By Charles Douglas Wehner |
16 May 2004 |
| This is an account of the discovery of the essence of stabilized optics (also called stabilised optics, vibration-compensated optics or shakeproof lenses). The story begins in the early nineteen-seventies. The film "The Sound of Music" had been made, using a device called a DYNALENS from a helicopter. The dynalens used an oil-filled variable prism.
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| Nippon Kogaku of Japan patented the use of a BOSKOVIC PRISM for optical vibration-compensation. The author recognised that neither method would give images free of colour fringes.
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| After some deep thought on the subject, the author realised that it is in the nature of a lens to convert an angular movement into a linear one. A new law of nature had been discovered.
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The first or fundamental law. If any image-forming optical system is in a state of neutral balance about its infinity focus, it will convert all angular vibration, relative to the axis of that system, of the optical axis through that focus into parallel vibration relative to the axis of that system. |
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The beauty of the method lies in the use of existing elements of the optical system, which now serve a dual purpose. As nothing is added to the optical path, there is no degradation of the image. Further, if correct centration is assured in the absense of shake, the performance is as it was before the vibration-compensation was added. ![]() The Greeks had a word for it. ATROMEROS signified all that did not cause a tremble. An optical system constructed so as not to cause a tremble would be ATROMERIC or ATROMEROUS. One reason for the devising of a new technical term is that vibration, once introduced into an optical system, cannot be removed. It can, however, be manipulated so as to become indiscernable in many instances. Another reason is the corruption of lawyers. The term "shakeproof lens" would be used interchangeably with the word "unbreakable", leading to unnecessary lawsuits. So as this new technology is made public, we look forward to the days when optics are not only ACHROMATIC and ANASTIGMATIC, but ATROMERIC also. |
| The trick works because every lens element is in effect a continuously varying prism. The top of a convex lens is an upward-pointing prism, the centre is like an optical flat, and the bottom "prism" points down. There is no need to contrive a variable prism.
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| A negative lens has much the same properties, except that the directions are reversed. The top "prism" points downwards and the bottom one points up.
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| Simple lenses, and also simple prisms, give colour errors - the rainbow effect, known as chromatic aberration. If the lens has been corrected for this - if it is an achromat - the prismatic action will also be colour-corrected.
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Mirror systems do not need achromatisation (colour correction). These catoptrics rely on reflection. Sir Isaac Newton believed that all lens systems (dioptrics), which rely on refraction, would always give colour fringes, until Dollond proved him wrong. |
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| Here we see a simple example of the method. We have two positive lenses with an "optical hinge" at their meeting point. The front element has to be slightly oversized to allow for movement. Achromatisation is not displayed..
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| When the rear element hinges about the common focus, the centre of the image is unchanged. The front element, in neutral balance about that point, now uses its lower part and so delivers prismatic action.
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| A good starting point for atromeroptic lens design is the Cooke triplet rather than the Doppelgauss, because the central element has a very short focus, and is suitable as an atromeric element. If only tiny vibration is to be compensated, the vibration-proofing might justify the colour error.
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We will take the elements of such a three-element design in turn, and see
how the variation in parameters affects the atromerisation..
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| This is not the standard picture of an image projected by a lens, but it is not wrong to draw the analogy. The arrow represents the movement of the centre of the image away from the axis of the front element.
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| That image is picked up by the middle element. Let us assume in this design, that the negative lens is set up for one-to-one magnification. The object distance and image distance will both be twice the focal length.
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| If the negative element lifts by half the amount of the vibration, half is left. At one-to-one, MINUS one half appears in the image. The tip of the arrow has been restored to the original axis, because the one-half lift and the minus one-half cancel each other.
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By the law of the lever, a one-half lift can only take place if the fulcrum is half as far away as the object - ie. at a distance equal to the focal length of this middle element.
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| Let us now assume that the design is for a reversed telephoto objective. The object distance is now 3F, where F is the focal length of the element. The image distance is half that, giving a half-scale image.
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| The atromeric element must lift by one third of the length of the red arrow, leaving two thirds. This distance will be halved in the image, giving one third downwards - which again cancels the lift and restores the head of the arrow to the old axis.
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By the law of the lever, we again get the fulcrum F units away from the atromeric element. A similar study of a telephoto design delivers the same result.
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| The final element is fixed with respect to that old axis. It delivers the image to its final destination. As the movement has been cancelled, the centre of the original object is at the centre of the final image.
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The Embedding Law. An atromeric part, embedded in an optical system, delivers optimal compensation for small vibrations when balanced about its infinity focus regardless of the manipulation of scale of the image by the other optical elements. |
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This comes about because the dimensions of vibration are time and distance, whilst that of geometry is simply distance. Geometrical manipulation does not affect time. Thus, when the scale of an image is manipulated, there is a pro rata manipulation of the vibration contained within it.
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| When computing the requirements for geometrical correction of the image, the question arises as to whether the atromeric part should tilt or remain parallel to the other elements.
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| It is a property of simple elements that the oblique ray will cut through a "virtual lens" that is thicker - for example, root-two times at forty-five degrees. This makes the off-axis focus fall short.
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| Although the curvature is in the correct direction, the ideal curve at the virtual object of that element is a circle centred on the balance point.
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| The virtual image, however, is closer to the balance point of the atromeric part, and in the ideal case also requires a circular field - yet of much smaller radius.
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| Fortunately, the virtual object is made by the front element, which also has a parabola-like distortion. In consequence, the virtual image can for part of its extent approximate to the required curve.
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When computing the geometry of the lens, therefore, one must take the deviation of the image due to vibration into account, in exactly the same way as one would with production tolerances. The tolerances due to atromerisation that are permitted are a question of design specification. Of course, if the atromeric part were a rectilinear cluster of components, one would take the other option - and keep it parallel to the remaining elements. However, the complexity of a rectilinear element-group rules it out for all but the most expensive designs. |
| In the diagram, the front element makes two images, A and B where the former is from some close object and the latter from infinity. These become converted by the atromeric element to D and E respectively.
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But according to the second law of atromeroptics, the vibration compensation is independent of manipulations of scale. Thus, both D and E will be restored to the axis by the same atromeric element. Relative to the optical centre C of the entire structure, the images will be vibration compensated - and simultaneously in focus - at F for the infinity object, and 2F for the object at distance 2F, where F is the focal length of the entire assembly. |
The Euatromeric Law. When an atromeric optical system contains an element in neutral balance about its infinity focus, there will be zero optical vibration from an object at infinity. When the focus is shifted, by moving the entire system, to objects at other distances, there will be zero optical vibration from there also. |
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The image does not shiver because a virtual prism has been generated by the atromeric element. This follows the lens law to correct for objects at all ranges and create vibration-compensated images along the system AXIS. However, when the focus falls short of the image plane and crosses the system axis, as with an object at infinity whilst the system is focused nearer, the vibration will re-emerge in the reversed direction. Similarly, if the focus is beyond the image plane, the rays will not reach the axis before striking that image plane. Thus, for defocused objects nearer than the plane of focus some vibration will remain. The behaviour is identical to what you see when you examine one of your fingers whilst bobbing your head up and down. When your head goes up, the defocused background goes up. However, if you place another finger even nearer than the one you are concentration on, it will go down when your head goes up. We see that atromeroptics do not eliminate vibration, but emulate the behaviour of optical systems, such as the eyes, that are TRAINED ON or DIRECTED AT an object in relative motion. |
| If the front element of an atromeric system is moved forward from a position such as G to H, for close focusing, its image will be enlarged. That image will still be in the same position relative to the atromeric element, which will give the original compensation for vibration, which will now be insufficient.
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The Disappointing Law. When the front element, or cluster of front elements, ahead of an atromeric part is made adjustable for close focusing, the distance of the balance-point of the atromeric part to that atromeric part must vary in proportion to the distance of the image of the front element or cluster of elements from that front element or cluster of elements, for vibration compensatiom to be maintained. |
| Ouch! A favourite trick of opticians - front-element focusing - goes out of the window. The complexities of creating a variable balance-point spoil the simplicity of the design. So it is best to focus the assembly by moving it in its entirety. |
Fortunately, REAR-element focusing is still allowed, because the vibration compensation has already taken place before the light reaches the rear. This gives the designer some choice.
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It is important to bear in mind that the four laws are based on small angles, where the sine of an angle approaches that angle itself (in radians). It also requires that over the required deflection range there is no substantial barrel or pincushion distortion within the (curved) object and image fields. Special exceptions will arise when huge deviations, or non-standard arrangements of elements, are employed. It is of course possible to create designs where two atromeric parts are each balanced at half their focal length, and variants of this kind. Such concepts are based upon the principle that for small angles the sine of the total angle is equal to the sum of the sines, to a reasonable approximation. Such complexities are best avoided if possible.
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| The kind of mounting used depends on the application, but for two degrees of motional freedom, Cardano`s mechanism - the gimbals - will usually be employed. It can be seen that the common axis of swivel is in the optic axis. The symbolic diagram does not show this, but it is common sense. For clarity, a dot may be added beneath the hinge.
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Generally, some form of centration clamp will be required - if only for transit. For still photography, it might be an instant-return clamp, released only during exposure. For motion pictures, it may require a button to snap the lens to its central position.
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Human, and most animal, eyes blink. We are accustomed to a transient disappearance of vision for a few milliseconds. Film makers make use of this fact by means of a cut in the filming. So when the atromeric part has exceeded its allowable excursion, the cameraman may have to press a button to recentre the element. This will often pass unnoticed. |
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If a flexible band or wire, such as phosphor bronze, preferably gold plated for good electrical contact, is suspended around the mounting, it can make contact with the mounting when the maximum excursion is near. |
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In a motion-picture system, this might sound an alarm in an earpiece, to prompt the cameraman to centre the atromeric element by pressing a button. In a still camera, it might prematurely close the shutter. If there is a microprocessor in that camera, it could be programmed with "patience". So if the exposure is only 20% (over 2 stops down), it might wait in the hope that the electrical contact is broken. When the contact is broken, the timeout begins again. That "patience" might diminish as the exposure progresses. |
| Hairsprings may be fitted to the suspension - and this is particularly useful in motion-picture lenses. However, the result will be a resonance, and special procedures such as the provision of dashpots will be needed to suppress that resonance. |
One ingenious form of dashpot invented by the author consists of thin sheets of ferromagnetic material and of copper or diamagnetic material, which are interleaved with each other without touching. The ferromagnetic material is magnetised, and damping takes place due to electrical eddy currents induced in the copper. Either the magnets or the copper sheets form the counterweight. The other set of vanes is secured to the housing.
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| When a magnet is used as a counterweight, it brings the motion-control of the atromeric part within reach of either analogue or digital control. Active filter systems might be used, or digital (autocorelation) functions might adjust the frequency-response. |
When a DC deflection current is applied to the coils in addition to the vibration-compensation waveform, it becomes possible to provide remote control of framing such as in a hand-held television camera. DC shift will, however, limit the available vibration excursion.
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| What we have seen so far is that when we want to take a photograph from a vibrating or moving camera, it will not give an ideal result except with an infinitesimally short exposure.
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| During the period of exposure, the lens will smear the image along its focal plane. This effect is due to the angular vibration, which magnifies the lens movement by the law of the optical lever.
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| The first effect of atromeroptics is to convert the angular vibration into linear vibration, shown here exaggerated. Vibration-proofing is perfect only at infinity.
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| Pulling focus brings the euatromeric axis forwards onto the subject. "Eu" is Greek, and sometimes Latin, for "good" or "optimum". |
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This axis is at right-angles to the direction of vibration. The images are exaggerated, to display the principle clearly. It can be seen, therefore, that there is no more smearing, but the problem has been reduced to one of perspective error as the lens views the scene from its changing position. Such perspective error is often trivial - particularly on distant objects. There is a euatromeric point, where the vertical and horizontal axes of vibration cross. This will be along the optical axis as it was at the moment the atromeric part was unclamped, and at the focusing distance, in the systems described. Hairsprings may make this point drift, by imparting the mean thrust of the lens system to the atromeric part. Similarly, as we shall see, the inertia of the atromeric part may also cause such drift.
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| Dynamic atromerisation allows the atromeric part to continue to move in the direction that the camera is taking. The background becomes blurred, but if the lens tracks with the object, the object is sharp. |
| Static atromerisation forces the atromeric part to come to rest, so that despite the camera movement the background is sharp. Anything moving relative to that background will have motion blur. |
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Viewed from the rear, the atromeric mounting consists of a hollow tube mounted on gimbals, and with a circular weight around it to counterbalance the mass of the element.
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The question arises as to whether a gyroscope can be constructed by fitting bearings to this weight, and arranging for it to spin. |
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Alternatively, with bearings on the gimbals, the entire tube can spin. Bell and Howell of Chicago, U.S.A., patented the idea of spinning the lens in the Seventies. The disadvantage is that centration error spoils the sharpness of the image. |
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Whatever the choice, a set of coils can induce a "magnetic footprint" into the ring. Let us say that coil 1 goes N, and the "footprint" is S. Switching on coil 2 causes N to be between 1 and 2. The ring is turned by the moment acting on the "footprint". Then 1 is turned off. Then 3 is turned on - and so on. This is a linear motor. |
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A danger is that if both the rotating ring and the coil assembly are of soft iron, there may be some magnetic attraction between them that upsets the performance. Fortunately, there is a good choice of ferrites that can be used, for example as the coil-assembly core. This design is introduced for its simplicity. We can already see what kinds of features might be available on CPU-based cameras: Program 1 The user half-presses the shutter button, and the CPU delivers voltage to the coils in the order 1, 1 with 2, 2, 2 with 3, 3 and 3 with 1. This sequence speeds up, to allow the rotor to accelerate. Upon full pressure on the button, voltage is cut. The coil assembly may or may not swing free of the atromeric part to allow for movement. The centration clamp is released and the exposure takes place. During this time, the flywheel is free-spinning with no drive. The outcome is STATIC atromerisation. Such methods would allow a choice of features, but the free-spinning gyro would not be able to stabilise exposures of more than a second or two. For more serious work, it becomes necessary to invent a hollow electrically-maintained gyroscope. Here is one such example: |
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An annular pre-aged magnet has, say, its north in the middle (shown red). It is covered in resin (shown yellow) that has a few thousand volts set into it, forming an electret. Two more rings (north outside) form with this ring a magnetic bearing. |
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The outer jacket of the assembly - attached to the inner rings - has at least three electrically-conductive films coated upon it. When several hundred volts DC are applied to such a film, the electret will rotate on its magnetic bearing. Sequencing the application of voltages to the films creates a linear-motor action as before. |
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With the trend towards increasing miniaturisation, there is a need to create designs which by virtue of their simplicity can be made small. The electrostatically-driven gyroscope meets that criterion, in that there are no wound components. The disadvantage is that high voltages - albeit at low current - are present in the system. One aspect to be borne in mind is that the drive is capacitive. Whereas a system with coils will accept less current as the frequency rises, a system with capacitive drive will accept more. The starting torque will be low, but the running torque high. Another aspect is that magnets without keepers run down, as do electrets. A target life-expectancy of ten years might reasonably be set - but in the absense of standardisation of parts, repair of old equipment might prove problematical when a magnet-electret gyro is used. |
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A further requirement is to limit the burden placed upon the atromeric part by discouraging the user from creating camera-shake. Those skilled in the art of electronic design will know how to detect vibration and so RE-INTRODUCE it into the liquid-crystal display by adding it to the X and Y co-ordinates of that display. When a liquid-crystal display is not available, as with a single-lens reflex camera, ANTI-ATROMERIC techniques will be needed to make the image, complete with its viewing screen, vibrate. This forces the user to struggle to hold the equipment steady. |
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Here we see a sketch of a typical application. The objective lens has an atromeric part with two elements, in order that colour fringes will not appear. Beyond the pentaprism, the ocular lens is balanced in the reverse direction, and reintroduces vibration to the image. |
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The foregoing has put the emphasis on photographic lenses. However, when a natural law is discovered it finds application in a very wide range of fields. What have been shown above are examples of the use. |
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At the time of writing, the atromeroptic laws have still not been published. That is to say, the Dynalens and other systems gave way to the STEADICAM, which is a camera platform that holds the entire equipment steady. Professionals might in future combine atromeroptics with the Steadicam. After all, avoidance of vibration is better than "repair". The stabilisation of the optical path by dynamically balancing an existing part or parts is the essence of atromeroptics. A few attempts are being made to stabilise images by adding prisms in various ways, but there is no precedent for what was described above. In the nineteen-seventies, the author applied for patents in London and Munich. He contacted the Association of Swiss Rosskopf Watch Manufacturers (Schweizerischen Rosskopf-Verband), suggesting that their industry would soon die out due to the arrival of electronic watches. The suggestion was made that atromeric mountings might be put on the market for optical manufacturers. This would allow the slow growth of this new technology to compensate for the slow decline of the pin-pallet "Dollar Watch" - a seamless transition. There was no response from the Association, and today a search of the Internet reveals practically no mention of them - not even in an historical context. It is as if they never existed. Nevertheless, there are still components from the watchmaking "SORTIMENT" industry, such as INCABLOC shockproof bearings, that are ideally suited for the construction of atromeric mountings. An approach was made to Ernst Leitz, in Wetzlar, Germany. The negotiations lasted for several months, before they declined the offer. It is not clear what the reasons for the rejection were - but they had been taken over by Wild of Heerbrugg, Switzerland. Perhaps they had limited decision-making power. To their credit, they maintained secrecy in the matter of vibration-compensated optics, as agreed. In Britain, the author bought a house and filled it with his antique furniture, personal effects such as family photos, and at least a tonne of industrial components, ready to create industry. Amongst the components were thousands of optical parts. Before he could start work, the British government - which had destroyed the whole of British industry through blunders - decided on a course of WAR. The "DARK FORCES" that the Queen spoke of concluded that industry was not the way ahead. Instead, they would return to robbing the world in an attempt at restoring their fortunes. The author`s house was totally wrecked, and he took refuge with those things he could rescue with a good landlord in Hampstead, London. In 2002, the "DARK FORCES" themselves acquired the house in Hampstead by cheating that landlord. They threw the author onto the street in severe medical difficulties, having already secured the alibi that the DISEASE was the cause of death. Temperatures were at that time sub-zero. The quetion might be raised as to why the author was targetted. It appears that this was not the case. Instead, the "DARK FORCES" had ordained that their servants must gain experience of bestial behaviour in preparation for the Iraq war. The author, with a major illness, was a suitable victim to practice on. Barely alive, the author escaped to Europe in March 2003 - just as the Iraq war was commencing. Throughout the rest of 2003 and the beginning of 2004, the author spent his time creating web-pages of his original inventions and of the laws of nature he has discovered. The first reason is that it would be a waste to have spent a lifetime gathering knowledge and then to die with it. The second reason is that there are those who are in a position to turn such knowledge into cash. Prior to publishing these details, the author contacted the German Ministry of Industry and Commerce. As a German national, the author offered that ministry a monopoly. There was no reply, and so the details are now published worldwide as promised. The author has at the time of writing become sixty years of age, has an untreated illness and was robbed of everything by the British government. Under such circumstances, he cannot create industry alone.
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AddendumSkew25 May 2004 | |
![]() | Although not part of the atromeroptic laws, there exist methods by which skew errors in an optical system may be corrected. The following concepts from the author are believed to be unique. A right-angled roof prism will allow straight-through mirror-reversal of the image. This is because the image undergoes only a single reflection. |
An investigation of the behaviour of mirrors shows that the image will rotate at twice the angle of tilt of the mirror. This reduces the problem to one of arranging for the prism or mirror in the light-path to rotate at half the rate at which the entire equipment rotates. |
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![]() | In the diagram, A is a flywheel, B is a connecting gear and C is a tube containing the roof prism. Our first consideration is to imagine that the moment of inertia of the flywheel is infinitely greater than that of the prism and its tube. | ||||||||||||
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Under such conditions, we would expect the gear ratio to be exactly 2:1. A mathematical study of the real-world situation shows that if R is the ratio of the turning moment of the prism and tube to that of the flywheel, then: GEARING=ROOT(4+3R) This leads to the following table of results: | |||||||||||||
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![]() Here we have pounced upon the result where the ratio is three quarters. The rotational moment of the prism assembly C is low because the mass is concentrated at its centre. We deliberately concentrate the mass of the flywheel A at its periphery, however, to give a high torque-to-mass ratio. The diagram also shows the use of a pulley B. Although gear-wheels can be used, there is a danger of chatter. A third option, shown later, is the use of rollers clad in rubber or non-perishable synthetic rubber such as silicone. If the pulley is removed, the energy will be distributed as 1 unit in the flywheel and 0.75 in the prism assembly. With the pulley restored, the prism rotates at half speed, with one quarter of the energy it had before, or 3 sixteenths of a unit. Due to the 2.5-to-one transformation, the flywheel turns at 5/4 times its previous speed, with 25/16 the previous energy. Total energy is therefore 28/16, which is unchanged. Hairsprings may be used to encourage the prism to drift to a central position, but to combat resonance, a dashpot will be needed and the system must be critically damped. | |||||||||||||
![]() | Here we see a possible final design. The prism is connected by a soft roller to the flywheel. |
No attempt is made to reverse the image. This is because the long optical path has already restricted the exit pupil diameter. With modern electronics, it is just as convenient to reverse an image in the central processor. For example, the Z80 had both LDIR (load, increment and repeat) and LDDR (load, decrement and repeat). The Pentium series have a direction flag. So it is quite general with central processors that there will be no time penalty if the software must load the image in reverse. Avoidance of camera skew is, of course, better than its removal. However, there will be occasions when avoidance is impossible. | |
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(C) 1973-2004 Charles Douglas Wehner.
Use freely but do not plagiarise.