Abstract: Transmission and reflection type holograms may be formed utilizing a novel polymer-dispersed liquid crystal (PDLC) material and its unique switching characteristics to form optical elements. Applications for these switchable holograms include communications switches and switchable transmission, and reflection red, green, and blue lenses. The PDLC material of the present invention offers all of the features of holographic photopolymers with the added advantage that the hologram can be switched on and off with the application of an electric field. The material is a mixture of a polymerizable monomer and liquid crystal, along with other ingredients, including a photoinitiator dye. Upon irradiation, the liquid crystal separates as a distinct phase of nanometer-size droplets aligned in periodic channels forming the hologram. The material is called a holographic polymer-dispersed liquid crystal (H-PDLC).

Abstract: Holographic data storage media having a sandwiched construction are described in which a holographic recording material is sandwiched between two substrates. A variety of different formulations of the holographic recording material are also described. By improving the formulation of the photosensitive material, holographic media can be improved.

Abstract: A method of fabricating a hologram screen having a large visual range and a hologram imaging apparatus used for the particular method of fabricating the hologram screen are disclosed. A plurality of mirrors (3) extended toward a plurality of photosensitive members (5) are arranged at a plurality of end portions (21), respectively, of a light diffuser (2). At least a reference beam (41) and object beams (42) passed through the light diffuser (2) are radiated on a plurality of the photosensitive members (5) individually thereby to form a plurality of holograms. These holograms are integrated with each other by being arranged two-dimensionally thereby to fabricate a hologram screen. Among the mirrors (3), a reference beam-side mirror (31) arranged nearer to the light source of the reference beams (41) is extended from the light diffuser (2) by a length varied with the position of the photosensitive member (5) to be exposed.

Abstract: The invention relates a lithograph for producing computer-generated holograms in a storage medium (13), provided with a source for generating a write beam (2), a moving lens (4) for focussing the write beam (2), means for displacing the moving lens (4) along a direction of movement (6), and with a means for displacing the write beam (2) in relation to the storage medium (13) in a manner that is perpendicular to the direction of movement (6). The aim of the invention is to provide a lithograph in which disruptions in the movement of a lens perpendicular to the direction of movement thereof do not effect this end, the moving lens (4) has refractive power only essentially in a first direction that is parallel to the direction of movement (6). In addition, a stationary lens (9) is provided, and this stationary lens (9) has refractive power only essentially in a second direction (5), whereby the second direction (5) is perpendicular to the first direction and to the write beam (2).

Abstract: It is a main object of the present invention to provide a volume hologram layer with good foil cutting property which is used for a volume hologram transfer foil and the like. The present invention provides a volume hologram layer wherein when the layer thickness thereof is 20 &mgr;m, breaking strength is in a range from 10 MPa to 30 MPa and breaking strain is in a range from 0.1% to 3% at 25° C., and breaking strength is in a range from 0.1 MPa to 1 MPa and breaking strain is in a range from 0.1% to 5% at 130° C., to thereby solve the above problem.

Abstract: An interferometric lithography method includes providing a first layer of material over a substrate and providing a second layer of material over the first layer of material. The method further includes providing a layer of photoresist over the first and second layers of material and providing coherent light to the first and second layers. The coherent light has an intensity insufficient to chemically transform the photoresist. The coherent light reflects off the first and layers to interfere with an intensity sufficient to chemically transform the photoresist.

Abstract: A radiation sensitive refractive index changing composition comprising (A) a decomposable compound, (B) a non-decomposable compound having a lower refractive index than the decomposable compound (A), (C) a radiation sensitive decomposer and (D) a stabilizer. By exposing the composition to radiation through a pattern mask, the above components (C) and (A) of an exposed portion are decomposed and a refractive index difference is made between the exposed portion and unexposed portion, thereby forming a pattern having different refractive indices.

Abstract: Quality of a reproduced light beam is improved, and rewriting and recording are performed at high speed without erasing data. Each page of a hologram is newly recorded so that the maximum point of diffraction light beam intensity in reproducing the newly recorded hologram is located at a position where diffraction light beam intensity from a data page of a hologram which has been previously recorded in a hologram recording medium is minimized at the time of reproducing the data.

Abstract: A method is disclosed for replicating (copying) a master hologram into a photosensitive layer to produce a copy of the hologram in a manner such that the copy of the hologram is an accurate and true replication of the master hologram with minimum interface-related defects. A holographic element containing a master hologram for use in contact copying is also disclosed.

Abstract: The present invention relates to a method of producing digital holograms in a storage medium, in which the technical problem of writing computer-generated holograms by means of optical lithography as quickly as possible and with little effort with simultaneous accurate control of the timed triggering and the positioning of the write beam is achieved in that a write beam is focused onto the storage medium and moved one-dimensionally relative to the storage medium, in that a scanning beam is focused onto a trigger mask having a plurality of trigger lines and moved one-dimensionally transversely relative to the trigger lines, the movement of the scanning beam being coupled with the movement of the write beam, in that, during the scanning of the trigger lines, a timed trigger signal is generated as a function of the arrangement of the trigger lines, in that, with the aid of the timed trigger signal, the intensity of the write beam on the storage medium is controlled, and in that the hologram is written line by li

Abstract: A ferroelectric material in which the refractive index change can be induced by irradiation with light at two different wavelengths without performing a reduction treatment or doping impurities. The ferroelectric material of the invention in which the refractive index change is induced by irradiation with light at two different wavelengths is a lithium tantalate single crystal with the composition of Li2O/(Li2O+Ta2O5)=0.4966 to 0.4995. Preferably, the ferroelectric material is a lithium tantalate single crystal with the composition of Li2O/(Li2O+Ta2O5)=0.4974 to 0.4989. Preferably, the infrared absorption coefficient in the [OH] stretching mode falls within a range of 0 cm−1 to 0.15 cm−1 (0 cm−1 and 0.15 cm−1 are included in the range).

Abstract: A grating interference device with adjustable resolution has high stability and precision adjustment functions. The invention has two reflectors and a beam splitter. One of the reflector is installed on a rotating axis along with an optic fiber or a platform of planar waveguide. Through the rotating axis, this reflector and the platform are maintained at a fixed relative angle and rotate with respect to the other reflector and the beam splitter. The period of the interference grating is controlled by the angle change, producing a grating with a micrometer-order period on the optic fiber or the planar waveguide.

Abstract: A new photopolymerizable material allows single-step, fast recording of volume holograms with properties that can be electrically controlled. Polymer-dispersed liquid crystals (PDLCs) in accordance with the invention preferably comprise a homogeneous mixture of a nematic liquid crystal and a multifunctional pentaacrylate monomer in combination with photoinitiator, coinitiator and cross-linking agent. Optionally, a surfactant such as octancic acid may also be added. The PDLC material is exposed to coherent light to produce an interference pattern inside the material. Photopolymerization of the new PDLC material produces a hologram of clearly separated liquid crystal domains and cured polymer domains. Volume transmission gratings made with the new PDLC material can be electrically switched between nearly 100% diffraction efficiency and nearly 0% diffraction efficiency. By increasing the frequency of the switching voltage, switching voltages in the range of 50 Vrms can be achieved.

Abstract: A photopolymerisable system is disclosed which can be polymerised by exposure to UV light, for example, to form a solid, light-transmitting sheet material having volume refractive index variations defining an optical diffuser or a hologram, for example. The system includes a silicone monomer, prepolymer, macromonomer or co-monomer capable of undergoing free radical initiated polymerization and further includes a photoinitiator.

Abstract: A post-exposure treatment method of a silver halide emulsion layer in the manufacture of a hologram, a hologram manufacturing using the post-exposure treatment method, and a holographic optical element including the hologram are provided. The post-exposure treatment method of a silver halide emulsion layer involves: pre-hardening the silver halide emulsion layer after exposure; developing the pre-hardened silver halide emulsion layer using a developer solution; bleaching the developed silver halide emulsion layer; hardening the bleached silver halide emulsion layer; drying the hardened silver halide emulsion layer; surface-hardening the dried silver halide emulsion layer; fixing the hardened silver halide emulsion layer; treating the fixed silver halide emulsion layer using warm water; and drying the silver halide emulsion layer which has been treated using warm water.

Abstract: The present invention relates to a volume hologram laminate with low generation of spotty hologram flaws in the volume hologram layer even when kept under pressurized conditions during storage, and to a volume hologram laminate-fabricating label. The volume hologram laminate 1 of the invention has a first adhesive layer 3, a volume hologram layer 5, a second adhesive layer 4 and a surface protective film 6 formed in that order on a substrate 1, wherein the volume hologram layer is a hologram recording in a recording material comprising a matrix polymer and a photopolymerizable compound, having a glass transition point of 30° C.-70° C. and a dynamic storage elastic modulus of 5×105 Pa-5×107 Pa at 50° C. when measured at 6.28 rad/s, and the second adhesive layer has a dynamic storage elastic modulus of no greater than 5×104 Pa or at least 2.5×105 Pa at 50° C. when measured at 6.28 rad/s.

Abstract: Holographic data storage media having a sandwiched construction are described in which a holographic recording material is sandwiched between two substrates. The substrates may be formed with fluid containment features in proximity to outer edges of the respective substrates. Also, the substrates may be formed with centerpieces that are recessed relative to the outer surfaces of the respective substrates. Such substrate features can improve and simplify the media fabrication process and may improve media quality.

Abstract: An optical storage medium of the present invention enables storage of data with high precision at high speed, and rewriting of data at high speed without an erasing process. Optical storage, reading and retrieving methods and optical storage, reading, and retrieving apparatuses using the medium are also provided. The optical storage medium has at least a polarization-sensitive member having the photo-induced birefringence property, such as a member made of polyester polymer having cyanoazobenzene as a side chain. The above apparatuses have spatial light modulator capable of modulating polarization. The modulator provides information of bit of two-dimensional data to each corresponding pixel by application or non-application of a voltage, and modulates the polarization of the beam incident on each pixel. Thereby, a signal beam transmitted through the spatial light modulator having a spatial polarization modulation corresponding to the two-dimensional data is obtained.

Abstract: A holographic recording medium comprising a first substrate and a second substrate having a holographic recording layer between the first substrate and the second substrate, the holographic recording layer containing:

Abstract: A holographic image shrinkable film and the manufacture thereof is to spread a UV resin film on a shrinkable film; stick the UV resin film tightly against a metal wheel engraved with a holographic pattern, holographic film or separating type hot stamping film; illuminate the UV resin film with an UV lamp so as to harden the UV resin film instantly; and remove the harden UV resin film from the metal wheel, the holographic film, or separating type hot stamping film; the holographic pattern on the metal wheel or the holographic film is copied onto the UV resin film, or a separating type hot stamping film substrate is combined on the UV resin film. The manufacturing method according to the present invention is rather not dangerous, and a specialist is not need. Therefore, a mass production can be practiced to save production cost can be saved.

Abstract: The invention is a method of packaging volume holographic filters to modify the temperature sensitivity using fixed volume holographic grating filters (VHG). These filters are recorded using either a phase mask or a two-beam method. A mechanical constraint is provided to the filter by way of a stress. This stress can be applied equally to both simple reflection grating as well as slanted reflection grating. One way is to use a filter-anisotropic tube arrangement where the tube is made by either stacking washers of precise inner diameter or by wrapping a wire around a central filter core. To modify the thermal wavelength coefficient of the filter, clamps comprising plates and screws are used, the filter is inserted into a substrate, or the filter is sandwiched between substrates.

Abstract: A holographic optical recording medium includes a plastic substrate, a first inorganic intermediate layer formed on the plastic substrate, and an organic recording layer on which information is recorded by using holography. The organic recording layer is formed on the first inorganic intermediate layer.

Abstract: There was found a metallocenyl-phthalocyanine or its metal complex of a divalent metal, oxometal, halogenometal or hydroxymetal, in which at least one of the four phenyl rings of the phthalocyanine contains, bound via a bridge unit E, at least one metallocene radical as substituent, E being composed of a chain of at least two atoms or atom groups selected from the group consisting of —CH2—, —C(═O)—, —CH(C1-C4alkyl)—, —C(C1-C4alkyl)2—, —NH—, —S—, —O— and —CH═CH—, as well as mixtures of the novel compounds which comprise, inter alia, isomers, a process for the production, the use and recording media comprising the novel compounds.

Abstract: Copolymer structures are formed by exposing a substrate with an imaging layer thereon to two or more beams of selected wavelengths to form interference patterns at the imaging layer to change the wettability of the imaging layer in accordance with the interference patterns. A layer of a selected block copolymer is deposited onto the exposed imaging layer and annealed to separate the components of the copolymer in accordance with the pattern of wettability and to replicate the pattern of the imaging layer in the copolymer layer. Stripes or isolated regions of the separated components may be formed with periodic dimensions in the range of 100 nm or less.

Abstract: Disclosed is a holographic recording medium. The novel holographic recording mediums disclosed herein comprises: a) at least one polyfunctional epoxide monomer or oligomer which undergoes acid initiated cationic polymerization. Each epoxide in the monomer or oligomer is linked by group comprising a siloxane to a silicon atom and each monomer or oligomer has an epoxy equivalent weight of greater than about 300 grams/mole epoxide; b) a binder which is capable of supporting cationic polymerization; c) an acid generator capable of producing an acid upon exposure to actinic radiation; and optionally d) a sensitizer.

Abstract: Blue-sensitized holographic media suitable for recording with a blue laser is disclosed. The blue-sensitized holographic media provides greater dynamic range and a higher sensitivity than a green-sensitized holographic media, thereby providing more rapid hologram writing times.

Abstract: Diffractive optical structures are written within crystal optical elements using ultrafast near-infrared laser pulses. The crystal optical elements preferably perform an optical function such as focusing or chromatically dispersing light. The diffractive optical structures within the crystal optical elements perform additional optical functions that augment or refine the functions performed by the crystal optical elements.

Abstract: A method for producing a holographic stereogram, comprising the steps of:

Abstract: The present invention relates to a lithograph for producing digital holograms in a storage medium, having a light source (8) for producing a write beam (10), having drive means (12, 14) for the two-dimensional movement of the write beam (10) relative to the storage medium (4) and having a first objective (16) for focusing the write beam (10) onto the storage medium (4) to be written.

Abstract: The volume hologram recording photosensitive composition provided by the present invention contains at least a fluorine-contained photoreactive compound represented by the following formula (1): R1—R3—(CF2)n-R4-R2 wherein R1 and R2 are photoreactive groups which can be bonded to each other by photoreaction, and each of R3 and R4 is independently a single bond or a bivalent hydrocarbon group having 1 to 5 carbon atoms, and n is an integer of 1 or more. This volume hologram recording photosensitive composition is used to form a recording section of a recording medium, and then the section is exposed to light, whereby a bright volume hologram can be obtained.

Abstract: Charge-transfer materials are demonstrated to be useful for generating femtosecond holographic gratings. Using semiconducting polymers sensitized with varying concentrations of C60, absorption holographic gratings with diffraction efficiencies of 1.6% were recorded with individual ultrafast laser pulses; the diffraction efficiency and time decay of the gratings were measured using nondegenerate four-wave mixing. High quantum efficiency for electron transfer reduces the effects of early recombination which otherwise limits the density of excitations in pure polymers, and the metastability of the charge transfer enables tuning of the decay dynamics by controlling the concentration of acceptors in the mixture.

Abstract: There is provided a manufacturing method of an optical device having a micro-asperity pattern that has various kinds of accurate three-dimensional shapes and is realized as thin films. A substrate is coated with a resin thin film made of a photosensitive resin, and the temperature of the resin thin film is controlled so as to be lower than the photosensitivity extinction temperature of the resin thin film. A micro-asperity pattern of a stamper is pressed against the resin thin film when the resin thin film is in a softened or melted state by pressurizing means, whereby a micro-asperity pattern is formed on the surface of the resin thin film.

Abstract: A method of producing holographic iridescent film includes the steps of applying an adhesion coating upon a corona or plasma treated iridescent film, holographically embossing the adhesion coating, thermosetting the holographically embossed adhesion coating, and applying a high-resolution index (HRI) coating to the thermo-set holographically embossed adhesion coating.

Abstract: The present invention provides a volume hologram laminate by which a desirable reproduced wavelength is controlled and set optionally. The laminate has a first adhesive layer 3, a volume hologram layer 5, a second adhesive layer 4 and a surface protecting film 6 formed on a substrate 2 in the described order, wherein a substance for shifting a recorded wavelength to the volume hologram layer is contained in the first and/or the second adhesive layer(s) and a reproduced wavelength of hologram recorded in the volume hologram layer is controlled with shifting the substance between the layers.

Abstract: The invention is concerned with a volume hologram medium obtained by multiple recording of holograms, which is improved in terms of just only security for forgery prevention but also aesthetics. A volume hologram medium 29′ comprises a reflection hologram in which a stereoscopic image of a three-dimensional object and an image of a plane pattern of a mask plate are recorded by interference of the same reference light beams having the same angle of incidence and the same wavelength with object light beams having mutually different angles of incidence. The stereoscopic image of the three-dimensional object is reconstructed in the form of diffracted light 31 in a single color and in angle relations close to recording conditions, and the image of a plane pattern of the mask plate is reconstructed as diffracted light 32b, 32′b at various angles of incidence of white illumination light 30 and in different colors depending on those angles of incidence.

Abstract: Achromatic multilayer diffractive pigment flakes and foils are provided having diffractive structures thereon. The diffractive pigment flakes can have a symmetrical stacked coating structure on opposing sides of a reflective core layer, an asymmetrical stacked coating structure on one side of a reflective layer, or can be formed with one or more encapsulating coatings around the reflective core layer. The diffractive pigment flakes can be interspersed into liquid media such as paints or inks to produce diffractive compositions for subsequent application to a variety of objects. The foils can be laminated to various objects or can be formed on a carrier substrate. The diffractive pigment flakes and foils can be formed with a variety of diffractive structures thereon to produce selected optical effects. The diffractive foils and diffractive compositions applied to an object exhibit an iridescent diffractive effect over an achromatic background.

Abstract: A rapid mass production of the high performance holographic recording articles including the process and composition are described. To prepare a high performance holographic recording article based on two-component urethane matrix system, for example, polyols and all the additives must be virtually free of moisture contents. Deaeration must be carried out, once isocyanate and polyols including catalysts and all other ingredients are mixed together, to eliminate all entrapped air that is introduced into the mixture during mixing. The deaeration takes time, and the urethane reaction must not be allowed to take place until all air bubbles are evacuated from the isocyanate-polyols mixture. The rapid mass production of this invention overcomes such process limitations and results in a high-volume production of the high performance holographic recording articles.

Abstract: In the manufacture of an array total internal reflection hologram for printing a pattern of high-quality microfeatures over a large area, a mask defining just a part of the pattern is used to record an array of sub-holograms, the holographic recording medium or the mask being moved with respect to each other subsequent to the recordal of each sub-hologram, thereby building up a hologram of the complete pattern to be printed.

Abstract: An object of the present invention is to provide a hologram recording material composition which is excellent in transparency and diffraction efficiency. The hologram recording material composition comprises a thermoplastic resin (A) which is soluble in a solvent, a radical polymerizable compound (B) which is solid at an ordinary temperature and at ordinary pressure and has the 9,9-diarylfluorene skeleton and at least one radical polymerizable unsaturated double bond, a plasticizer (C) and a photopolymerization initiator (D). A weight percentage ratio of the thermoplastic resin (A), the radical polymerizable compound (B) and the plasticizer (C), (A):(B):(C) is 10 to 80:10 to 80:10 to 80. A refractive index of the radical polymerizable compound (B) is larger than a weighted mean of that of the thermoplastic resin (A) and that of the plasticizer (C).

Abstract: The present invention offers increased efficiency and quality in the duplication of a master hologram utilizing an improved method of contact printing. This improved method of contact printing employs a polymer-dispersed liquid crystal (PDLC) recording medium as the duplication blank and/or the master hologram material. The optical qualities of the PDLC material described herein provide an improved method of duplication using single beam contact printing regardless of the material comprising the master hologram. Thus, master holograms originally recorded using highly complex optical geometries (e.g., computer generated holograms) are capable of duplication without the need for multiple beam power/intensity balancing and long recording times. The improved hologram contact printing method described herein works with virtually any type of master hologram, including both reflection and transmission holograms.

Abstract: A method for patterning a layer on a substrate can include projecting coherent radiation toward a reflector surface so that the coherent radiation is reflected off the reflector surface to provide a holographic projection of a desired image wherein the reflector surface includes information that corresponds to an inverse of the holographic projection of the desired image. The substrate including the layer can be maintained in the path of the reflected radiation so that the holographic projection is projected onto the layer. Related systems are also discussed.

Abstract: The present invention relates to a three-dimensional micropattern using a hologram which can not be counterfeited with color copying machines or diffraction grating image forming devices. The three-dimensional micropattern comprises a hologram composed of a three-dimensional aggregation of a large number of very small micro-letters A-Z or geometric micro-figures. The micro-letters or geometric micro-figures are three-dimensionally aggregated to constitute a three-dimensional object (conical object) to allow reconstruction of a three-dimensional image of the specific three-dimensional object.

Abstract: The invention relates to a method of providing a decorative coating or text or the like on articles, like shavers, GSM's, cards, etc. The coating comprises a region-wise optically modified (patterned) cholesteric liquid crystalline layer, which is transferred onto a surface of the article by means of a transfer operation. The so-called in-mold decoration technique has been found to be very advantageous for the transfer of decorative (patterned) cholesteric liquid crystalline layers. In this technique the layer is (releasably) deposited on a plastic carrier foil and provided with a layer of adhesive. The assembly is inserted in an injection mold before the injection molding of polymer material starts. In this way decorative coatings (e.g. multi color images) and texts or the like can be even applied onto, non-even and slightly curved substrates.

Abstract: A method of fabricating a diffraction grating by utilizing a single substrate comprises the steps of forming a photosensitive material layer and a light transmission reducing film having a predetermined pattern integrally with each other on the substrate, exposing the photosensitive material layer by exposure irradiation light via the light transmission reducing film, and developing the photosensitive material layer after exposure. It is composed so that the direction of exposure and the direction of development are opposite to each other. It is possible to fabricate a diffraction grating in which each grating is formed on a predetermined substrate at a predetermined pitch and a root portion in a cross-section of each diffraction grating is constricted. In this way, it is possible to reduce or eliminate interfaces, so that the generation of noise light can be effectively suppressed and a diffraction grating having a high diffraction efficiency can be made.

Abstract: A photoreactive composition comprises (a) at least one reactive species that is capable of undergoing an acid- or radical-initiated chemical reaction; and (b) a photoinitiator system comprising photochemically-effective amounts of (1) at least one type of semiconductor nanoparticle quantum dot that has at least one electronic excited state that is accessible by absorption of two or more photons, and (2) a composition, different from said reactive species, that is capable of interacting with the excited state of the semiconductor nanoparticle quantum dot to form at least one reaction-initiating species.

Abstract: A holographic recording medium includes a holographic recording carrier including a first light transmittable substrate, a second light transmittable substrate and a holographic recording layer sandwiched therebetween, a first antireflection film formed on the surface of the first light transmittable substrate and a second antireflection film formed on the surface of the second light transmittable substrate, and optical characteristics of the first antireflection film and those of the second antireflection film are determined to be different from each other the thus constituted holographic recording medium can achieves improved data recording characteristics and data reproducing characteristics using an object beam and a reference beam, and concurrently enables desired positioning of an object beam and a reference beam, or only the reference beam, and detection of the address of the region in which data are being recorded or from which data are being reproduced using a position control beam.

Abstract: Processes for producing a holographic material involve producing the holographic image on a polished, substantially smooth surface and then transferring the holographic image to a substrate. A metallic coating is applied to a smooth surface of a printing element to provide a coated surface, the coated surface is embossed to provide the holographic image, and the holographic image is transferred to a substrate via a bonding material, thereby producing the holographic material. The holographic material may be used to provide a decorative cover for an object or item, such as a floral grouping or a potted plant.

Abstract: A substrate surface 10 having a photo-sensitive material surface thereon is simultaneously exposed to four plane waves of light at angles of incidence &thgr;, −&thgr;, &phgr; and −&phgr; subtending from the normal of the surface. The four plane waves create an interference pattern on the substrate so as to cause the formation of a periodic structure on the photo-sensitive material surface of the substrate.

Abstract: A holographic recording material coupled to a plastic substrate can be exposed to an interference pattern formed by at least one coherent light source, and subsequently processed, thereby eliminating the need to transfer the holographic recording material from a glass substrate to the plastic substrate. Additionally, by performing a post-exposure heating step in a liquid bath, the formation of unwanted bubbles between the plastic substrate and the holographic recording material is at least in part prevented.

Abstract: A packaging tape (3) which comprises a polymer film is used as a holographic data carrier. The packaging tape (3) is set up for the storage of holographic information. Holographic information can be put into the packaging tape (3) with the aid of a writing device (4), before an object (1) is packaged by using the packaging tape (3), but also afterwards.