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
(Off topic) left or right
This subject seems to have strayed. Let us bring it back to the shadows, where it belongs. In some countries they drive on the right. In others they drive on the left. In the sunny Mediterranean island of Malta, where I lived for a couple of years, they drive in the shade. -- Frank Evans
a peculiar sharpener
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?)
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
picture of sun tracking device
I've put a picture of what I think is a sun tracking device on my web page at linux.bbn.com/~koolish. If anybody has seen one or knows how it was used, let me know. There are no markings on it.
Re: (Off topic) Left or Right?
Mike, It would be fair to tell us which week, so that tourists would know when to avoid the aulde countrie when scheduling visits. Somehow I've lost the connection to the moving shadow edge. Except for... The only vehicular direction that seems to relate to the edge of the moving shadow is traffic flow around a roundabout. In those countries where the steering wheel is on the sinister side folks would round around the roundabout in a clockwise or dialwise direction. I.e., the left hand rule applies so that the thumb is up! On the other hand, right side steering wheeled carriages usually turn counterdialwise or antidialwise around the roundabout and the right hand rule rules. As in Britannia. I think that I have the hands, rotations and rules right, right? Knighty Knight, t The Shaws wrote: We (UK) keep to the left side of the road, so that our (normally) strongest hand is available to fight an enemy with a sword - a throwback to the days of King Arthur and his Knights I suppose. There was a rumour going round that the governmment were considering changing us to driving on the right - but they would introduce the system gradually: Bicycles and motorbikes would change on Monday Cars would change on Wednesday Lorries and Buses on Friday Mike Shaw [EMAIL PROTECTED] 53.37N 3.02W -- Tom Semadeni O [EMAIL PROTECTED] o aka I (Ned) Ames . Britthome Bounty * Box 176 Britt ON P0G 1A0 'Phone 705 383 0195 fax 2920 45.768* North 80.600* West
Re: (Off topic) Left or Right?
Troy contributed: I've heard of at least one European country that made the switch from left to right (though I forget which one), the switch took a 10 year plan. Possibly the one which swapped around mid-day some years ago - can't remember which? All traffic stopped for five minutes, during which time they slowly moved over to the other side of the road and recommenced on the 'wrong' side, which of course was now the 'right' side having left the 'right' which was now the 'wrong' side - right? I guess they chose mid-day to avoid forgetful people setting out in the morning against the flow. Tony Moss
