New apodizers that arbitrarily decrease sensitivity to defocusing or to the variation of spherical aberration

1988 ◽  
Vol 66 (10) ◽  
pp. 878-882
Author(s):  
Richard Boivin
Keyword(s):  
Spherical Aberration ◽  
The Other ◽  
Optical Systems ◽  
Depth Of Focus ◽  
Rotationally Symmetric

Two families of pupil amplitude filters, or apodizers, are devised for rotationally symmetric optical systems. One type of apodizer, pertaining to systems with circular pupils, arbitrarily reduces their sensitivity to the variation of primary spherical aberration, when this is combined with defocusing to optimally compensate for the aberration. The other type of apodizer, pertaining to systems with slit pupils, arbitrarily extends their depth of focus.

Modelling of influence of spherical aberration coefficients on depth of focus of optical systems

2017 ◽  
Author(s):  
Petr Pokorný ◽  
Filip Šmejkal ◽  
Pavel Kulmon ◽  
Antonín Mikš ◽  
Jiří Novák ◽  
...  
Keyword(s):  
Spherical Aberration ◽  
Optical Systems ◽  
Depth Of Focus

Dependence of depth of focus on spherical aberration of optical systems

2016 ◽  
Vol 55 (22) ◽  
pp. 5931 ◽  
Author(s):  
Antonín Mikš ◽  
Jiří Novák
Keyword(s):  
Spherical Aberration ◽  
Optical Systems ◽  
Depth Of Focus

MAXIMUM OF THE FACTOR OF ENCIRCLED ENERGY

1961 ◽  
Vol 39 (1) ◽  
pp. 158-188 ◽  
Author(s):  
Guy Lansraux ◽  
Germain Boivin
Keyword(s):  
Diffraction Pattern ◽  
Spherical Aberration ◽  
Asymptotic Expression ◽  
Radiant Energy ◽  
The Other ◽  
Optical Systems ◽  
Rigorous Analysis ◽  
Gauss Function ◽  
Taylor’S Series

It is recognized that the most favorable distribution of radiant energy in a diffraction pattern is that which corresponds to the best concentration around the center O. This hypothesis is expressed by an extremal condition on the factor of encircled energy E(W), that is, the ratio of the energy inside a circle of radius W and centered on the diffraction pattern, to the total energy in the same.A study of the effects of spherical aberration on this factor of encircled energy has shown that aberration always tends to decrease the factor from the value obtained with an Airy pattern. However, this factor may be increased by the use of an amplitude filter at the pupil of the optical system.In treating the case of amplitude filters one may use a rigorous analysis in terms of Taylor's series in (1−x2)p−1 or a polynomial Tn(x) of degree n−1 in terms of (1−x2).The corresponding amplitudes in the diffraction pattern are Г(W) and Гn(W); the maximum factor of encircled energy E(Wm) and En(Wm). The following convergences are established: En(Wm) → E(Wm), Tn(x) → T(x), and Гn(W) → Г(W) as n → ∞.When the interval (0, Wm) of the diffraction pattern is made to correspond to the interval (0, 1) of the pupil by means of a suitable normalization the amplitude distributions T(x) and Г(W)—with W = Wmx—are identical. Some properties are deduced from this relation; for example, the Airy pattern is the limit of Г(W) when Wm → 0; on the other hand, the Gauss function [Formula: see text] is an asymptotic expression of T(x) when Wm → ∞. In any case, the factor of encircled energy is connected to the marginal amplitude in the pupil by the relation E(Wm) = 1−T2(1).The numerical determination of E(W) given up to W = 10 and Wm = 2, 3, 4, and 5 can be extended by use of an asymptotic expression of the factor of encircled energy.Finally, a curve M(W) has been obtained, which is an envelope of the curves E(W) corresponding to various values of Wm. This gives the locus of the maximum factor of encircled energy and represents the limiting performance of optical systems.

Practical Correction of Three Fold Astigmatism in the Philips CM TEM

1996 ◽  
Vol 54 ◽  
pp. 418-419
Author(s):  
Arno J. Bleeker ◽  
Mark H.F. Overwijk ◽  
Max T. Otten
Keyword(s):  
Optical Properties ◽  
Phase Contrast ◽  
The Other ◽  
Objective Lens ◽  
Symmetric Part ◽  
A Posteriori ◽  
Contrast Transfer Function ◽  
High Brightness ◽  
Rotationally Symmetric ◽  
Brightness Field

With the improvement of the optical properties of the modern TEM objective lenses the point resolution is pushed beyond 0.2 nm. The objective lens of the CM300 UltraTwin combines a Cs of 0. 65 mm with a Cc of 1.4 mm. At 300 kV this results in a point resolution of 0.17 nm. Together with a high-brightness field-emission gun with an energy spread of 0.8 eV the information limit is pushed down to 0.1 nm. The rotationally symmetric part of the phase contrast transfer function (pctf), whose first zero at Scherzer focus determines the point resolution, is mainly determined by the Cs and defocus. Apart from the rotationally symmetric part there is also the non-rotationally symmetric part of the pctf. Here the main contributors are not only two-fold astigmatism and beam tilt but also three-fold astigmatism. The two-fold astigmatism together with the beam tilt can be corrected in a straight-forward way using the coma-free alignment and the objective stigmator. However, this only works well when the coefficient of three-fold astigmatism is negligible compared to the other aberration coefficients. Unfortunately this is not generally the case with the modern high-resolution objective lenses. Measurements done at a CM300 SuperTwin FEG showed a three fold-astigmatism of 1100 nm which is consistent with measurements done by others. A three-fold astigmatism of 1000 nm already sinificantly influences the image at a spatial frequency corresponding to 0.2 nm which is even above the point resolution of the objective lens. In principle it is possible to correct for the three-fold astigmatism a posteriori when through-focus series are taken or when off-axis holography is employed. This is, however not possible for single images. The only possibility is then to correct for the three-fold astigmatism in the microscope by the addition of a hexapole corrector near the objective lens.

Atomic Resolution in Crystal Aperture Stem

1990 ◽  
Vol 48 (1) ◽  
pp. 236-237
Author(s):  
J T Fourie
Keyword(s):  
Optical System ◽  
Spherical Aberration ◽  
Three Dimensional ◽  
Transmission Function ◽  
Optical Systems ◽  
Bragg Angle ◽  
Electron Optical System ◽  
Intimate Contact ◽  
Diffraction Effects ◽  
Design Aspect

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.

New Feasible Concepts of Aberration Correction for Realizing High-Resolution Electron Microscopes

1990 ◽  
Vol 48 (1) ◽  
pp. 202-203
Author(s):  
H. Rose
Keyword(s):  
Spherical Aberration ◽  
Wave Length ◽  
Electron Wave ◽  
Optical Lens ◽  
Resolution Electron ◽  
Rotationally Symmetric ◽  
Electron Microscopes ◽  
The Cost ◽  
Imaging Performance ◽  
Acceleration Voltage

The imaging performance of the light optical lens systems has reached such a degree of perfection that nowadays numerical apertures of about 1 can be utilized. Compared to this state of development the objective lenses of electron microscopes are rather poor allowing at most usable apertures somewhat smaller than 10-2 . This severe shortcoming is due to the unavoidable axial chromatic and spherical aberration of rotationally symmetric electron lenses employed so far in all electron microscopes.The resolution of such electron microscopes can only be improved by increasing the accelerating voltage which shortens the electron wave length. Unfortunately, this procedure is rather ineffective because the achievable gain in resolution is only proportional to λ1/4 for a fixed magnetic field strength determined by the magnetic saturation of the pole pieces. Moreover, increasing the acceleration voltage results in deleterious knock-on processes and in extreme difficulties to stabilize the high voltage. Last not least the cost increase exponentially with voltage.

Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus

2014 ◽  
Vol 35 (1) ◽  
pp. 28-38 ◽  
Author(s):  
Renfeng Xu ◽  
Arthur Bradley ◽  
Norberto López Gil ◽  
Larry N. Thibos
Keyword(s):  
Image Quality ◽  
Refractive Error ◽  
Spherical Aberration ◽  
Depth Of Focus

Relationship between Induced Spherical Aberration and Depth of Focus after Hyperopic LASIK in Presbyopic Patients

Ophthalmology ◽  
2015 ◽  
Vol 122 (2) ◽  
pp. 233-243 ◽  
Author(s):  
Benjamin Leray ◽  
Myriam Cassagne ◽  
Vincent Soler ◽  
Eloy A. Villegas ◽  
Claire Triozon ◽  
...  
Keyword(s):  
Spherical Aberration ◽  
Depth Of Focus

scholarly journals Optical axes of catadioptric systems including visual, Purkinje and other nonvisual systems of a heterocentric astigmatic eye

2010 ◽  
Vol 69 (3) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Visual System ◽  
Optical Axis ◽  
The Other ◽  
Optical Systems ◽  
Numerical Examples ◽  
Straight Line ◽  
Optical Axes ◽  
Catadioptric Systems ◽  
Reflecting Surfaces ◽  
Special Case

For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system.  Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique.  Formulae were derived for the locations of any optical axes.  The purpose of this paper is to extend those results to allow for reflecting surfaces in the system in addition to refracting elements.  Thus the paper locates any optical axes in catadioptric systems (including dioptric systems as a special case).  The reflecting surfaces may be astigmatic and decentred or tilted.  The theory is illustrated by means of numerical examples.  The locations of the optical axes are calculated for seven optical systems associated with a particular heterocentric astigmatic model eye.  The optical systems are the visual system, the four Purkinje systems and two other nonvisual systems of the eye.  The Purkinje systems each have an infinity of optical axes whereas the other nonvisual systems, and the visual system, each have a unique optical axis. (S Afr Optom 2010 69(3) 152-160)

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