Abstract: The invention relates to a system comprising a series of data carriers, in particular identity cards, papers of value or the like, whereby the data carriers belonging to the system exhibit diffraction structures containing standard information and parts of the series are changed by additional measures in the area of the diffraction structures or combined with other elements and they differ from the rest of the series in optically recognizable fashion, whereby the change in the diffraction structures and/or the combination with other elements convey an esthetic overall impression and the change and/or combination with the other elements cannot be undone without destruction of the diffraction structures.

Abstract: A diffraction grating generates even-order, odd-order, and 0th-order exit-pupil images. The even-order exit-pupil images have brightness levels within a first range and the odd-order exit-pupil images have brightness levels within a second range that is different from the first range. In one example, the even-order exit-pupil images are virtually invisible, i.e., missing, the odd-order exit-pupil images have the same or approximately the same intensities, and the 0th-order exit-pupil image has an intensity greater than the respective intensities of the odd-order exit-pupil images.

Abstract: Methods and compositions are provided for detecting biomolecular interactions. The use of labels is not required and the methods can be performed in a high-throughput manner. The invention also provides optical devices useful as narrow band filters.

Abstract: An optical pickup apparatus for reproducing information from an optical information recording medium or for recording information onto an optical information recording medium, is provided with a first light source for emitting first light flux having a first wavelength; a second light source for emitting second light flux having a second wavelength, the first wavelength being different from the second wavelength; a converging optical system having an optical axis and a diffractive portion, and a photo detector; wherein in case that the first light flux passes through the diffractive portion to generate at least one diffracted ray, an amount of n-th ordered diffracted ray of the first light flux is greater than that of any other ordered diffracted ray of the first light flux, and in case that the second light flux passes through the diffractive portion to generate at least one diffracted ray, an amount of n-th ordered diffracted ray of the second light flux is greater than that of any other ordered diffracted

Abstract: Compact systems with reduced insertion loss, and increased switch isolation and switching speed. The switching and/or routing devices utilize a separating sub-system, a switching and/or routing sub-system, and a recombining sub-system.

Abstract: A first diffractive optical element pattern with a pattern pitch that is no greater than a wavelength of incident light is formed on a first main surface of substrate such as a glass plate. Second diffractive optical element patterns are formed at positions that are respectively incident to positive first-order diffracted light and negative first-order diffracted light produced by the first diffractive optical element pattern. Negative first-order diffracted light produced by each second diffractive optical element pattern is incident upon a boundary face of the substrate at an angle that is smaller than the critical angle, and so exits the substrate.

Abstract: An optical security component for authenticating a document or a product including a transparent plastic film embossed to form an embossed surface and to have at least one diffraction grating; a layer of dielectric material of high optical index at least partially coated on the embossed surface and producing a colored effect of a first color for a first orientation of the component and a second different color for orientation perpendicular to the first orientation; a low optical index layer coated on a side opposite the viewing direction of the dielectric material; and a colored contrast layer having transparent zones and colored zones on the low optical index layer.

Abstract: A diffraction optical element including an element body having a large number of grooves formed on its surface to form a grating, and a grating shape adjusting layer deposited on a grating surface of the element body by oblique incidence or material particles onto the grating surface, wherein the grating shape adjusting layer per se is made of a reflecting film material. By the grating shape adjusting layer, the contour shape of the resulting grating surface in a section perpendicular to a lengthwise direction of the grooves is made not similar to the sectional shape of the element body. A reflecting film may be formed on a grating shape adjusting layer made of another material. A reflecting film may be provided on the element body before a grating shape adjusting layer made of a transparent dielectric material is provided on the reflecting film.

Abstract: A method of manufacturing an element having a microstructure of an excellent grating groove pattern or the like is obtained. This method of manufacturing an element having a microstructure comprises steps of forming a metal layer on a substrate, forming a dot column of concave portions on the surface of the metal layer and anodically oxidizing the surface of the metal layer formed with the dot column of concave portions while opposing this surface to a cathode surface thereby forming a metal oxide film having a grating groove pattern. When the interval between the concave portions of the dot column is reduced, therefore, a linear grating groove pattern having a large depth with a uniform groove width along the depth direction is easily formed in a self-organized manner.

Abstract: A layered diffractive optical element is disclosed, with which a high diffraction efficiency is attained over a broad region of used wavelengths, and with which diffraction light of unnecessary diffraction orders can be suppressed. A diffractive optical element of the present invention includes a plurality of diffraction gratings made of materials with different Abbe numbers, the plurality of diffraction gratings being layered with each other. Moreover, the partial dispersion ratio with respect to a g-line and a F-line of the material constituting at least one of the plurality of diffraction gratings satisfies the condition represented by a specified expression.

Abstract: In order to achieve highly dispersive spectrometry in wide wavelength with the use of a single grism, but not a plurality of grisms, the grism is composed of a prism the vertex angle of which can be varied and a volume phase holographic (VPH) grating. More specifically, the grism comprises a prism the vertex angle of which can be varied; and a VPH grating being a diffraction grating and disposed substantially orthogonal with respect to a side including the vertex angle of the prism; the VPH grating being rotated around an axis being substantially orthogonal to the side of the prism, whereby a slope angle defined by the VPH grating and a predetermined plane is varied.

Abstract: An optical signal processing apparatus has a diffraction grating element, first condenser lens, Faraday rotation elements, polarization beam splitter, ?/2 plate, second condenser lens, third condenser lens, and diffraction grating element. The magnitude of a magnetic field of each of the Faraday rotation elements is controlled on the basis of an externally input control signal. The rotation angle of the plane of polarization of signal light is set to 0 or ?/2 in accordance with the magnitude of the magnetic field. Each Faraday rotation element receives signal light having wavelengths ?1 to ?4, which has arrived from the first condenser lens, and outputs the signal light as a polarized light component in the first azimuth (parallel to the z-axis direction) or second azimuth (parallel to the y-axis direction).

Abstract: A security element (2) comprising a plastic laminate (1) has a surface pattern which is composed mosaic-like at least from surface elements, wherein in the surface elements a reflecting interface (8) between a shaping layer (5) and a protective layer (6) of the plastic laminate (1) forms optically effective structures (9). Light (11) which is incident on the plastic laminate (1) and which passes through a cover layer (4) of the plastic laminate (1) and through the shaping layer (5) is deflected in a predetermined manner by means of the optically effective structures (9). Shaped in the surface of at least one of the surface elements is a diffraction structure which is produced by a superimposition of a linear asymmetrical diffraction grating (24) with a matt structure. The linear asymmetrical diffraction grating (24) has a spatial frequency from the range of values of between 50 lines/mm and 2,000 lines/mm.

Abstract: A diffractive element used in conjunction with a grating to move a desired order beam off-axis, thereby reducing interference by undesired orders. Use of the off-axis grating allows a more uniform beam in the presence of manufacturing defects, such as etch depth errors. The diffractive element used with the off-axis grating may include a beam shaper, a one-dimensional beam splitter, or a two-dimensional beam splitter.

Abstract: A light coupling element is proposed with a surface (3) of a material which is transparent to light of a given wavelength (?). In order for the light coupling element to act independently of the direction of the vectorial parameters of the light, such as in particular of the polarization, on the surface of the light coupling element line-form indentations or elevations (51, 52) are provided which are equidistantly parallel and which intersect at given angles (?).

Abstract: An electrostatic micromechanical device with continuously variable displacement, that includes: a movable member having a first electrode; an opposing surface having a second electrode; a channel separating the movable member from the opposing surface; a liquid situated in the channel, wherein the liquid has a sufficiently high dielectric constant so as to enable continuously variable and stable control of a displacement of the movable member over a travel range spanning at least half of the channel; the displacement being a result of a voltage applied between the first electrode and the second electrode; and at least one solid dielectric layer physically situated between the first electrode and the second electrode.

Abstract: An achromatic Fresnel optic that combines a Fresnel zone plate and a refractive Fresnel lens. The zone plate provides high resolution for imaging and focusing, while the refractive lens takes advantage of the refraction index change properties of appropriate elements near absorption edges to recombine the electromagnetic radiation of different energies dispersed by the zone plate. This compound lens effectively solves the high chromatic aberration problem of zone plates. The AFO has a wide range of potential applications in lithography, microimaging with various contrast mechanisms and measurement techniques.

Abstract: In a holographic pattern provided in a holographic optical element, a pattern 1a twists a diffracted light beam in a clockwise direction, to form a semi-circular light spot Sa on photodetection parts A and B so as to extend over a dividing line LX in a four-segment photodetection part. A pattern 1b similarly twists the diffracted light beam in a clockwise direction, to form a semi-circular light spot Sb on photodetection parts C and D so as to extend over a dividing line LX in the four-segment photodetection part.

Abstract: A light diffusive protective film for a surface light source device for protecting other base material and improving the luminance of information display is disclosed which comprises a transparent plastic film and a concave/convex layer stacked on the surface of the transparent plastic film and satisfies requirements that: (1) the ten-point mean roughness of the uneven surface in the concave/convex layer is 0.5 ?m to 2.0 ?m; and (2) the count number of profile peaks is 16 to 60 as determined by measuring a roughness curve for the uneven surface of the concave/convex layer and determining the count number of profile peaks by a peak count method.

Abstract: When a Gaussian power distribution laser beam is converted into a uniform power density beam by a converging homogenizing DOE and is divided into a plurality of homogenized beams by a diverging DOE, the power of the separated beam spatially fluctuates. For alleviating the power fluctuation of the beams, an aperture mask having a window wider than a section of the homogenized beam but narrower than a noise region at a focus of the converging homogenizer DOE. Since a homogenized beam can pass the aperture mask as a whole, the power fluctuation, in particular, near edges is reduced.

Abstract: A security element (2) comprising a plastic laminate has a surface pattern (12) composed mosaic-like from surface elements (13; 14; 15). Shaped into at least two of the surface elements (14; 15) is a respective diffraction structure {B(x, y, T)} produced from a superimposition of a low-frequency grating structure {G(x, y)} with a high-frequency relief structure {R(x, y)}. In the one surface element (14) a grating vector of the grating structure {G(x, y)} and a relief vector of the relief structure {R(x, y)} are parallel and in the other surface element (15) the grating vector (16) and the relief vector (17) include a substantially right angle. In addition the grating vectors (16) of the grating structures {G(x, y)} in the two surface elements (14; 15) are parallel. A common boundary (18) of the two surface elements (14; 15) is visible only upon lighting with linearly polarized light, in daylight both surface elements (14; 15) have the same surface brightness.

Abstract: The invention refers to electrically reconfigurable optical devices based on the use of a layer of dielectric and transparent viscoelastic material (G) opposing at least a first electrode structure (ES1). According to the invention the arrangement of the individual electrode zones in the first electrode structure (ES1) in order to deform the viscoelastic layer (G) complies with one of the following alternatives. According to the first alternative, the electrode zones of the first electrode structure (ES1) are grouped into groups composed of two or more adjacent electrode zones and within each of said groups individual electrode zones are supplied each with a substantially different voltage. According to the second alternative, the electrode zones of the first electrode structure (ES1) are substantially annular, elliptical, rectangular or polygonal closed-loop electrodes. The invention allows, for example, for creating electrically reconfigurable blazed gratings (30) or Fresnel zone lenses (40).

Abstract: A beam splitting element having a diffraction grating is designed by careful selection of device parameters such as grating period, duty cycle, depth and refractive index. In particular, the parameters are selected in such a way that the product of refractive index, depth and duty cycle is equal to or bigger than a predetermined value. The diffraction grating device designed by these rules exhibits a high diffraction efficiency and small polarization dependence.

Abstract: An optical gain flattening filter for attenuating the wavelength power levels of an optical beam to a threshold value. The filter has a series of volume phase gratings which each have a loss spectrum. The sum of the loss spectra for the volume phase gratings is about equal to the opposite of the gain spectrum of the optical amplifier. As the optical beam passes through the volume phase gratings, the sum of the loss spectra is added to the gain spectrum of the optical amplifier such that the optical beam is attenuated to the threshold value.

Abstract: The present invention is directed to an improvement in a diffractive display suitable for presenting graphic and the like displays. Broadly, a novel embodiment is realized from a holographic diffraction pattern carried by a magnet or element and an electrically energizable coil magnetically coupled with said magnet that is energizable for movement of the magnet. Rotation of the holographic diffraction pattern generates a display using the diffracted light from the holographic diffraction grating. Another novel embodiment is realized from a faceted rotatable element (FRE) having an array of facets each bearing a diffraction grating and a source energizable for rotation of the FRE from a resting station to a viewing station. Rotation of the FRE generates a display using the diffracted light from the diffraction gratings.

Abstract: Imaging system for a microscope based on extreme ultraviolet (EUV) radiation. The present invention is directed to a reflective imaging system for an x-ray microscope for examining and object in an object plane, wherein the object is illuminated by rays of a wavelength of less than 100 nm, particularly less than 30 nm, and is imaged in a magnified manner in an image plane. In the imaging system, according to the invention, for a microscope based on extreme ultraviolet (EUV) radiation with wavelengths in the range of less than 100 nm, with a magnification of 0.1× to 1000× and a structural length of less than 5 m, at least one of the imaging optical elements 2 and 3 in the beam path has a diffractive-reflective structure which is arranged on a spherical or plane area and has a non-rotationally symmetric, asymmetric shape. The arrangement according to the invention provides an imaging system which avoids the disadvantages of the prior art and ensures a high imaging quality.

Abstract: There is disclosed an optical device in which a first light source for outputting a first wavelength light is apart from a second light source for outputting a second wavelength light by a predetermined distance. An information recording medium is irradiated with the first and second wavelength lights transmitted through a holographic optical element having first and second diffraction areas. The first and second diffraction areas are provided with grating arrangements in which grating axis directions are parallel to each other and grating pitches are different from each other. The first and second wavelength lights reflected by the information recording medium are transmitted through the holographic optical element and diffracted by the first and second diffraction areas.

Abstract: In a method of making a replication tool, replication parts for both two dimensional optical elements, such as are fabricated using micro-forming techniques, and three dimensional optical elements, that are typically formed using cutting techniques are present on the replication tool. A method of manufacturing a replication tool for a planar optical sheet includes mounting at least one optical element part on a base to form a master part and forming a conductive metal layer over the master part. The method also comprises electrochemically depositing over the conductive metal layer to form an electrochemically deposited layer, separating the electrochemically deposited layer from the master part. The invention also relates to the replication tool itself and optical circuits formed using the replication tool.

Abstract: An optical head device having an optical element capable of transmitting without diffracting light having a wavelength emitted from a two-wavelength semiconductor laser and capable of diffracting light having another wavelength, to provide high utilization efficiency of light in a stable manner.

Abstract: An optical packet header identifier having a simplified configuration and being superior in reliability, stability, and economical efficiency, an optical router incorporating the identifier therein, and a routing method using the optical router are provided. The optical packet header identifier includes an optical waveguide, optical focusing elements, and a photo receiver. Tilted gratings for diffracting an incident optical beam and emitting the beams as diffracted optical beams to the outside of the waveguide are formed within the optical waveguide. The tilted gratings are not formed uniformly in a longitudinal direction of a core of the optical waveguide, but are arranged at intervals. The length of a portion containing a set of gratings and the length of a portion containing no gratings can be defined in increments of length “L”. “L” equals to the spatial length which 1 bit in an optical signal occupies.

Abstract: In an optical scanning device 1, a housing 3 has a space 3a in the inside thereof. A floating rotational plate 2 is housed in the space 3a, and is caused to float and to rotate by a magnetic force. The floating rotational plate 2 has an optical deflection layer 6 thereon. A diffraction grating 71 is formed on the optical deflection layer 6 on and around the center axis Z of the floating rotational plate 2. When a beam of light falls incident on the diffraction grating 71 in a direction normal to the surface of the optical deflection layer 6, the diffraction grating 71 diffracts the light in a radius direction of the circular-shaped floating rotational plate 2. The light is transmitted through optical waveguides 20 and 51 to be emitted outside from the housing 3. By rotating the small-sized floating rotational plate 2 at a high speed inside the housing 3, it is possible to scan the light at a high speed and with a high resolution.

Abstract: A surface pattern (18) is in the form of a visually visible mosaic comprising a number of surface portions (8; 9; 15; 16; 17) and is embedded in a laminate (1) comprising at least a transparent cover layer (2) and a protective layer (5). The surface portions (8; 9; 15; 16; 17) are transparent, scatter or reflect incident light (10) or diffract the incident light (10) at microscopic relief structures (4). The surface portions (8; 9; 15; 16; 17) are at least partially covered with a reflection layer (3). At least one of the surface portions occupied by a microscopic relief structure (4), an area (16), is a ZOM-structure (4?) with a predeterminedly slowly varying profile height h and a spatial frequency f, wherein the product of a predetermined limit wavelength ?G of the visible spectrum and the spatial frequency f is greater than or equal to one.

Abstract: An aberration compensating optical element includes: a diffractive structure having a plurality of ring-shaped zone steps formed into substantially concentric circles on at least one surface of the aberration compensating optical element; wherein the aberration compensating optical element is adapted for being disposed on an optical path between a light source for emitting a light having a wavelength of not more than 550 nm, and an objective lens made of a material having an Abbe constant of not more than 95.

Abstract: An electro-optical converter assembly is described. The electro-optic converter includes an optically transparent substrate with a plurality of alignment apertures and an optical device disposed on a first planar surface of the optically transparent substrate in alignment with the plurality of alignment apertures so that an axis of transmission of the optical device passes directly through the optically transparent substrate.

Abstract: A tunable optical device for adding or dropping one or more channels in a wavelength division multiplexing communication system is disclosed. The tunable optical device comprises one or more filters, wherein at least one filter comprises (a) one or more elastimers and (b) one or more gratings. An elastimer is a polymer that expands and contracts with a change in a voltage applied across the polymer or when a certain wavelength of light is diffracted from or transmitted through the polymer.

Abstract: An athermal package for fiber photonic devices includes at least two bonding regions at each end of the optical fiber containing the photonic device. At each end of the optical fiber, the bonding region nearest the photonic device (i.e., the inner bonding region) has a width that is less than that of the other bonding region (i.e., the outer bonding region). The smaller widths of the inner bonding regions allow for relatively precise control of the positions on the optical fiber that the inner bonding regions are attached. The larger widths of the outer bonding regions help provide reliable attachments.

Abstract: A method of moving a MEM system mirror in a well defined trajectory that allows longer seeks to be used to reach a target position as compared with known methods that employ small step sizes due to lack of well defined seek trajectories. One method uses the same seek trajectory (scaled in amplitude for seek length) for both axes (x-axis and y-axis) associated with the MEM mirror. This forces both axes to take the same length of time and to use the same “shape” to perform the move, and results in a straight line path between two points. Multiple straight line moves can be employed to provide a more complex trajectory. Another method uses a different trajectory with the same length, but a different shape, for each axis to force the MEM mirror along substantially any desired path such as an arc and/or straight line, among others.

Abstract: A plane diffraction grating based on surface normal rotation according to the present invention is designed so that the profile of the grooves at a radial area is determined depending on a rotational position of the area about a rotational center defined as a foot of the rotational axis on the surface of the plane diffraction grating. An optical system such as a spectrometer or a monochromator according to the present invention uses such a plane diffraction grating, and requires a special arrangement. The optical system includes: a plane diffraction grating as described above; a mechanism for rotating the plane diffraction grating about the rotational axis; an incidence optical system for casting a converging beam of light on a point of the surface of the plane diffraction grating, where the point is set apart from the rotational center.

Abstract: Optical systems are provided. One such optical system includes an optical source that propagates a source beam of light. A diffracting component is optically coupled to the optical source and is operative to receive the source beam and produce a diffracted beam. A target is located to receive the diffracted beam. Additionally, a compensating system repositions at least one of the optical source, the diffracting component, and the target in response to a detected change in refractive index of a medium through which the diffracted beam propagates so that the diffracted beam continues to be received by the target. Methods and other systems also are provided.

Abstract: To obtain an optical element that can reduce Fresnel (surface) reflection on a lens surface to be a cause of flare or ghost, and a scanning optical system having the same.

Abstract: A method includes configuring an imaging lens section to be free of structure with optically refractive power and to have a lens with an optically diffractive characteristic, and passing radiation from a scene through the imaging lens section, the imaging lens section causing the radiation to form an image at an image plane. An apparatus includes an imaging lens section which is responsive to radiation from a scene for causing the radiation to form an image at an image plane, the imaging lens section being free of structure with optically refractive power and including a lens which has an optically diffractive characteristic.

Abstract: The invention reduces the effects of stitching errors from re-scaling or re-positioning in the fabrication of fiber Bragg gratings or the mask used in such fabrication. A first embodiment of the invention preferably uses characteristics of stitching errors to compensate for the stitching errors themselves. By increasing the number of stitching errors, errors caused by the stitching errors can be reduced. A second embodiment uses continuous writing of the desired pattern, wherein the desired pattern is snapped to a grid that can be written by the fabrication equipment. Using continuous writing eliminates stitching errors in the resulting gratings.

Abstract: An optical device for enlarging an eye box, the optical device comprising: (a) a first optical expander being carried by, or formed in, a first light-transmissive substrate engaging a first plane; and (b) a second optical expander being carried by, or formed in, a second light-transmissive substrate engaging a second plane being spaced apart from the first plane. The first and the second optical expanders designed and configured such that light passing through the first optical expander is expanded in a first dimension, enters the second light-transmissive substrate through the second optical expander, and exits from the second light-transmissive substrate, expanded in a second dimension, hence enlarging an eye box of the optical device in both the first and the second dimensions.

Abstract: A diffraction grating generates even-order, odd-order, and 0th-order exit-pupil images. The even-order exit-pupil images have brightness levels within a first range and the odd-order exit-pupil images have brightness levels within a second range that is different from the first range. In one example, the even-order exit-pupil images are virtually invisible, i.e., missing, the odd-order exit-pupil images have the same or approximately the same intensities, and the 0th-order exit-pupil image has an intensity greater than the respective intensities of the odd-order exit-pupil images.

Abstract: The invention concerns a rectangular response optical filter for partitioning a limited spectral interval in a light flux with large spectrum comprising: a preferably monomode input optical fiber having one end; an array-reflector assembly in Litmann-Metcalf configuration; a converging optical system collimating at whose focus is set the input fiber end; a converging focusing optical system set between the array and the reflector; one or several output fibers of the same type as the input fiber. At least one reflector is placed in the focal plane of the focusing optical system and has a limited dimension in the dispersion plane, the position and the limited dimension of the dispersion plane determining the partitioned spectral interval.

Abstract: A diffractive optical element includes a first layer having a relief-type grating, a second layer having a relief-type grating, and a third layer having a relief-type grating. The first, second and third layers are formed of different materials. The diffractive optical element has at least three diffraction optical parts in the boundary areas of the respective layers. The diffractive optical element is set so that at least wavelengths, the diffraction efficiency thereof for diffracted light of a predetermined order may be maximum. The three wavelengths are substantially coincident with the main wavelengths of the three primary colors.

Abstract: A bi-directional wavelength division multiplexing/demultiplexing device is disclosed. In an exemplary embodiment, the bi-directional wavelength division multiplexing/demultiplexing device comprises a diffraction grating for combining a plurality of monochromatic optical input beams into a multiplexed, polychromatic optical output beam, and for separating a multiplexed, polychromatic optical input beam into a plurality of monochromatic optical output beams; and a transmissive/reflective optical element for transmitting the plurality of monochromatic optical input beams on an optical path toward the diffraction grating, and for reflecting the plurality of monochromatic optical output beams received on an optical path from the diffraction grating.

Abstract: A prism optimally separating and synthesizing a light beam of a wide angle of incidence. A diffraction prism 15 of the present invention is so constructed that a diffraction grid 21 is sandwiched between a pair of diffraction grid substrates 22, a pair of prism substrates 24 are bonded to the surfaces of the prism substrates 22 facing the diffraction grid 21 with interposition of adhesive layers 23, and a diffraction grid medium 25 having a refractive index substantially equal to that of the prism substrates 24 is charged in a gap defined by the diffraction grid 21 and the prism substrates 24, with the respective component members being optically combined together. An incident light is led to the diffraction grid 21 and separated on transmission or reflection by the operation of diffraction by the diffraction grid 21.

Abstract: Provided is a Fresnel lens the manufacture of that is unlikely to be affected by the working errors of the die in the optical axis and its neighborhood. Two lens surfaces 11, 11 that are disposed in the vicinity of the optical axis are disposed in the way they are shifted from each other in a direction along the optical axis, whereby the height Ha in this direction of the optical axis of a non-lens surface 12 located at the boundary between the two lens surfaces 11, 11 is made greater than an original height Ha of the non-lens surface 12 in a case where it is assumed that the lower ends 11a, 11a of each of these lens surfaces 11, 11 has been placed on the same flat plane intersecting the optical axis OA at a right angle with respect thereto. Also, the lens angle &thgr;a of at least one piece of lens surface 21 that is disposed in the vicinity of the optical axis is set to be greater than the original lens angle that should be given according to the focus calculation with respect to the lens angle 21.

Abstract: Aluminium oxide doped with a divalent metal oxide, produced by flame hydrolysis and which has no spinell structures or alpha-aluminium detectable in an x-ray diffractogram. It is produced by a pyrogenic process in which, during the flame hydrolysis of aluminium halogenides, an aerosol, which contains an aqueous solution of a divalent metal salt is added to the gas mixture. The doped aluminium oxides can be used in aqueous dispersions for chemical-mechanical polishing.