Abstract: A system includes determination of a treatment plan for delivering convergent radiation to a target based at least on a decrease in intensity of the convergent radiation due to material intercepted by the convergent radiation prior to reaching the target and on an increase in intensity of the convergent radiation due to a geometry of the convergent radiation. Some aspects include determination of a dose enhancement at the target over time due to contrast agent located at the target, wherein the determination of the treatment plan is based at least on the dose enhancement over time.

Abstract: A method for testing a surface includes finding respective first and second critical angles for total external reflection of radiation from an area of the surface at first and second wavelengths. The first and second critical angles are compared to determine an orientation of a tangent to the surface in the area.

Abstract: The present invention consists of a multilayer structure having at least one triad of layers where each of the three layers is a predetermined material. One of the materials is from a group including lanthanum, lanthanum oxide, or lanthanum-based alloys. A second material is disposed between the first material and a third material. The second material is from a group including carbon, silicon, boron, boron carbide or silicon carbide. The third material is from a group including boron or boron carbide. Alternatively, a fourth material is added to further strengthen and increase the water resistance of the multilayer structure. The fourth material is selected from a group including silicon, boron, boron carbide or silicon carbide. The fourth material is disposed between the third layer of multilayer period n and the first layer of multilayer period n−1.

Abstract: In an apparatus and a method for generating monochromatic X-ray radiation, an X-ray source, a monochromator and a slit collimator are arranged relative to one another such that X-rays of a specific energy among the X-rays emanating from the X-ray source are reflected at the monochromator and emerge through the slit of the slit collimator as a fan-shaped beam of monochromatic X-radiation. For scanning an examination subject with the X-ray beam, the monochromator is adjustable relative to the X-ray source and the slit collimator such that the condition for the reflection angle required for the reflection of X-rays of the specific energy at the monochromator remains substantially satisfied during the adjustment, and essentially only X-rays of the specific energy pass through the slit of the slit collimator.

Abstract: A fluorescent X-ray analysis apparatus includes: an X-ray generation source for radiating a primary X-ray; plural spectroscopic elements circularly arranged so that their inner surfaces constitute a circle centering on an optical axis of the primary X-ray and adapted for monochromatizing the primary X-ray and condensing it on a surface of an irradiation object; a spectroscopic element position adjusting means for adjusting the positions of the plural spectroscopic elements; a secondary X-ray detector for detecting a secondary X-ray radiated from the surface of the irradiation object upon irradiation with the monochromatized primary X-ray; a secondary X-ray detector position adjusting means for adjusting the position of the secondary X-ray detector; an irradiation object surface position detecting means for detecting the position of the surface of the irradiation object; and a control means for adjusting the positions of the plural spectroscopic elements by the spectroscopic element position adjusting means so

Abstract: The reflectivity of multilayered EUV mirrors tuned for 11-16 nm, for which the two-component Mo/Be and Mo/Si multilayered systems are commonly used, is enhanced by incorporating additional elements and their compounds mainly from period 5 of the periodic table. In addition, the reflectivity performance of the multilayer stacks is further enhanced by a numerical global optimization procedure by which the layer thicknesses are varied for optimum performance in, contradistinction to the constant layer thickness—i.e. constant partition ratio—multilayer stacks commonly designed and, fabricated hitherto. By incorporating additional materials with differing complex refractive indices in various regions of the stack, or by wholly replacing one of the components (typically Mo), we have observed peak reflectivity enhancements of up to 5% for a single reflector compared to a standard unoptimized stack.

Abstract: An X-ray diffractometer has an X-ray source (10), a double pinhole collimator (14), a sample (22) mounted on a rotatable sample stage (20), an analyser crystal (30) and a detector (34). The analyser crystal and detector are arranged to rotate together about an axis (21) that is coaxial with the axis of rotation of the sample stage. Very few scattered X-rays (26) reach the detector (34). The diffractometer has particular use for routine quality control measurements.

Abstract: Multilayer-film mirrors are disclosed that include multiple units of Mo and Si layers formed on the surface of a mirror substrate and that exhibit reduced internal stress and hence improved imaging properties. Hence, the mirrors are especially suitable for use in X-ray optical systems such as used in X-ray lithography systems. In an exemplary mirror, a molybdenum oxide layer is formed on at least one Mo layer at the interface surface between the Mo layer and an adjacent Si layer. The molybdenum oxide layer is formed by irradiation with oxygen ions, or by forming at least a portion of the Mo layer in an atmosphere including oxygen.

Abstract: An X-ray optical system with an X-ray source, an element that focuses the X-rays and an element that reflects them. In order to generate parallel X-radiation with small beam cross-section and high photon density, the X-radiation of the X-ray source is directed with its focusing element to the convex, parabolic and reflecting surface of the reflecting element. The X-ray optical system is useful for X-ray analysis, e.g., in X-ray diffractometry, reflectometry and/or fluorescence analysis.

Abstract: Provided is a novel density-nonuniform multilayer analyzing method that readily and highly accurately enables analyzing the state of distribution and interfacial condition of particulate matter in a density-nonuniform multilayer film. The method includes the step of, by using a scattering function representing an X-ray scattering curve according to a fitting parameter indicating a state of distribution of particulate matter, calculating a simulated X-ray scattering curve under the same conditions as those under which an actually measured X-ray scattering curve is measured, and the step of performing fitting between the simulated X-ray scattering curve and the actually measured X-ray scattering curve while the fitting parameter is being changed.

Abstract: The invention relates to a device for X-ray analytical applications such as X-ray diffractometry, reflectometry and/or fluorescence analysis. The aim of the invention is to monochromatize, focus and optionally transform the X-radiation of a focal spot of a point of an X radiation source into a parallel, high photon density radiation in a highly precise manner. Parallel X radiation having a point-shaped primary beam cross-section is thus directed at a concavely curved, parabolic reflecting element which is used to focus and monchromatize the X radiation by means of a gradient and multilayered system embodied on the reflecting element. At least one screen is arranged between the X radiation source and the reflecting element.

Abstract: Parallel X-ray beams with two kinds of wavelength are taken with the use of a single parabolic multilayer mirror. A single parabola prepared for a CuK&agr; X-ray is used for taking parallel X-ray beams of both the CuK&agr; X-ray and the CoK&agr; X-ray. The CuK&agr; ray emitted from a first X-ray focal spot located at the focus of the parabola is reflected at a reflecting surface composed of the parabola to become a parallel beam going out. When a second X-ray focal spot is arranged at the position apart from the first X-ray focal spot by a predetermined distance, the CoK&agr; X-ray emitted from the second X-ray focal spot is reflected at the same reflecting surface to become a parallel beam going out.

Abstract: A method for producing microstructures for use for x-ray lenses using extrusion techniques and a variable focus x-ray lens assembly are provided. An elongated strip of multiple x-ray lenses and cavities of arbitrary cross-section are produced by an extrusion step. A predefined lens profile of the multiple x-ray lenses has, for example, a parabolic profile for x-ray focusing. The elongated strip of multiple cylindrical compound x-ray lenses can be cut into multiple uniform small lengths, for example, 50 mm lengths, and positioned within a support member. Cutting the assembled support member and x-ray lenses at a selected angle provides a variable focus x-ray lens assembly.

Abstract: A unitary support device for a polycapillary optic is provided wherein a housing has a central opening therethrough and at least two locating structures, such as positioning shoulders, formed therein. Each locating structure is sized and positioned to accommodate a different polycapillary positioning component within the housing. Each polycapillary positioning component has at least one opening for holding at least one polycapillary of the polycapillary optic. One or more coaxial bores can define the central opening of the housing and the locating shoulders in one continuous fabrication operation. Depending upon the polycapillary positioning components employed, i.e., location of the openings therein for accommodating the polycapillaries, the positioning components can be oriented within the housing such that radiation from one of a divergent beam, a focused beam, or a parallel beam is collected by the optic, and such that the optic can output one of a collimated beam, a focused beam or a divergent beam.

Abstract: The parallel radiation (12) emanating from a sample 4 in a known apparatus for X-ray analysis (for example, for diffraction) is analyzed according to wavelength and focused in a focus 20 by a parabolic multilayer mirror 14. A collimator 28 is positioned around said focus. The resolution of the apparatus can be enhanced by making the angular passage width of the collimator smaller than the maximum range of its reflection angle &agr;max. In accordance with the invention the resolution of the apparatus will be better defined and hence enhanced by implementing the exit collimator 28 in such a way that the angular value for the passage width from every reflecting point A or B of the mirror surface is substantially independent of the position of the reflecting points. Preferably, the exit collimator 28 is implemented in the form of two mutually parallel knife edges which are situated at different distances from the reflecting points of the multilayer mirror.

Abstract: There is provided an optical apparatus for radiation with a wavelength ≦160 nm. The apparatus comprises a mirror with a mirror surface, and a first device for generating elastic oscillations with different acoustic wavelengths on the mirror surface due to surface deformations. Radiation impinging on the mirror surface is diffracted in a predetermined range of angles (&agr;).

Abstract: Apparatus and methods are disclosed for producing a flux of X-rays, from a plasma, wherein the flux remains rotationally symmetrical about a propagation axis over a period of use, even if the plasma produce flying debris. The plasma can be generated by a laser-plasma source or a discharge-plasma source, for example. The X-rays produced by the plasma are directed by an optical element to a downstream location. To such end, the optical element is located where it is subject to deposition and accumulation of flying debris from the plasma. The optical element has an axis of rotational symmetry. A rotational actuator is situated relative to the optical element and is configured to rotate the optical element about the axis of rotational symmetry during use. Hence, if deposits of flying debris form on the optical element, the deposits will be rotationally symmetrical and thus have an identical affect on the X-ray flux at any angle about the axis of rotational symmetry.

Abstract: A method for testing a surface includes finding respective first and second critical angles for total external reflection of radiation from an area of the surface at first and second wavelengths. The first and second critical angles are compared to determine an orientation of a tangent to the surface in the area.

Abstract: The invention makes possible to increase the degree of radiation focusing by the lens, to use particles of higher energies, and to increase the coefficients, depending on these factors, of the devices, the lens is used in. Thus the sublens 18 of the least degree of integration represents a package of the channels 5, which is growing out of joint drawing and forming the capillaries, which are laid in a bundle. The sublens of each higher degree of integration represents a package of sublenses of the previous degree of integration, which is growing out of their joint drawing and forming. The sublenses are growing out of performing the said operations at the pressure of the gaseous medium inside the channels being higher than the pressure in the space between the sublenses of the previous degree of integration and at the temperature of their material softening and splicing the walls.

Abstract: In the production of optical elements, not only flat substrates but also spherical or aspherical substrates are used. The costs of such a substrate can exceed the coating costs by a multiple. Particularly in development work, cost savings may be achieved if a substrate can be used repeatedly. To recover a substrate, it is proposed to provide an interlayer between the substrate and the functional layers, which comprises at least one layer of chromium and one layer of scandium. By immersing the optical element into a hydrochloric acid solution, this interlayer is dissolved, so that the functional layer is also removed from the substrate and the substrate is ready for reuse.

Abstract: The present invention refers to a refractive arrangement for X-rays, and specially to a lens comprising: a member of low-Z material, said member of low-Z material having a first end adapted to receive x-rays emitted from an x-ray source and a second end from which emerge said x-rays received at said first end. It further comprises a plurality of substantially saw-tooth formed grooves disposed between said first and second ends, said plurality of grooves oriented such that said x-rays which are received at said first end, pass through said member of low-Z material and said plurality of grooves, and emerge from said second end, are refracted to a focal point.

Abstract: An X-ray diffractometer comprising an X-ray source (10) from which X-rays are guided to a sample (11) to be investigated, an X-ray detector (12) for receiving X-rays diffracted or scattered from or reflected by the sample (11), and a goniometer for adjustment of sequential relative angular positions between the X-ray source (10), the sample (11) and the X-ray detector (12) for detecting X-ray diffraction lines, X-ray scattered signals or X-ray reflectograms of the sample (11) to be investigated, wherein the X-rays can be guided at least sectionally along different optical paths, is characterized in that the X-rays can be guided from a position 1 to a position 2 along n≧2 different switchable optical paths, wherein the different optical paths are rigidly disposed relative to each other between position 1 and position 2 and form a unit (13), wherein the sample (11) assumes either position 1 or position 2 and wherein the switching over between the different optical paths can be effected by turning the unit (1

Abstract: In an apparatus and a method for the analysis of atomic or molecular elements contained in a sample by wavelength dispersive X-ray spectrometry, wherein primary x ray or electron radiation is directed onto the sample whereby fluorescence radiation is emitted from the sample, the fluorescence radiation is directed onto a mirror or focussing device consisting of a multi-layer structure including pairs of layers of which one layer of a pair consists of lanthanum and the other consists of carbon and the fluorescence radiation is reflected from the mirror or focussing device onto an analysis detector for the analysis of the atomic or molecular elements contained in the sample.

Abstract: A system includes substantial focus of radiation on a focal area, the focused radiation following a radiation path from a lens to the focal area, and projection of light on a surface so as to substantially indicate an intersection of the radiation path with the surface. In some aspects, the light projected on the surface substantially indicates a distance between the surface and the focal area.

Abstract: An optical element for diffracting x-rays that includes a substrate, a diffraction structure applied to the substrate, the diffraction structure including an exterior surface facing away from the substrate and the diffraction structure capable of diffracting x-rays and a protective layer applied to the exterior surface.

Abstract: A mirror element for the reflection of x-rays, particularly for EUVL exposure systems for the manufacture of semiconductor structures, wherein the x-rays reach the mirrors under a certain incident angle, consists of a substrate with a multilayer structure disposed thereon which multilayer structure comprises at least a first layer of a lanthanum-containing compound and a second layer of a boron-containing compound alternately disposed on the substrate.

Abstract: In a device and a method for the analysis of atomic and molecular elements by way of wavelength dispersive x-ray spectrometric structures including at least one mirror or focussing device having a multi-layer structure onto which fluorescent radiation generated by primary x-ray or electrons beams from a sample to be examined is directed and the reflected fluorescence radiation is supplied to a measuring device for determining the nature of impurities contained in the sample, the multi-layer structure consists of at least a lanthanum layer and a boron carbide layer.

Abstract: Disclosed are methods and apparatus for simultaneously flooding a sample (e.g., a semiconductor wafer) to control charge and inspecting the sample. The apparatus includes a charged particle beam generator arranged to generate a charged particle beam substantially towards a first portion of the sample and a flood gun for generating a second beam towards a second portion of the sample. The second beam is generated substantially simultaneously with the inspection beam. The apparatus further includes a detector arranged to detect charged particles originating from the sample portion. In a further implementation, the apparatus further includes an image generator for generating an image of the first portion of the sample from the detected particles. In one embodiment, the sample is a semiconductor wafer. In a method aspect, a first area of a sample is flooded with a flood beam to control charge on a surface of the sample. A second area of the sample is inspected with an inspection beam.

Abstract: An x-ray generation apparatus includes an x-ray reflecting mirror and x-ray generation part. The x-ray reflecting mirror is formed on an inner surface of a concave aspheric surface. The x-ray generation part receives at least one incident energy beam. The x-ray generation part is arranged near a focal point including a focal point of a paraboloid, and the x-ray reflecting mirror has at least one aperture formed in a position except for a part of the concave aspheric surface crossing an axis including the focal point of the concave aspheric surface, and an incident energy beam irradiates the x-ray generation part through the aperture.

Abstract: A reflective lens with at least one curved surface formed of polycrystalline material. In an example embodiment a lens structure includes a substrate having a surface of predetermined curvature and a film formed along a surface of the substrate with multiple individual members each having at least one similar orientation relative to the portion of the substrate surface adjacent the member such that collectively the members provide predictable angles for diffraction of x-rays generated from a common source. A system is also provided for performing an operation with x-rays. In one form of the invention the system includes a source for generating the x-rays and a polycrystalline surface region having crystal spacings suitable for reflecting a plurality of x-rays at the same Bragg angle along the region and transmitting the reflected x-rays to a reference position.

Abstract: To provide an X-ray monochromator capable of sufficiently removing the harmful X-rays while the intensity of the main reflected line can be sufficiently maintained, an X-ray monochromator 4 is formed by depositing a plurality of layer pairs on a substrate 4c and each being made up of a reflecting layer 4a and a spacer layer 4b, with first and second multilayered films 4e1 and 4e2 including one or a plurality of layer pairs having a predetermined periodic length d, wherein so that of X-rays reflected from the first multilayered film 4e1 adjacent the substrate 4c, the X-rays of a desired energy can be removed by interference with X-rays reflected by the second multilayered film 4e2 remote from the substrate 4c, the predetermined periodic length d2, the material for the reflecting layers 4a or the material for the spacer layers 4b in the second multilayered film 4e2 are different from those in the first multilayered film 4e1 and, also, the second multilayered film 4e2 has a properly chosen number of the layer pa

Abstract: To provide an X-ray monochromator capable of providing properly monochromated primary X-rays having a sufficiently high integrated intensity, the X-ray monochromator 4 for use in a X-ray fluorescence analysis for monochromating X-rays 2, emitted from an X-ray source 3, to provide primary X-rays 5 that are subsequently emitted towards a sample 1. The X-ray monochromator 4 is formed by depositing a plurality of layer pairs on a substrate 4c and each being made up of a reflecting layer 4a and a spacer layer 4b, with a plurality of multilayered films 4e including one or a plurality of layer pairs having a predetermined periodic length d, wherein the closer multilayered film 4e is to the substrate 4c, the smaller is set the above described predetermined periodic length d.

Abstract: A novel dual beam low energy electron microscope (LEEM) apparatus for inspecting semiconductor circuits or masks. Direct imaging records many pixels in parallel, offering higher inspection rates than prior art scanning methods. A low energy flood beam is superimposed with a second, higher energy flood beam. The use of two beams avoids charging effects upon insulating or partially insulating substrates. Under appropriate conditions, the net charging flux to each image element can be balanced on a pixel by pixel, as well as global basis. Either the low energy or the higher energy beam may be used to form an image of the surface. An electron optical apparatus and configuration for this dual beam LEEM is described.

Abstract: An illumination system for wavelengths ≦193 run comprises (a) a first raster element upon which a light bundle emitted from a light source impinges, for producing a convergent light bundle having a focal point, and (b) a second raster element. The convergent light bundle impinges on the second raster element outside the focal point. There is also provided an illumination system for wavelengths ≦193 nm, comprising (a) a first plurality of raster elements upon which a light bundle emitted from a light source impinges, for producing a plurality of convergent light bundles, where a member of the first plurality of raster elements produces a member of the plurality of convergent light bundles having a focal point, and (b) a second plurality of raster elements. The member of the plurality of convergent light bundles impinges on a member of the second plurality of raster elements outside the focal point.

Abstract: A method for testing a surface includes finding respective first and second critical angles for total external reflection of radiation from an area of the surface at first and second wavelengths. The first and second critical angles are compared to determine an orientation of a tangent to the surface in the area.

Abstract: A reflective lens with at least one curved surface formed of polycrystalline material. In one embodiment, a lens structure includes a substrate having a surface of predetermined curvature and a film formed along a surface of the substrate with multiple individual members each having at least one similar orientation relative to the portion of the substrate surface adjacent the member such that collectively the members provide predictable angles for diffraction of x-rays generated from a common source. A system is also provided for performing an operation with x-rays. In one embodiment, a system includes a source for generating the x-rays, a polycrystalline surface region having crystal spacing suitable for reflecting a plurality of x-rays at the same Bragg angle along the region, and transmitting the reflected x-rays to a reference position.

Abstract: A reflective lens with at least one curved surface formed of polycrystalline material. In an example embodiment a lens structure includes a substrate having a surface of predetermined curvature and a film formed along a surface of the substrate with multiple individual members each having at least one similar orientation relative to the portion of the substrate surface adjacent the member such that collectively the members provide predictable angles for diffraction of x-rays generated from a common source.

Abstract: X-ray diagnostic system. The system includes a source of x-rays which communicates with an x-ray beam concentrator spaced apart from the x-ray source and disposed for receiving x-rays from the x-ray source. An x-ray spectrometer is disposed for receiving x-rays from the concentrator. In a preferred embodiment, the concentrator is formed of a cylindrical spiral of a metal-coated plastic material having a surface for reflecting x-rays. In another embodiment, the concentrator includes a plurality of concentric nested cylinders of a metal-coated plastic material for reflecting x-rays. In yet another embodiment, the concentrator is a glass capillary bundle. The concentrator allows the spectrometer to be spaced away from the source of x-rays such as scanning electron microscope.

Abstract: An optical element for diffracting x-rays that includes a substrate, a diffraction structure applied to the substrate, the diffraction structure including an exterior surface facing away from the substrate and the diffraction structure capable of diffracting x-rays and a protective layer applied to the exterior surface.

Abstract: A modular x-ray lens system for use in directing x-rays comprising a radiation source which generates x-rays and a lens system which directs the x-rays, wherein the x-ray lens system may be configured to focus x-rays to a focal point and vary the intensity of said focal point.

Abstract: An X-ray optical system with two X-ray mirrors (A,B) for imaging an X-ray source (S) on a target region is characterized in that the X-ray mirrors (A,B) are mutually tilted by an angle other than 90° such that the combined region of acceptance of the X-ray mirror (A,B) is adjusted to the shape of the X-ray source (S) and/or the target region. This increases the intensity of the focused X-ray radiation on the sample for a given emission of the X-ray source (S) power using a few, technically simple modifications.

Abstract: A method and system for detecting an image of an object, particularly a soft tissue material. A generated x-ray beam is transmitted through the soft tissue material. A transmitted beam is directed at an angle of incidence upon a crystal analyzer. An image of the object is detected from a beam diffracted from the crystal analyzer either at or near a peak of a rocking curve of the crystal analyzer. The method and system of this invention is particularly useful for analyzing images of cartilage.

Abstract: In a device and a method for the analysis of atomic and molecular elements by way of wavelength dispersive x-ray spectrometric structures including at least one mirror or focussing device having a multi-layer structure onto which fluorescent radiation generated by primary x-ray or electrons beams from a sample to be examined is directed and the reflected fluorescence radiation is supplied to a measuring device for determining the nature of impurities contained in the sample, the multi-layer structure consists of at least a lanthanum layer and a boron carbide layer.

Abstract: A channel-cut monochromator has at least two kinds of reflecting surface pairs processed on a common single crystal block. Each reflecting surface pair has a first and a second reflecting surfaces between which X-rays are reflected even-number times. The channel-cut monochromator can be rotated around an axis of rotation perpendicular to a reference plane so as to switch the reflecting surface pair which reflects X-rays. An X-ray beam incident on any reflecting surface pair or its extension line is tangent to a common imaginary circle whose center coincides with the axis of rotation. With this structure, the switchover of the reflecting surface pair is accomplished by only the rotation of the channel-cut monochromator around its axis of rotation, so that various X-ray beams reflected by various Miller indices can be taken out selectively. The channel-cut monochromator may have a direct path through which an X-ray beam passes in no contact with any reflecting surface.

Abstract: Thin film thickness measurement accuracy in x-ray reflectometry systems can be enhanced by minimizing scattering and beam spreading effects. An oblong x-ray beam can be produced by shaping the electron beam in an x-ray microfocus tube, or by creating a target with a metal strip having the desired beam cross section. The elongation allows the beam direction dimension to be substantially reduced, without causing overheating of the target. By blocking portions of the x-ray beam focused on the thin film and generating reflectivity curves in increments, the effects of scattering can be minimized.

Abstract: The present invention provides methods and instruments for focusing and imaging x-rays using grazing incidence optics and medical and microscopic uses thereof.

Abstract: An x-ray or neutron apparatus for the transmission of x-ray or neutron images is described, which includes x-ray- or neutron-three-dimensional (3-D) arrays or mosaics, including a plurality of x-ray or neutron lenses positioned so that they form a two-dimensional (2-D) mosaic of compound refractive lenses to provide a plurality of separate x-ray or neutron paths between an object and an image at an x-ray- or neutron-detector. The apparatus is so constructed that it permits separate parts of an object to be imaged such that a total composite image is formed from these various parts. An imaging apparatus of the detection of carcinoma in breast tissue is formed using such an apparatus. Methods of microscopy and imaging are obtained using this apparatus.

Abstract: A grating that includes a multilayer structure that has alternating layers of materials, a plurality of grooves formed between a plurality of lands, wherein at least one structural parameter of the plurality of grooves and plurality of lands is formed randomly in the multilayer structure.

Abstract: An X-ray condenser for condensing X-rays radiated from an X-ray source to a very small condensing spot is disclosed. X-rays from the X-ray source are formed to a parallel X-ray beam by a parallel type parabolic reflection mirror. The parallel X-ray beam is made monochromatic by an analyzing crystal and condensed to the condensing spot by a zone plate. The zone plate is constructed by alternately arranging a plurality of X-ray transmitting bands and a plurality of X-ray shielding bands and can condense the parallel X-ray beam to a very small focus point.

Abstract: Microlithography apparatus and methods are disclosed for achieving high-resolution pattern transfer of a pattern onto a substrate, such as a semiconductor wafer, using extreme ultraviolet (EUV, also termed soft X-ray) radiation. The apparatus include an imaging-optical system (projection-optical system) capable of receiving pattern-encoding EUV light from a mask and forming an image of the pattern on the substrate. The desired wavelength of the EUV light is 20 nm to 50 nm, and the imaging-optical system includes multiple reflective mirrors having aspherical surficial profiles and multilayer-film reflective surfaces. The apparatus are configured especially to achieve a pattern-element resolution, of the projected image, of 70 nm or finer.