Characteristics of the thick, compound refractive lens

Pantell, R. H.; Feinstein, J.; Beguiristain, H. R.; Piestrup, M. A.; Gary, C. K.; Cremer, Jay Theodore

doi:10.1364/ao.42.000719

Cited by 23 publications

(16 citation statements)

References 9 publications

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“…Owing to a favorable ratio between wavelength and the aperture of the CRL, a combination of geometrical optics and the Abbe diffraction limit is believed to be adequate for describing simple imaging set-ups. As such, ray transfer matrix (RTM) formalisms have been developed to describe CRLs (Protopopov & Valiev, 1998;Pantell et al, 2003;Poulsen & Poulsen, 2014), leading to ISSN 1600-5775 # 2018 International Union of Crystallography exact analytical solutions for the numerical aperture, vignetting, chromatic aberration and resolution for the general thick-lens case . This work has since been extended to describe the reciprocal-space resolution for darkfield microscopy and to identify schemes for sampling sixdimensional direct space-momentum space .…”

Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.

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Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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“…7 when s is replaced by (s). As noticed by Pantell et al (2001a), a transverse shift does not influence the image shape but reduces the CRL transmission by adding a thickness Ád = 2 /p to the effective thickness of a double concave lens. This results in the following reduction of the CRL transmission, The integral intensity detected at the screen versus the transversal shift s.…”

Section: Misalignment Of Parabola Axes: Transversal Shiftmentioning

confidence: 92%

The role of single element errors in planar parabolic compound refractive lenses

Andrejczuk

Krzywiński

Sakurai

et al. 2010

J Synchrotron Radiat

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The propagation of X-rays through a compound refractive lens (CRL) with imperfect CRL elements is investigated. The trajectories of random rays within the geometrical optics regime are calculated in one plane using Monte Carlo methods. Three different lenses were simulated: Be, Al and Ni lenses designed for photon energies of 20 keV, 60 keV and 175 keV, respectively. The results show that while transverse displacements of single elements in a CRL do not influence imaging resolution, rotational errors can be important. Systematic calculations of aberrations owing to the deviation of the element's surface from a perfect parabolic shape are also presented.

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“…This result should be corrected for effect of lens thickness. As it was shown in [17], the focal length f t of a "thick" lens is calculated as :…”

mentioning

confidence: 99%

“…Result is f t = 106.3 mm for the discussed 137-unit lens and 8-keV X-rays. For a "thick" lens the lens formula (1) may be rewritten as [17]:…”

mentioning

confidence: 99%

Projection-type x-ray microscope based on a spherical compound refractive x-ray lens

et al. 2007

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New projection-type X-ray microscope with a compound refractive lens as the optical element is presented. The microscope consists of an X-ray source that is 1-2 mm in diameter, compound X-ray lens and X-ray camera that are placed in-line to satisfy the lens formula. The lens forms an image of the X-ray source at camera sensitive plate. An object is placed between the X-ray source and the lens as close as possible to the source, and the camera shows a shadow image of the object. Spatial resolution of the microscope depends on the lens focal length, lens aperture and the distance from the source to the object. One to two micron resolution may be achieved by placing the object at a distance of 1-5 mm from the source. The X-ray source may be designed with the target deposited on a 200-µm thick Be window, which permits the object to be placed very close to the emitting surface. The tube focal spot is equal to 1-2 mm. Results of imaging experiments with an ordinary copper anode X-ray tube and a 10-cm focal length spherical compound refractive X-ray lens are discussed.

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Characteristics of the thick, compound refractive lens

Cited by 23 publications

References 9 publications

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

The role of single element errors in planar parabolic compound refractive lenses

Projection-type x-ray microscope based on a spherical compound refractive x-ray lens

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