The optimum image plane in an optical system with chromatic aberration

1967 ◽  
Vol 17 (6) ◽  
pp. 527-542 ◽  
Author(s):  
V. Blumová
Keyword(s):  
Optical System ◽  
Image Plane ◽  
Chromatic Aberration

Electron Holography Improving Transmission Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 208-209
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
Transfer Functions ◽  
Imaging System ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Wave Aberration

Generally, the electron object wave o(r) is modulated both in amplitude and phase. In the image plane of an ideal imaging system we would expect to find an image wave b(r) that is modulated in exactly the same way, i. e. b(r) =o(r). If, however, there are aberrations, the image wave instead reads as b(r) =o(r) * FT(WTF) i. e. the convolution of the object wave with the Fourier transform of the wave transfer function WTF . Taking into account chromatic aberration, illumination divergence and the wave aberration of the objective lens, one finds WTF(R) = Echrom(R)Ediv(R).exp(iX(R)) . The envelope functions Echrom(R) and Ediv(R) damp the image wave, whereas the effect of the wave aberration X(R) is to disorder amplitude and phase according to real and imaginary part of exp(iX(R)) , as is schematically sketched in fig. 1.Since in ordinary electron microscopy only the amplitude of the image wave can be recorded by the intensity of the image, the wave aberration has to be chosen such that the object component of interest (phase or amplitude) is directed into the image amplitude. Using an aberration free objective lens, for X=0 one sees the object amplitude, for X= π/2 (“Zernike phase contrast”) the object phase. For a real objective lens, however, the wave aberration is given by X(R) = 2π (.25 Csλ3R4 + 0.5ΔzλR2), Cs meaning the coefficient of spherical aberration and Δz defocusing. Consequently, the transfer functions sin X(R) and cos(X(R)) strongly depend on R such that amplitude and phase of the image wave represent only fragments of the object which, fortunately, supplement each other. However, recording only the amplitude gives rise to the fundamental problems, restricting resolution and interpretability of ordinary electron images:

scholarly journals A proposed Mathematical Expression for Computer Design of Electrostatic Mirror

2012 ◽  
Vol 9 (1) ◽  
pp. 148-152
Author(s):  
Baghdad Science Journal
Keyword(s):  
Optical System ◽  
Focal Length ◽  
Mathematical Expression ◽  
Optical Element ◽  
Chromatic Aberration ◽  
Computer Design ◽  
Computational Investigation ◽  
Beam Path ◽  
Runge Kutta Method ◽  
Electrostatic Mirror

A computational investigation has been carried out on the design and properties of the electrostatic mirror. In this research, we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The electron beam path under zero magnification condition had been investigated as mirror trajectory with the aid of fourth – order – Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. each optical element in optical system has suffer from the chromatic aberration, for this case, it is use to operate the mirror in optical system at various values of chromatic aberration to correct it in that system.

Application of Dynamic Optical Theory in Zoom System

2007 ◽  
Vol 364-366 ◽  
pp. 539-543
Author(s):  
Yuan Hu ◽  
Yue Gang Fu ◽  
Zhi Ying Liu ◽  
Tian Yuan Gao ◽  
Lei Zhang ◽  
...  
Keyword(s):  
System Design ◽  
Optical System ◽  
Image Plane ◽  
Image Motion ◽  
Object Image ◽  
Motion Group ◽  
Imaging Quality ◽  
Optical Theory

Dynamic optical is a theory which we can deduce the object-image conjugated rations of optical system by researching motion group in optical system. It can unify various formula and methods of optical system which have motion group. Zoom system is a typical dynamic optical system. This paper will discuss how to apply the dynamic optical theory to zoom system design. With dynamic optical theory, we can derive the image motion compensating formula and the trace curve of the image motion compensating group. The cam can be fabricated according to compensating curve, which can ensure the stabilization of image plane and keep imaging quality. Moreover, a example of 30× zoom system is presented, which proves that the dynamic optical theory has some practicability for zoom system design.

Non-Gaussian intensity fluctuations in the image plane of an optical system

1997 ◽  
Author(s):  
Ivan A. Popov ◽  
Nikolay V. Sidorovsky ◽  
Leonid M. Veselov
Keyword(s):  
Optical System ◽  
Image Plane ◽  
Intensity Fluctuations ◽  
Non Gaussian

scholarly journals CALCULATION OF THE ACHROMATIC DIFFRACTION SYSTEM WITH CORRECTED SPHERICAL ABERRATION (part 2)

2020 ◽  
Vol 8 (1) ◽  
pp. 127-133
Author(s):  
Yury Ts. Batomunkuev ◽  
Alexandra A. Pechenkina
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Optical Element ◽  
Diffraction Order ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Real Image ◽  
Optical Elements ◽  
A Value ◽  
Analytical Expressions

Achromatization of a three-component diffraction system consisting of one thick and two thin hologram optical elements is considered in the work. Analytical expressions are obtained for correcting the chromatic aberration of the position of a thick focusing hologram optical element by two scattering thin hologram optical elements in a given spectrum range. It is shown that achromatization is achieved for such a three-component system using two thin hologram elements located symmetrically on both sides of the thick element and having a value of the working diffraction order greater than the ratio of the focal length to the distance from the thin element to the image plane (at a given wavelength). The proposed three-component holographic system can be used to convert both an imaginary image into a real image and a real into an imaginary image in predetermined spectral regions of the visible, ultraviolet or infrared ranges of the spectrum.

scholarly journals ACHROMATIZATION OF THE VOLUME HOLOGRAPHIC OPTICAL ELEMENS

2020 ◽  
Vol 8 (1) ◽  
pp. 139-145
Author(s):  
Yury Ts. Batomunkuev
Keyword(s):  
Spectral Range ◽  
Optical System ◽  
Optical Element ◽  
Chromatic Aberration ◽  
Lens Model ◽  
Base Element ◽  
First Approximation ◽  
Two Component ◽  
Diffraction Structure ◽  
Analytical Expressions

The work considers a two-component holographic optical system having a base element in the form of a thick (volume) hologram optical element and intended for use in a given spectral range. The calculation of a two-component holographic system is carried out using formulas obtained from the mirror-lens model of the thick hologram element proposed by the author. It is indicated that according to the mirror model a thick hologram optical element is achromatic in a first approximation. For this the local period of the volume diffraction structure of the hologram element must be many times greater than the working wavelength, and the transverse dimensions of the element must be less than its thickness. Analytical expressions are given for the mutual correction of the chromatic aberration of the position of a thick hologram optical element and a relief kinoform element. The condition for achromatization of this two-component holographic system is formulated.

New Direct Methods for Phase and Structure Retrieval in HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 26-27
Author(s):  
D. Van Dyck ◽  
M. Op de Beeck
Keyword(s):  
Electron Micrographs ◽  
Structural Information ◽  
Spherical Aberration ◽  
Direct Method ◽  
Direct Methods ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Variation Method ◽  
First Results ◽  
Image Area

Reliable interpretation of high resolution electron micrographs is only possible by comparison with computer simulations. However, simulation is a tedious trial and error technique which can only be successful if the experimental parameters are known and if the number of plausible structure models is small. For instance the interpretation of images of amorphous objects by simulation is hopeless. This makes the power of HREM very much dependent on the amount of prior information available from other techniques such as X-ray diffraction. HREM would be much more powerful and independent if a direct method could be established to retrieve the structural information of the object directly from the electron micrographs.We present a new “focus variation method” in which the phase is retrieved in the image plane in a deterministic way from a combination of images at closely spaced focus values, as inspired on the method proposed in [1] [2]. In a sense the whole information is used in the 3D image area of the electron microscope. The method allows to correct for chromatic aberration, spherical aberration and focus and is robust against noise. In a second stage we retrieve the projected structure of the object directly from the knowledge of the wavefunction at the exit face, using the channelling theory proposed in [3]. The first results are very promising.

Resolution in Emission Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 360-361
Author(s):  
G. F. Rempfer
Keyword(s):  
Current Density ◽  
Intensity Distribution ◽  
High Intensity ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Emission Current Density ◽  
Emission Current ◽  
Object Size ◽  
Emission Microscopy

A commonly used estimate for the resolution limit imposed by spherical aberration in electron microscopes is the radius of the circle of least confusion rℓc. The radius of least confusion is calculated for a point object and a single energy, and is referred to object space. There are a number of reasons for questioning the usefulness of the radius of least confusion as a measure of resolution. If the intensity were uniformly distributed over the circle of confusion at different depths in the image it would be natural to assume that best resolution occurs in the plane in which the circle of confusion is smallest. However, the intensity is not uniform. Furthermore the effect of a distribution of electron energies and a non-zero object size (required for a non-zero current) should be included in calculating resolution, especially in emission microscopy, where the chromatic aberration can be very large, and low emission current density can limit the smallness of details which can be viewed or recorded. In an earlier work Storbeck, and recently my colleagues and I using a different approach, have taken these effects into account in resolution studies based on the intensity distribution in the image.In emission microscopy the aberrations introduced by the accelerating field as well as those due to the objective lens must be considered. In our calculations the spherical aberration coefficients due to the field and the lens are referred to virtual specimen space (the image space of the accelerated electrons) at unit magnification, where they are combined, as are the chromatic aberration coefficients. The object for the microscope is a small disc centered on the axis. The emission current density is uniform, with a cosine angular distribution, and an emission energy distribution chosen to fit the particular application. The intensity distribution in the image plane is calculated first for monoenergetic beams, as a function of the axial position of the plane. The distribution curves in Fig. 1 exhibit the effects of spherical aberration and object size as the defocus changes. The shapes of the curves are due to the behavior of the image disc as a function of the emission angle αe. Between the plane of least confusion and the paraxial plane, as αe increases from 0° the image disc at first moves away from the axis in the azimuth of emission (retrograde direction). After reaching a maximum displacement, which depends on the distance from the paraxial plane, the image disc moves back to the axis and into the opposite azimuth as αe continues to increase. The intensity on the axis is highest when the retrograde displacement is equal to the image disc radius, Fig. 1c. This intensity distribution turns out to be more favorable for resolution than does the distribution in the plane of least confusion, Fig. If, even though the beam spreads over a larger area. The smaller the object radius and spherical aberration coefficient are, the closer the high-intensity plane is to the paraxial plane. For a monoenergetic beam the high-intensity plane for the smallest object which can provide the required current in the image is the optimum image plane for geometrical resolution. For a beam with a range of energies the total intensity distribution is obtained from the weighted sum of single-energy distributions calculated for a series of values in the energy range and for a given position of the image plane, Fig. 2. A good approximation to the plane providing best resolution for the beam as a whole is the high-intensity plane for the average energy.

Study of Chromatic Aberration of Pan-Cassegrain Optical System

2012 ◽  
Vol 32 (7) ◽  
pp. 0722002
Author(s):  
韦晓孝 Wei Xiaoxiao ◽  
许峰 Xu Feng ◽  
余建军 Yu Jianjun
Keyword(s):  
Optical System ◽  
Chromatic Aberration
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