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From: Wm. S. Maddux, 75211,2555 TO: John Carmichael, INTERNET:[EMAIL PROTECTED] CC: SUNDIAL, INTERNET:[email protected] DATE: 5/6/99 2:46 PM RE: Copy of: RE: a peculiar sharpener John, Here is my interpretation of what is going on with the bead and hole shadows: First off, any attempt to estimate the center of the 'fuzzy' edge shadow of a style's edge is subject to uncertainty because of the properties of the eye and/or visual system. The eye is able to function over a range of about 8 orders of magnitude. For photoptic (not dark adapted, non-rods) vision, the range is about 6 orders of mag. To realize this large dynamic range, the visual system, VS, adjusts to overall brightness and then functions over a restricted range of RELATIVE brightness within the overall total range. The edge light- gradient is non-linear, the VS' response is non- linear, and shifts with the amount of diffuse light, from sky, and from illuminated, non-zero-albedo objects in the surroundings of the dial. Finding the geometric 'center' of the 'fuzz' is not in the cards. As for the bead in the hole, I don't think that diffraction effects play a major role. Think of the ring aperture as producing many fuzzy circular (1/16 in. pinhole images) of the sun's 1/2 degree disk, each with its center on a 3/16 inch diameter circle. The result will be a ring of light. Because of the curve of the ring, these circles will overlap more on the inner edge of the ring than on the outer edge. A cross-section of the 3-D light intensity distribution will resemble that of a miniature volcanic mountain, with a fairly deep steep-walled central crater and sloping sides that at first drop steeply, but then taper off into the general light level. Since the plate that the hole is drilled through casts a shadow on the immediate surround, the eye sees the ring as bright, and VS response to lower light in the center is reduced, making it look darker in contrast. In the case of the bead alone, the analemma plate is in full sun, but the 1/8 in. bead's penumbral shadow is seen in relative contrast to that, while any small umbral center is not very noticeable on the VS' sliding scale of sensitivity. Sciagraphically, Bill Maddux
