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The states of the three-dimensional quantum harmonic oscillator classify optical aberrations of axis-symmetric systems due to the isomorphism between the two mathematical structures. Cartesian quanta and angular momentum classifications have their corresponding aberration classifications. The operation of concatenation of optical elements introduces a new operation between harmonic oscillator states.
Deformable mirrors are increasingly used in astronomy. However, they still are limited in stroke for active correction of high-amplitude optical aberrations. Magnetic liquid deformable mirrors (MLDMs) are a new technology that has the advantages of high-amplitude deformations and low costs. In this paper, we demonstrate extremely high strokes and interactuator strokes achievable by MLDMs which can be used in astronomical instrumentation. In particular, we consider the use of such a mirror to suggest an interesting application for the next generation of large telescopes. We present a prototype 91 actuator deformable mirror made of a magnetic liquid (ferrofluid). This mirror uses a technique that linearizes the response of such mirrors by superimposing a large and uniform magnetic field on the magnetic field produced by an array of small coils. We discuss experimental results that illustrate the performance of MLDMs. A most interesting application of MLDMs comes from the fact they could be used to correct the aberrations of large and lower optical quality primary mirrors held by simple support systems. We estimate basic parameters of the needed MLDMs, obtaining reasonable values.
The presence of optical aberrations in the entrance pupil of a coronagraph causes the stellar light to scatter about the occulting spot, reducing the effective contrast achievable. Even if these aberrations are sufficiently corrected with a deformable mirror to enable planet detection, small drifts in the optical alignment of the telescope introduce additional low-order aberrations.
Unlike focal-plane coronagraphs that use occulting spots and Lyot stops to eliminate diffraction, pupil-plane coronagraphs operate by shaping the pupil to redirect the diffracted stellar light into a tight core. As in focal-plane coronagraphs, the optical aberrations in the telescope must be sufficiently corrected to enable high contrast imaging. However, in shaped-pupil coronagraphs, the low-order aberrations resulting from misalignment and optical figure drift have a much smaller influence upon the contrast at at the inner working angle. These weaker sensitivities greatly relax the strict low-order wavefront stability required for high-contrast imaging the cost of some throughput. In this paper, we present the simulated performance of the concentric ring shaped pupil concepts comparing them to focal-plane coronagraphs that are optimized for the same inner working angles.
Gruneisen (sup 1-3), has shown that small, light weight, liquid crystal based devices can correct for the optical distortion caused by an imperfect primary mirror in a telescope and has discussed the efficiency of this correction. In this paper we expand on that work and propose a semi-analytical approach for quantifying the efficiency of a liquid crystal based wavefront corrector for this application.
Due to their short wavelength, X-rays can in principle be focused down to a few nanometres and below. At the same time, it is this short wavelength that puts stringent requirements on X-ray optics and their metrology. Both are limited by today’s technology. In this work, we present accurate at wavelength measurements of residual aberrations of a refractive X-ray lens using ptychography to manufacture a corrective phase plate. Together with the fitted phase plate the optics shows diffraction-limited performance, generating a nearly Gaussian beam profile with a Strehl ratio above 0.8. As a result, this scheme can be applied to any other focusing optics, thus solving the X-ray optical problem at synchrotron radiation sources and X-ray free-electron lasers.
Presented is a method that tailors the geometry of a mirror’s core structure as well as the mounting interface such that a desired set of aberrations is reduced. It will be shown that targeting specific aberrations as opposed to reducing overall surface figure error (SFE) is a valid method to reduce weight or improve performance. Analyzed first is the self-weight deflection of a thin circular plate of uniform thickness continuously supported along its outer edge. The Kirchhoff-Love plate bending equations are related to the radially symmetric Zernike polynomials of piston, defocus, and primary spherical aberration. Next, the mirror’s radial thickness is optimized to eliminate primary and secondary spherical aberrations when the outer edge is simply supported. As an example, the method is demonstrated using a 2-meter diameter aluminum mirror where surface deflections can have an appreciable effect at mid-to-near infrared wavelengths
Method for correcting radial aberrations of a circular mirror continuously supported at the outer edge.
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Signal-to-noise ratio of a coherent lidar is directly proportional to heterodyne efficiency, which is a measure of the mixing of the local oscillator and signal beams. Formulation of heterodyne efficiency is presented and then extended to include the primary, or Seidel, aberrations arising from optical systems. Animations of the intensity pattern for mixing of truncated Gaussian beams in the presence of Seidel aberrations are shown to illustrate the effect on heterodyne efficiency. Results showing the degradation of heterodyne efficiency with an increasing amount of Seidel aberration are given for the same Gaussian beams. This is further extended to predict the change in heterodyne efficiency of a coherent lidar as a result of its optical components by including aberration data derived from optical testing.
Optical metasurfaces are two-dimensional arrays of nano-scatterers that modify optical wavefronts at subwavelength spatial resolution. They are poised to revolutionize optics by enabling complex low-cost systems where multiple metasurfaces are lithographically stacked and integrated with electronics. For imaging applications, metasurface stacks can perform sophisticated image corrections and can be directly integrated with image sensors. Here we demonstrate this concept with a miniature flat camera integrating a monolithic metasurface lens doublet corrected for monochromatic aberrations, and an image sensor. The doublet lens, which acts as a fisheye photographic objective, has a small f-number of 0.9, an angle-of-view larger than 60° × 60°, and operates at 850 nm wavelength with 70% focusing efficiency. The camera exhibits nearly diffraction-limited image quality, which indicates the potential of this technology in the development of optical systems for microscopy, photography, and computer vision.
This paper examines the polarization aberrations in optical systems of isotropic radially symmetric weak polarizers in the paraxial approximation. Optical systems which fit this description are composed of uncoated and coated lenses and mirrors. Polarization aberrations are variations in phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear polarization, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at interfaces.
Single and double mirror systems geometrical optical image aberrations noting focal number, angle of field, secondary magnification and mutual position tolerances
White-light phase-conjugate mirrors would be incorporated into some optical systems, according to a proposal, as means of correcting for wavefront distortions caused by imperfections in large optical components. The proposal was given impetus by a recent demonstration that white, incoherent light can be made to undergo phase conjugation, whereas previously, only coherent light was known to undergo phase conjugation. This proposal, which is potentially applicable to almost any optical system, was motivated by a need to correct optical aberrations of the primary mirror of the Hubble Space telescope. It is difficult to fabricate large optical components like the Hubble primary mirror and to ensure the high precision typically required of such components. In most cases, despite best efforts, the components as fabricated have small imperfections that introduce optical aberrations that adversely affect imaging quality. Correcting for such aberrations is difficult and costly. The proposed use of white-light phase conjugate mirrors offers a relatively simple and inexpensive solution of the aberration-correction problem. Indeed, it should be possible to simplify the entire approach to making large optical components because there would be no need to fabricate those components with extremely high precision in the first place: A white-light phase-conjugate mirror could correct for all the distortions and aberrations in an optical system. The use of white-light phase-conjugate mirrors would be essential for ensuring high performance in optical systems containing lightweight membrane mirrors, which are highly deformable. As used here, "phase-conjugate mirror" signifies, more specifically, an optical component in which incident light undergoes time-reversal phase conjugation. In practice, a phase-conjugate mirror would typically be implemented by use of a suitably positioned and oriented photorefractive crystal. In the case of a telescope comprising a primary and secondary mirror (see figure) white light from a distant source would not be brought to initial focus on one or more imaging scientific instrument(s) as in customary practice. Instead, the light would be brought to initial focus on a phase-conjugate mirror. The phase-conjugate mirror would send a phase-conjugate image back, along the path of the incoming light, to the primary mirror. A transparent, highly efficient diffractive thin film deposited on the primary mirror would direct the phase-conjugate image to the imaging instrument(s).
This presentation discusses work done to assess the design of a focusing column in a miniaturized Scanning Electron Microscope (SEM) developed at the NASA Marshall Space Flight Center (MSFC) for use in-situ on the Moon-in particular for mineralogical analysis. The MSFC beam column design uses purely electrostatic fields for focusing, because of the severe constraints on mass and electrical power consumption imposed by the goals of lunar exploration and of spaceflight in general. The resolution of an SEM ultimately depends on the size of the focused spot of the scanning beam probe, for which the stated goal here is a diameter of 10 nanometers. Optical aberrations are the main challenge to this performance goal, because they blur the ideal geometrical optical image of the electron source, effectively widening the ideal spot size of the beam probe. In the present work the optical aberrations of the mini SEM focusing column were assessed using direct tracing of non-paraxial rays, as opposed to mathematical estimates of aberrations based on paraxial ray-traces. The geometrical ray-tracing employed here is completely analogous to ray-tracing as conventionally understood in the realm of photon optics, with the major difference being that in electron optics the lens is simply a smoothly varying electric field in vacuum, formed by precisely machined electrodes. Ray-tracing in this context, therefore, relies upon a model of the electrostatic field inside the focusing column to provide the mathematical description of the "lens" being traced. This work relied fundamentally on the boundary element method (BEM) for this electric field model. In carrying out this research the authors discovered that higher accuracy in the field model was essential if aberrations were to be reliably assessed using direct ray-tracing. This led to some work in testing alternative techniques for modeling the electrostatic field. Ultimately, the necessary accuracy was attained using a BEM/Fourier series hybrid approach. The presentation will give background remarks about the MSFC mini Lunar SEM concept and electron optics modeling, followed by a description of the alternate field modeling techniques that were tried, along with their incorporation into a ray-trace simulation. Next, the validation of this simulation against commercially available software will be discussed using an example lens as a test case. Then, the efficacy of aberration assessment using direct ray-tracing will be demonstrated, using this same validation case. The discussion will include practical error checks of the field solution. Finally, the ray-trace assessment of the MSFC mini Lunar SEM concept will be shown and discussed. The authors believe this presentation will be of general interest to practitioners of modeling and simulation, as well as those with a general optics background. Because electron optics and photon optics share many basic concepts (e.g., lenses, images, aberrations, etc.), the appeal of this presentation need not be restricted to just those interested in charged particle optics.
The Facility for Advanced Accelerator and Experimental Tests (FACET) is a new user facility at the SLAC National Accelerator Laboratory, servicing next-generation accelerator experiments. The 1.5% RMS energy spread of the FACET beam causes large chromatic aberrations in optics. These aberrations necessitate updated quadrupole scan fits to remain accurate.
For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.