THE YOLO REFLECTOR

Arthur S. Leonard

-Figure 1-

     The Yolo Reflector is an unobstructed reflecting telescope consisting of two concave mirrors, both tilted relative to the approaching light path, and having the general configuration shown in Figure 1. Many variations on this basis design are possible, depending on aperture, focal length, and optical excellence desired.

     The design of the Yolo optical systems are based on the following general principles:

1.     When a mirror or lens in an otherwise perfect optical system is tilted, a wave-front aberration, or error, is introduced into each ray traversing the system. The magnitude of this error, in terms of path-length difference,  w, may be expressed as follows:(1)*

where the  C's  are constants whose values depend on the amount of convergance or divergance of the cone of rays striking the surface, the index of refraction (if a

lens surface is involved), and the radius of curvature of the surface; is the angle of tilt of the optical axis of the surface relative to the approaching central ray; and 

z  and designate the point (in polar coordinates) where the ray in question strikes the optical surface.

____________*References are listed at the end of the paper.

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2.     Because of the cyclic nature of the individual terms (proportional to ,

, etc.), it is possible, by tilting  N elements (mirrors or lenses having curved surfaces), and each tilted through the correct angle and having its tilt-axis oriented in the proper direction, to make  N-1  of the terms cancel out completely.

3.     By applying a properly designed warping harness to one of the mirrors of the

system, acceptable control or cancellation of the residual astigmatism ( terms) can be affected.

4.     If the radii of curvature of the two mirrors are made great enough in comparison with the aperture of the instrument, only the first two terms in the infinite series indicated by Eq. (1) will be large enough to require cancellation.

     The first term in the series (the term) is coma and the second, astigmatism. In the Yolo designs the tilt angles are adjusted to make the coma term of the secondary mirror just cancel the coma of the primary, and the astigmatism terms from the two mirrors are taken care of by some additional stratagem. If a third tilted element, such as a lens of long focal length and which itself may introduce a small coma term, is employed, the tilts of the two mirrors may be altered slightly so as to cancel this small additional amount of coma.

     With small apertures and relatively long radii of curvature, the residual uncompensated tilt-aberrations (mainly astigmatism, in this case) may be so small as to be tolerable. In this case no additional optical or mechanical device is necessary. With slightly larger apertures and higher standards of optical excellence, the addition of a small cylindrical lens or a tilted spherical lens of relatively long focal length, located in the light path a

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short distance ahead of the focal plane, gives a very satisfactory instrument. Another variation employs a tilted simple lens of very long focal length located in the light path ahead of the primary mirror. Where reasonably good optical performance is required, all of these designs are limited to rather small apertures and rather long focal lengths.

     For instruments of large apertures and top optical performance, one or the other of two additional stratagems must be employed. Either the surface curves of one or both mirrors must have predetermined amounts of astigmatism figured into them, or a properly designed and adjusted warping harness must be applied to one of the mirrors.

     Although the equations and comments contained herein may be applied to more than one of the variations just described, the bulk of the material of this paper is concerned with the harness-warped-secondary Yolo reflector.

General Equations

     The effective focal length,  F, is given as follows (see Figure 1):

where  R1  and  R2  are the radii of curvature of the primary and secondary mirrors, respectively, and  S  is separation distance (slant-distance) from the center of the primary to the center of the secondary.

     Equation (3) gives the diameter of the illuminated area of the secondary,  D2:

where  D1  is the illuminated aperture of the primary.

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     The slant distance,  T, from the center of the secondary to focal point of the system is given by Eq. (4):

Finally, the relationship between the angles of tilt of the two mirrors is given by Eq. (5):

where  A  and  B  are the angles of deflection of the central ray by the primary and secondary mirrors respectively (see Figure 1).

     Experience with the design of the light-baffle system for the Yolo reflector has shown that by designing the optical system to bring the focal point well back of the plane of the primary mirror, the "muffle" (that part of the light-baffle system which is located forward of the secondary mirror) can be shortened very appreciably. It is recommended, therefore that  T  be made about 1.2 times  S. When this condition is combined with Eq. (4), the following is obtained:

     Although  R1  and  R2  need not be made equal, in most practical designs they will turn out to be not greatly different; and there is no good reason why

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they should not be made the same. Furthermore, when the warping harness is placed on the secondary mirror (see "The Mirror Warping Problem," ahead) other conditions dictate that the secondary mirror blank should be nearly the same size as the primary. If we make the two mirrors the same diameter and the same radius of curvature, then one grinding tool and one pitch lap will suffice for both. This represents an appreciable saving in time and expense in constructing the telescope and is, therefore, recommended. If  R1  and  R2

are replaced by the single quantity,  R, and  T  is made equal to 1.28S, Eqs. (2) through (6) reduce to the following:

Parabolization of the Primary Mirror

     Theoretically, the primary mirror should be a paraboloid, and the secondary, an hyperboloid. Both mirrors have such long radii of curvature, however, that neither one deviates very much from a perfect sphere. In Yolo reflectors of small aperture and moderately long focal length, this deviation is practically undetectable, and instruments employing spherical mirrors will show no need for correction. However, instruments of eight-inches aperture or larger, made with spherical mirrors, will be found to be under-corrected by an appreciable amount. This defect can be eliminated by a small amount of parabolization applied to the primary mirror only.

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     The amount of parabolization,  Y, which when applied to the primary mirror, will correct for both mirrors, is given by the following expression:

     When  R1  is equal to  R2  and  T  is 1.2 times  S, the following is true:

     This means that the primary mirror should be parabolized by 416 percent. Although this might sound like a lot of parabolization, in actual amount it is quite small and will be

difficult to measure. To test for this amount of parabolization, we recommend either a caustic tester or a null test such as that proposed by Dall(2). Another alternative is to have the secondary mirror aluminized and then mount both mirrors in the telescope tube and test on a bright star with a high-power eyepiece. This method will require good seeing and may be much less convenient than a shop test, but it is very effective in obtaining the right amount of overall correction for the system.

Design Procedure

     Although the design procedure to be described here may seem somewhat unorthodox, it has the effect of forgiving the telescope maker for some of his mistakes in meeting tolerances or allowing him to just about ignore them. The first step, after the aperture has been decided upon, is to select a good value for the effective focal length,  F. The few Yolo reflectors which have been

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built (or started) to date have been designed as f/15 and f/17 instruments. Throughout this paper reference will be made to two of these, an 8-inch f/15 design described very briefly in Sky and Telescope (3) , and a 12-inch f/17 design currently under construction for the Sacramento Valley Astronomical Society Observatory at Colfax, California. Although there seems to be no inherent reason why fairly short focal lengths should not be satisfactory, the prospective telescope maker is cautioned to not try anything much shorter than about f/12 or f/10 until some Yolo designs of these focal ratios have been built and thoroughly tested.

     With values for  D, and  F  decided upon, values for R, D2,  S, and  T  are calculated, using Eqs. (7), (8), (9), and (10). Next, a scale drawing is made showing the two mirrors and the light-path, much like Figure 1. The secondary mirror blank is located so that it clears the parallel bundle of rays going to the primary by about one-twentieth of its diameter. This, then, permits angle,  A, to be measured or calculated. With this known value for  A, a value for angle,  B, is calculated, using Eq. (11). This permits the focal point to be located and the outline of the light-path to be drawn to scale. Following this, the system of light-baffles is designed (see "Light-Baffle System," ahead) and drawn to scale.

     At this point we are ready to start work on the construction of the telescope itself. The first step here is to rough-grind both blanks to the desired radius of curvature, thin-down the secondary blank (if this has been decided upon) and smooth up the backs of both blanks until they are reasonably flat and parallel to the front surfaces. Next, the mirror cells and warping

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harness are constructed and fitted to the glass blanks. After this has been completed, the mirror blanks are fine-ground and polished.

     After the mirrors have been tested and found to have the desired surface curves, the warping harness is tested with the secondary mirror in the test set-up shown in Figure 4. After the warping harness has passed its test, the radii of curvature of the two mirrors are measured carefully, and a second design is made, based on the measured values of the radii of curvature of the two mirrors as they have actually turned out, Eq. (6). Usually, the new value of mirror-separation,  S, will turn out to be not greatly different from the first calculated value, and the plans as first laid out can be altered fairly easily to conform to the new values.

     The telescope tube and baffle system is constructed next, based on this second design. Finally, after the tube has been built, the actual separation distance,  S, is measured, and the angle  B, is calculated from measurements of the primary mirror relative to the line running from the center of the eyepiece tube to the center of the secondary mirror. With these final values for  S  and  B, a third design is calculated (mainly the angle, A) using Eq. (5). Final collimation of the instrument is carried out according to this final design.

The Mirror-Warping Problem

     The purpose of the warping harness is to produce, by mechanical flexure, a displacement of the mirror surface which is everywhere equal and opposite (to within acceptable optical tolerances) to the wave-front aberration, astigmatism. The aberration, astigmatism, is given by the following equation:

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This equation tells us that the amount of flexure should be proportional to the square of the distance from the center of the mirror and in going around the edge of the mirror (say clockwise) the displacement should take the shape of a sine-curve and it should go through two complete cycles (two maxima and two minima) in going once around the mirror.

     If we were to balance a mirror blank, face-up, on a small rigid support located under the center of the mirror and then hang two equal weights from the edge of the blank at opposite sides, the glass would bend under the load as a simple beam. The following formula gives the flexure,  h, for a beam so supported and loaded:

where  Kh  is a quantity which is determined by the force applied and other factors,  Z  is the radial distance from the center to the point in question and  r  is one half the diameter of the mirror blank. This equation tells us that in the central part of the mirror the flexure will be proportional to  Z2, but out toward the edge it will flatten out a little compared with this curve. This suggests that as far as the  Z2  feature of the astigmatism formula is concerned, our flexed mirror will follow the desired curve fairly well in its central part, but out toward the edge it may deviate a little from the desired curve.

     If we should support the mirror blank at two points at opposite sides at its outer edge instead of at its center, and then hang our two equal weights at points midway between the two points of support (90° each way from the

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support points) the edge of the mirror will be flexed upward over the two support points, and downward under the other two points, midway between. In going once around the edge of a mirror so loaded we will encounter two high areas (maxima) and two low areas (minima). Although the curve may not be a perfect sine-curve, it will be a fair approximation to such a curve.

     The first warping harness to be constructed was designed to apply flexure forces to the edge of the mirror blank in just this way - two "pushes" and two "pulls". Tests of this device in the optical shop showed it to do a fairly good job on a 6-inch-diameter mirror everywhere except in the immediate vicinity of the the pressure-points, where the flexure was found to be too great. This is just the opposite of what might be expected from a consideration of just the Z2 and Z3 features of the flexure curve. It indicates that other factors are acting to increase the curvature of the mirror blank in the areas where the simple beam formula says the curvature might be found to be a little too small.

     Another way of looking at the problem is to consider the actual flexure curve as we go around the edge of the mirror (in contrast to going across the face of the mirror). From this point of view the actual flexure curve peaks too sharply at the maxima and minima (as compared with the desired sine-curve shape). A rather obvious solution to this difficulty is to distribute the loads at the edge of the mirror as compared with the single-point design. To carry out this idea, a short bar was placed under each of the four pressure members and each of these divided the load equally and distributed it to two points separated 30° apart around the edge of the mirror.

     The original warping harness was modified to employ this stratagem and then tested on a 6-inch-diameter mirror. The final design of this warping

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harness is shown in Figure 2. As far as could be determined by sensitive tests in the optical shop, this warping harness was completely satisfactory in every respect. Although the warping harness for the SVAS telescope shown in Figures 3a and 3b is more sophisticated in its entirety, it employs the same basic pattern of load distribution.

     A second stratagem, which can be used to reduce the excess deflection of the mirror surface in the immediate vicinity of the pressure points, is to reduce the thickness of the mirror blank. The total deflection of the mirror surface at any given point is largely due to bending of the mirror blank; but in addition, and to a lesser extent, is due to shear-action. The deflection due to shear-action varies directly as the applied load, inversely as the thickness of the mirror, and builds up rather rapidly as we approach the pressure point. The deflection due to bending, on the other hand, varies inversely as the square of the thickness. A moderate reduction in thickness will, therefore, result in a rather large reduction in the force required to bend the mirror; and this will result in reduction of the shear-action component of the total deflection at each point on the mirror surface.

     Even if we were to make the mirror blank wafer-thin, the deflection of the mirror surface would not fit the desired curve perfectly, so we should not try to carry this idea to an extreme. If we should make the mirror blank too thin, the optician would have difficulty in controlling the surface curve of the mirror to within the desired tolerances. In order to give some idea as to what is recommended in this respect - the 12.5-inch-diameter pyrex blank for the secondary of the SVAS 12-inch Yolo was thinned down from the standard 2.125-inch thickness to 1.75 inches.

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     The third stratagem which can be employed to eliminate localized excess deflections produced by the warping harness is to use what might otherwise considered an oversize glass blank and thus move the pressure-points on the glass well outside of the area of the mirror which is used to reflect the cone of rays of light. This stratagem has the further advantage of relieving the optician of some of his working tolerances and making an optical surface with a fairly bad turned edge perfectly acceptable - as long as the turned part of the edge does not extend too far in from the edge of the blank.

     This device has the disadvantages that it increases the cost of the glass blank and it makes necessary larger angles of tilt in the design. Although larger tilt-angles result in larger tilt-aberrations (which are compensated for in the Yolo design) we should charge only a small fraction of this disadvantage against this idea since the larger tilt-angles reduce very appreciably the problem of baffling out the unwanted stray light which might get into the eyepiece. Although the warping harness might be applied successfully to either the primary or the secondary mirror, the increase in the cost of the blank resulting from the employment of this stratagem will be much less if secondary is warped rather than the primary. Furthermore, if the amount of this increase in blank diameter is chosen properly, the diameter of the blank for the secondary will be equal to that of the primary. When this is done, one grinding tool and one polishing lap will suffice for both mirrors; and the economics from this may more than offset the added cost of the increased diameter of the secondary blank. It is for this reason that we recommend that the warping harness be applied to the secondary rather than to the primary mirror.

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Design of the Warping Harness

       And Mirror-Mount       

     The principal structural part (or parts) of the warping harness consists of either a pair of crossed beams, as shown in Figure 2, or an x-member, as shown in Figure 3a. It should be capable of providing four equal forces - two pushes and two pulls - equally distributed (90° apart) around the edge of the mirror. The four forces will be equal if, in the crossed beam design, the two beams are pivoted at their midpoints or, in the x-member design, opposite arms are of equal lengths. Preferably, all four arms should be of equal length. Tolerances for lengths of the arms have not been calculated, but it is felt that if reasonable care is exercised in laying out the lengths of the four arms, this specification will have been met satisfactorily.

     The force required to warp a glass mirror has not yet been measured or calculated. As a result we can only give a rough value for the strength requirements of the warping harness. The force (at each of the four points on the edge of the mirror) required to bend the mirror is given by the following formula:

where  P  is the required force,  K  is a constant which depends primarily on the modulus of elasticity of the glass,  t  is the thickness of the glass blank,  D2  is the calculated illuminated diameter (not the diameter of the glass blank), and  wa  is the amount of astigmatism which must be produced

Fig 3A

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by the warping harness. This is given by the following equation:

where U is the calculated separation between the artificial star and eyepiece to be used in the test set-up for checking the performance of the warping harness in the optical shop, and is given by Eq. (19).

     The weight of the warping harness shown in Figures 3a and 3b is carried by a thin sheet-metal spider and a set of counterweights. With this design the actual weight of the warping harness is unimportant so far as flexure is concerned. With the design shown in Figure 2, however, the total weight of the harness is carried by the mirror. This will produce unwanted deflections, or errors, in the surface curve of the mirror. In order to

keep these errors to a minimum, the warping harness should be designed as light as possible. Lightness could be achieved by constructing the harness out of high-strength aluminum alloy; but it is felt that the high coefficient of thermal expansion of aluminum alloys might make this material unsatisfactory for this application. For this reason steel is preferred as the material for the warping harness. In order to avoid excessive weight with steel, some guide lines are needed.

     The warping harness shown in Figure 3a was made of annealed mild steel. Assuming a yield strength of 40,000 lb per square inch and dimensions as measured, it should have been capable of sustaining a load of about 250 lb at the ends of each of its four arms. Substituting this value for  P  and putting the known values for  t,  D2, and  wa  for this unit into Eq. (14), a value of K = 14.5x106 lb/in3 is obtained. This warping harness was tested

Figure 3B

Figure 2

The two angles indicated in the Plan View are 15° and 30°.The text between the two views reads "Pressure pads".The text below the isometric drawing, between the two detail drawings reads "Relieved with oversized drill".The text below the rightmost detail drawing reads "All pivot joints of similar construction".

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on a 12.5-inch mirror and found to be adequately strong. A value of  K  equal to 14.5x106

will, therefore, give a maximum force that the warping harness need be able to provide. The actual working force needed to produce the required amount of flexure in a pyrex mirror is considerably less than this.

     In order to keep the weight of the warping harness to a minimum, the cross-beams or x-member should be designed to have the material of that member stressed to its yield strength when a load of this magnitude or a little less is applied to the ends of each of its four arms. If the crossed-beams or x-member is made of annealed, or hot-rolled mild steel, this condition will be met if the maximum width (at midsection)  b, and the depth, or thickness,  a, conform to the following equation:

where  D  is the actual diameter of the mirror blank.

     For small telescopes where only a small amount of warpage will be sufficient, a simple design of harness which contacts the glass blank with four small circular shoes should be satisfactory. These shoes should be articulated, or pivoted so that they can seat themselves well on the surface of the glass. In larger telescopes, where larger amounts of astigmatism must be neutralized, the shoe design shown in Figures 2, 3a, and 3b should be employed. These shoes have two contact areas each, separated by a distance which subtends an angle of 30° at the edge of the mirror blank. The force from the crossed-beams or x-member is applied to the midpoint of each shoe which, in turn, divides it equally between its two contact areas. Each shoe is pivoted or articulated so that it

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can seat itself properly on the surface of the glass. The forces developed in the crossed-beams or x-member are transmitted to the shoes by tension or compression-struts.

     In the crossed-beam design, the amount of astigmatism provided by the harness is varied by merely turning the pivot screw at the midpoint of the two beams (see Figure 2). In the x-member design, adjustment is accomplished by merely tightening a single screw against one of the compression struts. (see Figure 3a). In both of these designs the warping harness contacts the glass at eight points and the linkage is such that the applied force is the same at all points, no matter what its magnitude might be.

     One of the requirements of the warping harness is that it should hold its adjustment more or less indefinitely. When we say "hold" we mean that flexures should remain constant to within less than one-millionth of an inch. Since the forces involved are considerably more than the weight of the mirror blank, and since one-millionth of an inch is a much closer tolerance for mechanical parts than we are accustomed to dealing with, some new precautions must be observed. Since the pressures in the system will normally take up all play at the joints, the main precautions to be observed are to be sure that all joints are fitted well and that no material is used in the harness which might creep or otherwise yield slowly to the forces. One joint in particular which is important is the joint between the shoe and the glass blank. In order that this joint should fit well, the shoe should be lapped-in against the glass. This can best be done after the mirror is rough-ground or during fine-grinding stages. This should be done without any abrasive between the metal shoe and the glass. If abrasive is used, the contact areas will usually turn out to have turned-down edges.

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     The most that should be put between the metal and the glass is a single sheet of onion-skin paper. A material such as sheet cork should not be used between the metal and glass because, under the existing pressures, it will yield slowly and thus make the harness lose its adjustment. All the articulated joints, or pivot points in the warping harnesses shown in Figures 2 and 3a consist of one-eighth-inch steel balls pressed into drilled recesses in mild steel members. In order to facilitate assembly, the balls were soldered to one of the members at each joint, care being taken not to overheat the balls to the point of discoloring them in the soldering operation. It is felt that this construction is preferable to sharpened points, because with small points, pressures may easily reach the yield strength of one of the materials of the joint thus permitting plastic flow to take place.

     Even though the areas of plastic flow may be quite small, they are still subject to a small amount of creep in the metal, and in time, may allow the warping harness to get out of adjustment.

     One more adjustment - rotation - must be provided. In order to obtain satisfactory cancellation of the astigmatism, not only must the tension in the warping harness be adjusted to within about one-half of one percent, or less, of the required magnitude, but the phase, or rotation of the warping harness must be corrected to within about one-tenth of a degree. Provision for this adjustment can be made by attaching the secondary mirror-mount to a circular plate (parallel to the mirror blank) and then attaching this plate to the telescope tube so that it can be rotated a few degrees in either direction within its plane.

     So far, we have spelled out requirements to be met by the warping harness. Since the mirror blank is a partner in this warping operation, it too must be

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manufactured to close tolerances. Its modulus of elasticity must be quite uniform throughout, it must be closely circular, and uniform in thickness. The glass as it is manufactured is probably uniform enough in modulus of elasticity, and the molded pyrex blanks are probably close enough to circular. Since flexure varies inversely as the cube of the thickness of the blank, the thickness must meet fairly close tolerances. It is recommended that the back of the mirror to be warped be ground flat or slightly concave or convex and the thickness of the blank at the edge should be made uniform to within about 0.001 inch.

     The warping harness of Figure 2 has a fairly firm grip on the mirror. This suggests that the mirror-mounting lugs might simply be attached to the warping harness. If this is done, any adjustment of the warping harness will change the collimation of the mirror and make recollimation necessary. This is not in itself a serious objection to its use. If the mirror is to be used in a fixed position, such would be the case in a wind-tunnel application, this method of mounting the mirror is probably worth considering.

     With this method of mounting, gravity acts on the mirror which, in turn exerts forces against the warping harness. Equal and opposite forces are automatically set-up in the warping harness. These will, in general, merely change all the individual forces exerted by the warping harness by an equal amount. This might throw the warping harness out of adjustment, but if the mirror is mounted this way and then adjusted, the difference in pressure will be taken care of automatically - and no one will be aware of it. If the mirror is mounted this way in a movable telescope, however, each time the telescope is pointed in a new direction, the magnitude and distribution of these forces

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in the warping harness will change and this in turn will change the amount of warp in the mirror. This means that with this method of mounting the mirror each time the telescope is pointed in a new direction, a small adjustment of the warping harness may be required. In small telescopes where the weight of the mirror is small, this method of mounting may not produce changes in the tension of the warping harness large enough to necessitate readjustment each time the telescope is moved, and so, may be quite acceptable. In larger instruments (eight inches aperture and up) this method of mounting the mirror may be found to be objectionable because of the necessity of making frequent adjustments of the warping harness.

     The warping harness and mirror-mount shown in Figures 3a and 3b grips the mirror firmly at three points around its edge. This carries the weight of the mirror and provides positive collimation no matter what direction the telescope is pointed. The x-member of the warping harness is held in position by a thin, flexible sheet metal spider which maintains it in the proper position relative to the mirror, but does not otherwise restrain its movement. Counterweights balance the weight of the warping harness in all positions of the telescope so that only the flexure forces produced by the x-member are exerted against the mirror. All gravitational forces on the warping harness are taken care of by the sheet-metal spider and the counterweights. Thus the net warping forces exerted on the mirror remain constant no matter in what direction the telescope points. It is felt that with this design of mirror-mount and warping harness, Yolo reflectors in sizes up to 30- or 36-inch aperture can be made to operate successfully.

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Shop-Test of Warping Harness

     Part of the success of the Yolo reflector can be attributed to a simple but rigid test which is available for certifying the design of the warping harness. For this purpose, the mirror with its warping harness is set up as shown in Figure 4. The separation-distance, U, is given by the following expression:

where the angle,  B, is expressed in radians.

     Where  R1  and  R2  are equal and  T  is 1.2 times  S, the following formula will hold:

     The artificial star, in order to be suitable for this test, should be reasonably round, and its diameter,  d, should be no greater than that given by Eq. (21):

     Since this is smaller than the pin-hole light sources used by many telescope makers, optical reduction must be resorted to in order to adapt available equipment for this service. A microscope objective is recommended for this purpose.(4)

-Figure 4-

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     With the light source, mirror, and eyepiece set up as shown in Figure 4, and the warping harness unstressed, the image seen in the eyepiece should show only one aberration - astigmatism - but lots of that. When the eyepiece is moved toward the mirror, the image should take on the appearance of a sharp vertical line. When the eyepiece is moved away from the mirror, a point will be reached where the image has the appearance of a sharp horizontal line. Next, put a little stress on the warping harness. Now, in the eyepiece, the vertical and horizontal line-images will be shorter and will become sharp with less travel of the eyepiece. As the stress on the warping harness is increased, the images will continue to shorten and may start to rotate a little. If image rotation is observed, the mirror and warping harness should be rotated a little in the same direction. This should make the images return to the vertical and horizontal attitudes. Further increases in the stress and rotation of the warping harness should eventually result in a perfect Airy diffraction pattern in the eyepiece. Until a very good Airy diffraction pattern can be achieved in this test, there is little point in putting the mirror and warping harness into a telescope.

Light-Baffle System

     In order to provide good performance on deep sky objects, the Yolo reflector needs a well designed system of light baffles. Since its eyepiece looks right up at the sky through the open end of the tube, it has some of the problems of the Cassegrainian reflector. Its main problem differs from that in the Cassegrainian, however, in that the open end of the Yolo is confined to only one side of the secondary and does not extend all the way around, as it does

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in the Cassegrainian. The eyepiece and eyepiece tube are, or course, pointed right at the secondary. By designing the Yolo so that the tilt angles are a little greater than the minimum required to make the light path just clear mirrors of the minimum required diameters, the central illuminated part of the secondary is moved a short distance away from the open end of the tube. This helps very appreciably in the solution of this problem and is a device which cannot be used in the Cassegrainian.

     Having the eyepiece located at the bottom of the tube and looking up instead of at the top of the tube and looking across, as is the situation in the Newtonian reflector, is both a disadvantage and an advantage. It is a disadvantage in that it makes the light baffle system necessary in the Yolo; but it is an advantage in that once the system of baffles is installed, the field of view in the Yolo is much darker than that which can be obtained in Newtonian. In the Newtonian, the eyepiece is pointed squarely at the diagonal mirror, but it also "sees" the far side of the telescope tube surrounding the diagonal. This part of the tube is quite close to the open end and thus is fairly well illuminated by direct starlight, general sky light, and perhaps light from other sources. Thus the eyepiece in the Newtonian is looking right at a surface which receives quite a lot of illumination. Since the eyepiece in the Newtonian is quite close to the diagonal, it gets a fairly good look at the mirror cell of the primary and any surface roughness or baffles located in the lower part of the tube, all of which are looking right up at the sky and are, therefore, fairly well illuminated. This feeds more unwanted light into the eye of the observer and spoils his view of faint objects.

     Once the baffles,  B  and  G, in the Yolo (see Figure 5) are properly adjusted, all direct starlight, and any other light coming down the tube, is

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screened off; and the eyepiece can see only the back sides of the baffles. Since these surfaces are not directly illuminated through the open end of the tube, they provide a very dark background for the eyepiece. Since the secondary mirror in the Yolo is relatively far from the eyepiece, the eyepiece does not get to see much of the primary mirror cell reflected in the secondary; and, since the primary in the Yolo is located at the bottom of a much longer tube than in the Newtonian, it receives many times less illumination (roughly inversely as the squares of the tube-lengths) than its counterpart in the Newtonian. Very little light from this source, therefore, gets into the eyepiece of the Yolo.

     The light-baffle system for the Yolo reflector is designed as shown in Figure 5. First, the two mirrors and the field lens of the largest eyepiece (or photographic plate) are laid out to scale. Next, the outline of the cone of rays from a point source is laid out (light solid lines). Then the outline of the cone of rays from an extended source which will just fill the field is drawn in (light dashed lines). The next step is to locate baffle  G. If the telescope is intended for visual observation only and the field lens of the largest eyepiece is no more than about 2 inches in diameter, baffle  G  can be located as close as two primary mirror diameters in front of the tube proper. If, on the other hand, the instrument is to be used in photography, with a plate as large as 5" by 7", then baffle  G  may need to be located as far out as four- or five-diameters.

     With the location of baffle  G  decided upon, lay a straight edge on the drawing so that it will pass through points  O,  B, and  G. With point  O  (inside edge of eyepiece or plate holder) as a pivot, adjust the straight edge until both points  B  and  G lie about the same fraction of the distance between

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the solid and dashed lines.  If  B  and  G  are quite close to the solid lines, there may be an objectionable amount of vignetting for objects near the edge of the field.  In this case, baffle  G  should be located a little farther out from the main structure of the telescope tube.  When a satisfactory location for baffle  G  has been found, points  B  and  G  are marked on the layout.  The locations of all the other baffles are then decided upon and laid out in plan approximately as shown in Figure 5. 

     Once the locations of all baffles has been decided upon, the baffles themselves can be designed.  The outside outline of each baffle must conform to the inside cross section of the telescope tube at its location.  These can be laid out to scale as shown in Figure 5.  From the plan view we locate the center and radius of the cross section of each cone of rays that passes through a baffle.  These centers are the located on the baffle layout and the cross sections are drawn in as circles.  Points  B  and  G  locate the straight portions of the inside outlines of baffles  B  and  G.  The rest of the inside outlines are drawn as arcs of circles which clear the cones of rays by about one-inch, all the way around.  This is done so that possible convection currents in the air inside the tube can get around the edge of a baffle without being pushed too far into one of the light paths. 

     If the telescope is intended for use on bright objects only, such as the moon and planets, the baffle system may be omitted entirely.  However, even on these objects, a baffle system will give more pleasing views.  A very good compromise between the complete baffle system which has just been described and no baffles at all, is a muffle with baffle  G  on its front end plus just the straight portion of baffle  B.  These two baffles by themselves will screen out all direct starlight from the eyepiece, and will give a field of view which

-Figure 5-

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is noticeably darker than that which can be obtained in a good Newtonian reflector.

Tube Design

     Because of the shape of the light path in the Yolo reflector, a tube of rectangular cross section will generally be found to be advantageous. Plywood is a satisfactory material for its construction. If the light-baffles too are made of plywood, they may be built integrally with the sides and thus serve as internal stiffeners for the tube. The muffle (that part of the baffle system extending forward of the secondary mirror) can be made of relatively light-weight material, circular in cross section, and detachable from the telescope tube, proper.

     In order to minimize the deleterious effects of possible convection currents in the air within the tube it is recommended that the inside surface of the tube should be no closer to the light path than one-half of the radius of the primary mirror. This means that the shorter dimension of the rectangular cross section of the inside of the tube should be no less than one and one-half times the aperture of the telescope.

Collimation

     Collimation of the Yolo reflector requires both mirrors to be tilted through the proper angles and the tilt-lines of both mirrors to be aligned accurately perpendicular to the principal plane of the instrument (the plane of the paper in Figures 1 and 5). When the warping harness is properly oriented, the two tension members ("pullers") which reach around to the front surface of

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the mirror (see Figure 3b) should be accurately in the principal plane of the system. The two "pushers" lie approximately one mirror radius above and below this plane.

     Satisfactory collimation can be achieved with the aid of a pair of fixtures, one made for each end of the telescope. Each fixture consists of a slender rod which can be attached to - or mounted directly in front of - a mirror. Each rod is long enough to extend across the mirror and out past the center of the light-path passing that mirror. Each rod carries two movable markers.

     The following procedure is recommended:

     1.  Attach each fixture to its mirror, and make adjustments to have each rod pass directly in front of the center of its mirror and slide the mirror-marker along each rod until it is squarely in front of the center of its mirror.

     2.  Sight along the center of the eyepiece tube to the secondary mirror-marker and then rotate primary fixture until its rod falls in the line of sight.

     3.  Slide light-path marker along the rod until it is on the line of sight to the center of the secondary. This, then, places the light-path marker on the line running from the focal point to the center of the secondary. The primary mirror-marker is now on the line running from the center of the primary to the center of the secondary.

     4.  Measure the distance between these two markers; and, with the measured distance, S, calculate the angle,  B.

     5.  With this value of  B  and Eq. (5), calculate angle,  A. With  A  and  S, calculate the distance from the center of the secondary mirror to the center of the light-path to a star.

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     6.  Slide the light-path marker for the secondary fixture until it is at the calculated distance from the mirror-marker (center of secondary).

     With the rod of the primary fixture passing through the centerline of the light-path running from the secondary mirror to the focal point and passing directly in front of the center of the primary, the principal plane of the optical system is now defined by this rod (a straight line) and the center of the secondary mirror (a point).

     7.  While sighting along the centerline of the eyepiece tube adjust the three collimating screws on the secondary mirror mount until the light-path marker on the eyepiece axis and the two mirror-markers appear to fall one behind the other on a single straight line. When this has been accomplished, the secondary mirror has been adjusted to the proper tilt-angle and its tilt-line must be accurately perpendicular to the principal plane.

     8.  Rotate secondary fixture about the axis of the secondary mirror until secondary rod appears to be parallel to - and lie on top of - the primary fixture rod. This then places the light-path marker of the secondary fixture in the principal plane of the instrument.

     9.  Adjust the three collimating screws of the primary mirror until the light-path marker of the secondary fixture appears to fall in line with the others. This, then places the primary mirror at the proper angle of tilt and leaves its tilt-line perpendicular to the principal plane. Remove both collimation fixtures from the telescope.

     10.  With the telescope pointed at a bright star high in the sky and a high-power eyepiece, adjust tension and rotation of the warping harness until a perfect star image is obtained. Follow the procedures as described under the heading of "Shop-Test of Warping Harness."

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References

1. ‘First Order Tilt Aberrations in Mirrors and Lenses,’ by Arthur S. Leonard,Proc. Of Seventeenth Annual Convention of Western Amateur Astronomers,University of Nevada, Reno, Nevada, August 19-21, 1965 

2. ‘A Null Test for Paraboloids,’ by Horace E. Dall, A.T.M. Book 3, pp. 49-155.  

3. ‘Convention Highlights from Reno,’ by Allan McClure and Leif J. Robinson,Sky and Telescope, Vol. XXX, No. 4, October 1965, pp. 206-210. 

4. ‘Schmidt Camera Notes,’ by Henry E. Paul, A.T.M. Book 3, pp. 149-155.

NOTE: 

Fig. 3a 

Secondary mirror, mirror-mount, and warping harness.Rear view. SVAS 12-inch Yolo reflector.

Fig. 3b 

Secondary mirror, mirror-mount, and warping harness,Front view. SVAS 12-inch Yolo reflector

-Equation Summary-