Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration

2010 ◽  
Vol 27 (12) ◽  
pp. 2563 ◽  
Author(s):  
Aleksey N. Simonov ◽  
Michiel C. Rombach
Author(s):  
J T Fourie

The attempts at improvement of electron optical systems to date, have largely been directed towards the design aspect of magnetic lenses and towards the establishment of ideal lens combinations. In the present work the emphasis has been placed on the utilization of a unique three-dimensional crystal objective aperture within a standard electron optical system with the aim to reduce the spherical aberration without introducing diffraction effects. A brief summary of this work together with a description of results obtained recently, will be given.The concept of utilizing a crystal as aperture in an electron optical system was introduced by Fourie who employed a {111} crystal foil as a collector aperture, by mounting the sample directly on top of the foil and in intimate contact with the foil. In the present work the sample was mounted on the bottom of the foil so that the crystal would function as an objective or probe forming aperture. The transmission function of such a crystal aperture depends on the thickness, t, and the orientation of the foil. The expression for calculating the transmission function was derived by Hashimoto, Howie and Whelan on the basis of the electron equivalent of the Borrmann anomalous absorption effect in crystals. In Fig. 1 the functions for a g220 diffraction vector and t = 0.53 and 1.0 μm are shown. Here n= Θ‒ΘB, where Θ is the angle between the incident ray and the (hkl) planes, and ΘB is the Bragg angle.


1991 ◽  
Vol 127 ◽  
pp. 68-76
Author(s):  
W.H. Jefferys ◽  
G.F. Benedict ◽  
R.L. Duncombe ◽  
O.G. Franz ◽  
L.W. Fredrick ◽  
...  

AbstractThe Fine Guidance Sensors (FGSs) are the instrument of choice for most astrometric measurements with the Hubble Space Telescope (HST). The observed amount of spherical aberration in the Ritchey Chretien optical system does not affect positional measurements with perfectly aligned FGSs because they are interferometers. The FGSs combine wavefronts from points in the exit pupil with other points which are at the same radial distance from the optical axis. Asymmetric aberrations such as coma and astigmatism do affect the measured positions. The current knowledge of the HST wavefront error, the FGS operation and the implications for milliarcsecond relative astrometry are discussed. It is still planned to use the HST to tie the HIPPARCOS and VLBI Reference Frames together at the few milliarcsecond level.


2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Johannes Stock ◽  
Matthias Beier ◽  
Johannes Hartung ◽  
Sebastian Merx ◽  
Herbert Gross

Abstract In recent years, the precision of the manufacturing process for optical surfaces has improved tremendously. As a result, freefrom surfaces have become more attractive options for imaging applications with increased accuracy requirements. However, with regards the integration into an optical system, performance is often limited due to surface imperfections, such as mid-spatial frequency errors and alignment errors. This demonstrates the need for a more holistic description of systems, including multiple freeform components, which enable performance predictions based on the system as a whole. In this work, a solution for such a simulation is presented and verified by a comparison with the experimental data. This procedure not only predicts system performance but also supports tolerancing and easier alignment.


Molecules ◽  
2019 ◽  
Vol 24 (6) ◽  
pp. 1018
Author(s):  
Tina Sabel

Holographic volume phase gratings are recorded in an epoxy-based, free-surface, volume holographic recording material. Light-induced gratings are formed by photo-triggered mass migration caused by component diffusion. The material resolution enables a wide range of pattern spacings, to record both transmission and reflection holograms with many different spatial frequencies. An optimum spatial frequency response is found between the low spatial frequency roll-off and the high spatial frequency cut-off. The influence of the energy density of exposure on the spatial frequency response is investigated. Secondary volume holographic gratings (parasitic gratings) are observed in the high frequency range. The possibility of distinguishing the regular grating from the secondary grating is discussed in the form of probe wavelength detuning.


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