A secure lens sheet or layer suitable for use in a micro-optic system, which is made up of a plurality of joined fine lens arrays (e.g., joined fine lenticular and/or joined fine non-cylindrical lens arrays), is provided. Each array has a lens pitch different from adjacent or contiguous arrays and/or is orientated in a direction different from adjacent or contiguous arrays. A micro-optic security device, which utilizes the inventive secure lens sheet and one or more overlying or underlying arrangements of micro-sized image icons (e.g., line data), is also provided. The image icon arrangement(s) and the secure lens layer are configured such that one or more synthetic images are projected by the security device. These projected images may show a number of different optical effects. With such a combination lens layer, some regions could be optically active when the device is tilted in one direction, some could be active when tilted in the opposite direction, and some areas could be active when the device is tilted in either (or any) direction. The inventive micro-optic security device may be partially embedded in and/or mounted on a surface of a security article (e.g., paper or polymer security document, label, card), or integrated therein.

A lenticular tag display system and a lenticular tag are provided. The tag display system includes a display structure having an axis of rotation and a set of the lenticular tags, removably connected to the display structure. Each tag in the set of lenticular tags has a first lenticular image selected by a name program and a second lenticular image that is a souvenir image. Each tag is oriented relative to the display structure such that an axis of lenticulation of the lenticular tag is parallel to the axis of rotation of the display structure.

A lenticular tag display system and a lenticular tag are provided. The tag display system includes a display structure having an axis of rotation and a set of the lenticular tags, removably connected to the display structure. Each tag in the set of lenticular tags has a first lenticular image selected by a name program and a second lenticular image that is a souvenir image. Each tag is oriented relative to the display structure such that an axis of lenticulation of the lenticular tag is parallel to the axis of rotation of the display structure.

Toy apparatus (1) which is constructed to travel from place to place and which provides an optical illusion for a viewer, and wherein the toy apparatus (1) comprises: i) a device (17) having a plurality of separate images (18); ii) the separate images (18) are displayed on panels (19); iii) the panels (19) are rotatable; iv) the panels (19) are such that when they are rotating and when the separate images (18) are viewed by the viewer, they provide an optical illusion due to the viewer's persistence of vision; and v) the toy apparatus (1) is movable from place to place

Toy apparatus (1) which is constructed to travel from place to place and which provides an optical illusion for a viewer, and wherein the toy apparatus (1) comprises: i) a device (17) having a plurality of separate images (18); ii) the separate images (18) are displayed on panels (19); iii) the panels (19) are rotatable; iv) the panels (19) are such that when they are rotating and when the separate images (18) are viewed by the viewer, they provide an optical illusion due to the viewer's persistence of vision; and v) the toy apparatus (1) is movable from place to place

A method, a system, and a computer program product for tracking an object moving relative to a moving platform, the moving platform moving relative to an external frame of reference. The system includes An inertial sensor for tracking the object relative to the external reference frame, a non-inertial sensor for tracking the object relative to the moving platform, and a processor to perform sensor fusion of the inertial and non-inertial measurements in order to accurately track the object and concurrently estimate the misalignment of the non-inertial sensor's reference frame relative to the moving platform.

A method, a system, and a computer program product for tracking an object moving relative to a moving platform, the moving platform moving relative to an external frame of reference. The system includes An inertial sensor for tracking the object relative to the external reference frame, a non-inertial sensor for tracking the object relative to the moving platform, and a processor to perform sensor fusion of the inertial and non-inertial measurements in order to accurately track the object and concurrently estimate the misalignment of the non-inertial sensor's reference frame relative to the moving platform.

A 3-dimensional object may contain tunnels passing through the object so that when the object rotates, if the object is viewed from a certain angle, the tunnel is only visible for the moment that the tunnel is pointed directly at the viewer's eye. This system of tunnels can be used to create an animated system of dots when the shape rotates, and the dots can be positioned so that they create the animated illusion of dots moving along the surface of the shape in the opposite of the true direction of rotation.

A 3-dimensional object may contain tunnels passing through the object so that when the object rotates, if the object is viewed from a certain angle, the tunnel is only visible for the moment that the tunnel is pointed directly at the viewer's eye. This system of tunnels can be used to create an animated system of dots when the shape rotates, and the dots can be positioned so that they create the animated illusion of dots moving along the surface of the shape in the opposite of the true direction of rotation.

An optical device includes an array of lenses and a plurality of segments disposed under the array of lenses. The plurality of segments corresponds to a plurality of images. Upon tilting the device at different viewing angle, the array of lenses presents images sequentially. In some examples, individual ones of the segments can comprise specular reflecting, transparent, diffusely reflecting, and/or diffusely transmissive features. In some examples, individual ones of the segments can comprise transparent and non-transparent regions. The images can produce one or more optical effects.