R: Copy of: RE: a peculiar sharpener
Hello Bill, your description of the shadow produced by the system gnomon-bead ( sent to the List almost one year ago ! ) coincide exactly with my conclusions I am sorry: if I had read your message I would have let notice the coincidence , but I've not received the messages sent in the first days of May 99 for a breakdown to my modem. Now I have looked for peculiar sharpener in the archive for the Sundial Mail List and I have found, late, some interesting considerations Best wishes, Gianni your description,
Copy of: RE: a peculiar sharpener
-- Forwarded Message -- From: Wm. S. Maddux, 75211,2555 TO: John Carmichael, INTERNET:[EMAIL PROTECTED] CC: SUNDIAL, INTERNET:SUNDIAL@RRZ.UNI-KOELN.DE 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
Re: a peculiar sharpener
Message text written by Jim Cobb I remember many years ago during a partial eclipse looking at the shade under a young tree. On the ground was a profusion of pinhole images of the eclipsed sun, formed by the random gaps between the leaves. Subsequently I've read of this effect in astronomy magazines. It's worth looking for, if you get the chance. I have seen this too - it was almost surrealistic! Chuck
Re: a peculiar sharpener
Hi Charles: Your explanation makes a great deal of sense, and it is easy to understand! There is so much e-mail coming in on this question, that I think I'll wait to hear what everybody has to say until I make up my mind as to what is going on. Because nobody seems really clear as to what the exact mathematical explanation is, (or an easy-to-use formula that predicts bead and hole diameters based on desired focal length), then maybe the best way to design bead-in-a-hole styles is by experimentation, not math. (at least for mathematically challenged people like me!) Thanks, John Carmichael The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. snip I don't know why this works, but it does. Can any of you explain this? John Carmichael Although there may be some slight effect due to diffraction, it is negligible. The open ring between the bead and the edge of the hole can be described another way, as follows: The open ring is comprised of an infinite number of round holes, 1/16th inch in diameter, each with it's center on the circumference of a circle 3/16ths inch in diameter which is coaxial with the bead and the hole. Each of these 1/16th inch holes acts as a shadow sharpener (pinhole) which projects an image of the sun onto a surface. On the surface, there are then projected an infinite number of images of the sun arranged in a circle. The images overlap each other to form a bright ring with a dark center. As the bead/hole aperture is moved further away from the surface, the images of the sun will grow larger, overlapping more and more which causes the dark center to diminish in size. If the aperture is moved a large enough distance away, the dark center will disappear and the infinite number of sun images will almost merge into a single image of the sun. I say almost, because the centers (indeed any point on the sun) will still form a ring 3/16ths inch in diameter. Does that make any sense? Charles
Re: a peculiar sharpener
The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. snip I don't know why this works, but it does. Can any of you explain this? John Carmichael Although there may be some slight effect due to diffraction, it is negligible. The open ring between the bead and the edge of the hole can be described another way, as follows: The open ring is comprised of an infinite number of round holes, 1/16th inch in diameter, each with it's center on the circumference of a circle 3/16ths inch in diameter which is coaxial with the bead and the hole. Each of these 1/16th inch holes acts as a shadow sharpener (pinhole) which projects an image of the sun onto a surface. On the surface, there are then projected an infinite number of images of the sun arranged in a circle. The images overlap each other to form a bright ring with a dark center. As the bead/hole aperture is moved further away from the surface, the images of the sun will grow larger, overlapping more and more which causes the dark center to diminish in size. If the aperture is moved a large enough distance away, the dark center will disappear and the infinite number of sun images will almost merge into a single image of the sun. I say almost, because the centers (indeed any point on the sun) will still form a ring 3/16ths inch in diameter. Does that make any sense? Charles
Re: a peculiar sharpener
[EMAIL PROTECTED] (John Carmichael) wrote: Actually, nobody has mentioned this yet but as a kid I remember that we used a pinhole to look at the image of a solar eclipse. Now I know that it is called a shadow sharpener... I remember many years ago during a partial eclipse looking at the shade under a young tree. On the ground was a profusion of pinhole images of the eclipsed sun, formed by the random gaps between the leaves. Subsequently I've read of this effect in astronomy magazines. It's worth looking for, if you get the chance. Jim --- -- | Jim Cobb | 540 Arapeen Dr. #100 | [EMAIL PROTECTED] | | Parametric| Salt Lake City, UT | (801)-588-4632 | | Technology Corp. | 84108-1202 | Fax (801)-588-4650 | --- -- I threw spot remover on my dog and he disappeared. -- Steven Wright
Re: a peculiar sharpener
Earlier I wrote: I remember many years ago during a partial eclipse looking at the shade under a young tree. On the ground was a profusion of pinhole images of the eclipsed sun, formed by the random gaps between the leaves. It occurs to me that I should have mentioned that the tree's shadow lay in large part on a sidewalk. The pinhole images need to be cast on a pretty good surface to be easily visible. Jim --- -- | Jim Cobb | 540 Arapeen Dr. #100 | [EMAIL PROTECTED] | | Parametric| Salt Lake City, UT | (801)-588-4632 | | Technology Corp. | 84108-1202 | Fax (801)-588-4650 | --- -- Every program has at least one bug and can be shortened by at least one instruction -- from which, by induction, one can deduce that every program can be reduced to one instruction which doesn't work.
Re: a peculiar sharpener
HI patrick: Thanks for your feedback. Actually, nobody has mentioned this yet but as a kid I remember that we used a pinhole to look at the image of a solar eclipse. Now I know that it is called a shadow sharpener... There is one part of your message that I don't understand: What I find interesting about the effect is whether or not it was used in the design of meridian lines where a spot of light crossing a marked meridian line was used to establish all sorts of astronomical parameters. I suspect the variation in image distance was too great. Thanks again, John Carmichael Tucson
Re: a peculiar sharpener
Dear Dan: Here in town we have a funny little store called the Beadshop. The bead that I used was of solid brass with a tiny 1/32 inch hole clear through. I passed a thin brass wire through the hole and cemented it there with epoxy. I fixed the wire to brass nuts and bolts which were in the 1/16 inch thick (#14 grade) brass plate through which I drilled the 1/4 inch hole, being careful to center the bead exactly. John Carmichael Tucson Hello dialists: Three years ago I built an equitorial interactive mechanical heliochronometer of brass and wood based on the design described in chapter xII, pgs. 193-202 of the Mayall's book. The heliochronometer consists of four basic parts: base, dial plate, alidade or sighting instrument, and analemma. The alidade is attached to the dial plate so that it can be rotated about its center, which is coincident with the center of the dial plate. Consisting of a flat plate, the alidade has two fixed upright arms perpendicular to the dial plate. One arm contains the style or nodus, the other the analemma. The Mayall's suggest that the style or nodus may be either a simple pinhole (a shadow sharpener), the intersection of two crosshairs, or a bead centered inside of a small hole. They didn't say which type is better, however. To determine this, because I didn't know the necessary optical mathematics, I conducted over thirty different experiments using all sorts of hole, crosshair and bead diameters. The objective, of course, was to find the style which cast the smallest point of light or shadow onto the analemma. The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. This arrangement somehow has the ability to sharpen the shadow of the bead. I don't know how this works, but it does. It probably has something to do with the wavelength of light or diffraction. My experiments showed that this effect only worked for a style with these dimensions; larger or smaller beads, holes or gaps did not exhibit this strange focusing phenomena. I don't know why this works, but it does. Can any of you explain this? John Carmichael p.s. I believe I sent photos of this style on my heliochrometer to several of you to whom I sent copies of my manual (Roger, Ross, Susan, Harold, Fred?) John I wonder if you could tell me how you suspended the bead with the wires? Seems like a good bit of fine construction. What was the bead made off? I am tempted to make such an item to use with my dial. Thank you. Dan Wenger Daniel Lee Wenger Santa Cruz, CA [EMAIL PROTECTED] http://wengersundial.com http://wengersundial.com/wengerfamily
RE: a peculiar sharpener
Hello Art: Don't forget that even though I used a 1/4 hole, most of that hole space is occupied by a 1/8 inch bead. So, in effect, what we have is a small 1/16 th inch donut-shaped ring of light around the bead. John Carmichael Tucson John Carmichael wrote: The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. And Richard M. Koolish calculated: The linear diameter of the diffraction spot (Airy disk) produced by a pinhole of a given diameter is: spot = (2.44 * wavelength * focal_length) / diameter The optimal size is where spot = diameter, so: diameter * diameter = (2.44 * wavelength * focal_length) diameter = sqrt (2.44 * wavelength * focal_length) An example of a pinhole for a distance of 100 mm and a wavelength of 550 nm is: diameter = sqrt (2.44 * .000550 * 100) = sqrt (.01342) = .366 mm Using a distance of 24 inches = 610 mm, this becomes 0.9 mm = 1/32 inch, still several times smaller than John's hole. I think the explanation lies in simple geometrical optics. Imagine putting your eye where the shadow is being cast and looking back toward the style and the sun. I would like to suppose that the distance to the style was something closer to 14 (subject to objection and correction from John), so that the image of the sun would be just eclipsed by the 1/4 inch bead, giving a black shadow at the center. Just a little off-center, an arc of the sun would show around the bead, so the brightness would grow, but only until the disk of the sun runs into the edge of the hole. Thereafter the brightness would decrease slowly until the sun is entirely outside the hole. This would lead to a shadow with a diameter-at-half-brightness of about 1/16 inch, within a diffuse bright field with diameter on the order of 1/4 inch. The size of the shadow is reduced at the cost of reducing the contrast with the surrounding lighted area. The principle is much the same as a sundial that images the sun through a pinhole: a sharper image is a dimmer image. --Art Carlson
RE: a peculiar sharpener
John Carmichael wrote: The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. And Richard M. Koolish calculated: The linear diameter of the diffraction spot (Airy disk) produced by a pinhole of a given diameter is: spot = (2.44 * wavelength * focal_length) / diameter The optimal size is where spot = diameter, so: diameter * diameter = (2.44 * wavelength * focal_length) diameter = sqrt (2.44 * wavelength * focal_length) An example of a pinhole for a distance of 100 mm and a wavelength of 550 nm is: diameter = sqrt (2.44 * .000550 * 100) = sqrt (.01342) = .366 mm Using a distance of 24 inches = 610 mm, this becomes 0.9 mm = 1/32 inch, still several times smaller than John's hole. I think the explanation lies in simple geometrical optics. Imagine putting your eye where the shadow is being cast and looking back toward the style and the sun. I would like to suppose that the distance to the style was something closer to 14 (subject to objection and correction from John), so that the image of the sun would be just eclipsed by the 1/4 inch bead, giving a black shadow at the center. Just a little off-center, an arc of the sun would show around the bead, so the brightness would grow, but only until the disk of the sun runs into the edge of the hole. Thereafter the brightness would decrease slowly until the sun is entirely outside the hole. This would lead to a shadow with a diameter-at-half-brightness of about 1/16 inch, within a diffuse bright field with diameter on the order of 1/4 inch. The size of the shadow is reduced at the cost of reducing the contrast with the surrounding lighted area. The principle is much the same as a sundial that images the sun through a pinhole: a sharper image is a dimmer image. --Art Carlson
RE: a peculiar sharpener
Hello All, The discussion about 'shadow sharpeners' is interesting. When diffraction was mentioned I wondered if a 'double-slit' diffraction apparatus and the resulting interference pattern could be used as (or with) a vernier scale to further increase resolution... I'll have to play with this! Chuck
Re: a peculiar sharpener
On Wed, 5 May 1999, Phil Pappas wrote: Hello dialists: I conducted over thirty different experiments using all sorts of hole, crosshair and bead diameters. The objective, of course, was to find the style which cast the smallest point of light or shadow onto the analemma. The design which worked the best was a 1/8 inch spherical bead, suspended by thin brass crosswires, in the exact center of a 1/4 inch round hole. (The style was about 24 inches from the analemma). A very curious thing happens with this type of style. The bead alone, by itself, casts a shadow that was twice as big as the bead; but when the 1/8th in. bead is in the center of a 1/4 hole, with a space of 1/16th of an inch between the bead's edge and the hole edge, the bead's shadow miraculously sharpens into a tight, dark shadow that is only 1/16th of an inch in diameter, smaller than the bead itself The wires which keep the bead suspended in the middle of the hole are so thin that they don't cast a visible shadow onto the analemma. At first glance, this sounds like you're creating a sort of zone plate lens, relying upon diffraction, as you suggest. I'll have to play with this a bit - I can see lots of applications! Since the alidade is always rotated so the light path is on axis, the bead is always centered in a circular aperture. That being the case, a flat disk should work as well. I'm thinking of printing an image if the bead-in-ring style onto transparency film with a laser printer. That way, we can try many combinations without the effort of machining a finished product each time. For a final design, the brass parts have much more class, and never get dirty or scratched! Dave
Re: a peculiar sharpener
Patrick Powers wrote: It is simply the pin hole camera effect again. Light passing through any small aperture is focused . As the hole's size is changed the focusing parameters are changed too. So with a fixed distance from hole to plate there will be one size that works. A different size would be needed for different image distances. The pinhole doesn't really do any focussing. It allows a small beam of light from a point on the subject to travel to the image. The fact that the pinhole is small allows small areas of the subject to be sampled and therefore produce a reasonable copy of the subject, without mixing different points on the subject too much. However, the light doesn't pass through the pinhole, or any aperture, without being affected by diffraction, which causes the image of a point source to turn into a diffraction pattern consisting of a central disk surrounded by alternating dark and bright rings. For a circular aperture, the linear size of the diffraction disk is determined by the size of the aperture, the distance to the image, and the wavelength of light involved. One common theory says that the smallest image is produced when the diffraction disk is the same size as the pinhole. The linear diameter of the diffraction spot (Airy disk) produced by a pinhole of a given diameter is: spot = (2.44 * wavelength * focal_length) / diameter The optimal size is where spot = diameter, so: diameter * diameter = (2.44 * wavelength * focal_length) diameter = sqrt (2.44 * wavelength * focal_length) An example of a pinhole for a distance of 100 mm and a wavelength of 550 nm is: diameter = sqrt (2.44 * .000550 * 100) = sqrt (.01342) = .366 mm The zone plate does have a focussing effect due to the interference between the light coming from the various zones. For an explanation see: http://www.freeyellow.com/members6/glsmyth/zone_Plate.htm http://www.stanford.edu/~cpatton/pinhole.html
