The opaque square

The problem of finding small sets that block every line passing through a unit square was first considered by Mazurkiewicz in 1916. We call such a set {\em opaque} or a {\em barrier} for the square. The shortest known barrier has length $\sqrt{2}+ \frac{\sqrt{6}}{2}= 2.6389\ldots$. The current best lower bound for the length of a (not necessarily connected) barrier is $2$, as established by Jones about 50 years ago. No better lower bound is known even if the barrier is restricted to lie in the square or in its close vicinity. Under a suitable locality assumption, we replace this lower bound by $2+10^{-12}$, which represents the first, albeit small, step in a long time toward finding the length of the shortest barrier. A sharper bound is obtained for interior barriers: the length of any interior barrier for the unit square is at least $2 + 10^{-5}$. Two of the key elements in our proofs are: (i) formulas established by Sylvester for the measure of all lines that meet two disjoint planar convex bodies, and (ii) a procedure for detecting lines that are witness to the invalidity of a short bogus barrier for the square.Comment: 23 pages, 8 figure

Generalizations of Kijowski's time-of-arrival distribution for interaction potentials

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the ``crossing state'' concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.Comment: 5 inlined figures: some typo correction

Operator normalized quantum arrival times in the presence of interactions

We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator-normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding ``tunneling time'' obtained at the transmission side of the barrier becomes independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultra-opaque, classical-like regime dominated by wave packet components above the barrier.Comment: 10 pages, 5 figures, RevTe

Rectangular-Mask Coronagraphs for High-Contrast Imaging

We present yet another new family of masks for high-contrast imaging as required for the to-be-built terrestrial planet finder space telescope. The ``best'' design involves a square entrance pupil having a 4-vane spider, a square image-plane mask containing a plus-sign shaped occulter to block the starlight inside 0.6 lambda/D, and a Lyot-plane mask consisting of a rectangular array of rectangular opennings. Using Fraunhofer analysis, we show that the optical system can image a planet 10^{-10} times as bright as an on-axis star in four rectangular regions given by {(xi,zeta): 1.4 < | xi | < 20, 1.4 < | zeta | < 20}. Since the design involves an image plane mask, pointing error is an issue. We show that the design can tolerate pointing errors of about 0.05 lambda/D. The inclusion of a 4-vane spider in the entrance pupil provides the possibility to build a mirror-only on-axis system thereby greatly reducing the negative effects of polarization. Each of the masks can be realized as two masks consisting of stripes of opaque material with the stripes oriented at right angles to each other. We call these striped masks barcode masks. We show that it is sufficient for the barcode masks by themselves to provide 10^{-5} contrast. This then guarantees that the full system will provide the required 10^{-10} contrast.Comment: 12 pages, 5 figure

Predicting the readability of transparent text

Will a simple global masking model based on image detection be successful at predicting the readability of transparent text? Text readability was measured for two types of transparent text: additive (as occurs in head-up displays) and multiplicative (which occurs in see-through liquid crystal display virtual reality displays). Text contrast and background texture were manipulated. Data from two previous experiments were also included (one using very low contrasts on plain backgrounds, and the other using higher-contrast opaque text on both plain and textured backgrounds). All variables influenced readability in at least an interactive manner. When there were background textures, the global masking index (that combines text contrast and background root mean square contrast) was a good predictor of search times (r = 0.89). When the masking was adjusted to include the text pixels as well as the background pixels in computations of mean luminance and contrast variability, predictability improved further (r = 0.91)

Integrating photovoltaic cells into decorative architectural glass using traditonal glasspainting techniques and fluorescent dyes

Photovoltaic cells can be integrated into decorative glass, providing a showcase for this renewable technology, whilst assisting in the creation of sustainable architecture through generation of electricity from the building surface. However, traditional, opaque, square, crystalline-silicon solar cells contrast strongly with their surroundings when incorporated into translucent, coloured glazing. Methods of blending photovoltaic cells into their surroundings were developed, using traditional glass painting techniques. A design was created in which opaque paint was applied to the areas of glass around underlying photovoltaic cells. Translucent, platinum paint was used on the glass behind the photovoltaic cells. This covered the grey cell backs whilst reflecting light and movement. The platinum paint was shown to cause a slight increase in power produced by photovoltaic cells placed above it. To add colour, very small amounts of Lumogen F dye (BASF) were incorporated into a silicone encapsulant (Dow Corning, Sylgard 184), which was then used hold photovoltaic cells in place between sheets of painted glass. Lumogen dyes selectively absorb and emit light, giving a good balance between colour addition and electricity production from underlying photovoltaic cells. When making sufficient quantities of dyed encapsulant for a 600 x 450 mm test piece, the brightness of the dye colours faded, and fluorescence decreased, although some colour was retained. Improvement of the method, including testing of alternative encapsulant materials, is required, to ensure that the dyes continue to fluoresce within the encapsulant. In contrast, the methods of adding opacity variation to glass, through use of glass painting, are straightforward to develop for use in a wide variety of photovoltaic installations. Improvement of these methods opens up a wide variety of architectural glass design opportunities with integrated photovoltaics, providing an example of one new medium to make eco-architecture more aesthetically pleasing, whilst generating electricity

The effect of transparency on recognition of overlapping objects

Are overlapping objects easier to recognize when the objects are transparent or opaque? It is important to know whether the transparency of X-ray images of luggage contributes to the difficulty in searching those images for targets. Transparency provides extra information about objects that would normally be occluded but creates potentially ambiguous depth relations at the region of overlap. Two experiments investigated the threshold durations at which adult participants could accurately name pairs of overlapping objects that were opaque or transparent. In Experiment 1, the transparent displays included monocular cues to relative depth. Recognition of the back object was possible at shorter durations for transparent displays than for opaque displays. In Experiment 2, the transparent displays had no monocular depth cues. There was no difference in the duration at which the back object was recognized across transparent and opaque displays. The results of the two experiments suggest that transparent displays, even though less familiar than opaque displays, do not make object recognition more difficult, and possibly show a benefit. These findings call into question the importance of edge junctions in object recognitio