Analysis of Seidel aberration coefficients of thick lens with arbitrary focal length

2018 ◽  
Author(s):  
Jirí Novák ◽  
Antonín Mikš ◽  
Pavel Novák ◽  
Petr Pokorný ◽  
Filip Smejkal
Keyword(s):  
Focal Length ◽  
Thick Lens

scholarly journals Simulating and optimizing compound refractive lens-based X-ray microscopes

2017 ◽  
Vol 24 (2) ◽  
pp. 392-401 ◽  
Author(s):  
Hugh Simons ◽  
Sonja Rosenlund Ahl ◽  
Henning Friis Poulsen ◽  
Carsten Detlefs
Keyword(s):  
Focal Length ◽  
Numerical Aperture ◽  
Chromatic Aberration ◽  
Matrix Analysis ◽  
Full Field ◽  
X Ray ◽  
Transfer Matrix Analysis ◽  
Thick Lens ◽  
Lens Material ◽  
Analytical Expressions

A comprehensive optical description of compound refractive lenses (CRLs) in condensing and full-field X-ray microscopy applications is presented. The formalism extends ray-transfer matrix analysis by accounting for X-ray attenuation by the lens material. Closed analytical expressions for critical imaging parameters such as numerical aperture, spatial acceptance (vignetting), chromatic aberration and focal length are provided for both thin- and thick-lens imaging geometries. These expressions show that the numerical aperture will be maximized and chromatic aberration will be minimized at the thick-lens limit. This limit may be satisfied by a range of CRL geometries, suggesting alternative approaches to improving the resolution and efficiency of CRLs and X-ray microscopes.

Third-order aberration coefficients of a thick lens with a given value of its focal length

2018 ◽  
Vol 57 (15) ◽  
pp. 4263 ◽  
Author(s):  
Antonín Mikš ◽  
Jiří Novák
Keyword(s):  
Focal Length ◽  
Third Order ◽  
Thick Lens

scholarly journals Measuring the effective focal length and shape factor of a thick lens using a microscope

Optik ◽  
2015 ◽  
Vol 126 (19) ◽  
pp. 1965-1969
Author(s):  
Julián Espinosa ◽  
Jorge Pérez ◽  
Consuelo Hernández ◽  
David Mas ◽  
Carmen Vázquez
Keyword(s):  
Shape Factor ◽  
Focal Length ◽  
Effective Focal Length ◽  
Thick Lens

scholarly journals Software for Teaching through Interactive Demonstrations about Converging Lenses

2019 ◽  
Vol 3 (1) ◽  
pp. 15
Author(s):  
Pavlos Mihas
Keyword(s):  
Graphical Representation ◽  
Focal Length ◽  
Least Square ◽  
Image Point ◽  
Focal Distance ◽  
Spherical Surfaces ◽  
Step Procedure ◽  
Linear Fit ◽  
Principal Points ◽  
Thick Lens

<p><em>In this paper, Software is presented for teaching through interactive demonstrations about lenses. At first we explore lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts. Then there is a page for understanding the thick lens model. We introduce a step by step procedure to find the focal length and find the principal planes and finally the use of the focal length and principal points to construct the image. There is a page for finding the position of the image not by the formula but by the method we use on an actual experiment: We move the screen back and forth until we can get the sharpest possible image. This is done by finding the minimum of a standard deviation of the position of the rays for a given position of the screen. Then there is a simulation of an experiment for finding the focal length. This uses a macro to simulate the finding of several image points b for several object points a. These values are used first in the graphical representation of the image point as a function of b and the image points as a function of a. With suitable least square fits we get two lines with parameters that give values for the focal length and principal plane. Then there is a simulation of two experiments of finding the focal length of a lens. The spreadsheet calculates the distance b vs a, the image y, and there ar graphs of y as a function of a and y as a function of b from which we find 1) a hyperbolic fit for y vs a and a linear fit for y vs b from which we calculate the focal distance, 2) it calculates 1/a and 1/b and then finds a linear fit and a parabolic fit for the data. Also we get the same parameters by finding the cuts of lines uniting the point (a,0) and (0,b).. 3) there is a plot of a+b vs a and then the points are fitted with a hyperbola whose asymptotes give the sum of focal length and principal planes. Then there is a page where we can see two lenses for which the shape can change to have a perfect focusing at a given distance. These two lenses are based on Huygens’ ideas, Spherical and Huygen Lenses.</em></p>

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

The Reduction of Chromatic Aberrations Due to Instrumental Instabilities

1971 ◽  
Vol 29 ◽  
pp. 14-15
Author(s):  
J. S. Lally ◽  
R. Evans
Keyword(s):  
Electron Microscope ◽  
High Voltage ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Usual Practice ◽  
Voltage Electron ◽  
Short Focal Length ◽  
Chromatic Aberrations ◽  
Electron Microscopes

One of the instrumental factors often limiting the resolution of the electron microscope is image defocussing due to changes in accelerating voltage or objective lens current. This factor is particularly important in high voltage electron microscopes both because of the higher voltages and lens currents required but also because of the inherently longer focal lengths, i.e. 6 mm in contrast to 1.5-2.2 mm for modern short focal length objectives.The usual practice in commercial electron microscopes is to design separately stabilized accelerating voltage and lens supplies. In this case chromatic aberration in the image is caused by the random and independent fluctuations of both the high voltage and objective lens current.

A Superconducting Microscope

1971 ◽  
Vol 29 ◽  
pp. 10-11 ◽  
Author(s):  
R. E. Worsham ◽  
J. E. Mann ◽  
E. G. Richardson
Keyword(s):  
Liquid Helium ◽  
Focal Length ◽  
Vacuum System ◽  
Objective Lens ◽  
Electrical Instability ◽  
Radiation Shields ◽  
And Control ◽  
Thermal Oscillations ◽  
Flux Pump

This superconducting microscope, Figure 1, was first operated in May, 1970. The column, which started life as a Siemens Elmiskop I, was modified by removing the objective and intermediate lenses, the specimen chamber, and the complete vacuum system. The large cryostat contains the objective lens and stage. They are attached to the bottom of the 7-liter helium vessel and are surrounded by two vapor-cooled radiation shields.In the initial operational period 5-mm and 2-mm focal length objective lens pole pieces were used giving magnification up to 45000X. Without a stigmator and precision ground pole pieces, a resolution of about 50-100Å was achieved. The boil-off rate of the liquid helium was reduced to 0.2-0.3ℓ/hour after elimination of thermal oscillations in the cryostat. The calculated boil-off was 0.2ℓ/hour. No effect caused by mechanical or electrical instability was found. Both 4.2°K and 1.7-1.9°K operation were routine. Flux pump excitation and control of the lens were quite smooth, simple, and, apparently highly stable. Alignment of the objective lens proved quite awkward, however, with the long-thin epoxy glass posts used for supporting the lens.

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