Slightly out of focus: star-testing your telescope: the stars that entice us can also help us optimize our telescopes.
Under steady skies and using high magnification (25x or more per inch of telescope aperture), we will see a star's image as a tiny disk (called the Airy disk) surrounded by a bull's-eye pattern of faint diffraction rings. The rings grow increasingly dimmer farther out from the center, and you'll probably see only one or two. This image is a consequence of the wave nature of light. (For an interesting, readable discussion of light's nature, I recommend Richard Feynman's 1985 book QED: The Strange Theory of Light and Matter.)
The size of the Airy disk is determined by the telescope's aperture and the light's wavelength. With green light (555-nanometer wavelength) and aperture (D) measured in millimeters, the angular diameter of the dark ring just outside the Airy disk is 280/D arcseconds. In an optically perfect, unobstructed telescope, 84% of a star's light gathered by the telescope objective is concentrated in the Airy disk, with the rest distributed in the diffraction rings.
This simple mathematical formula easily shows why larger apertures have an advantage. Double the aperture's diameter and your telescope collects four times as much light. But the Airy disk's angular diameter is halved, so the light is now concentrated in one quarter the area. The result is an Airy disk that is 16 times brighter. Illustrations comparing the light distribution for star images in different-sized telescopes are often normalized (portrayed with the same height), which obscures this advantage of a larger aperture. Smaller Airy disks are also the reason why larger telescopes have better resolution, which translates into better views of double stars and lunar and planetary detail.
The diffraction pattern of a flawless in-focus star image is lovely, but atmospheric turbulence (seeing) often conceals it, especially when we're observing with large-aperture telescopes. Luckily, a star's image slightly inside and outside focus more readily helps us diagnose problems, and it's easier to discern details blurred by poor seeing in this larger image.
In a telescope free of optical faults, with its optics properly aligned, and at thermal equilibrium, a star's diffraction pattern just inside of focus will be identical to the pattern at the same distance outside of focus. This is true of any telescope design.
In a fine, unobstructed telescope, the expanded diffraction pattern seen just inside or outside of focus is a set of concentric rings, with the outermost ring slightly brighter and broader than the rest. The pattern is different in a telescope with a central obstruction. Other than the very center, the area in the middle is quite dark, the ring structure is coarser, and the inner rings are no longer of uniform brightness. Nevertheless, the patterns at equal distances inside and outside of focus are identical.
Preparing for a Star-Test
For star-testing, you should set your telescope outside early and allow an hour or more for it to acclimate to the ambient temperature. Although a star-test will quickly reveal if your optics are out of alignment, it's best to start out with the telescope as well collimated as you can make it ahead of time.
For moderate apertures, say 6 to 10 inches, select a 1st- or 2nd-magnitude star. With smaller instruments use a brighter star, and with larger ones, go fainter. Select a star high in the sky where the atmospheric seeing is better. Pick an eyepiece giving an exit pupil of 1 mm or slightly smaller. A simple way to determine the exit pupil of a telescope setup is to divide the eyepiece's focal length in millimeters by your telescope's focal ratio. Thus, an eyepiece with a focal length of 5 mm will yield a 1-mm exit pupil with an f/5 telescope. For large-aperture telescopes, seeing may require you to use lower magnifications--longer focal-length eyepieces and larger exit pupils.
Star-testing is easier with a tracking telescope. Otherwise you have to continuously nudge the telescope along to keep the star closely centered in the eyepiece field while watching for moments of good seeing. For those of us in the northern seats, Polaris is a good target for modest-aperture telescopes that lack motorized tracking.
If you're testing a refractor, try adding a green or yellow filter to the eyepiece. Even the best apochromats may have some color artifacts visible on out-of-focus star images that veil the diffraction patterns. Reflective optics do not require a filter, but they can sometimes help you see what's going on. Experiment.
For most testing, defocus the star image enough to see four to eight rings. Move quickly between the view inside and outside of focus, and carefully compare their appearances. This is a very sensitive test of optical quality and you will likely see some differences, but minor ones will not have a noticeable effect on the telescope's performance for in-focus observing.
Interpreting What You See
Artifacts in a diffraction image can arise if your telescope is not at thermal equilibrium. As a telescope with a solid tube cools, the colder, denser air slides down the lower side of the tube while warmer, lighter air rises along the upper side. This variation in air density can alter the out-of-focus patterns. The effects of large temperature differences are blatant, appearing as amorphous blobs moving slowly across the out-of-focus patterns. A nearly cooled scope will show a dent in one side of the pattern well inside focus, and a bulge on the opposite side of it when well outside of focus. Thermal effects are oriented vertically. If you change the tube's orientation, you'll disturb them briefly, but they'll soon reorient themselves.
If your optics are not quite aligned, the rings in the out-of-focus pattern will be eccentric and the shadow of any central obstruction will appear off-center. The in-focus image will have incomplete diffraction rings squeezed off to one side. Gary Seronik's column "No-Tools Collimation" (S&T: Oct. 2013, p. 64) describes a very easy way for collimating a reflector with a star-test.
Bad seeing often blurs the planets and hides fine detail. It can also make star-testing difficult. In his highly recommended book, Star Testing Astronomical Telescopes (Willmann-Bell, 2008), Harold Richard Suiter explains that poor seeing makes the outside-focus star image look as if the dappling of sunlight on the bottom of a pool is washing across the aperture. Under these conditions you'll need to wait for moments when you can separate the true, unchanging features of the pattern from the effects of seeing. On some nights it may be a hopeless task, but on most nights patience will prevail.
Inside- and outside-focus patterns that don't appear round are signs of astigmatism. A small amount of astigmatism results in oval rings, and moving the eyepiece from one side of focus to the other will change their orientation by 90[degrees] in the field of view. But astigmatism may not mean a problem with the telescope's optics. Turn your head. If the oval pattern also turns, the astigmatism is in your eye. You should also rotate your eyepiece to see if it is a source of astigmatism. In a Newtonian, note the orientation of the oval pattern and rotate the primary mirror 45[degrees]. If the oval also rotates, then the primary is the problem. In a Newtonian reflector, a slightly concave or convex secondary mirror may cause images to appear astigmatic.
If the pattern shows rings that are irregular, especially if they show sharp points, you may have some stress in the way the telescope optics are mounted. Make sure any clips holding a mirror in place or retaining rings securing lens elements are not overly tight.
A common and significant problem with Newtonian mirrors is what opticians call a turned-down edge, meaning that the very outer part of the mirror is too flat. In such cases, inside focus the rings appear washed out and there's a wide, diffuse glow beyond them. Outside focus the contrast of the rings is increased. As a reality check, you can make a circular mask that covers the very outer part of the mirror and repeat the star-test. If you verify that your mirror has a turned-down edge, the telescope's optical performance will be improved by permanently masking the mirror's outer edge.
If a scope's primary mirror or lens has a hill or a trough in the form of a circular band around its center, this "zone" will create a brightened ring on one side of focus that becomes a darkened ring on the other side.
Often a consequence of fast polishing, surface roughness on a lens or mirror causes the rings to appear uneven in brightness, with blotches of light and dark that remain at fixed locations within the rings and gaps. Seeing can produce similar effects, but the positions of the blotches are ever changing.
There's a fair chance your telescope will show some spherical aberration, which is a smooth variation of focus depending on where the incoming light falls on the radius of the scope's objective. A common form of spherical aberration comes from a mirror being undercorrected, where the light from the center of the mirror focuses slightly long relative to light reflected from the edge. The opposite is true in the case of an overcorrected mirror.
Ideally, the outer diffraction ring should appear equally bright inside and outside of focus. If the optics are undercorrected, inside focus the outer ring will brighten and light will be lost in the inner part of the pattern. Outside focus the outer ring will darken and the inside will brighten. With overcorrection the reverse happens. A mirror's correction can change as it cools during the night.
For most of us, the biggest hindrance to star-testing is bad seeing. To avoid it, you can star-test early in the day using the Sun's reflection off a distant, shiny sphere. Early in the day, the air is often still over long stretches of lawn. You can also buy or make a portable artificial star for use at night. If you use the Sun's reflection or an artificial star, it must be sufficiently far from the telescope. (In the May 1991 issue, page 528, Roger Sinnott detailed the aberrations caused by focusing a scope closer than infinity.)
Star-testing is often described as easy. The basics are certainly simple, but it takes time to become a proficient tester, especially given the vagaries of seeing and a telescope's thermal behavior. Spend time learning the nuances of being a tad "out of focus," and you'll know how and when you'll get your finest in-focus views.
Notes on the Diffraction Images with this Article
Except where noted, the images of diffraction patterns appearing with this article were made with high-quality telescopes--an 85-mm refractor and a 90-mm Maksutov-Cassegrain. Both were fitted with appropriate Barlow lenses to yield effective focal lengths of approximately 3,000 mm. In order to enlarge the in-focus appearance of the Airy disk and improve its visibility in the images, each scope was stopped down to a 50-mm aperture. This also enhanced the brightness of the diffraction rings in the Maksutov's images because the scope's central obstruction now represented 55% of the aperture's diameter, transferring more light from the Airy disk into the rings.
An artificial star was created by reflecting the beam of a helium-neon laser located near the telescopes off a small, convex mirror located about 50 feet (15 meters) away. As noted in Alan French's accompanying text, because this artificial star was relatively close to the telescopes, it introduced a small amount of spherical aberration in the images--something that would not have occurred if the telescopes had been focused for infinity.
It's in the Book
There's one-stop-shopping for anyone wanting to learn all the nuances that can be gleaned from a star-test--the second edition of Harold Richard Suiter's Star Testing Astronomical Telescopes (Willmann-Bell, 2008). An applied physicist, Suiter gives detailed theory and background on star-testing amateur telescopes. A highlight of the book, however, is the computer-generated diffraction images that will help you determine what level of errors exist in an optical system. Subtitled "A Manual for Optical Evaluation and Adjustment," the book is a proverbial gold mine of material for extracting the most information from a star-test. A copy belongs on every serious telescope-user's bookshelf.
Telescope maker and observer Alan French wrote about eyepieces in our September 2013 issue, page 68. His wife, Sue, authors our monthly Deep-Sky Wonders column.
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|Title Annotation:||Quick Optical Evaluation|
|Publication:||Sky & Telescope|
|Date:||Jul 1, 2014|
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