Circular Zones and Turned Edges

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This chapter discusses zonal defects and a common type of zonal error, a turned edge. It will make four chief points:

1 On mirrors of amateur size, interior zones are seldom large enough to be troublesome.

2. Zonal defects can be detected by defocusing a larger amount than is usual.

3 Turned edge is a persistent problem that yields contrasts worse than the smaller aperture inside the turned annulus.

4. Narrow turned edges can be treated by masking or painting the edge.

11.1 Causes of Zonal Defects

Zones are slight circular corrugations in the polished surface of the glass. The improper use of fast polishing materials may lead to zones in optical elements. For example, the lap is typically pressed against the optical piece to achieve uniformity of polishing action. If too little pressing is done, or if part of the lap overhangs during pressing, sections of the polisher can ride the optical piece with more pressure than the rest. Because the lap and the stroke direction rotate with respect to the mirror, this uneven pressure digs a trench around a certain radius of the mirror. Many other mechanisms can also result in zonal defects. When too short a stroke is used, good statistical averaging of the two surfaces doesn't take place. Channeling a lap with a centered pattern will often result in a profusion of thin rings. If a piece of the brittle pitch breaks off and is trapped beneath the rest of the lap, it will plow a furrow in the mirror during the next few minutes until the piece is forced back into the lap.

However, these causes are minor compared to the chief reason for zones. Fast aspherical mirrors demand the use of smaller polishers. The old style of optical work (common in the days of long-focus mirrors) involved the use of two identical disks. Telescope makers modified their stroke slightly for a few minutes, but still used an equal-diameter lap to achieve the aspherical figure. Unfortunately, that method won't work on mirrors of low focal ratio. The sphere is so different from the correct shape that the maker struggles for proper conformance. A lap of equal size won't ever reach the correct form. The natural tendency toward statistical averaging will keep dragging its curve back toward a sphere. Also, full-diameter laps are cumbersome when the optical piece is large, regardless of its focal ratio.

The optician chooses a sub-diameter lap, usually one about half the size of the disk being worked (unless the optical piece is really huge—then it's even smaller). The aspherical shape can be approached merely by rubbing the center of the disk more than the outside. Using a smaller lap is dangerous though. The optician must enforce an artificial randomness on the polishing machine to prevent the unnatural precision of the mechanism from digging trenches at fixed radii and, by implication, leaving ridges at other radii. A partially worked surface must be blended or smoothed.

Happily, interior zones on most commercial mirrors are detectable in sensitive bench tests, but they are usually so slight that they are unseen in the eyepiece. Most common is a small depression or nipple at the center, an error that is largely obscured by the secondary mirror. In leaving this error untreated, the optician is saving time and money by ignoring an error that will not be illuminated. (A central zone is shown in Fig. A-3.)

Another common type of interior zone consists of one or more ghostly thin rings appearing about halfway out. They can usually be seen in the Foucault test when the surface figure is very near a sphere, but such an error is only cosmetic. The slight ringing is evidence that the blending is going well.

On the other hand, if the maker is hurried and testing is inadequate, a severe zone may be left in the mirror. One form of interior zonal defect has two competing radii of curvature—one inside the zone, the other outside the zone. This condition may be more damaging to the image than light scattered from the vicinity of the zone itself. Light deflected from the immediate area of the zone will appear as diffuse glow if the zone is sharp enough, but these large areas of the mirror on either side of the zone are directing a great deal of light on interfering focal points. They cover sufficient area that light is attempting to come to two tight disks at different focal distances.

The most debilitating form of a zone is turned edge. It can result from even a full-diameter lap. It is caused by excessive wear at the edge of the disk during polishing. If too much pressure is applied while the tool is teetering on the edge of the optical surface, or if the lap is not maintained in good conformance to the shape of the disk being worked, a turned edge can result (Texereau 1984). Turned edge also seems to be a problem associated with a rocking motion of the mirror disk during polishing.

Turned-down edge, because it happens at the very periphery of the optical surface, is not limited in amplitude. Interior zones are temporary intruders. If good contact between the mirror and tool is maintained and the stroke is not too short, the averaging effects of many strokes at many different angles will eventually average the zone out. It will be automatically blended away.

Turned edge, on the other hand, is derived from bad figuring habits or improper use of materials. Once it starts, the cause generally doesn't go away. It just keeps on occurring or even becomes worse. Turned edges are usually deep, and since the edge is on the perimeter of the optics, it covers a surprisingly large fraction of the aperture's surface area. A 5% turned-edge zone is struck by about 10% of the light incident on the aperture.



Normalized aperture radius

Fig. 11-1. Turned edge is modeled by a 60th-order term of Eq. 11.1.

Normalized aperture radius

Fig. 11-1. Turned edge is modeled by a 60th-order term of Eq. 11.1.

Zonal aberration is connected to the expression for general spherical aberration. Remember, the equation for the wavefront involved terms like

W(p) = constant + focus term + Ap4 + Ap6 + Ap8 + A1(p10 + ... (11.1)

Normally, for global figuring errors, the coefficient of p4 is largest, with a smaller coefficient of p6. All of the remaining terms are much smaller. But a zone is a special case where one or more of the higher order terms contributes. A zone is like a switch that turns on very high-order spherical aberration, suddenly waking up errors that were best left asleep.

A simple example is graphed in Fig. 11-1. Turned edge is modeled as a term — A6(p60. There is nothing special about the 60th order. Similar results would have been derived from 58th order or 62nd order.

Interior zones are more complicated. They are combinations of many highorder terms. Broad zones are described by lower orders than sharp zones.

11.2 Interior Zones

Something should be emphasized at the beginning to avoid frightening the reader. Interior zonal defects on amateur-sized optics are rarely more than cosmetic defects. Although they are common during brief periods of fabrication, reasonably careful work is enough to lessen them. Few opticians would release a small mirror with a significant interior zone on it. Large mirrors, however, are typically figured face-up with polishers much smaller than their diameters. Such optics often show persistent zones. These mirrors require more careful evaluation to determine if their zonal defects are negligible.

Two types of interior zones are considered here. The first is a narrow trench where the deformation is isolated or does not persist over the rest of the surface. Huge observatory optics often suffer from this type of zone, because the surface is worked by very small polishers. Usually, opticians working on large optics are no fools and will not let conditions that generate these zones endure for long. Still, the skeletal remains of zonal grooves will sometimes appear on test photographs from big mirrors.

The star-test pattern in Chapter 2 was calculated from such a 1/4 wavelength trench zone. It was modeled as a narrow Gaussian-function dip in an otherwise flat mirror. The particular extrafocal patterns shown in Fig. 2-9 had defocusing aberrations of 20 wavelengths. A general feature of the star test for zones is that one must rack farther out of focus to see the effect of zones well.

A zone produced commonly in the fabrication of small mirrors has a profile that looks like an "S" or "Z," and is called an "S-zone" here. The zone remains after global figuring errors below sixth order are subtracted from the wave front. This zone can have different radii on either side of its sharpest slope.

11.2.1 Aberration Function of S-Zones

Zones can be described by linear combinations of many spherical aberration terms, but that method is somewhat cumbersome. Instead, the zone is specified here with three parameters: amplitude, width, and radius. The optical surface is then divided into three regions, and the surface is constructed by fitting cubic polynomials through the points defined by those three parameters. At the border of each region, the slope of the wavefront is set to zero. Figure 11-2 shows a narrow zone at a 40% radius. A cupped plateau is inside the zone and a shallow dish surrounds it. Less evident is the slightly different curvature of those areas.

Fig. 11-2. A sharp S-zone at a radius of 40% of the aperture. It divides up the surface into two broad areas with different radius of curvature, as well as providing a rapidly inclined scattering ridge.

11.2.2 Filtering of S-Zones

Interior zones have two characteristic scales. Light diffracted from the vicinity of the zone itself is scattered into a broad fuzzy halo, so one anticipates that the modulation transfer function should dip rapidly at low spatial frequencies. When such zones have a large diameter, more or less like a big central obstruction, the MTF oscillates similarly at higher spatial frequencies.

The behavior of the MTF matches both predictions in Fig. 11-3 for two radii and two amplitudes. One radius is just the 40% zone described in the last section. The other is the same zonal defect moved out until it is centered on 70% of the radius. Both zones are plotted with total aberrations of 1/8 and 1/4 wavelength, and both zones have width equal to 0.1 aperture radii. The 1/4-wavelength zones yield a slightly better Strehl intensity ratio than the 0.8 value that marks the Rayleigh 1/4-wavelength limit

Fig. 11-3. Modulation transfer functions for a single zone. The MTF curves are for two values of zonal aberration (1/4 wavelength and 1/8 wavelength) and two zonal radii (0.7 and 0.4 of the full aperture). The aperture is unobstructed.

for spherical aberration. The V8-wavelength amplitude zones are well inside of the 0.8 Strehl ratio tolerance.

The slight wiggles of the zonal defect MTF at high spatial frequency don't concern the tester much. More troublesome is the brisk drop at low spatial frequency. It is this degradation that Danjon and Couder were talking about when they made the distinctions between the slope of the defect and its amplitude (mentioned in Chapter 1). A smooth surface is the difference between merely adequate optics and those rare instruments that take the observer's breath away.

Notice another characteristic of these plots. A zone appearing at 70% of the aperture is much worse than an equal-depth zone appearing closer to the center. At low spatial frequencies, the contrast drops more precipitously for the larger-radius zone. Lowered performance in this case is purely a function of how much area the defect covers.

Of course, interior zonal defects are not well described by peak-to-valley wavefront error. The RMS deviation is a much better way of characterizing zones. Zones are unacceptable when their RMS deviation is 1/14 wavelength, which corresponds roughly to the 1/4 wavelength curve of Fig. 11-3 at a radius of 0.7. This deviation is much worse than any self-respecting optician would tolerate. For deviations half that size, the MTF only shows a slight dip. This amount of aberration is acceptable.

11.2.3 Detecting Interior Zones in the Star Test

In his 1891 work on star testing, Taylor gave a brief description of how he detected a zone in a refractor:

In order to detect such zonal aberration, which is caused by imperfect figuring of one or more of the surfaces, it is best to direct the telescope to a very bright star, using a moderately high power, and rack in and out of focus as before, only it is best to rack out until 8 to 20 interference rings can be counted, for the irregular zonal effect is most easily detected under such conditions Counting from the edge inwards, it may be noticed, for instance, that the outer ring is poor and weak, while the next one or two appear disproportionately strong, the next two or three weak, while those about the center are strong again... (Taylor 1983).

Even though Taylor was writing about refractors and referring to smoother deformations that those modeled here, he described the two essential techniques to detect zones. First, bright stars are used to test for zonal defects. Second, the telescope is defocused farther than is recommended to detect other types of aberration. Defocusing long distances is especially handy because it lessens the effect of other aberrations almost to the vanishing point. Also, because light near focus is hopelessly muddled together, the zone doesn't tend to isolate itself from the rest of the diffraction structure.

Star-test patterns for unobstructed optics with an S-zone at 40% the radius of the aperture and 1/8-wavelength total aberration on the wavefront are shown in Fig. 11-4 (corresponding to one curve of the MTF chart in Fig. 11-3). The defocusing aberrations are 10 and 20 wavelengths, whereas most of other aberrations appearing in this book are all depicted inside of 8 or 10 wavelengths. The telescope is a long way out of focus, but still this zone is easily visible.

The zone is most distinct at ±20 wavelengths, where it appears near its proper radius, but it has some anomalous features even here. It dips before it crests. In fact, the zone seems to be located at the crossover point between the extra bright ring and the depressed ring, presumably because it is an S-zone. Trench or hill zones are located at the correct radius but are bracketed by opposite-brightness rings. A dark area is always associated with a bright one because energy must be conserved. Energy that makes one ring look brighter always must be scooped from a nearby ring.

The patterns at ±10 wavelengths defocusing aberration show another interesting zonal property noticed by Taylor—the pattern at 10 wavelengths

S-zone=1/8 rad=0.4 10 perfect 10

S-zone=1/8 rad=0.4 10 perfect 10

Fig. 11-4. Star-test patterns for an S-zone at 40% radius with amplitude of 1/8 wavelength. The perfect patterns are in the column on the right. The aperture is unobstructed.

Fig. 11-4. Star-test patterns for an S-zone at 40% radius with amplitude of 1/8 wavelength. The perfect patterns are in the column on the right. The aperture is unobstructed.

seems to be the complement of the —10 wavelengths pattern. The reversal is not perfect, only approximate. In portions of the disk far from the edge and close to the radius of the zone, the pattern seems to be a negative of the pattern on the other side of focus.

The in-focus pattern indicates that such a zone will frighten a tester more than it will disturb an image. The Strehl ratio is reduced only to about 0.95, well within the tolerance for excellent optics.

Another pattern appears in Fig. 11-5. This time the zone has been moved to a radius of 0.7 of the full aperture and the aperture is obstructed by 20%. Here we see really complicated behavior. The localized effects of the aberration have not yet unmixed from the image at 20 wavelengths defocus. This fact teaches something important about identifying zones. Zones are easy to detect, but their radius and number is hard to pin down. The most we can say, unless very clean separation is seen, is that the surface exhibits zones.

In casual conversations, one hears star-testers speaking confidently about locating zones, saying things like "I detected two zones, one at 50% and the other at 75% of the radius." These claims assume that the structure of the out-of-focus pattern is completely unmixed, which is probably false. Figure 11-5 is a calculated pattern from one zone at a known radius, yet this aperture seems afflicted with many zones. The multiple ringing will separate out at 30 or 40 wavelengths defocusing aberration (not shown) but in an obscure manner. Since this zone is so far out on the aperture, it interferes with the ever-present dark ring on the inside of the bright outer ring.

One final conclusion can be drawn from both Figs. 11-4 and 11-5. The star test is almost too sensitive to interior zonal aberrations. The filtration of Ye-wavelength total aberration of either situation is mild. The in-focus patterns are nearly the same as the unaberrated optics. Yet the zones look severe when defocused. If you can only barely detect the existence of zones with defocused optics, then you have nothing to fear. They will not damage the focused image in most dark-field observing situations. In fact, I have never seen a zone as bad as the one depicted in Fig. 11-5.

11.3 Turned Edges

Turned-down edge is common enough in both amateur and commercial mirrors although it usually takes different forms. In amateur-made mirrors, it is often wide and shallow, starting at a radius somewhere around 80% or 90% of full aperture and rolling gradually toward the edge. In commercial mirrors, turned-down edge is usually right at the perimeter, but it is steeper. The reasons for this dichotomy are obscure. Perhaps amateurs, who usually work by hand, are capable of putting less pressure on the mirror, or maybe they use a pitch with different working characteristics. Commercial mirrors are likely polished with stiff pitch and hence are not prone to turned edge, but the machines are capable of putting enormous force on the tools.

For the purpose of this chapter, which is less concerned with mirror making than mirror testing by observers, the type of turned edge described is the narrow one. Wide turned-down edges will be classified as zones that happen to be at the boundary of the mirror. Their behavior at best focus is similar to simple spherical overcorrection. Since lower orders of spherical aberration (4th and 6th) have already been discussed in Chapter 10, this

Spherical Aberration Fringe Patterns

Fig. 11-5. Star-test patterns of an S-zone at 70% of the disk radius. Total aberration is 1/8 wavelength. Normal patterns are in the column on the right.

Fig. 11-5. Star-test patterns of an S-zone at 70% of the disk radius. Total aberration is 1/8 wavelength. Normal patterns are in the column on the right.

section will concentrate on the other limiting case.

Turned edge seems to be more prevalent in fast, large, or thin mirrors, but this rule is not rigid. It appears often enough in slow, small, or thick optics. One mirror-making author advises that during design of large thin-mirror telescopes, observers plan a larger surface than will be expected in the final instrument. Then they can cheerfully (and somewhat fatalistically) mask the far edge (Kestner 1981).

11.3.1 Aberration Function

Again, a turned edge can be handled by a very high-order term in the spherical aberration equation. Here we choose a much easier path. It is much more convenient simply to allow the mirror to be flat out to a certain radius and then start a quadratic fall toward the edge. The quadratic nature of the downward trend is not based on any physical evidence or theory of the way these edges are put on optical surfaces. It is chosen arbitrarily. Other ways to describe the descent were tried, and the results didn't change much.

Figure 11-6 shows such a turned edge as a skirted table. This figure is not quite accurate. Best focus for turned edges demands that the inner flat area become a very shallow bowl. The aberration function actually used to generate the patterns was modified so that it had a minimum variance.

11.3.2 MTF of Turned Edge

The filtering of a turned edge is shown in Fig. 11-7. This aberration is very compact and highly sloped, so it is no surprise that the light diffracted from the edge is diverted far from the center. The MTF drops quickly to reflect the damage to the widely spaced bar patterns of a low spatial frequency target. At the other end of the scale, the contrast preservation at high spatial frequency is much like that of a smaller aperture with a radius the size of the unturned area. Light is driven so far from the central core that it doesn't interfere with the focused spot, but the outer portion of the aperture is not contributing appreciably to the image. A telescope with a turned edge behaves no better than a smaller telescope. Worse, at low spatial frequencies, the spurious light from the edge region actually harms the image.

11.3.3 Image Pattern of Turned-Down Edge

Figure 11-8 shows a focus run of the previous section's turned edge. Since this aberration is much more common with reflectors than refractors, a moderate obstruction has been added for realism.

A diffuse glow spreads over the field of view inside focus. Contrast between the rings is appreciably lessened. The reverse is true as well—the contrast between the rings visible outside of focus is increased. Of course, this effect is easier to see with a filter that passes only one color (perhaps a deep green or a crimson red), but using such a filter requires a very bright source of light. Also, the edge of the diffraction disk softens inside focus. Turned edge, like other zones, is easier to detect at long defocus distances.

Fig. 11-6. An example aberration function of a turned edge.

Turned edge starting at 95% radius Total aberration = 0.63 wavelength

Turned edge starting at 95% radius Total aberration = 0.63 wavelength

Fig. 11-7. Filtration of an unobstructed aperture caused by an example turned edge that reaches 0.63 wavelength at the far edge. The Hat area inside covers 95% of the diameter. The Strehl ratio is slightly higher than 0.8, so this error is about the maximum tolerable. A comparison is made to an aperture with the turned portion masked or painted out. The MTF goes to zero at about 0.95 of the maximum spatial frequency just as the smaller aperture would.

Fig. 11-7. Filtration of an unobstructed aperture caused by an example turned edge that reaches 0.63 wavelength at the far edge. The Hat area inside covers 95% of the diameter. The Strehl ratio is slightly higher than 0.8, so this error is about the maximum tolerable. A comparison is made to an aperture with the turned portion masked or painted out. The MTF goes to zero at about 0.95 of the maximum spatial frequency just as the smaller aperture would.

At greater distances inside focus, the hazy glow of turned-down edge condenses into a smaller bundle, and the edge of the disk seems to bleed light into the outside. This behavior appears in Fig. 11-9, where the defocus is shown at 30 wavelengths inside and outside of focus.

Other aberrations also render the diffraction rings more distinct on one side of focus than the other—an example is lower-order spherical aberration—but none of them show a uniformity of disk illumination. One might well wonder if a turned edge is detectable in the presence of spherical aberration or if it is too difficult to tease out of the confused image.

Fig. 11-8. Image patterns of turned edge starting at 95% the radius and having the value of -0.63 wavelength right at the edge. Obstruction is 25%, and the normal unaberratedpatterns appear in the column to the right.

Fig. 11-8. Image patterns of turned edge starting at 95% the radius and having the value of -0.63 wavelength right at the edge. Obstruction is 25%, and the normal unaberratedpatterns appear in the column to the right.

Chapter 11. Circular Zones and Turned Edges normal, defocused 150

TE inside focus 150

Fig. 11-9. Turned edge ±30 wavelengths out of focus. Normal appearance is also shown. The Maltese crosses are a moiré effect caused by the sampling rate of the calculated image. They would not appear in a real view.

If, say, a turned edge as severe as Fig. 11-8 is added to 1/4 wavelength of spherical aberration, the turned edge would be visible beyond 20 wavelengths defocus (image not shown). The spherical aberration becomes hard to detect with 20 wavelengths defocusing aberration, but the turned edge is still there to see. Thus, turned edge can indeed be detected in the presence of mild correction error.

When the image is focused inward a long way, the low-brightness soft edge of the disk becomes hard to see. Low contrast in the rings is a surer indicator of turned edge, and the delicate appearance of the boundary is further evidence.

Ellison and other subsequent authors pointed out that the edge of the disk inside of focus looked "hairy" (Ingalls 1976). It would not be surprising if the uncontrolled way a turned edge is applied to a mirror would lead to some structuring in the scattered light, thus causing a "hairy" edge. However, I have never been sure such an effect is generated by the turned edge or is caused by the common turbulence-induced aberration acting on slight low-order spherical aberration.

With the wider and less deeply turned edges characteristic of amateur-made mirrors, some modifications of these patterns should be expected. The turned area diverts light to lower angles and looks more compact. Also, the optimum distance for detecting a soft edge is somewhat nearer the focus than the 20-wavelength number recommended above.

Refractors can have turned-down edges, too, but the appearance is reversed. Contrasty rings are found inside focus; the soft edge and low contrast rings are outside. However, refractors don't tend to exhibit turned edge unless it is wide. Normally, the lens cell hides the far edge of the objective behind retaining rings. In a way, this advantage compensates for not being able to hide a central zone behind a secondary. Few refractors are made so badly that they show noticeable turned edges.

The in-focus images of Fig. 11-8 display the almost negligible effect of turned edge on high-resolution applications. The diffuse glow is still there, but is unseen compared to the dazzling stellar image. Other than the slightly reduced effective aperture, turned edge disturbs low spatial frequencies (or wide details) preferentially.

11.3.4 Signal-to-Noise Ratio of a Turned Edge

The effect of turned edge is very similar to dirty optics in that it "scatters" light throughout the field of view. Therefore, it is instructive and revealing to make an equivalent signal-to-noise calculation. In most dark-field observing situations, turned edge is like dusty optics or spider diffraction in that small amounts matter little. A tiny fraction of an already dim object's light is negligible. However, in the case of lunar-planetary astronomy or attempted observation of a dim object next to a bright one, turned edge can become a serious source of trouble. How much can be tolerated?

For planetary astronomy, two things are important: 1) the diameter of the induced halo of the turned edge and 2) the amount of light removed from the image. The diameter is easy to estimate. Consulting the MTF chart in Fig. 11-7, we see that the halfway-down point in the initial sharp drop (marked with oval) occurs at about 2% the maximum spatial frequency. This number inverts to a radius of about 50A/D, or about 40 Airy disk radii for a 5% turned edge. In a 200 mm aperture using yellow-green light, the radius of the glow is about 30 arcseconds. For a turned-edge amplitude of only 1/8 wavelength, the amount of energy removed from the image (and reappearing as noise) is slightly less than 1% of the total energy. Thus, the SNR can be as bad as 20 dB.

The really disturbing thing about turned edge is the relative compactness of the halo. It doesn't throw the light as far from the image as dust does. Thirty arcseconds means that much of the offending light is still inside planetary disks. Turned edges are pernicious errors that remove contrast far in excess of their nominal magnitudes. The amplitude of a 5% turned edge zone must be decreased to 1/25 wavelength before it reaches the 30 dB SNR that was given as the tolerance for dust. That amount is scarcely measurable. Of course, a turned edge of such a small magnitude hardly behaves in the manner of a turned edge. It has begun to compete with interior zones and roughness errors.

The best way of reducing turned-edge diffraction is to make sure that it is extremely narrow. The turned-edge halo will then appear much larger and correspondingly dimmer. It will divert light outside planetary disks and diffract less light to begin with. For a 2.5% turned edge of the same 1/8 wavelength amplitude as the case above, a 24 dB SNR is diffracted to a halo with twice the angle. Now, because much of the stray light misses the image and the area of the turned edge is smaller, the true SNR increases to 28-30 dB.

11.3.5 The Width of the Turned Edge

Usually, when turned edge is less detectable than in Figs. 11-8 and 11-9, you have very little to worry about. But if you have a serious problem with an edge zone, the radius at which the zone begins to roll is a useful bit of information. You can perhaps do further tests with edge masks to try to determine the turning radius and severity of the zone, but such checks are difficult to interpret.

Turning radius is easier to determine using a variation of the Foucault test. Try an occluding knife outside the focus of an artificial-source star test done at night. The source should be very bright, so move the flashlight close to the sphere or use a larger sphere. Mount the knife over one half of an empty tube of the same diameter as an eyepiece. (A fragment of a playing card or opaque slip of paper works almost as well as a true knife and offers less opportunity for accident.) You can do fine adjustments by rotating this "eyepiece." Defocus should be 5 mm or more. Arrange the telescope so the knife's shadow covers either 1/4 or 3/4 of the aperture, but not half. Do not replace this knife edge by a Ronchi ruling. The side-order images of the grating disturb interpretations of the edge.

If the shadow is perfectly straight on the aperture and seems rock-solid, try to put the knife nearer to the focus. If you see a blurred, quavery shadow that is disturbed by the slightest touch, you are probably too close to focus. Set the knife farther away. You are looking for a slight curl of the shadow very near the edge of the aperture. The curl becomes severe beyond the turning radius.

If you can detect the width of a turned edge in this manner, then the rolled region is probably too wide to paint as suggested below. What you want to see is little or no evidence of a turned edge from this crude test. You only want to paint a narrow turned edge. If you detect a wide turned edge, you will find it easier to mask the offending region. Use the turning radius determined here to calculate the size of the aperture through which you wish to allow light transmission.

11.3.6 Remedies for Turned Edge

As was shown in the MTF diagram above, the mirror with a turned edge performs no better than a smaller perfect aperture at high spatial frequencies and worse than the smaller aperture at low spatial frequencies. Clearly, the last bit of aperture on the periphery is doing less than nothing for the imaging performance. Turned edges gather worthless, imperfectly focused light and corrupt otherwise perfect images with it.

Masking is not an irreversible step, but it requires a little mechanical skill. Generally, it involves constructing a narrow annulus and finding a way of holding it over the mirror. A mask holder mounted above the mirror works best for open-tubed, Dobsonian mountings. Access to the region just above the mirror is easy with such a telescope, and installing and adjusting an edge mask is convenient.

Those mirror owners who have a definite diagnosis of turned edge and who are willing to accept the considerable risks involved, may significantly improve the performance of a telescope mirror by painting it. Painting should not be attempted with wide turned edges. The definition of "wide"

Chapter 11. Circular Zones and Turned Edges depends on aperture diameter. Ten millimeters sounds wide for a 150-mm mirror and narrow for a 500-mm mirror.

Painting the mirror, however, works with any telescope and requires only a steady hand. Remove the mirror and place it on a lazy-susan or other rotating platform. Make sure the mirror is larger than the rotating table under it. Spend some time carefully centering and leveling the mirror on the pivot, so that it doesn't wobble or rotate eccentrically.

Slowly spinning the disk, brace your hand in one spot and introduce the brush point gingerly onto the mirror's surface, working in from the edge. You are in no hurry, so try to lay down a clean line over many revolutions. I don't advise using a permanent marker but if you do, be advised the solvent tends to wipe up existing marks, so you may have to make repeated passes before the ink stays on the mirror. Brushes are less controllable, but painting in this manner results in a more saturated obscuration. Do not use an airbrush or spray paint of any sort.

Perform the painting operation in two steps. The first time, paint out just 1 or 2 mm of the far edge. If you are fortunate, this narrow ribbon will largely cure the edge problems. Star test the mirror again. If the image doesn't improve, extend the painted zone inward. At the end of such a procedure, the ugly appearance of the mirror can be shocking. Keep in mind, however, that you have, in effect, trimmed off the poorest part of the aperture.

The effect of a corrected turned edge can be seen in the star test. How it will improve actual observing is not immediately apparent. Remember, the most objectionable feature of a turned edge is a hazy glow in the vicinity of the bright point image—20 to 40 Airy radii out. Inspection of the MTF chart reveals a quick dip at low spatial frequency. For this 5% wide zone, most of the damage has already occurred by the time 2 to 5% of the maximum spatial frequency of the MTF target has been reached. If the aperture is 200 mm (8 inches), then detail separations less than about 10 to 30 arcseconds are degraded. Masking the turned edge will have the most benefit with richly-detailed large objects, such as the cores of tight globular clusters or planetary disks.

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