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

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 Rotational analysis of the first negative band spectrum of oxygen. II

1940 ◽  
Vol 174 (958) ◽  
pp. 371-378 ◽  
Keyword(s):  
Hollow Cathode ◽  
Focal Length ◽  
Second Order ◽  
Hollow Cathode Discharge ◽  
Resolving Power ◽  
Band Spectrum ◽  
Third Order ◽  
Negative Band ◽  
Single Plate ◽  
A Current

In a previous paper (Nevin 1938)*, the author has given an analysis of the (0, 1) λ 6438, (0, 0) λ 6026, and (1, 0) λ 5632 bands of the first negative band spectrum of oxygen and has shown that the system is due to a transition 4 ∑ - g → 4 Π u . The present paper contains an analysis of the (0, 2) λ 6856 and (2, 0) λ 5295 bands. Using the method described in (I) to excite the spectrum, a discharge through helium containing a small amount of oxygen, the plates of the band λ 6856 taken in the second order of the grating could be measured only as far as λ 6720 on account of the large number of ghosts and the blackening produced below this point by the enormously over-exposed helium line λ 6678. To photograph the remainder of the band it was necessary to use a hollow cathode discharge through commercial oxygen as described by Frerichs (1926). This source is considerably less intense than the discharge through helium the exposures with which, in the case of the present band, were between 12 and 18 hr. with Ilford Astra III plates. To reduce the exposures to a reasonable time a cylindrical lens made by Hilger, 15 cm. long and 5 cm. wide with a focal length of 30 cm., was mounted at right angles to the axis of the spectrograph between the grating and the plate as described by Oldenberg (1932). The lens was mounted so that its axis could be adjusted exactly perpendicular to the slit and the grating rulings, a point of the highest importance if the definition is not to be impaired. As far as could be judged there was no loss of resolving power over the length of plate covered by the lens. Satisfactory exposures of a range of 180A were obtained in about 6 hr. with the hollow cathode discharge taking a current of 0.8 amp. The plates were measured with respect to third order iron standards. The λ 5295 band had already been photographed in the second order at the same time as the bands analysed in (I). However, to complete the analysis it was found necessary to take a third order plate, and to save time the arrangement described above was used, the entire band being obtained on a single plate with an exposure of 5 hr. The resolving power attained on this plate with sharp lines was about 200,000. The theoretical resolving power of the grating in this order is 250,000, so the reduction caused by the lens must have been very small. * Referred to as (I) throughout this paper.

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.

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>

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