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Showing papers on "Zone plate published in 2003"


Journal ArticleDOI
TL;DR: Two new soft X-ray scanning transmission microscopes located at the Advanced Light Source (ALS) have been designed, built and commissioned and interferometer control implemented in both microscopes allows the precise measurement of the transverse position of the zone plate relative to the sample.
Abstract: Two new soft X-ray scanning transmission microscopes located at the Advanced Light Source (ALS) have been designed, built and commissioned. Interferometer control implemented in both microscopes allows the precise measurement of the transverse position of the zone plate relative to the sample. Long-term positional stability and compensation for transverse displacement during translations of the zone plate have been achieved. The interferometer also provides low-distortion orthogonal x, y imaging. Two different control systems have been developed: a digital control system using standard VXI components at beamline 7.0, and a custom feedback system based on PC AT boards at beamline 5.3.2. Both microscopes are diffraction limited with the resolution set by the quality of the zone plates. Periodic features with 30 nm half period can be resolved with a zone plate that has a 40 nm outermost zone width. One microscope is operating at an undulator beamline (7.0), while the other is operating at a novel dedicated bending-magnet beamline (5.3.2), which is designed specifically to illuminate the microscope. The undulator beamline provides count rates of the order of tens of MHz at high-energy resolution with photon energies of up to about 1000 eV. Although the brightness of a bending-magnet source is about four orders of magnitude smaller than that of an undulator source, photon statistics limited operation with intensities in excess of 3 MHz has been achieved at high energy resolution and high spatial resolution. The design and performance of these microscopes are described.

636 citations


Journal ArticleDOI
TL;DR: In this article, an electrically tunable Fresnel zone plate lens is demonstrated using nanoscale polymer-dispersed liquid crystal droplets, and the measured diffraction efficiency is close to the theoretical limit.
Abstract: An electrically tunable Fresnel zone plate lens is demonstrated using nanoscale polymer-dispersed liquid crystal droplets. In the voltage-off state, the zone plate behaves like a positive lens. The measured diffraction efficiency is close to the theoretical limit and is controllable by voltage. The major advantages of such a Fresnel lens are simple fabrication, large aperture size, polarization independent, and fast switching speed, although the required operating voltage is relatively high.

238 citations


Journal ArticleDOI
03 Jul 2003-Nature
TL;DR: An achromatic Fresnel optical system for EUV or X-ray radiation that combines a Fresnel zone plate with a refractive lens with opposite chromatic aberration is reported, which can deliver a resolution comparable to the highest resolution in the entire electromagnetic spectrum but with an improvement of two or more orders of magnitude in spectral bandwidth.
Abstract: Advances in extreme-ultraviolet (EUV) and X-ray optics are providing powerful new capabilities in high-resolution imaging and trace-element analysis of microscopic specimens1, and the potential for fabricating devices of smaller critical dimensions in next-generation integrated circuit lithography2. However, achieving the highest resolution with such optics usually requires the illuminating EUV or X-ray beam to be highly monochromatic. It would therefore be highly desirable to have large-field-of-view, sub-100-nm resolution optics that are achromatic to a significant degree, allowing more light to be utilized from broader bandwidth sources such as laser-produced plasmas. Here we report an achromatic Fresnel optical system for EUV or X-ray radiation that combines a Fresnel zone plate with a refractive lens with opposite chromatic aberration. We use the large anomalous dispersion property of the refractive lens material near an absorption edge to make its fabrication practical. The resulting structure can deliver a resolution comparable to that of the Fresnel zone plates that have achieved the highest resolution (25 nm; ref. 3) in the entire electromagnetic spectrum, but with an improvement of two or more orders of magnitude in spectral bandwidth.

178 citations


Journal ArticleDOI
TL;DR: It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture.
Abstract: Fractal zone plates (FZPs), i.e., zone plates with a fractal structure, are described. The focusing properties of this new type of zone plate are compared with those of conventional Fresnel zone plates. It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture.

172 citations


Journal ArticleDOI
TL;DR: A switchable Fresnel zone plate lens is demonstrated using a polymer-stabilized liquid crystal that can be operated below 10 volts with fast response time and works well for linearly polarized light.
Abstract: A switchable Fresnel zone plate lens is demonstrated using a polymer-stabilized liquid crystal. The fabrication process is relatively simple and the device can be operated below 10 volts with fast response time. Such a device works well for a linearly polarized light.

127 citations


Journal ArticleDOI
TL;DR: In this article, a soft x-ray microscope based on Fresnel zone plate lenses and partially coherent illumination was used to achieve a spatial resolution of 20 nm at 207nm wavelength.
Abstract: A spatial resolution of 20 nm is demonstrated at 207-nm wavelength by use of a soft x-ray microscope based on Fresnel zone plate lenses and partially coherent illumination Nanostructural test patterns, formed by sputtered multilayer coatings and transmission electron microscopy thinning techniques, provide clear experimental results

67 citations


Patent
17 Oct 2003
TL;DR: In this paper, the authors present methods for aligning the two optical elements during fabrication and maintaining the alignment during subsequent operation, and also address methods of maintaining the alignments during subsequent operations.
Abstract: Methods for fabricating refractive element(s) and aligning the elements in a compound optic, typically to a zone plate element. The techniques are used for fabricating micro refractive, such as Fresnel, optics and compound optics including two or more optical elements for short wavelength radiation. One application is the fabrication of the Achromatic Fresnel Optic (AFO). Techniques for fabricating the refractive element generally include: 1) ultra-high precision mechanical machining, e.g,. diamond turning; 2) lithographic techniques including gray-scale lithography and multi-step lithographic processes; 3) high-energy beam machining, such as electron-beam, focused ion beam, laser, and plasma-beam machining; and 4) photo-induced chemical etching techniques. Also addressed are methods of aligning the two optical elements during fabrication and methods of maintaining the alignment during subsequent operation.

50 citations


Patent
Wenbing Yun, Yuxin Wang1
10 Oct 2003
TL;DR: In this article, an extreme ultraviolet (EUV) AIM tool for both the EUV actinic lithography and high-resolution imaging or inspection is described, which can be extended to lithography nodes beyond the 32 nanometer (nm) node covering other short wavelength radiation such as soft X-rays.
Abstract: An extreme ultraviolet (EUV) AIM tool for both the EUV actinic lithography and high-resolution imaging or inspection is described. This tool can be extended to lithography nodes beyond the 32 nanometer (nm) node covering other short wavelength radiation such as soft X-rays. The metrology tool is preferably based on an imaging optic referred to as an Achromatic Fresnel Optic (AFO). The AFO is a transmissive optic that includes a diffractive Fresnel zone plate lens component and a dispersion-correcting refractive lens component. It retains all of the imaging properties of a Fresnel zone plate lens, including a demonstrated resolution capability of better than 25 nanometers and freedom from image distortion. It overcomes the chromatic aberration of the Fresnel zone plate lens and has a larger usable spectral bandwidth. These optical properties and optical system designs enable the development of the AFO-based AIM tool with improved performance that has advantages compared with an AIM tool based on multilayer reflective mirror optics in both performance and cost:

50 citations


Journal ArticleDOI
TL;DR: Through numerical experiments, it is confirmed that a Gaussian focal spot with a beam width of 7.7 nm can be produced by a modified Fresnel zone plate with a minimum structure size of 30 nm.
Abstract: A modified Fresnel zone plate that can produce an approximate Gaussian focal spot is proposed for the focusing and imaging of soft x rays and extreme ultraviolet radiation. The selection conditions for the positions and the widths of the concentric open rings are analytically presented. The focal spot size can be much smaller than the width of the narrowest open ring, and the sidelobes and the higher orders can be effectively suppressed. Through numerical experiments, we confirm that a Gaussian focal spot with a beam width of 7.7 nm can be produced by a modified Fresnel zone plate with a minimum structure size of 30 nm.

48 citations


Journal ArticleDOI
TL;DR: In this paper, a hard X-ray focusing test of a Fresnel zone plate has been performed with a synchrotron radiation source at the undulator beamline 20XU of SPring-8.
Abstract: A hard X-ray focusing test of a Fresnel zone plate has been performed with a synchrotron radiation source at the undulator beamline 20XU of SPring-8. A Fresnel zone plate with a radius of 150 µm, and an outermost zone width of 100 nm was used for the X-ray focusing device. The 248-m-long beamline provides fully coherent illumination for the focusing device. The focused beam was evaluated by the knife-edge-scan method and scanning microscope test using test charts. Nearly diffraction-limited focusing with a size of 120 nm was achieved for the first-order diffraction at 10 keV X-ray. Evaluation for the third-order diffraction was also performed at 8 keV X-ray, and a focal size of 50 nm has been obtained.

42 citations


Journal ArticleDOI
TL;DR: In this article, a sputtered-sliced Fresnel zone plate (ss-FZP) with an outermost zone width 0.16 μm was fabricated and characterized.
Abstract: Microfocusing of 100 keV x ray with a sputtered-sliced Fresnel zone plate (ss-FZP) has been performed at the 250-m-long beamline (20XU) of SPring-8. The ss-FZP with an outermost zone width 0.16 μm which is composed of 70 layers of alternating Cu and Al layers and having thickness ∼180 μm was fabricated and characterized. The minimum focal spot size attained for the first order focal beam was 0.5 μm with a focal distance 900 mm at a photon energy 100 keV. The total flux of the microprobe was ∼2×106 photons s−1 μm−2.

Patent
29 Apr 2003
TL;DR: In this paper, a mask blank inspection tool includes an AFO having a diffractive lens and a refractive lens formed on a common substrate, where the diffractive lenses are a Fresnel zone plate and the refractive lenses is a Refractive Fresnel lens.
Abstract: A mask blank inspection tool includes an AFO having a diffractive lens and a refractive lens formed on a common substrate. The diffractive lens is a Fresnel zone plate and the refractive lens is a refractive Fresnel lens. The AFO is used to image light from a defect particle on a multilayer mask blank or the surface of the multilayer mask blank to a detector.

Journal ArticleDOI
TL;DR: In this paper, a phase reconstruction of an atomic force microscope tip with a spatial resolution of better than 900 nm was presented using an X-ray energy of 1.83 keV using a zone plate based microscope at a third generation synchrotron, Advanced Photon Source at the Argonne National Laboratory.

Journal ArticleDOI
TL;DR: The intermediate-energy scanning x-ray microscope at beamline 2-ID-B at the Advanced Photon Source is a dedicated instrument for materials and biological research as discussed by the authors, which uses a zone plate lens to focus coherent I-4 keV x-rays to a 60 nm focal spot of 10 9 photons/ s onto the sample.
Abstract: The intermediate-energy scanning x-ray microscope at beamline 2-ID-B at the Advanced Photon Source is a dedicated instrument for materials and biological research. The microscope uses a zone plate lens to focus coherent I-4 keV x-rays to a 60 nm focal spot of 10 9 photons/ s onto the sample. It records simultaneous transmission and energy-resolved fluorescence images. We have used the microscope for nanotomography of chips and microspectroscopy of cells.

Proceedings ArticleDOI
05 Oct 2003
TL;DR: In this article, a Fresnel zone plate is realized which is capable of generating tight elevation foci using a large aperture, which can improve slice thickness compared with both a conventional lensed probe and a multi-row design.
Abstract: In contrast to PZT probes, capacitive microfabricated ultrasonic transducers (cMUTs) require a DC bias. We investigate elevation beam profile shaping by spatially varying this bias polarity. Such a scheme introduces a 180/spl deg/ phase shift in the device's impulse response. A Fresnel zone plate is realized which is capable of generating tight elevation foci using a large aperture. This paper presents measurements from a prototype Fresnel cMUT probe, and matching simulation results. The Fresnel probe is capable of improved slice thickness compared with both a conventionally lensed probe and a multi-row design. Also, combinations of bias polarity control and multiple firings can enable harmonic imaging without pre-distortion of the transmit signal. Multiple firing schemes further optimize slice thickness, and allow beam steering in elevation.

Journal ArticleDOI
TL;DR: A drastic increase in image contrast for a low-absorbing specimen is demonstrated for both the full-field imaging and scanning x-ray microscope methods, similar to the Nomarski DIC method for visible-light microscopy.
Abstract: We describe a novel approach for converting the specimens phase information into strong image contrast in the x-ray region, the differential interference contrast x-ray microscopy (X-DIC). In the used setup, X-DIC operation was accomplished by a twin zone plate (TZP), i. e. two zone plates on both sides of the same substrate, laterally shifted by about one outermost zonewidth. Once a TZP has been successfully produced by means of especially developed nanofabrication processes, it is as easy to use as a single zone plate, without any alignment difficulty or further requirements to the coherence of the illumination. The tremendeous contrast enhancement was demonstrated at the microscopy beamline ID21 at ESRF in Grenoble for test objects and biological samples. TZPs allow for full field X-DIC imaging as well as for DIC scanning transmission x-ray microscopy. The first experiments were carried out at 0.31 nm wavelength (4 keV photon energy), and features down to approx. 160 nm could be resolved in X-DIC.

Journal ArticleDOI
TL;DR: A comparison of the diffraction patterns in the focal region between pulsed and continuous-wave illumination shows that the focal shape produced by a zone plate can be significantly altered when an ultrashort pulse is shorter than 100 fs.
Abstract: The focal distribution produced by a zone plate under ultrashort pulsed laser illumination is investigated under the Fresnel approximation. A comparison of the diffraction patterns in the focal region between pulsed and continuous-wave illumination shows that the focal shape produced by a zone plate can be significantly altered when an ultrashort pulse is shorter than 100 fs. In particular, the focal width in the axial and the transverse directions is increased by approximately 5% and 85%, respectively, from continuous-wave illumination to 10-fs pulsed illumination.

Journal ArticleDOI
TL;DR: In this paper, a new method of spatial coherence profilometry is demon-strated, where the surface profile is measured by shifting the spatial degree of coherence gradually in its own space of existence, and modulating its phase angle.
Abstract: A new method of spatial coherence profilometry is demon- strated. The surface profile is measured by shifting the spatial degree of coherence gradually in its own space of existence, and modulating its phase angle. In each point of the sample we analyze the change of light intensity versus the phase of a Fresnel zone pattern used as the intensity distribution of an incoherent quasimonochromatic source. The tilt of the surface is measured by gradually shifting the Fresnel zone plate on its transverse plane. This shift of the light source rotates the spatial degree of coherence around the coordinate origin until the condition of maximum interference visibility is fulfilled. The method works without any mechani- cal movement and a quasimonochromatic light illuminates the interfero- metric system. Experimental demonstration of the new method is pre- sented. © 2003 Society of Photo-Optical Instrumentation Engineers.

Patent
17 Apr 2003
TL;DR: In this article, an alignment or overlay mark with improved signal to noise ratio is disclosed, which results in a greater depth of focus, thus improving the performance of the alignment mark, which is a zone plate having n concentric alternating opaque and non-opaque rings.
Abstract: An alignment or overlay mark with improved signal to noise ratio is disclosed. Improved signal-to-noise ratio results in greater depth of focus, thus improving the performance of the alignment mark. The alignment mark comprises a zone plate having n concentric alternating opaque and non-opaque rings. Light diffracted by either the odd or even rings are cancelled while light diffracted by the other of the odd or even rings are added.

Journal ArticleDOI
TL;DR: In this paper, a combination of the x-ray undulator and a zone plate enabled the authors to make a coherent X-ray source of around 0.1 μm size.
Abstract: Present status of our developments of x-ray holographic microscopes at SPring-8 BL20XU is described. A combination of the x-ray undulator and a zone plate enabled us to make a coherent x-ray source of around 0.1 μm size. Using this secondary source, two types of x-ray holographic microscopes were investigated. First, a Gabor microscope in point-projection geometry was tested. A tantalum 0.2 μm line-and-space pattern could be resolved. Second, using a zone plate as a beam splitter, a Fourier transform holographic microscope was tested. A tantalum 0.2 μm line-and-space pattern could be observed. Polystyrene beads of 2.8 μmand 0.8 μm in diameter could be observed. In Fourier transform holography, a reconstructed image of a specimen that is located out of the plane of the reference source is blurred. Numerical focusing of such an x-ray hologram could be successfully demonstrated.

Journal ArticleDOI
TL;DR: In this paper, the Zernike's phase contrast method has been implemented to the microscope with phase plates made of gold, and the photon energy was tuned to 12 keV just above the L3 absorption edge of gold (11.9 keV).
Abstract: A hard X-ray transmission imaging microscope has been in use at the beamline BL24XU of SPring-8. It makes use of a phase zone plate made of tantalum as its X-ray lens, and is capable of imaging the structure as fine as 125-nm line-and-space pattern. The Zernike's phase-contrast method has been implemented to the microscope with phase plates made of gold. The photon energy was tuned to 12 keV just above the L3 absorption edge of gold (11.9 keV) in order to increase the image contrast. Polystyrene micro particles as transparent specimens were imaged clearly in the opposite image contrast with phase plates to shift the phase of the central order spectra in the back focal plane of the objective by one-quarter and three-quarters of a period while the absorption contrast image showed little image contrast. Performance of the newly developed phase zone plate has been tested and it was confirmed that the structure as fine as 60-nm line-and-space pattern was able to be imaged.

Journal ArticleDOI
TL;DR: In this article, the possibility of creating a time lens, an analogue of the zone plate in X-ray optics, for ultracold neutrons is experimentally demonstrated by means of a purely quantum effect: the phase modulation of a neutron wave at a variable modulation frequency.
Abstract: The possibility of creating a time lens, an analogue of the zone plate in X-ray optics, for ultracold neutrons is experimentally demonstrated. The neutron energy was changed by means of a purely quantum effect: the phase modulation of a neutron wave at a variable modulation frequency. The modulator was a phase grating with vari- able spatial period moving across the neutron beam. © 2003 MAIK "Nauka/Interperiodica".

Journal ArticleDOI
TL;DR: In this article, a 13.9nm coherent X-ray laser is generated by means of a ps CPA glass laser system, whose pulse duration and number of photons are about 7ps and 10 12 photons/ pulse, respectively.
Abstract: A picosecond time-resolved soft X-ray microscopy system using an X-ray laser has been developed A 13.9nm coherent X-ray laser is generated by means of a ps CPA glass laser system. The pulse duration and the number of photons of the X-ray laser are about 7ps and 10 12 photons/ pulse, respectively. The X-ray laser pulse is condensed with a Schwarzschild optics and illuminated onto the sample. The transmitted X-ray image is magnified with a zone plate. X-ray images of a Cu mesh and a zone plate with spatial resolution of about 200nm has been obtained by a single shot of ps X-ray laser.

Patent
29 Jul 2003
TL;DR: In this article, the authors propose to use the refraction type Fresnel lens part and the outer periphery part thereof as a reflection type lens part to realize a large diameter and a short focus, that means, high NA by eliminating limit in terms of machining.
Abstract: PROBLEM TO BE SOLVED: To provide a Fresnel lens capable of realizing a large diameter and a short focus, that means, high NA by eliminating limit in terms of machining, and to provide a lighting device compact and thin and capable of condensing wide-angle light by using the Fresnel lens. SOLUTION: In the Fresnel lens, the center part of a plate-like lens member is set as a refraction type Fresnel lens part and the outer periphery part thereof is set as a reflection type Fresnel lens part. In the illuminator, at least one LED element is arranged near the center axis of at least one lens in the Fresnel lens. COPYRIGHT: (C)2005,JPO&NCIPI

Proceedings ArticleDOI
23 Mar 2003
TL;DR: Propagation of light at 1.5mm along an air hole is achieved within an air-silica structured Fresnel waveguide where the holes are distributed along the Fresnel zones of the fibre.
Abstract: Propagation of light at 1.5mm along an air hole is achieved within an air-silica structured Fresnel waveguide where the holes are distributed along the Fresnel zones of the fibre. Fresnel lensing is reported.

Patent
26 Mar 2003
TL;DR: In this paper, a Fresnel lens sheet consisting of a lenticular lens sheet and a rear projection screen is used to avoid the "collapse", "abrasion" and "moire" problems.
Abstract: The present invention provides a Fresnel lens sheet capable of successfully avoiding the “collapse”, “abrasion” and “moire” problems. A Fresnel lens sheet 10 constitutes, together with a lenticular lens sheet, a rear projection screen, which is mounted in the frame of a rear projection type display. The Fresnel lens sheet 10 includes, on one surface of its substrate, a Fresnel lens part 13 containing a plurality of lenses 11 concentrically formed on one plane. The apexes 11 a of the lenses 11 situated in the area between the center O and the outer edge P of the Fresnel lens part 13 are flattened to give flat faces 12 , and the widths W of the flat faces 12 of the lenses 11 on the outer edge P side are made greater than the widths W of the flat faces 12 of the lenses 11 on the center O side. The widths W of the flat faces 12 of the lenses 11 are from 0 to 30 μm.

Patent
17 Jan 2003
TL;DR: In this article, a zone plate device is used to provide frequency selective feedback to a laser diode, which can be used as a standalone component for filtering optical radiation from other sources or as a switch for switching the intensity or wavelength of optical radiation between different values.
Abstract: In a tunable optical source, a zone plate device 100 is used to provide frequency selective feedback to a laser diode 110. The zone plate device 100 is positioned to receive an output mode of the laser diode 110 and to return a frequency selected image of the mode spot to the laser diode 110. By changing the refractive index of material of the zone plate device 100, it is possible to change the frequency providing the image at the point of return to the laser diode 110. This allows the zone plate device 100 to be used in tuning the optical source, without using moving parts. In an embodiment, the zonc plate device 100 is at least partially fabricated in an electro-optic material such as SBN:75 and can therefore be tuned by using electrodes to apply an electric field across it. The zone plate device 100 can be coupled directly to the laser diode 110 or via a waveguide section 105 which can be used to increase the output mode spot size from the laser diode 110 for delivery to the zone plate device 100. The zone plate device 100 can alternatively be used as a standalone component for filtering optical radiation from other sources or as a switch for switching the intensity or wavelength of optical radiation between different values. Tunable or switchable optical devices can be used for instance in communications, such as in wavelength division multiplexing.

Journal ArticleDOI
TL;DR: In this article, a single plane fracture with an axially symmetric stress distribution behaves as a seismic lens that focuses seismic energy to a beam "waist" at a focal plane, and both phase and amplitude effects on a seismic wave propagating across the fracture contribute to the lensing behavior.
Abstract: [1] A single plane fracture with an axially symmetric stress distribution behaves as a seismic lens that focuses seismic energy to a beam “waist” at a focal plane. Both phase and amplitude effects on a seismic wave propagating across the fracture contribute to the lensing behavior. Radial gradients in the fracture specific stiffness cause wave refraction through a radially varying group time delay, while the fracture transmission amplitude approximates a Fresnel zone plate. This work demonstrates that a two-dimensional planar fracture, contrasted with three-dimensional geologic structures such as basins and domes, can focus seismic waves. Focusing of seismic waves by fractures should be considered in the interpretation of seismic data from fractured strata with heterogeneous stress distributions.

Patent
16 Apr 2003
TL;DR: In this paper, a light emitting device and a manufacturing method thereof and a display used the light-emitting device, in which fine patterning for the light emitting devices is realized by a simple process and the light leakage is prevented and the efficiency at extracting light is increased.
Abstract: A light emitting device and a manufacturing method thereof and a display used the light emitting device, in which fine patterning for the light emitting device is realized by a simple process and the light leakage is prevented and the efficiency at extracting light is increased, are provided. The light emitting device provides an organic electroluminescent (EL) device in which electrodes and a luminescent layer are formed, a diffraction grating or a zone plate, and a filter. Light emitted from the luminescent layer transmits through the diffraction grating or the zone plate, which is formed with a designated grating pitch, or is reflected at the diffraction grating or the zone plate. With this, the transmitting or reflecting light is controlled to be in a designated angle region. And when the light is transmitted through the filter, light having different color tone and chromaticity from those of the light emitted from the luminescent layer is extracted.

Journal ArticleDOI
TL;DR: In this article, phase contrast X-ray microscopy at 4 keV photon energy on copper interconnect structures, buried in silicon dioxide, was performed using 2.2 pm and 0.7 pm high Nickel phase rings with a contrast of 30 % and 39 %.
Abstract: X-ray microscopy in the multi-keV photon energy range offers unique possibilities to study relatively thick samples with high spatial resolution. When employing a high N.A. condenser zone plate for sample illumination in combination with a high resolution micro zone plate objective lens, a spatial resolution of currently 60 nm is achieved. We report here on phase contrast X-ray microscopy at 4 keV photon energy on copper interconnect structures, buried in silicon dioxide. While the amplitude contrast in these samples is only 7 %, negative as well as positive phase contrast were demonstrated using 2.2 pm and 0.7 pm high Nickel phase rings with a contrast of 30 % and 39 %, respectively.