Abstract: An authentication server includes a calculator configured to calculate, based on a first set and a second set, similarity indicative of how similar the second set is to the first set, and an authenticator configured to, based on the similarity, authenticate a person who carries the mobile device during the second period as a true user. The first set is representative of characteristics of a true user of a mobile device and has as elements identifiers of one or more cells where the mobile device was located during a first period previous to a time at which an authentication request was received. The second set has as elements identifiers of one or more cells where the mobile device was located during a second period differing from the first period.

Abstract: A liquid crystal lens device includes a first electrode unit, a counter electrode and a liquid crystal layer. The first electrode unit includes a first and a second electrode. The liquid crystal layer is provided between the first electrode unit and the counter electrode. A threshold voltage Vth of the liquid crystal layer, an absolute value V1 of a potential difference between the first electrode and the counter electrode, a distance P1 between a center of the first electrode and a center of the second electrode, a thickness d1 of the liquid crystal layer, an effective elastic constant keff of the liquid crystal layer, a dielectric anisotropy ?? of the liquid crystal layer, and a dielectric constant ?0 of a vacuum satisfy V1>Vth×(P1/2)/d1, V1<Vth×(P1/d1), and (P1/2)/d1<?0×(??/keff).

Abstract: According to one embodiment, a liquid crystal optical device includes a first substrate unit, a second substrate unit, a liquid crystal layer, and a driver. The first substrate unit includes first electrodes, a second electrode, and a third electrode. The second substrate unit includes an opposing electrode provided on a second surface opposing the first surface. The liquid crystal layer is provided between the first substrate unit and the second substrate unit. The driver sets the first electrodes, the second electrode and the third electrode to a first potential, a second potential and a third potential respectively. A distance between the first electrode and the second electrode is longer than a distance between the second electrode and the third electrode. A difference between the first potential and the second potential is larger than a difference between the second potential and the third potential.

Abstract: According to one embodiment, a liquid crystal optical device includes first and second substrate units and a liquid crystal layer. The first substrate unit includes a first substrate having a first surface and a first side extending in a first side direction, and first electrodes provided on the first surface. The second substrate unit includes a second substrate having a second surface, and second electrodes provided on the second surface. The liquid crystal layer includes liquid crystal molecules provided between the first and second substrate units. A first angle in a first rotation direction from the first side direction to the first direction is less than 90 degrees and more than 0 degrees. A second angle in the first rotation direction is different from the first angle. A third angle in the first rotation direction is different from the first and second angles.

Abstract: According to an embodiment, an image display device includes an optical element, a voltage controller, and a display. Regarding the optical element, the refractive-index distribution changes according to the voltage applied thereto. The voltage controller controls, in a first mode, the voltage applied to the optical element in such a way that a first-type refractive-index distribution is achieved which acts as a first-type Fresnel lens; and controls, in a second mode that is different than the first mode, the voltage applied to the optical element in such a way that a second-type refractive-index distribution is achieved which acts as a second-type Fresnel lens having a greater number of steps than the first-type Fresnel lens. The display is disposed on the back side of the optical element and displays images.

Abstract: According to an embodiment, a liquid crystal lens device includes an optical element and a voltage controller. The optical element includes: a refractive index modulation layer of which a refractive index distribution changes according to a voltage applied thereto; and electrodes to apply a voltage to the refractive index modulation layer. In a first voltage state, the voltage controller controls voltages applied to the electrodes such that a first refractive index distribution is arranged periodically in the optical element. In a second voltage state, the voltage controller controls voltages applied to the electrodes such that a second refractive index distribution is achieved. In an intermediate voltage state, the voltage controller controls a voltage applied to a first-type electrode, to which a first voltage that is the maximum value among the voltages applied to the electrodes in the first voltage state is applied, to a second voltage lower than the first voltage.

Abstract: According to one embodiment, a liquid crystal optical device includes first and second substrate units and a liquid crystal layer. The first substrate unit includes a first substrate having a first major surface, and a first electrode extending along a first direction. The second substrate unit includes a second substrate and a first opposing electrode. The liquid crystal layer is provided between the first substrate unit and the second substrate unit and includes a first portion provided on a side of the first substrate unit and a second portion provided on a side of the second substrate unit. The first portion has a vertical alignment. The second portion has a horizontal alignment. A long axis of liquid crystal molecules in the second portion aligns along a second direction perpendicular to the first direction.

Abstract: A refractive-index distribution type liquid crystal optical device includes an optical element and a controller. The optical element includes a first and a second substrate, a liquid crystal layer, a first electrodes and second electrodes provided between the first substrate and the liquid crystal layer, third electrodes and fourth electrodes provided between the second substrate and the liquid crystal layer. Each of the second electrodes is between a pair of the first electrodes. Each of the plurality of second electrodes has a pair of end portions and a center portion being between the pair of end portions. A pair of the third electrodes are provided between a pairs of the fourth electrodes. The third electrode overlaps with the end portions the second, electrode and the third electrodes are projected onto the surface of the first substrate. The controller applies voltages to each of the electrodes.

Abstract: A liquid crystal lens device includes a first electrode unit, a counter electrode and a liquid crystal layer. The first electrode unit includes a first and a second electrode. The liquid crystal layer is provided between the first electrode unit and the counter electrode. A threshold voltage Vth of the liquid crystal layer, an absolute value V1 of a potential difference between the first electrode and the counter electrode, a distance P1 between a center of the first electrode and a center of the second electrode, a thickness d1 of the liquid crystal layer, an effective elastic constant keff of the liquid crystal layer, a dielectric anisotropy ?? of the liquid crystal layer, and a dielectric constant ?0 of a vacuum satisfy V1>Vth×(P1/2)/d1, V1<Vth×(P1/d1), and (P1/2)/d1<?0×(??/keff).

Abstract: A liquid crystal optical device of an embodiment includes: a first substrate unit; a second substrate unit; and a liquid crystal layer interposed between the first substrate unit and the second substrate unit. The liquid crystal molecules on a side of a first alignment layer of the first substrate unit is aligned perpendicularly to a first principal surface of the first substrate unit while the liquid crystal molecules on a side of a second alignment layer of the second substrate unit are aligned horizontally along a second direction. The opposing electrode includes: a first region and a second region, the first region has N first openings, and the second region includes M second openings, N being an integer of 0 or greater, M being an integer of 1 or greater, M being greater than N.

Abstract: A liquid crystal lens device includes first electrodes, first and second sub electrodes, an opposite electrode, and a liquid crystal layer. The first electrodes extend in a first direction and are arranged in a second direction crossing the first direction. The first sub electrode is provided between a center in the second direction of two nearest ones of the first electrodes and one of the two nearest first electrodes. The second sub electrode is provided between the center and the other of the two nearest first electrodes. The opposite electrode is opposed to each of the first electrodes, the first sub electrode, and the second sub electrode. The liquid crystal layer is provided between the first electrodes and the opposite electrode, between the first sub electrode and the opposite electrode, and between the second sub electrode and the opposite electrode.

Abstract: A liquid crystal lens device and an image display apparatus are disclosed. According to certain embodiments, the liquid crystal lens device includes a liquid crystal optical unit and a drive unit. The liquid crystal optical unit includes a first substrate unit having a plurality of first electrodes and a plurality of second electrodes, and a second substrate unit having a first opposing electrode. The drive unit controls voltages between the first electrodes and the first opposing electrode and between the second electrodes and the first opposing electrode by changing the voltage between the second electrodes and the first opposing electrode from a third voltage to a fourth voltage after changing the voltage between the first electrodes and the first opposing electrode from a first voltage to a second voltage. In some embodiments, the liquid crystal lens device is included in the image display apparatus along with an image display unit.

Abstract: According to one embodiment, a device includes first and second substrate units, a liquid crystal layer. The first substrate unit includes a first substrate, first and second electrodes, an extraction electrode, and a dielectric material layer. The second substrate unit includes a second substrate and a third electrode. The liquid crystal layer is provided between the first and second substrates. The first electrodes are provided on the first substrate to extend in a first direction. The second electrodes are provided on the first substrate and extend along the first direction. The extraction electrode is for electrically connecting the second electrodes. The third electrode is provided on the second substrate to extend in a second direction intersecting the first direction.

Abstract: According to one embodiment, a liquid crystal optical device includes an optical unit and a controller. The optical unit includes first and second substrates, first electrodes, first and second counter electrodes, and a liquid crystal layer. The controller controls a voltage applied to the first electrodes, and the first and second counter electrodes. The controller performs a plurality of display modes based on at least one of image information and a control signal being obtained to forms a plurality of lens. The image information is inputted to an image display unit stacked with the optical unit and emits an image light.

Abstract: According to one embodiment, a liquid crystal optical element includes: a pair of first and second substrates; a liquid crystal layer provided between the first and second substrates; first electrodes provided on the first substrate on the liquid crystal layer side and arranged along a first direction; second electrodes provided on the second substrate on the liquid crystal layer side and arranged along a second direction; and a driving unit configured to apply a voltage between the first electrodes and the second electrodes. The first electrodes are divided into electrode regions arranged along a third direction. The first electrodes included in each of the electrode regions are electrically connected to an extension line.

Abstract: According to one embodiment, a liquid crystal optical element includes first and second substrate units, a liquid crystal layer, and spacers. The first substrate unit includes a first substrate and first electrodes. The first substrate has a first major surface. The first electrodes are provided on the first major surface, extend along a first direction, and have a first width in a second direction perpendicular to the first direction. The second substrate unit includes a second substrate and an opposing electrode. The second substrate has a second major surface opposed to the first major surface. The opposing electrode is provided on the second major surface. The liquid crystal layer is provided between the first and second substrate units. The spacers are in contact with the liquid crystal layer. A diameter of each spacer is larger than the first width.

Abstract: A liquid crystal lens device includes first electrodes, first and second sub electrodes, an opposite electrode, and a liquid crystal layer. The first electrodes extend in a first direction and are arranged in a second direction crossing the first direction. The first sub electrode is provided between a center in the second direction of two nearest ones of the first electrodes and one of the two nearest first electrodes. The second sub electrode is provided between the center and the other of the two nearest first electrodes. The opposite electrode is opposed to each of the first electrodes, the first sub electrode, and the second sub electrode. The liquid crystal layer is provided between the first electrodes and the opposite electrode, between the first sub electrode and the opposite electrode, and between the second sub electrode and the opposite electrode.

Abstract: A liquid crystal optical device includes a liquid crystal optical unit and a drive unit. The liquid crystal optical unit includes a first and second substrate unit, and a liquid crystal layer. The first substrate unit includes a first substrate, a plurality of first electrodes, a second electrode, and a third electrode. The second substrate unit includes a second substrate, a plurality of first opposing electrodes, a second opposing electrode, and a third opposing electrode. The drive unit is configured to implement a first operation including subjecting the first electrodes to a first potential, subjecting the second electrode to a second potential, subjecting the third electrode to a third potential, subjecting the first opposing electrodes to a first opposing potential, subjecting the second opposing electrode to a second opposing potential, and subjecting the third opposing electrode to a third opposing potential.

Abstract: According to one embodiment, liquid crystal optical apparatus includes a first substrate unit, a second substrate unit, and a liquid crystal layer. The first substrate unit includes a first substrate, first electrodes extending in a first direction, a first sub electrode, and a second sub electrode. The second substrate unit includes a second substrate and an opposing electrode. The liquid crystal layer is provided between the first and second substrate units and. The first substrate unit including at least one selected from: a first distance between the one electrode of the first electrodes and the first sub electrode longer than a second distance between the other electrode of the first electrodes and the second sub electrode; and a first width of the first sub electrode narrower than a second width of the second sub electrode.

Abstract: A gradient index liquid crystal optical apparatus according to an embodiment includes: a first substrate having a first face; a second substrate having a second face opposed to the first face of the first substrate; a liquid crystal layer sandwiched between the first substrate and the second substrate; a plurality of first electrodes provided on the first face of the first substrate, and arranged along a first direction; a plurality of second electrodes provided on the first face of the first substrate to correspond to the first electrodes, the plurality of second electrodes being arranged along the first direction; a plurality of third electrodes provided on the first face of the first substrate and arranged along the first direction; and a fourth electrode provided on the second face of the second substrate.