parameter-space search to find the optimal combination of free parameters in GBD to construct the analytical Airy function. The experiment is conducted on a consumer-grade CPU, and a high-performance GPU, where the new algorithm is 34 times faster than the previously published algorithm on CPUs, and 67,513 times faster on GPUs.

Single atom in a superoscillatory optical trap

Optical tweezers have become essential tools to manipulate atoms or molecules at a single particle level. However, using standard diffraction-limited optical systems, the transverse size of the trap is lower bounded by the optical wavelength, limiting the application range of optical tweezers. Here we report trapping of single ultracold atom in an optical trap that can be continuously tuned from a standard Airy focus to a subwavelength hotspot smaller than the usual Abbe’s diffraction limit. The hotspot was generated using the effect of superoscillations, by the precise interference of multiple free-space coherent waves. We argue that superoscillatory trapping and continuous potential tuning offer not only a way to generate compact and tenable ensembles of trapped atoms for quantum simulators but will also be useful in single molecule quantum chemistry and the study of cooperative atom-photon interactions within subwavelength arrays of quantum emitters.

Engineering of Aberrated PSF by Asymmetric Apodization with the Complex Shaded Aperture

The point spread function (PSF) produced by a coherent optical system under the influence of defocus, coma, and primary spherical aberration (PSA) is examined in this work. This paper deals with asymmetric apodization and pupil engineering to control monochromatic aberrations. To reduce the influence of monochromatic aberrations on the diffracted PSF, this approach uses amplitude and phase apodization. Analytical investigations on intensity PSF are carried out with varying amounts of aberrations and degrees of amplitude and phase apodization. Computed central peak intensity and full width at half maxima (FWHM) and analyzed. The resolution of a diffraction-limited optical imaging system is improved by using an asymmetric optical filter that minimizes the effect of defocus.

The Influence of the Aperture Stop Fractal Shape of an Optical System on the Illuminance Distribution

In the article the options for the application of aperture shapes with fractal properties in the design of optical systems are considered. Calculations of mathematical models of point spread functions of a diffraction-limited optical system are performed. The diffraction patterns of the light distribution in these systems are presented, and the point spread functions are considered for various shapes of the aperture stop. Analytical expressions are obtained for the light distribution depending on the pupil shape, which can be used to control the process of image formation. The pupil shape, which has the shape of an equilateral triangle, is chosen as the basic one, and the shape of the pupil as a "Koch snowflake" curve is also considered. Using the Fraunhofer integral, the dependences of the distribution of the spectral density of the complex amplitude on the aperture located on an opaque screen are derived in the Fraunhofer approximation and under the condition of illumination by a plane monochromatic wave. Using the relationship with the complex amplitude, the sought-for intensity distribution in the plane of the diffraction pattern is obtained. Taking into account the simplifications adopted in this article, the solution of the Fraunhofer integral is found, by setting the integration limits, depending on: the selected aperture profile, the coordinate system chosen for it, and the position of nodal points in this system

Study on Single-molecule Biophysics and Biochemistry in Dilute Liquids and Live Cells without Immobilization or Significant Hydrodynamic Flow: The Thermodynamic Single-molecule Demon.

Since mathematics provides a way to answer questions about the thermodynamic jitter in a clear, rational manner, with evidence to support it, mathematics is the reliable method necessary to get the best information on the movement of a single molecule / a single particle at the molecular scale in dilute liquids and live cells without immobilization or hydrodynamic flow. The Brownian movement (normal diffusive systems) and generally the thermodynamic jitter (anomalous diffusive systems) are ultimately the direct or indirect cause of every measurement signal at the molecular scale in diffraction limited and unlimited optical systems in dilute liquids and live cells without immobilization or hydrodynamic flow. For example, emitted photons are the epiphenomenon of the underlying process of thermodynamic jitter of single molecules / single particles at the molecular scale. The key question is: How far apart do two molecules / two particles have to be in the time domain so that the required degree of separation between the two individual molecules / the two individual particles can be quantified at the molecular scale in order to distinguish them as separate entities without immobilization or hydrodynamic flow? The Földes-Papp's limits of the singlemolecule time resolution in dilute liquids and live cells without immobilization or hydrodynamic flow are the exact answers. The diffusive process is complicated and not minimalist. A minimalist model has a third possibility, it may be right but irrelevant.

Spatial resolution of omni-resonant imaging.

Omni-resonance refers to the broadening of the spectral transmission through a planar cavity, not by changing the cavity structure, but by preconditioning the incident optical field. As such, broadband imaging can be performed through such a cavity with all the wavelengths simultaneously resonating. We examine here the spatial resolution of omni-resonant imaging and find that the spectral linewidth of the cavity resonance determines the spatial resolution. Surprisingly, the spatial resolution improves at longer wavelengths because of the negative angular dispersion intrinsic to Fabry-Pérot resonances, in contrast to conventional diffraction-limited optical imaging systems where the spatial resolution improves at shorter wavelengths. These results are important for applications ranging from transparent solar windows to nonlinear resonant image processing.

Three-dimensional transfer function of optical microscopes in reflection mode.

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can beobtained.

Calculation of ensquared energy of the diffraction-limited optical system with Higher-order parabolic filter

Mathematical properties of the ensquared energy functions for apodized point-spread function (PSF) are presented. An expression of ensquared energy for the apodized point Spread function of the optical system with a circular aperture was derived using a parabolic apodized filter with a different arrangement N =1, 2,3,4. The results obtained were discussed graphically.

Zernike coefficients of a circular Gaussian pupil

ABSTRACT We present a derivation of a formula for Zernike-Gauss circle coefficients expressed in terms of Zernike circle coefficients for a circular Gaussian pupil by revisiting a method in which theorthonormal Zernike-Gauss circle polynomials are not derived first. This is achieved by utilizing a new result, based on the extended Nijboer-Zernike diffraction theory, in which an analytical expression for the autocorrelation of any two Zernike circle polynomials in the circular Gaussian pupils is derived. We use the result to investigate the Strehl ratio of a nearly diffraction-limited optical system that is characterized using Zernike circle coefficients or classical peak-valley coefficients. The results show that aberration correction of the system with a circular Gaussian pupil is most effective if the aberrations are expressed in terms of orthonormal Zernike-Gauss circle coefficients.

MBE-grown MCT hetero- and nanostructures for IR and THz detectors

We present an overview of our technological achievements in the implementation of detector structures based on mercury cadmium telluride (MCT) heterostructures and nanostructures for IR and THz spectral ranges. We use a special MBE design set for the epitaxial layer growth on (013) GaAs substrates with ZnTe and CdTe buffer layers up to 3” in diameter with the precise ellipsometric monitoring in situ . The growth of MCT alloy heterostructures with the optimal composition distribution throughout the thickness allows for the realization of different types of many-layered heterostructures and quantum wells to prepare the material for fabricating single- or dual-band IR and THz detectors. We also present the two-color broad-band bolometric detectors based on the epitaxial MCT layers that are sensitive in 150–300-GHz subterahertz and infrared ranges from 3 to 10 μm, which operate at the ambient or liquid nitrogen temperatures as photoconductors, as well as the detectors based on planar HgTe quantum wells. The design and dimensions of THz detector antennas are optimized for reasonable detector sensitivity values. A special diffraction limited optical system for the detector testing was designed and manufactured. We represent here the THz images of objects hidden behind a plasterboard or foam plastic packaging, obtained at the radiation frequencies of 70, 140, and 275 GHz, respectively.

Ground-testing method of a zero gravity wavefront for space telescopes.

A ground-testing method and an algorithm are presented to demonstrate how to predict the image quality for an orbiting space telescope under 0g. By using a mathematical model of the ground-testing system, one has to change the gravity conditions to get a 0g wavefront. For the Hinode space telescope, one can change the gravity acceleration from +1 g to -1 g by rotating the telescope upside down, which is difficult for larger optical space telescopes. In this paper we introduce a new algorithm to get 0g results by measuring the wavefronts under different gravity acceleration sets. In this way we can predict the 0g image quality under any gravity acceleration value. With the algorithm, we propose to use oscillation in the vertical direction to mimic the change of the telescope figure under acceleration caused by gravity. Criteria of tests and estimates of errors are discussed in this paper. A test experiment is designed and performed for a scaled model of the space solar telescope (SST). The optical test system includes a 1.4-mm-thick, 101.6-mm-diameter flat mirror, and has almost the same gravity sag as the SST's 1-m-diameter primary has; thus, it can be compared to the Hinode method. As a suspending spring mass oscillation system, it provides a gravity environment varying sinusoidally around 1g. Gravity accelerations and response wavefronts are aligned in time. Test results and comparisons to Hinode's are achieved and listed. The differences between our method and Hinode's results is less than 1/20λ RMS, which is sufficient for testing a diffraction limited space optical system.

Super-Resolution Imaging Using Compressive Sensing and Binary Pure-Phase Annular Filter

Super-resolution is an important goal for the diffraction-limited optical system. In this paper, we present a novel technique that exceeds the limit of resolving power of the diffraction-limited optical system to achieve super-resolution imaging by combining compressive sensing with a binary pure-phase annular filter. This novel technique is achieved by using a classical 4F optical system with a pure-phase spatial light modulator. The feasibility of this imaging technique is theoretically analyzed and physically validated by laboratory experiments.

Design of Diffraction Limited Head Mounted Display Optical System Based on High Efficiency Diffractive Elements

A diffraction limited optical system for head mounted displays (HMDs) was designed. This optical system consists of four modules, including 1:5 mm and 5:30 mm beam expanders, polarization grating-polarization conversion system (PG-PCS) and refractive/diffractive projection optical module. The PG-PCS module transforms the unpolarized Gaussian beam to a linearly polarized beam and it simultaneously homogenizes the spatial intensity profile. The optical projector module has a 30° field of view, a 22 mm eye relief, and a 10 mm exit pupil diameter with a compact structure. Common acrylic materials were utilized in the optical design process; therefore, the final optical system was lightweight. The whole optical system is suitable for a 0.7 inch liquid crystal on silicon microdisplay (LCOS) with HDTV resolution (1920×1080) and 8.0 μm pixel pitch.

Simulation of Small-Pitch HgCdTe Photodetectors

Recent studies indicate as an important technological step the development of infrared HgCdTe-based focal plane arrays (FPAs) with sub-wavelength pixel pitch, with the advantage of smaller volume, lower weight, and potentially lower cost. In order to assess the limits of pixel pitch scaling, we present combined three-dimensional optical and electrical simulations of long-wavelength infrared HgCdTe FPAs, with 3 μm, 5 μm, and 10 μm pitch. Numerical simulations predict significant cavity effects, brought by the array periodicity. The optical and electrical contributions to spectral inter-pixel crosstalk are investigated as functions of pixel pitch, by illuminating the FPAs with Gaussian beams focused on the central pixel. Despite the FPAs being planar with 100% pixel duty cycle, our calculations suggest that the total crosstalk with nearest-neighbor pixels could be kept acceptably small also with pixels only $$3\,\mu \hbox {m}$$ wide and a diffraction-limited optical system.

Asymmetric apodization for the comma aberrated point spread function

This paper deals with the study of light flux distributions in the point spread function formed by an optical system with a one-dimensional aperture under the influence of the coma aberration. The traditional design of an asymmetric optical filter improves the resolution of a diffraction-limited optical imaging system. In this approach we explore the control of monochromatic aberrations through pupil engineering with asymmetric apodization. This technique employs the amplitude and phase apodization for the mitigation of the effects of third-order aberrations on the diffracted image. On introducing the coma wave aberration effect, the central peak intensity in the field of diffraction is a function of the edge strips width and the amplitude apodization parameter of a one-dimensional pupil filter, whereas the magnitude of the reduction of optical side-lobes is a function of the degree of phase apodization at the periphery of the aperture. The analytically computed results are illustrated graphically in terms of point spread function curves under various considerations of the coma aberrations and a different degree of amplitude and phase apodization. Hence, for the optimum values of apodization, the axial resolution has been analyzed using well-defined quality criteria.

Методи формування нанорозмірних структур на плівках халькогенідних склоподібних напівпровідників

The analysis of methods of micro- and nanorelief structures recording at chalcogenide vitreous semiconductors films is presented. It is shown that exposing of the chalcogenide vitreous semiconductors films by optical radiation focused by diffraction limited optical systems allows to obtain prints with much smaller size than the diffraction boundary by using of the photosensitive materials exposure characte-ristics nonlinearity. The data of the recording nanosize structures by near field and electron beam systems are revealed. Fig.: 6. Refs: 28 titles.

“MODAL NOISE” IN SINGLE-MODE FIBERS: A CAUTIONARY NOTE FOR HIGH PRECISION RADIAL VELOCITY INSTRUMENTS

Exploring the use of single-mode fibers (SMFs) in high precision Doppler spectrometers has become increasingly attractive since the advent of diffraction-limited adaptive optics systems on large-aperture telescopes. Spectrometers fed with these fibers can be made significantly smaller than typical 'seeing-limited' instruments, greatly reducing cost and overall complexity. Importantly, classical mode interference and speckle issues associated with multi-mode fibers, also known as 'modal noise', are mitigated when using SMFs, which also provide perfect radial and azimuthal image scrambling. However, these fibers do support multiple polarization modes, an issue that is generally ignored for larger-core fibers given the large number of propagation modes. Since diffraction gratings used in most high resolution astronomical instruments have dispersive properties that are sensitive to incident polarization changes, any birefringence variations in the fiber can cause variations in the efficiency profile, degrading illumination stability. Here we present a cautionary note outlining how the polarization properties of SMFs can affect the radial velocity measurement precision of high resolution spectrographs. This work is immediately relevant to the rapidly expanding field of diffraction-limited, extreme precision RV spectrographs that are currently being designed and built by a number of groups.

Superresolved imaging based on wavelength multiplexing of projected unknown speckle patterns

We propose a method for resolution enhancement of a diffraction limited optical system based on the capture of a set of low resolution images. These images are obtained after projection of an ensemble of unknown speckle patterns on top of the high resolution object that is to be imaged. Each speckle pattern is generated by the same thin (and unknown) diffuser, but illuminated with a slightly different wavelength. From the ensemble of low resolution images, we obtain a system of equations that can be solved in an iterative manner that enables reconstruction of the high resolution object. As a result, we also achieve the projected high resolution speckle patterns used for the encoding.

The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG

We report on the implemented design of a two-colour instrument based on electron multiplying CCD (EMCCD) detectors. This instrument is currently installed at the Danish 1.54m telescope at ESO's La Silla Observatory in Chile, and will be available at the SONG (Stellar Observations Network Group) 1m telescope node at Tenerife and at other SONG nodes as well. We present the software system for controlling the two-colour instrument and calibrating the high frame-rate imaging data delivered by the EMCCD cameras. An analysis of the performance of the Two-Colour Instrument at the Danish telescope shows an improvement in spatial resolution of up to a factor of two when doing shift-and-add compared with conventional imaging, and that it is possible to do high-precision photometry of EMCCD data in crowded fields. The Danish telescope, which was commissioned in 1979, is limited by a triangular coma at spatial resolutions below 0.5" and better results will thus be achieved at the near diffraction limited optical system on the SONG telescopes, where spatial resolutions close to 0.2" have been achieved. Regular EMCCD operations have been running at the Danish telescope for several years and have produced a number of scientific discoveries, including microlensing detected exoplanets, the detection of previously unknown variable stars in dense globular clusters and the discovery of two rings around the small asteroid-like object (10199) Chariklo.