scholarly journals On the aberrations of compound lenses and object-glasses

1833 ◽  
Vol 2 ◽  
pp. 146-147
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Considerable Advantage ◽  
Optical Instruments ◽  
Spherical Surfaces ◽  
Finite Distance ◽  
The Subject ◽  
Algebraic Investigation ◽  
Difficult Part

To those mathematicians who have investigated the theory of the refracting telescope, it has often, says Mr. Herschel, been objected, that little practical benefit has resulted from their speculations. Although the simplest considerations suffice for correcting that part of the aberration which arises from the different refrangibility of the different coloured rays, yet in the more difficult part of the theory of optical instruments which relates to the correction of the spherical aberration, the necessity of algebraic investigation has always been , acknowledged; although, however, the subject is confessedly within its reach, a variety of causes have interfered with its successful prosecution, and the best artists are content to work their glasses by empirical rules. In the investigations detailed in this paper, the author’s object is, first to present, under a general and uniform analysis, the whole theory of the aberration of spherical surfaces; and then to furnish practical results of easy computation to the artist, and applicable, by the simplest interpolations, to the ordinary materials on which he works. In pursuing these ends he has found it necessary somewhat to alter the usual language employed by optical writers;—thus, instead of speaking of the focal length of lenses, or the radii of their surfaces , he speaks of their powers and curvatures ; designating, by the former expression, the quotient of unity by the number of parts of any scale which the focal length is equal to; and by the latter, the quotient similarly derived from the radius in question. After adverting to some other parts of the subject of this paper, more especially to the problem of the destruction of the spherical aberration in a double or multiple lens, and to the difficulties which it involves, Mr. Herschel observes, that one condition, hitherto unaccountably overlooked, is forced upon our attention by the nature of the formulæ of aberration given in this paper; namely, its destruction not only from parallel rays, but also from rays diverging from a point at any finite distance, and which is required in a perfect telescope for land objects, and is of considerable advantage in those for astronomical use: 1st, The very moderate curvatures required for the surfaces; 2nd, That in this construction the curvatures of the two exterior surfaces of the compound lens of given focal length vary within very narrow limits, by any variation in either the refractive or dispersive powers at all likely to occur in practice; 3rd, That the two interior surfaces always approach so nearly to coincidence, that no considerable practical error can arise from neglecting their difference, and figuring them on tools of equal radii.

Experimental Study on Correction of Spherical Aberration in Electro-Magnetic Round Lens

1990 ◽  
Vol 48 (1) ◽  
pp. 234-235
Author(s):  
Ergang Chen ◽  
Chongjun Mu
Keyword(s):  
Electron Beam ◽  
Spherical Aberration ◽  
Focal Length ◽  
Image Point ◽  
Electron Trajectory ◽  
Optical Instruments ◽  
Concave Lens ◽  
In Series ◽  
Electron Microscopes ◽  
Electro Magnetic

As we know that the spherical aberration in a round electromagnetic lens can not be eliminated. Therefor,the correcting of such aberration is an important subject to improve the ultimate resolution of electron microscopes and the performance of other electron optical instruments, such as electron beam manufactureing machines, electron lithographic machine etc.A combination of quadrupoles and octupoles which was proposed by Scherzer is a reasonable way to correct this aberration, but it has been proved practically unsuccessful. Crewe suggested that the sextu-pole elements could be used as a device to correct the 3rd order aberration of a round lens. Later he has showed that a system of two sextupoles with a round lens placed in the middle of it can acturely act as an electromagnetical concave lens if the focal length of this middle lens be settled to satisfy certain condition. Instead of taking terms of z7 in series solution of motion equation of electron in sextu-pole which Crewe had done, we took it up to z20to compute the amplitude r and slope r' of electron trajectory at each specific point z1 , z2 , z3, and z4along the optical axis. The results show that the action of sex-tupole-lens-sextupole system does act as an optical concave lens. It produces a negative spherical aberration. Differing from optical concave lens, in this system the negative aberration can be varied in a wide rang by adjusting the strength of sextupole k. Fig.2 shows a series of computed performances of electron beam near Gaussian image point while the strength of sextupole k=0 incase(a) and k1< k2in case (b) and (c). Evidently, this system does produce a negative spherical aberration while k is not zero.

scholarly journals Rules and principles for determining the dispersive ratio of glass; and for computing the radii of curvature for achromatic object glasses, submitted to the test of experiment

1833 ◽  
Vol 2 ◽  
pp. 316-317
Keyword(s):  
Refractive Index ◽  
Spherical Aberration ◽  
Focal Length ◽  
Refractive Indices ◽  
Practical Application ◽  
Convex Lens ◽  
Astronomical Instruments ◽  
Rules And Principles ◽  
The Subject ◽  
Source Of Error

The author begins this paper by an enumeration of the various works on the subject extant in our language, and a general mention of the writings of foreign mathematicians, which he considers as leaving room for further inquiry and simplification. He then states the method employed in his experiments for determining the refractive and relative dispersive powers of his glasses, the former of which is that generally known and practised;—of measuring the radii and focal length of a lens, and thence deriving the refractive index; with some refinements in its practical application, consisting chiefly in using the lens as the object-glass of a telescope, and adapting to it a positive eye-piece and cross-wires, which are brought precisely to the true focus by the criterion of the evanescence of parallax arising from a motion of the eye, as is practised in adjusting the stops of astronomical instruments. The only source of error it involves is in the measurement of radii of the tools which it was found could always be performed within 1/500th of their whole values. The dispersive ratio of two glasses was determined by over-correcting the dispersion of a convex lens of the less dispersive glass by a concave of the greater, and then withdrawing the latter from the former till the achromaticity is perfect, or as nearly so as the materials will admit, and measuring the interval between the lenses and their foci, from which data the ratio of their dispersive powers is easily obtained. The refractive indices and dispersive ratio thus determined, the next step is to find the radii of curvature so as to destroy spherical -aberration. In this investigation, the author does not consider it as necessary to limit the indeterminate problem by any further condition, as others before him have done, but regarding it as a matter of great convenience to avoid contact of the interior surfaces in the centre of the glasses, leaves it open to the optician to make a choice within certain limits, thus avoiding what he considers as an intricate equation arising out of the fourth condition. He proceeds, therefore, to express analytically the aberrations of the glasses, and to deduce the equation expressive of its destruction, which of course involves one indeterminate quantity; this may be either of the radii, or any combination of them. The author chooses the ratio of the radii of the interior and exterior surfaces of his flint lens for this indeterminate, which he assumes, as well as may be, to satisfy the condition of the absence of contact and near equi-curvature of the adjacent surfaces; thence deduces, first, the radii of both of the surfaces of the flint lens; next, its aberration to be corrected; and thence, by the solution of a quadratic, or by the use of a table containing its solutions registered in various states of the data, the ratio of the radii of the convex, whence the radii themselves are easily deduced.

Resolution Attainable With the Present Day STEM

1973 ◽  
Vol 31 ◽  
pp. 230-231 ◽  
Author(s):  
J. S. Wall ◽  
J. P. Langmore ◽  
H. Isaacson ◽  
A. V. Crewe
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Aperture Size ◽  
Magnetic Lens ◽  
Peak Intensity ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Half Angle

The scanning transmission electron microscope (STEM) constructed by the authors employs a field emission gun and a 1.15 mm focal length magnetic lens to produce a probe on the specimen. The aperture size is chosen to allow one wavelength of spherical aberration at the edge of the objective aperture. Under these conditions the profile of the focused spot is expected to be similar to an Airy intensity distribution with the first zero at the same point but with a peak intensity 80 per cent of that which would be obtained If the lens had no aberration. This condition is attained when the half angle that the incident beam subtends at the specimen, 𝛂 = (4𝛌/Cs)¼

Improvements in the electron probe forming capabilities and x-ray hole counts in the Philips TEM

1983 ◽  
Vol 41 ◽  
pp. 376-377
Author(s):  
Richard L. McConville
Keyword(s):  
Field Strength ◽  
Electron Probe ◽  
Spherical Aberration ◽  
Focal Length ◽  
Objective Lens ◽  
Parallel Beam ◽  
Tilt Axis ◽  
X Ray ◽  
Small Probe ◽  
Specimen Height

A second generation twin lens has been developed. This symmetrical lens with a wider bore, yet superior values of chromatic and spherical aberration for a given focal length, retains both eucentric ± 60° tilt movement and 20°x ray detector take-off angle at 90° to the tilt axis. Adjust able tilt axis height, as well as specimen height, now ensures almost invariant objective lens strengths for both TEM (parallel beam conditions) and STEM or nano probe (focused small probe) modes.These modes are selected through use of an auxiliary lens situ ated above the objective. When this lens is on the specimen is illuminated with a parallel beam of electrons, and when it is off the specimen is illuminated with a focused probe of dimensions governed by the excitation of the condenser 1 lens. Thus TEM/STEM operation is controlled by a lens which is independent of the objective lens field strength.

Comparison of Deterministic and Linear Cosine Spatial Filtering of Transmission Electron Micrographs

1972 ◽  
Vol 30 ◽  
pp. 596-597
Author(s):  
David A. Ansley
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Spatial Filter ◽  
Operating Conditions ◽  
Objective Lens ◽  
List Type ◽  
Spatial Filters ◽  
Transmission Electron ◽  
Wide Range

The coherence of the electron flux of a transmission electron microscope (TEM) limits the direct application of deconvolution techniques which have been used successfully on unmanned spacecraft programs. The theory assumes noncoherent illumination. Deconvolution of a TEM micrograph will, therefore, in general produce spurious detail rather than improved resolution.A primary goal of our research is to study the performance of several types of linear spatial filters as a function of specimen contrast, phase, and coherence. We have, therefore, developed a one-dimensional analysis and plotting program to simulate a wide 'range of operating conditions of the TEM, including adjustment of the:(1) Specimen amplitude, phase, and separation(2) Illumination wavelength, half-angle, and tilt(3) Objective lens focal length and aperture width(4) Spherical aberration, defocus, and chromatic aberration focus shift(5) Detector gamma, additive, and multiplicative noise constants(6) Type of spatial filter: linear cosine, linear sine, or deterministic

A High Resolution Scanning Microscope

1968 ◽  
Vol 26 ◽  
pp. 356-357
Author(s):  
A. V. Crewe ◽  
J. Wall ◽  
L. M. Welter
Keyword(s):  
High Resolution ◽  
Field Emission ◽  
Spherical Aberration ◽  
Focal Length ◽  
Spot Size ◽  
Emission Source ◽  
Field Of View ◽  
Scanning Microscope ◽  
Magnetic Lens ◽  
High Quality

A scanning microscope using a field emission source has been described elsewhere. This microscope has now been improved by replacing the single magnetic lens with a high quality lens of the type described by Ruska. This lens has a focal length of 1 mm and a spherical aberration coefficient of 0.5 mm. The final spot size, and therefore the microscope resolution, is limited by the aberration of this lens to about 6 Å.The lens has been constructed very carefully, maintaining a tolerance of + 1 μ on all critical surfaces. The gun is prealigned on the lens to form a compact unit. The only mechanical adjustments are those which control the specimen and the tip positions. The microscope can be used in two modes. With the lens off and the gun focused on the specimen, the resolution is 250 Å over an undistorted field of view of 2 mm. With the lens on,the resolution is 20 Å or better over a field of view of 40 microns. The magnification can be accurately varied by attenuating the raster current.

scholarly journals On a cassegrain reflector with corrected field

1913 ◽  
Vol 88 (602) ◽  
pp. 188-191
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Straightforward Manner ◽  
Flat Field ◽  
Convex Mirror ◽  
Solution Proceeds ◽  
Characteristic Features ◽  
Working Out ◽  
Essential Problem ◽  
Single Focus

The purpose of this memoir is to discover an optical appliance which shall correct in a practical manner the faults in the field of a Cassegrain reflector, while leaving unimpaired its achromatism and the characteristic features of its design, which gives a focal length much greater than the length of the instrument, combined with a convenient position of the observer. The question touches an investigation by Schwarzschild as to what can be done with two curved mirrors the figures of which are not necessarily spherical. With these be corrects spherical aberration and coma, but in order to secure a flat field he is led to a construction in which the second mirror, which is between the great mirror and its principal focus, is concave, and therefore shortens the effective focal length, in place of increasing it. The deformations from spherical figures are also so great, especially for the great mirror, as to leave it doubtful whether the construction discussed could ever be the model for practicable instruments. If we keep to the Cassegrain form, spherical aberration and coma may equally be corrected by deformations of the mirrors which through large, are less extreme, but there remains a pronounced curvature of the field. For this reason I am led, in the present memoir, to consider more complicated systems produced by the interposition of systems of lenses, achromatism can be preserved completely for a single focus if there are three lenses of focal length determined when their position are given, and if all are made of the same glass. One of these lenses, which I call the reverser, is silvered at the back and replaces the convex mirror; the other two are placed close together in the way of the outcoming beam, about one third of the distance from the great mirror to the reverser; the members of this pair, which I call the corrector, are of nearly equal but opposite focal lengths, introducing very little deviation in the ray but an arbitrary amount of aberration, according to the distribution of curvatures between the two faces of each lens. All the surfaces are supposed spherical except that of the great mirror, The essential problem is to bring the necessary work into a form that will allow unknown quantities which express the distribution of curvature between the faces of each lens to be carried forward algebraically. The methods employed are those of a recent memoir by the author,* and a part of the paper is occupied in working out expressions to which this theory leads, for thin lenses, systems of thin lenses, mirrors, reversers and the like, and it may be regarded as an expansion and working illustration of that memoir. Ibis part does not lend itself to summary, When the expressions are obtained the solution proceeds in a straightforward manner, by approximation, which is somewhat complicated owing to the number of considerations which it is necessary to keep in view, but is not otherwise difficult. The solution is completed at the stage where the unextinguished aberrations are considered negligible.

scholarly journals Design of spherical aberration free liquid-filled cylindrical zoom lenses over a wide focal length range based on ZEMAX

2020 ◽  
Vol 28 (5) ◽  
pp. 6806 ◽  
Author(s):  
Licun Sun ◽  
Shuwu Sheng ◽  
Weidong Meng ◽  
Yuanfangzhou Wang ◽  
Quanhong Ou ◽  
...  
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Length Range

scholarly journals IV.On a supposed alteration in the amount of astronomical aberration of light, produced by the passage of the light through a considerable thickness of refracting medium

1872 ◽  
Vol 20 (130-138) ◽  
pp. 35-39 ◽  
Keyword(s):  
Royal Academy ◽  
Angular Displacement ◽  
Focal Length ◽  
The Sun ◽  
Change Of Direction ◽  
The Subject ◽  
The Difference ◽  
North Polar ◽  
Academy Of Sciences ◽  
Right Ascension

A discussion has taken place on the Continent, conducted partly in the 'Astronomische Nachrichten,’ partly in independent pamphlets, on the change of direction which a ray of light will receive (as inferred from the Undulatory Theory of Light) when it traverses a refracting medium which has a motion of translation. The subject to which attention is particularly called is the effect that will be produced on the apparent amount of that angular displacement of a star or planet which is caused by the Earth’s motion of translation, and is known as the Aberration of Light. It has been conceived that there may be a difference in the amounts of this displacement, as seen with different telescopes, depending on the difference in the thicknesses of their object-glasses. The most important of the papers containing this discussion are:—that of Professor Klinkerfues, contained in a pamphlet published at Leipzig in 1867, August; and those of M. Hoek, one published 1867, October, in No. 1669 of the 'Astronomische Nachrichten,’ and the other published in 1869 in a communication to the Netherlands Royal Academy of Sciences. Professor Klinkerfues maintained that, as a necessary result of the Undulatory Theory, the amount of Aberration would be increased, in accordance with a formula which he has given; and he supported it by the following experiment:— In the telescope of a transit-instrument, whose focal length was about 18 inches, was inserted a column of water 8 inches in length, carried in a tube whose ends were closed with glass plates; and with this instrument he observed the transit of the Sun, and the transits of certain stars whose north-polar distances were nearly the same as that of the Sun, and which passed the meridian nearly at midnight. In these relative positions, the difference between the Apparent Right Ascension of the Sun and those of the stars is affected by double the coefficient of Aberration; and the merely astronomical circumstances are extremely favourable for the accurate testing of the theory. Professor Klinkerfues had computed that the effect of the 8-inch column of water and of a prism in the interior of the telescope would be to increase the coefficient of Aberration by eight seconds of arc. The observation appeared to show that the Aberration was really increased by 7'' 1. It does not appear that this observation was repeated.

A Maximum-Minimum Method of Determining the Cardinal Points of a Lens System

1936 ◽  
Vol 32 (1) ◽  
pp. 138-143
Author(s):  
G. F. C. Searle
Keyword(s):  
Minimum Distance ◽  
Focal Length ◽  
Refractive Indices ◽  
Lens System ◽  
Coaxial System ◽  
Nodal Points ◽  
Finite Distance ◽  
The Media ◽  
Principal Points ◽  
Maximum Minimum

The method of determining the focal length f of a thin converging lens by finding the minimum distance Δ0 between image and object is well known. When the thickness of the lens is negligible, f = ¼Δ0.In the general coaxial system, the media at the two ends have refractive indices μ1, μ2, and there is a finite distance t between the principal or unite plances. The two focal lengths are unequal, since, f1/f2=μ1/μ2, and the nodal points do not coincide with the principal points.

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