Abstract: Methods for providing gaming advice are provided. For example, regarding a blackjack game, one or more first player cards are identified for a first player and one or more second player cards are identified for a second player. The first and second player cards are displayed to the first player. A probability associated with a first one of the plurality of playing options is determined based at least on a set of predetermined statistical blackjack data, the one or more first player cards, and the one or more second player cards. It is then determined, based at least on the determined probability associated with the first playing option, whether to display a first indication corresponding with first advice regarding the first playing option, a second indication corresponding with second advice regarding the first playing option, or a third indication corresponding with third advice regarding the first playing option.

Abstract: System and methods related to wagering, such as slot machines and/or other electronic games. Some wagering may relate to market indicators, market lines, and/or stop commands.

Abstract: An optical device is provided that comprises a multi-order diffractive Fresnel lens (MOD-DFL) and an achromatizing compensation mechanism that reduces refractive dispersion created by the MOD-DFL, thereby reducing the focal range of the MOD-DFL. A method is also provided of using the optical device in an image processing system to obtain images of an object and processing the images to perform image enhancement.

Abstract: An optical device is provided that comprises a multi-order diffractive Fresnel lens (MOD-DFL) and an achromatizing compensation mechanism that reduces refractive dispersion created by the MOD-DFL, thereby reducing the focal range of the MOD-DFL. A method is also provided of using the optical device in an image processing system to obtain images of an object and processing the images to perform image enhancement.

Abstract: An optical device comprising a freeform optical surface having a diffractive pattern formed thereon and a method and system for forming a diffractive pattern on a freeform optical surface are provided. The diffractive pattern can be formed with sufficient precision that the optical device is suitable for use in a telescope used in astrometry for exoplanet sub-micro-arcsecond resolution.

Abstract: A multi-order diffractive Fresnel lens (MOD-DFL) that is suitable for use in a space telescope for studying transiting earth-like planets of distant stars is provided. The MOD-DFL may comprise a MOD-DFL array comprising a plurality of MOD-DFL segments that are secured to a mounting surface of a deployment device, such as a balloon, for example, in a preselected arrangement to form the MOD-DFL. An array telescope may be formed of an array of deployment devices, such as an array of balloons, for example, each having a MOD-DFL secured to a mounting surface of the respective deployment device, an optics system disposed inside of the respective deployment device, and a camera disposed inside of the respective deployment device. Each MOD-DFL comprises a plurality of MOD-DFL segments arranged in a preselected arrangement to form the respective MOD-DFL.