Can a device that can perform hyperacuity vision tasks be built? In this paper, a feasibility study based on separation discrimination is conducted. Two types of ideal detectors are considered. The first is the stimulus defined statistically (SDS) detector by Geisler and Davilla. The second is one that estimates the uncertainty and then takes out its effect. In the first method, an array of many ideal stimulus defined exactly (SDE) detectors covers uncertainties and forms the ideal SDS detector. When the separation distance between the SDE detectors is around 1 arcmin, the SDS detector can achieve nearly optimal performance. To cover the motion uncertainty with nearly optimal performance, the SDE detector at each position needs to cover 16 directions, and at each direction, it needs to cover speeds with an increment of 0.5 degrees/s. Typically, the SDS detector needs 7776 SDE detectors to deal with a speed up to 2 degrees/s stimulus movement with a randomly selected direction and a 9 min x 9 min position uncertainty region. This ideal observer can achieve a hyperacuity threshold of 2-4 arcsec. Its threshold is almost constant over the range of speeds covered by the SDS detector. Using the second method, position estimation and motion tracking capability is examined. With perfect position estimation and motion tracking, the SDS detector can be reduced to a single SDE detector that is tuned to correct position and motion direction and speed. Two lower bounds on the estimation variance are examined, namely: 1) the Cramer-Rao bound and 2) the Ziv-Zakai bound. The results showed that if an estimation algorithm that can achieve the performance of bounds can be found, then the second method could achieve a hyperacuity capability of 1 s or less. The human visual system may more likely adopt the first method, but the second is simpler to use in building up a device using microprocessors. In this paper, dot-pair templates are used, which precisely match to dot-pair stimuli, to compute the likelihood and make a decision. The main difference between this paper and that of Geisler and Davilla lies in using a discrete sum over an array of SDE detectors to closely approximate continuous integration over the uncertain region, which makes it much easier in hardware implementation.

The paper develops four alternatives for modeling surfaces of the cornea and contact lenses. The cornea and contact lenses are generally smooth surfaces with possible discontinuities in circumferential or radial patterns. We define surfaces derived from semi-regular tensor product B-spline surfaces over a polar coordinate domain. The semi-regular partition allows finer control over the patch size, which is desirable for adaptive refinement. In geometric space, several patches meet at the origin, potentially resulting in a discontinuity. This is addressed by either imposing a system of constraints or blending the center region into a continuous function. The representations are fit to sampled data from a range of shapes and compared in terms of overall fit and fidelity at the origin. In the cases where constraint equations are used, their effectiveness and consequences on the resulting accuracy are assessed.

The Wiener-Lee-Schetzen scheme of using Gaussian white noise to test a nonlinear dynamical system is extended in two ways. 1) An arbitrary non-Ganssian white noise stationary signal can be used as the test stimulus. 2) An arbitrary function of this stimulus can then be used as the analyzing function for cross correlating with the response to obtain the kernels characterizing the system. Closed form expressions are given for the generalized orthogonal basis functions. The generalized kernels are expanded in terms of Volterra kernels and Wiener kernels. The expansion coefficients are closely related to the cumulants of the stimulus probability distribution. These results are applied to the special case of a Gaussian stimulus and a three-level analysis function. For this case a detailed analysis is Lade of the magnitude of the deviation of the kernels obtained with the ternary truncation as compared to the Wiener kernels obtained by cross correlating with the same Gaussian as was used for the stimulus. The deviations are found to be quite small.

The phase-slipping behavior of second-order squaring and quadrupling phase-locked loop configurations is investigated by digital computer simulation. Statistics are obtained for the mean time between batches of phase slips and the duration of the batches, as a function of the effective loop signal-to-noise ratio (SNR).