Micro-optic anticounterfeiting elements for currency and other items using virtual lens systems

An optical security element, comprising:

• a lens array comprising a plurality of spot focusing lenses on a first side, wherein the spot focusing lenses are arranged into 2 by 2 lens sets, at least one spot focusing lens of each lens set focuses on only one whole pixel per spot focus direction;
• and
• an interlaced image on or proximate to a second side of the lens array opposite the first side, wherein:
• the interlaced image comprises a matrix having a number of pixels under each lens set of each spot focusing lens of the plurality of spot focusing lenses wherein the number of pixels for each lens set divided by the number of lenses in each lens set is a non-integer;
• the pixels of each of the matrices under each set of lenses are interlaced based on a ray tracing program along orthogonal interlacing axes of each lens set;
• and
• the interlacing of the pixels in the matrix is configured to provide a pre-determined mismatch, whereby at least one pixel is located between adjacent lenses of the lens sets.

An optical security element for application to a product to limit counterfeiting, comprising:

• a lens array with a first side and a second planar side opposite the first side;
• a plurality of lenses formed on the first side of the lens array, at least one lens of each lens set focuses on only one whole pixel per spot focus direction;
• and
• an interlaced image on or proximate the second planar side, wherein:
• the interlaced image is formed based on a ray tracing program in both directions to define a matrix having a number of pixels under each lens set of a plurality of lens sets within the lenses formed on the first side of the lens array wherein the number of pixels for each lens set divided by the number of lenses in each lens set is a non-integer:
• each lens set of the plurality of lens sets comprises at least a unit of four lenses arranged to have an equal or unequal number of lenses on a side;
• and
• the pixels provided in the interlaced image in both directions is selected to position at least one of the pixels between each pair of adjacent ones of the lens in each unit of at least a unit of four lenses of each lens set of the plurality of lens sets to create a pre-determined mismatch.