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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.
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.
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.
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.
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.
A metrology system for measuring aspheric test objects by subaperture stitching. A wavefront-measuring gauge having a limited capture range of wavefront shapes collects partially overlapping subaperture measurements over the test object. A variable optical aberrator reshapes the measurement wavefront with between a limited number of the measurements to maintain the measurement wavefront within the capture range of the wavefront-measuring gauge. Various error compensators are incorporated into a stitching operation to manage residual errors associated with the use of the variable optical aberrator.
An apparatus for eliminating beamsplitter generated optical aberrations in a pupil concentric optical system providing a plurality of spatially separated images on different focal planes or surfaces is presented. The system employs a buried surface beamsplitter having spherically curved entrance and exit faces which are concentric to a system aperture stop with the entrance face being located in the path of a converging light beam directed there from an image forming objective element which is also concentric to the aperture stop.
As astronomical observations benefit from improved sensitivity, the effectiveness of scientific programs is becoming limited by systematics that often originate in poorly understood image sensor behavior. Traditional, bottom-up detector characterization methods provide one way to model underlying detector physics, and generate ever more faithful numerical simulations, but this approach is vulnerable to preconceptions and over-simplification. The alternative top-down approach is laboratory emulation, which enables observation, calibration, and analysis scenarios to be tested without relying on a complete understanding of the underlying physics. This complements detector characterization and simulation efforts by testing their validity. We describe a laboratory facility and experimental testbed that supports the emulation of a wide range of mission concepts such as gravitational weak lensing measurements by WFIRST and high precision spectrophotometry of transiting exoplanets by JWST. An Offner relay projects readily customizable "scenes" (e.g. stars, galaxies, spectra) with very low optical aberration over the full area of a typical optical or near infrared image sensor. f/8 and slower focal ratios may be selected, spanning those of most proposed space missions and approximating the point spread function (PSF) size of seeing limited ground based surveys. Diffraction limited PSFs are projected over a wide field of view and wavelength range to deliver highly predictable image patterns down to sub-pixel scales with stable intensity and fine motion control. The testbed enables realistic validation of detector performance on science-like images, which aids mission design and survey strategy, as well as targeted investigations of various detector effects.
A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.
Two approaches to reducing optical aberrations of concave grating spectrographs have been used, holographically controlling the groove curvature and spacing and reshaping the optical substrate while ruling the grooves conventionally. The latter approach, slightly deforming an ellipsoidal grating blank, can lead to diffraction-limited performance at a single FUV wavelength. When such a grating is used in a slitted Rowland circle spectrograph, the result is an extremely efficient spectrograph with spectral resolving power of about 30,000 and low astigmatism. Optical fabrication technology has advanced to the point where these exotic surface gratings are becoming practical.