# Stopping down a telescope to reduce brightness by 5 magnitudes

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Suppose we have a variable star with a change in magnitude between maximum and minimum of 5 mag.

How much would you need to stop down a telescope (block some of the area) so that the star at maximum brightness appears to be the same brightness as when it is at minimum magnitude with no stop.

Treating as a school question

Each change of 1 magnitude changes brightness by how much? So by what factor will a change of 5 magnitudes give? (5 magnitudes is a very convenient number for this question)

You will need to reduce the area of the telescope by the same factor.

## Resolution and Seeing

There is much emphasis, when discussing telescope optics, on the resolution capabilities of the instrument. The quantification of telescopic resolution is somewhat a subjective process. Examples are the Rayleigh, Dawes, and Sparrow criteria. For more detail on this topic, please refer to “Telescope Optics” by Rutten and van Venrooij. The well-known theoretical Rayleigh resolution limit, similar to Dawes but more restrictive, is based on diffraction [ α = 1.22 λ / D ] where α is the resolution in radians, λ is the wavelength and D is the objective size. We typically select a λ of 550 nanometers (5500 Angstroms), which is the wavelength the eye is most sensitive to. With this wavelength, and D in meters, the formula for α in arcseconds simplifies to [ α = 0.1384 / D ]

Therefore, AAI’s diffraction resolution for its 10-inch (0.25 m) and 24-inch (0.61 m) telescopes would be 0.54 and 0.23 arcseconds, respectively. We know, of course, that our telescope’s resolution is nowhere near as good as the Rayleigh diffraction formula implies. The reason is atmospheric seeing.

Earth-based telescopes, including our naked eyes, must contend with image distortion and scintillation caused by atmospheric disturbances as light reaches us from outer space. That’s why stars twinkle and images blur and dance when viewed with telescopes or binoculars. This effect worsens as the zenith angle increases. Recall that the zenith angle is the angular distance from the zenith, and equals 90 degrees at the horizon. Temperature changes and winds create variations in atmospheric refractive indices resulting in these image distortions. This condition is called “seeing”, and is a prime consideration in selecting the location of an observatory.

Atmospheric seeing varies considerably based on location, weather conditions and time of day. The average seeing in Muana Kea, a prime location, is about 0.5 arcseconds, while the Mount Wilson observatory has seeing in the 1 arcsecond range. These are mountain locations, which have better seeing than our local New Jersey sites. Our conditions typically result in 1 to 4+ arcsecond seeing. So if our seeing is in the 1 to 4 arcsecond range, what does this imply about effective telescope resolution apertures?

[ D = 0.1384 / α ]

For 1 arcsecond seeing, the effective aperture is 0.138 meters or 5.45 inches and for 4 arcsecond seeing, it’s 0.0346 meters or 1.36 inches. In other words, the effective resolution capability of AAI’s large telescopes is that of a 5 1/2-inch instrument, or likely, even smaller. This is especially the case in solar viewing, where the Sun’s energy creates significant atmospheric turbulence and seeing in daytime degrades to the 2 to 4+ arcsecond range. Since AAI’s telescopes are larger than our seeing limitation, their greatest benefit over smaller telescopes is their light gathering capability, an important nighttime advantage. It should also be pointed out that when viewing with larger apertures, there might be brief moments of near diffraction limited resolution. However, when used photographically, seeing will usually be the limiting resolution.

How can the effects of seeing be minimized? Ideal locations are remote mountain peaks with prevailing winds coming from the ocean. Hawaii, the Chilean ranges and the Canary Islands are prime examples. In our area, avoiding weather fronts and locating instruments on grass will help. In my personal solar photography experience, stopping down a telescope’s aperture to 4 – 6 cm consistently yields the best results.

A good amateur Internet site on estimating seeing effects is by the Portland, Oregon based Rose City Astronomers http://www.rca-omsi.org/seeing.htm

Of course, professional observatories have begun to deal with seeing using active and adaptive optics, where mirrors are tilted or deliberately distorted to compensate for atmospheric effects. These adjustments can take place in the millisecond range, yielding resolutions rivaling that of the Hubble Space Telescope. As an aside, one should recognize that radio telescopes are not bothered by seeing (or light pollution) because they deal with much larger wavelengths, in the decimeter or meter range.

## Contents

For an ND filter with optical density d, the fraction of the optical power transmitted through the filter can be calculated as

where I is the intensity after the filter, and I0 is the incident intensity. [1]

The use of an ND filter allows the photographer to use a larger aperture that is at or below the diffraction limit, which varies depending on the size of the sensory medium (film or digital) and for many cameras is between f/8 and f/11, with smaller sensory medium sizes needing larger-sized apertures, and larger ones able to use smaller apertures. ND filters can also be used to reduce the depth of field of an image (by allowing the use of a larger aperture) where otherwise not possible due to a maximal shutter speed limit.

Instead of reducing the aperture to limit light, the photographer can add a ND filter to limit light, and can then set the shutter speed according to the particular motion desired (blur of water movement, for example) and the aperture set as needed (small aperture for maximal sharpness or large aperture for narrow depth of field (subject in focus and background out of focus)). Using a digital camera, the photographer can see the image right away and choose the best ND filter to use for the scene being captured by first knowing the best aperture to use for maximal sharpness desired. The shutter speed would be selected by finding the desired blur from subject movement. The camera would be set up for these in manual mode, and then the overall exposure adjusted darker by adjusting either aperture or shutter speed, noting the number of stops needed to bring the exposure to that which is desired. That offset would then be the amount of stops needed in the ND filter to use for that scene.

Examples of this use include:

• Blurring water motion (e.g. waterfalls, rivers, oceans).
• Reducing depth of field in very bright light (e.g. daylight).
• When using a flash on a camera with a focal-plane shutter, exposure time is limited to the maximal speed (often 1/250th of a second, at best), at which the entire film or sensor is exposed to light at one instant. Without an ND filter, this can result in the need to use f/8 or higher.
• Using a wider aperture to stay below the diffraction limit.
• Reduce the visibility of moving objects.
• Add motion blur to subjects.
• Extended time exposures.

Neutral-density filters are used to control exposure with photographic catadioptric lenses, since the use of a traditional iris diaphragm increases the ratio of the central obstruction found in those systems, leading to poor performance.

ND filters find applications in several high-precision laser experiments because the power of a laser cannot be adjusted without changing other properties of the laser light (e.g. collimation of the beam). Moreover, most lasers have a minimal power setting at which they can be operated. To achieve the desired light attenuation, one or more neutral-density filters can be placed in the path of the beam.

Large telescopes can cause the Moon and planets to become too bright and lose contrast. A neutral-density filter can increase the contrast and cut down the brightness, making the Moon easier to view.

A graduated ND filter is similar, except that the intensity varies across the surface of the filter. This is useful when one region of the image is bright and the rest is not, as in a picture of a sunset.

The transition area, or edge, is available in different variations (soft, hard, attenuator). The most common is a soft edge and provides a smooth transition from the ND side and the clear side. Hard-edge filters have a sharp transition from ND to clear, and the attenuator edge changes gradually over most of the filter, so the transition is less noticeable.

Another type of ND filter configuration is the ND-filter wheel. It consists of two perforated glass disks that have progressively denser coating applied around the perforation on the face of each disk. When the two disks are counter-rotated in front of each other, they gradually and evenly go from 100% transmission to 0% transmission. These are used on catadioptric telescopes mentioned above and in any system that is required to work at 100% of its aperture (usually because the system is required to work at its maximal angular resolution).

In practice, ND filters are not perfect, as they do not reduce the intensity of all wavelengths equally. This can sometimes create color casts in recorded images, particularly with inexpensive filters. More significantly, most ND filters are only specified over the visible region of the spectrum and do not proportionally block all wavelengths of ultraviolet or infrared radiation. This can be dangerous if using ND filters to view sources (such as the Sun or white-hot metal or glass), which emit intense invisible radiation, since the eye may be damaged even though the source does not look bright when viewed through the filter. Special filters must be used if such sources are to be safely viewed.

An inexpensive, homemade alternative to professional ND filters can be made from a piece of welder's glass. Depending on the rating of the welder's glass, this can have the effect of a 10-stop filter.

### Variable neutral-density filter Edit

The main disadvantage of neutral-density filters is that different situations might require a range of different filters. This can become an expensive proposition, especially if using screw filters with different lens filter sizes, which would require carrying a set for each diameter of lens carried (although inexpensive step-up rings can eliminate this requirement). To counter this problem, some manufacturers have created variable ND filters. These can work by placing two polarizing filters together, at least one of which can rotate. The rear polarizing filter cuts out light in one plane. As the front element is rotated, it cuts out an increasing amount of the remaining light, the closer the front filters comes to being perpendicular to the rear filter. By using this technique, the amount of light reaching the sensor can be varied with almost infinite control.

The advantage of this approach is reduced bulk and expenses, but one drawback is a loss of image quality caused by both using two elements together and by combining two polarizing filters.

### Extreme ND filters Edit

To create ethereal looking landscapes and seascapes with extremely blurred water or other motion, the use of multiple stacked ND filters might be required. This had, as in the case of variable NDs, the effect of reducing image quality. To counter this, some manufacturers have produced high-quality extreme ND filters. Typically these are rated at a 10-stop reduction, allowing very slow shutter speeds even in relatively bright conditions.

In photography, ND filters are quantified by their optical density or equivalently their f-stop reduction. In microscopy, the transmittance value is sometimes used. In astronomy, the fractional transmittance is sometimes used (eclipses).

## Stopping down a telescope to reduce brightness by 5 magnitudes - Astronomy

hy would anyone want to do astrophotography with a regular camera lens instead of a telescope? There are many reasons. Some objects, like the Milky Way and the Veil Nebula, are too big for the field of view of most telescopes. A regular lens gives you the flexibility to set up quickly, without the hassle and expense of a heavy telescope, wires, large batteries, and (for some cameras) a laptop computer, Windows, device drivers, and software. Wide-field images of the Milky Way or the stars can also be very beautiful. And sometimes you can take more interesting pictures with a regular lens than are possible with a big telescope, such as a picture of a flock of geese flying in front of the Moon, the optical distortion caused by a jet exhaust, or the Moon rising over a mountain in Yosemite National Park.

The criteria for a good lens for photographing stars and photographing during daylight are quite different. In this article I will discuss some of the technical and photographic aspects of selecting and using a camera lens for astrophotography.

#### Lens criteria for telescope-free astrophotography

Image of a portion of the Milky Way in the constellation of Cygnus. This image was made without a telescope&mdashonly an 80&ndash200mm f/2.8D zoom lens (set at 100 mm) on an ordinary tripod, using an unmodified Nikon D7000. A total of 28 5-second exposures, taken in Raw mode at ISO 3200, were combined in software to reduce the amount of noise. This image was also re-sized and contrast-adjusted. The reddish area in the center-right is the North America Nebula. Compare this image with the one under Nebulae.

For cameras, there is no dispute that a DSLR camera is as low as you can realistically go if you want to take good quality pictures at night (although there are some people who still use film cameras, and get good results). But there's a great deal of confusion about lenses. Some camera review websites ridicule the idea of obsessing over lens size. They advise you to just move closer to the subject. That's great advice if you're taking pictures of your dog, which might be three feet away, but when the subject is 1,800,000 light years away, it's not really an option. (However, if you have a few billion bucks of taxpayer money lying around, as NASA does, it's still very good advice.)

Astrophotography is a science. The golden rule in science is: always make the raw data as good as you can get it. To do astrophotography well, you're better off spending money on good lenses than buying a cheap one and trying to fix the image in Photoshop. Photoshopping your images will only make them look unnatural. For example, one mistake people often make with Photoshop is to make the background black, thereby removing all the faint detail from the image. Experienced astrophotographers can spot this instantly and would diss your image.

That said, it's possible to get great results with lenses costing around a hundred bucks. The biggest factor in widefield astrophotography is not the lens, but the amount of light pollution at your site. The worse the light pollution, the harder it is to subtract it out.

#### Distortion

Before I start, let me dispel a few myths. Using a camera lens instead of a telescope will not necessarily make your task easier. You will have much more trouble with light pollution with a regular lens than with a telescope. You will also have the additional task of making your photograph into an interesting composition. That's not usually an option with a telescope. Although many people are attracted to camera lens astrophotography because they think it's cheaper, this is not necessarily so. You can easily spend one or two thousand dollars for a good camera lens. For that amount of money, you could get a very good telescope and a computerized mount.

Coma distortion at the edge of a 35-mm f/1.8 lens at different apertures. This is considered to be an excellent lens, but for star fields it's only usable when stopped down four steps. A slower lens, such as an f/2.8, would have to be stopped down four more steps, which means you're already down to f/4.5. (D7000, 10 sec, ISO 1600, daylight white balance, re-sized)

On the other hand, with a camera lens there's less of a need to be familiar with the sky. You just point in the general direction of "up" and take your picture. And if you get bored with it, you can use the lenses for other things, like throwing them at your dog when it barks too much because you're not taking any pictures of it. So it's a good way for beginners to get started.

The three factors that are most important in photographing stars are chromatic aberration (CA), speed, and sharpness.

Chromatic aberration Even some lenses labeled ED, which have some elements made of extra-low dispersion glass, have unacceptable CA. For a landscape photo, CA isn't too important. For stars, what you'll get is 2 or 3 separate stars in the corners - a red, white and blue star next to each other. Yes, you can sometimes fix this in software, but it's a pain. Don't waste your time with a non-ED lens.

Un-resized photo of the Moon taken with a Nikkor VR 18&ndash300mm f/3.5&ndash5.6G zoom lens (D7000, 1/100s, f/8, focal length 300 mm, focus mode manual, ISO 100, cropped, slight sharpening applied). A better lens would avoid the chromatic aberration visible here and give a sharper result.

The dispute about sharpness is probably a holdover from the old days when people used to print hard copies of their photos. Even so, it has a point: because of the optical low-pass filter in almost all DSLR cameras (the D800E and D7100 being the only exceptions that I know of), your images will always be slightly fuzzy when viewed full-size, even when they're taken with a multi-thousand-dollar lens. To get an artifact-free, sharp image, it's usually necessary to reduce it to about half its original size. I use the &ldquobin pixels - average&rdquo function in Imal for this, because this feature also reduces the image noise, but it can also be done in Photoshop.

An articulating screen is a big convenience. I used to use a portable TV, but they tend to suck up battery power.

Some other features are important for daytime photography, but less so for astrophotography:

Vibration Reduction A tripod or mount and a remote shutter release are essential for any kind of astrophotography. Vibration reduction doesn't help. Leave VR turned off if your lens has it. Most of my lenses don't even have it&mdashbut then, I learned photography with an old manual film camera and subsequently migrated to a Coolpix 880, which was so slow it forced me to learn the tricks of holding a camera steady (like, for instance, gluing it to a rock).

Lens creep distortion in infrared image of the planet Jupiter taken with a zoom lens and no duct tape. Settings: Modified D90, R72 filter, Nikkor 80&ndash200 f/2.8D, f/3.2, starting focal length 86 mm, 9 sec, ISO 1600.

Geometric distortion can create big headaches when you try to combine multiple frames. If distortion is present, some parts of the combined image will not be lined up, causing the image to appear out of focus. This could happen if the lens is off-center or tilted, or if there are imperfections in your filter, lens, or camera sensor.

#### Lenses

Satellite trail photographed with Nikkor 50mm f/1.2 lens (D7000, 2 sec, f/2, ISO 4000, cropped, resized to 50% width). This is a crop from a corner of the image, yet the lens is so good that no CA and very little coma are visible. Satellite trails are generally fainter than airplane trails, except for big satellites like the ISS. With experience, it is easy to tell the difference.

So, what is the best lens to use? As with daytime photography, that depends on what you want to photograph. Select your lens on the basis of how big your object is. A free Windows program (ccdcalc) can show you how some popular astronomical objects fit in the field of view for various telescopes and lenses.

Large objects Milky Way, constellations, star trails, meteors&mdashuse a short lens.

Nebulas are good subjects for telescope-free astrophotography, because some of them have angular sizes many times bigger than the Moon. The only problem is that most nebulas emit their light at 656 nanometers, which is almost completely blocked by the camera's internal filter. To capture that beautiful deep red glow of recombining hydrogen atoms, you have to have your camera modified for infrared. But some nebulas, like the Swan Nebula and the Orion Nebula, are bright enough that you can nail them even with an unmodified camera.

Some star clusters, such as the Pleiades and Hyades, are also big enough that a telephoto lens will work satisfactorily. But the result won't be as good as if you used a telescope, because a small lens will miss some of the finer details.

A 30-sec exposure of Ursa Major taken with a 35-mm f/1.8 lens on a Nikon D7000 at ISO 1600. Even though the sky looked completely dark to the eye, it appears light brown in this photo because of light pollution. (However, night photographs taken with a D7000 tend to appear a bit more brown than with other cameras.) Correcting this in software would be possible on this image, because there's lots of signal to work with. This particular image was photobombed by a firefly, which is visible as three yellow streaks in the upper right.

The same lens stopped down to f/4.0. This image would be harder to fix because the signal is fainter, but the camera noise is the same. You would have to take several images and combine them on the computer (using Deep Sky Stacker or some commercial software like Nebulosity) to get a noise-free image. These three images in this panel have been resized and converted from 48 to 24 bits/pixel, but not otherwise altered.

With a 70&ndash300mm zoom lens set at 300 mm, the stars are a little brighter than the 35mm lens because of the larger aperture. However, star trailing now becomes a problem. Also, f/4.5 is as far open as this lens will get. At 300mm, it's only f/5.6. Although it's not visible here, the stars in the corners are highly distorted. In real life, you'd probably have to stop this lens down to f/8 to get acceptable star shapes.

Camera lenses are measured by their focal length in millimeters. Telescopes are measured by the diameter of their primary lens or primary mirror in millimeters. To convert, use these formulas:
focal length mm / aperture mm = f-number.
focal length mm / f-number = aperture mm .

The number of photons collected, which determines maximum brightness, is proportional to aperture squared. Speed, that is, the ability to focus a lot of light efficiently onto a single pixel element, is inversely related to the f-number. Magnification is proportional to focal length. Resolution is determined by many factors, including the turbulence in the atmosphere and the aperture of the lens.

I am most familiar with Nikon lenses, since I've used a bunch of them, but Canon lenses are just as good. Nikons can be used on a Canon, if you add a special adapter, but Canon lenses will not work on a Nikon. Here is my brief review of some Nikon lenses for telescope-free astrophotography.

Nikkor 28&ndash300mm f/3.5&ndash5.6 (FX)(Aperture = 8&ndash53.6 mm). Some people complain that the focus ring on this one is too small. At higher zoom it goes down to f/5.6, which means it's fairly slow. This is a great travel lens, but it's not ideal for astrophotography. The difference between f/3.5 and f/1.8 is night and day&mdashliterally (see photos at right).

Aperture rings Some lenses don't have an aperture ring, so the aperture can only be set in the camera. These kinds of lenses are fine with a DSLR, but they don't work on CCD astronomy cameras, because most of them don't have any way of setting the aperture. If you ever upgrade to an astronomy camera, you'll have to jam a piece of plastic into the lens aperture lever to keep it from closing down to f/22. These lenses should be avoided if you ever plan to move to a cooled CCD camera.

Because FX lens format is bigger, lenses designed for FX are bigger and tend to gather more light, so they're generally preferable to DX lenses even on a DX camera. Bigger diameter = more resolution and shorter exposures.

#### Optical Aberrations: Problems and Solutions

Problem Characteristic Symptom Solution
Spherical aberration Halos around bright objects, can't get sharp focus Stop down the lens
Chromatic aberration Purple fringes, colors not lined up Use an ED lens
Coma Seagulls in corners Stop down the lens
Diffraction Fuzzy image at f/16 or higher Open up the lens
Out of focus Stars are uniform round disks, not points Use Live View to focus
Images getting darker over time Dew condensation on lens Battery-operated hair dryer
Color noise Colored splotches in image Use lower ISO and longer exposure
Chromatic focal shift Red halos around stars Use a filter or get a better lens
Barrel or pincushion distortion Straight objects appear curved Use a different focal length
Field curvature Out of focus in corners Use a better lens or field flattener
Astigmatism (rare) Asymmetrical stars Lens elements may be misaligned
Tilt Out of focus on one side of image Lens is mounted crooked, re-attach
Insufficient resolution Stars are big blobs instead of points Use a bigger aperture lens
Lens flare Large white circles on image Stop doing remakes of Star Trek

Airplane trails appear as two parallel strings of beads due to the 1-second wing strobe. The red center beacon strobe looks like a fuzzy star, but in this telescope image you can see reflections from parts of the fuselage. Color noise is also visible in the background.

Another common artifact is large red &ldquostars&rdquo that appear in some images and not in others. These are red strobes from airplanes, which flash at one-second intervals. They may be surrounded by a halo caused by reflections off the fuselage. Long time-exposures of the night sky commonly show many trails of red and white flashes going in many directions. If the plane has its landing lights on, you may see four or more solid lines.

Red halos around stars are very common. They're caused when the lens focuses red, green and blue to different points. Many camera lenses do this. That's one reason monochrome CCD cameras give sharper images than color cameras: with a monochrome camera you expose one color at a time, and refocus every time you change filters.

Long white streaks may be airplanes or satellites. Some satellites, especially Iridium satellites, show up as a brief flare that resembles a meteor trail. Or they may periodically get brighter and dimmer if the satellite is tumbling out of control.

#### Star sizes and Airy disks

Orion Nebula photographed with a Nikkor 18&ndash300mm lens (left) and a 4.3-inch refractor scope (right). The image on the right has been shrunk to make the star fields the same size. Even with a three-second exposure, the stars in the left image are not round, and they are larger and fewer in number than the telescope image. Of course, the fact that a tree branch got in the way of the camera doesn't help, either. However, the camera image covered a much wider field of view. Also, the telescope image had to be exposed for 39 times longer to get comparable brightness, because the same photons were spread out over a much wider area on the sensor.
Settings: Left = D7000 on fixed tripod, Nikkor 80&ndash200 f/2.8D at 200 mm, f/3.2, ISO 1600, 49 frames of 3 sec stacked resized to 1/16 original area, cropped, sharpened and contrast-stretched. Right = modified D90 on WO FLT-110 + 0.8x reducer/flattener, f/5.6, CGEM, no guiding, total exposure 96 min, resized to 1/159x original area.

Optically, stars are point sources. However, because of the wave nature of light, an image of a star always appears as a disk, known as an Airy disk, which has a finite size. Several factors determine the size of a star image on your sensor:

Seeing At high magnification, stars are not found at fixed positions, but move around randomly, due to atmospheric turbulence. This is called seeing and it is measured in the number of arcseconds that the star moves, 2&ndash4 arcsec being typical.

One result of this is that it's harder to photograph nebulas with a small lens than a big one because the stars, being proportionally bigger in a small lens, block more of the view.

The Cambridge Photographic Star Atlas is a good example of the trade-offs of doing astrophotography without a telescope. Mellinger and Stoyan used a high-end SBIG 16-bit camera and Minolta 50mm f/1.4 lens, stopped down to f/4, and no telescope, to photograph the stars as seen from both the Northern and Southern hemispheres. The resulting images are spectacular for star fields, but mediocre for nebulae and terrible for galaxies. Photographing small objects such as galaxies and planets is a challenge with a regular lens, because of its lower resolution. The result is typically a saturated white oblong blob with little or no detail. Even Andromeda and the Large Magellanic Cloud, which have a large apparent angular size, can be difficult with a small lens.

#### Mounts

Using an ordinary tripod, how long can you expose before star trailing becomes a problem? Trailing is influenced by four factors:

1. Time The longer you expose, the more trailing you will get.
2. Aperture The more light you can get onto your sensor, the shorter your exposure can be.
3. Magnification With a 35-mm lens and a camera with a DX or APS-C sensor, star trailing becomes objectionable after about 20 seconds. With a 200-mm lens on the same camera, stars begin to change into streaks after only 5 seconds.
4. Declination The amount of trailing per unit time depends on the cosine of the angle from the celestial equator. In plain language, that means if you point directly at the north or south pole, there will be no trailing, and you will get the most trailing for objects on the equator. For example, with a 200mm lens you can expose stars in Ursa Major for up to 5 seconds, but the longest you can expose the Orion Nebula without trailing is about 2 seconds.

There are several ways to deal with this:

Motorized mount Inexpensive motorized mounts made specifically for this purpose are available. As your magnification approaches that of a telescope, getting more precise movement and aligning the mount with the Earth's axis become more and more important. If you're in the northern hemisphere, aligning it is done by pointing the axis of rotation of the mount toward Polaris. The more expensive German equatorial mounts used by amateur astronomers will also work, but they aren't needed at these levels of magnification, unless you want very long time exposures. Some people use a homemade device known as a &ldquobarn-door mount.&rdquo

As mentioned above, trailing can also be caused by zoom lenses zooming by themselves.

#### Nebulae (Added Sep 24, 2013)

Image of a portion of the Milky Way in the constellation of Cygnus using filters. This image was made without a telescope, using a Nikon D90 modified for infrared, and a CGEM motorized mount. The red channel is a single 10-minute exposure with a Baader 7 nm H-alpha filter. The green and blue channels are a single 10-minute exposure with a Celestron 8-nm OIII filter. Lens: Nikkor f/1.2 50 mm, set at f/2.0, ISO 400, no guiding (Cropped and resized).

I mentioned above that nebulas are ideal subjects for astrophotography with a regular camera because they are so big. But what exactly do you need to take good pictures of a nebula? Here's a shopping list:

1. A motorized mount is essential, because you will be exposing for 5 minutes to an hour.
2. At least one two-inch diameter narrow-band filter. Hydrogen-alpha (H&alpha) filters and Oxygen-III (OIII) filters are good to start. (Watch out: some filters marked as H&alpha are really long-pass filters and will give terrible results.)
3. A 52&ndash48 mm step-down ring, plus a set of step-down rings if your lens is something other than 52 mm in diameter.
4. A fast, sharp lens. If your lens isn't sharp, the stars will be so big that they will tend to cover up the nebula.
5. A clear, dark sky.
6. A camera modified for infrared. Some people modify their own camera, but there are many vendors who will do it for a fee. It's a simple modification, and the modified camera can usually still be used for regular photography. If you save the parts it's not difficult to convert it back.
7. For DSLRs, the newest bunch of cameras are preferred because they're much more sensitive. Since you'll be using a narrow-band filter, Live View focusing won't work with the older cameras. You can still focus by trial and error, but a more sensitive camera, like Nikon's D7100 or the Canon equivalent, will make the task much easier.

Some nebulas are bright enough that you can dispense with some of the above items. For example, I've taken reasonably good pictures with a H&alpha narrowband filter of objects that were only a few degrees away from the full moon (dispensing with item no. 5). For a blue oxygen III filter, though, you need dark. A modified camera is only needed for H&alpha and SII, which are in the near-infrared. If you don't want to risk modifying your camera, you can still take great pictures of some nebulas with an unmodified camera, using an OIII filter, but they will appear blue. Unfortunately, not all nebulas emit blue radiation.

Photographic lenses are ideal for wide-angle shots like the photo of the nebulae in Cygnus shown above. This image combines the nebulas around the star Sadr, which is the center of the &ldquocross&rdquo in Cygnus. The butterfly-shaped IC 1318 nebula in the center and the tiny C-shaped Crescent Nebula (NGC 6888) above and to its right appear red. The large white nebula at the lower left is the North America Nebula (NGC 7000). Just above it is the Pelican Nebula. The white parentheses-shaped one at lower right is the Veil Nebula (IC 1340). No telescope was used, but the camera was attached to a CGEM German equatorial mount.

Compare this image with the image at the top of the page, where the North America nebula is just a faint pink smudge superimposed on the Milky Way background. Without a filter, it is virtually impossible to photograph the Veil nebula with a camera lens. With a filter, you almost can't miss it.

The sharpness of the lens makes a huge difference in pictures like this, because the stars are point sources. Don't listen to people who tell you a sharp lens is not necessary. I tried the same nebula on the same night with a f/1.8 35-mm lens, focused to perfection, and instead of sharp points, the stars came out as big fuzzy blobs. So I switched to a manual f/1.2 50-mm lens. The trade-off with this particular lens is that near-infrared and blue don't focus to exactly the same point, so it's necessary to re-focus when switching filters.

Some objects are so large that it's virtually impossible to photograph them with a telescope. That's where the power of telescope-free astronomy comes in. Most people are probably familiar with the gigantic Orion Nebula (see photo above), but they might not realize that it's surrounded by an even larger nebula called Barnard's Loop (Sh2-276), which is over 12 times bigger, both in actual size and apparent size, with an angular size of almost 840 minutes of arc. That's 28 times bigger than the angular size of the Moon. Barnard's Loop covers nearly 15% of the distance from the celestial equator to the pole. Yet despite its size, it is far too faint to be seen with the naked eye, or even through the eyepiece of a typical telescope.

At this scale, the entire Orion Nebula, which is about twice the apparent size of the moon, is only a small white blob in the center, and the Horsehead Nebula is a tiny dark blip near Alnitak (the leftmost of the three large stars in Orion's belt). Photographing Barnard's Loop with a telescope would be like photographing the Empire State Building with a microscope. You could do it, and you'd certainly get better resolution and finer detail, but it would take weeks of exposing and painstakingly stitching images together. The image below took less than an hour to photograph, plus another ten or twenty minutes of computer processing time.

Barnard's Loop in Orion is 320 light years across and only 1300 light years away, so its angular size is 13.8 degrees. (Modified D90 and 50-mm f/1.2 lens.) Compare this image with the one below from a monochrome CCD camera.

Here's the equipment that was used for this image.

1. A DSLR partially modified for infrared, set at ISO 800.
2. CGEM motorized mount (aligned with Polaris using a polar scope).
3. 2-inch H-alpha, 7 nm filter and a 52&ndash48 mm step-down ring.
4. Nikkor 50 mm f/1.2 lens set at f/2.0.
5. A copy of Deep Sky Stacker.
6. Image processing software (Imal or equivalent) to adjust the contrast.

To make this image, I took 11 exposures of 5 minutes each with the H&alpha filter and 8 color exposures of 15 seconds with no filter. At f/2, with moderate levels of light pollution, you can only expose for 10&ndash15 seconds before the the sky background starts to saturate the image sensor. If your lens is slower, you will need proportionately longer exposures. Because Barnard's loop is so faint, the H-alpha filter is essential for blocking out the starlight. Almost nothing is visible through an O III filter hydrogen is by far the strongest signal, so you need a camera that can photograph the near-infrared wavelength of hydrogen. That means either a modified DSLR or a specialized CCD astronomy camera.

In Deep Sky Stacker, make sure to load the color images first, or the software may get confused and make the image completely red. The rule of thumb is: one second without a filter is equivalent to one minute with a filter.

#### Cooled astronomy cameras

Compare this image with the one below taken using a cooled astronomy camera (total exposure 40 min). CCD cameras are more sensitive and have higher resolution than a DSLR. Images are smoother because of the greater pixel depth, but the cameras are harder to use. Generally they're controlled by a laptop computer through a USB, ethernet, or serial cable.

You can get comparable images with a DSLR, but it takes a lot longer. See linuxsetup137.html for details on setting up a CCD camera. What an astronomy camera buys you is more efficient use of your limited observing time.

Barnard's Loop photographed with the same Nikkor f/1.2 lens, but using a cooled astronomy camera instead of a DSLR. Left: Red=H&alpha, green=luminance and blue=blue. Right=Halpha only. These images were taken on a night when lots of airplanes were flying around, so they are crisscrossed with airplane trails. Nebulae are often shown in grayscale to make it easier to see the detail. Technically this was a cooled CCD camera, but in this instance additional cooling was not actually necessary. It was so cold that when I set the camera to &minus15C, instead of cooling down, the heater came on.

Cropped, unresized image of Crescent Nebula (NGC 6888) taken with a Nikkor 50mm f/1.2 lens without a telescope using a cooled CCD camera and filters. Red=H&alpha, Green and Blue = OIII. Notice how the nebula is partially obscured by the stars. A telescope image would show more detail and the stars would be smaller, while a DSLR image would be fuzzier and many of the fainter stars would be lost in the noise. (Contrast-stretched and cropped to 1.46% of original area. CGEM motorized mount total exposure 90 min.)

Veil nebula photographed with a 180 mm f/2.8 telephoto camera lens. Because the Veil Nebula is so big, most telescopes can only capture part of it at a time, but it's a perfect match for this lens. I used a cooled monochrome CCD camera for this image. That allows you to re-focus after changing filters, which is necessary with most camera lenses. The limiting factor here was the blue-green background from the Moon, which was out while the picture was taken. I subtracted that from the image. Even so, it only took 20 minutes with each filter to get this image. (Red = H-alpha filter Green and blue = OIII filter. Not cropped, but contrast-stretched and resized. CGEM motorized mount, no guiding total exposure was 20 min H-alpha and 20 min O-III.)

Jupiter and Saturn conjunction photographed without a telescope. Three of Jupiter's moons are visible around Jupiter (at left). (D7000, ISO 500, 300 mm lens, f/11, five frames of 1 sec stacked manually, cropped and sharpened)

Update (Mar 31, 2015) Nikon has a new DSLR designed for astrophotography called the D810A. It's a 36.3 MP CMOS camera sensitive to wavelengths out to 656 nm that does long exposures up to 15 minutes, and has no optical low pass filter.

See Mounting big lenses for astrophotography for the basics of how to attach things together when doing astrophotography without a telescope.

Update (Dec 23, 2020) Think it's impossible to photograph the moons of Jupiter without a telescope? Think again. At right is a photo of the conjunction of Jupiter and Venus on December 22, 2020. Three of Jupiter's moons are visible. In the time it would have taken to set up a telescope and find the target, the planets would have set behind the trees. Then again, extreme close-ups of trees are nice too.

See Mounting big lenses for astrophotography for the basics of how to attach things together when doing astrophotography without a telescope.

## Lens VS Telescope: does aperture affect resolving power/sharpness?

So this is basically a continuation of an idea from another thread talking about different sensors and their ability to resolve. One poster brought up telescopes to make a point, but the thread maxed out and I thought this was worth discussing (if you don't I will respect that and let you quietly leave the thread, without assassinating you ).

So, Here's the meat n potatoes. One can read nearly everywhere, web, books, personal logs, astrophotographers (AP) will swear by this, that greater aperture will improve resolution. When I say aperture I don't mean F stop, I mean actual size of the front element (objective element). To get us started here is a quote from Telescope.com,

"A telescope's most important attribute is its aperture, which determines the brightness and sharpness of everything you see through your scope. Technically, this is the diameter of the main lens or mirror and as the aperture increases so does the details of the image you see. Depending on the aperture you will either see an open or a restricted field of view. For example a good 10" aperture scope shows sharper images than even a well-made 6" aperture telescope."

So, im trying to sort out the context of this claim. To say the details of the image you see improves with aperture size isn't something we hear with camera photography much, but why? Does this not apply to camera lenses? And if not why not? A prime lens is not much different than a telescope, in fact they are nearly identical. Even using a telescope tube assembly attached to a camera is called prime scoping.

So what gives here? They physics behind it will have to be sorted out, which is why I hope this thread attracts those of you who can do so. As I understand it, larger aperture would possibly reduce affects of diffraction (but at a point diffraction may already be un-noticeable?), and it would add more light for better SNR. But if a photo is already at base ISO with proper exposure, more light won't help SNR right? So for an increase in detail, it must be either diffraction reduction or something else.

This brings up another question, is the severity of diffraction based on the F stop or the diameter of the front element (of lens or scope)? To me this is all important information. A lot of these AP guys are very serious into their stuff, I find it hard to accept that they are just wrong. I have met some serious AP buffs and they put any photographer I know to shame when it comes to enthusiasm.

So the question, does front element diameter (in refractors) impact detail and resolving power, or is something else going on here, either they are wrong or misunderstood? I know there are other factors that will affect detail, like quality of glass and aberrations, so lets understand that we are speaking about even playing fields with those. If all else is equal, ie if quantity of light isn't a factor with ISO ect, will a larger aperture offer more detail?

"Run to the light, Carol Anne. Run as fast as you can!"

Astronomers and makers of telescopes know that resolving power increases with lens diameter. For telescopes, it's kind of obvious. 1.) it's like triangulation, where the wider the two measurement points, the more precise the measurement 2.) assuming DOF is a don't care, the wider the opening, the less diffraction.

There are probably a few things that make photography different. 1.) Larger lenses are more expensive and harder to make, and so may not be manufactured as precisely as smaller ones 2.) if the real world, you do care about DOF, and for the same DOF, you have equal diffraction 3.) larger lenses cost a heck of a lot more, and if you already have enough resolution, why spend more? 4.) very few consumer lenses are diffraction limited.

In my opinion, the increase in resolving power due to larger lenses, while theoretically correct, doesn't mean that much to cameras.

The real reason I brought up the point is to change people's mindset about sensor size and light gathering. Everyone's been taught that a larger sensor gives better results than a smaller one, but most haven't thought it through and realized that's because of the larger lenses. Astronomers pick a telescope size first, a sensor second. Photographers pick the sensor size, then the lenses.

What astronomers do makes more sense to me. The difference between equivalent lens F-stops can be 10:1 or greater, while the difference in sensor performance could never be more than say, 2:1. Lens first, sensor second.

I don't know why this concept meets such resistance. It means that a small sensor system could equal a larger one if you put big enough lenses on it. Which we know is pretty much true with the use of speed boosters. Sounds silly to some, but the Hubble has a medium format size sensor, which is TINY compared to the size of it's lens. Proportion wise, that worse that mating a cell phone to a Canon L lens.

A logical output of equivalence is that sensor size doesn't matter. For any given format, you can pick a lens which gives equivalent performance to another size format.

I've said it before. If smaller lenses give you the performance you need, you might as well buy into a smaller body system. If you think you need large lenses, may as well get a larger system. Doesn't make much sense to put huge lenses on a tiny body and vice versa.

Now, lets go out a get a beer while we watch this thread grow to 150 . . .

professional cynic and contrarian: don't take it personally
http://500px.com/omearak

Ontario Gone wrote:

So this is basically a continuation of an idea from another thread talking about different sensors and their ability to resolve. One poster brought up telescopes to make a point, but the thread maxed out and I thought this was worth discussing (if you don't I will respect that and let you quietly leave the thread, without assassinating you ).

So, Here's the meat n potatoes. One can read nearly everywhere, web, books, personal logs, astrophotographers (AP) will swear by this, that greater aperture will improve resolution. When I say aperture I don't mean F stop, I mean actual size of the front element (objective element). To get us started here is a quote from Telescope.com,

"A telescope's most important attribute is its aperture, which determines the brightness and sharpness of everything you see through your scope. Technically, this is the diameter of the main lens or mirror and as the aperture increases so does the details of the image you see. Depending on the aperture you will either see an open or a restricted field of view. For example a good 10" aperture scope shows sharper images than even a well-made 6" aperture telescope."

So, im trying to sort out the context of this claim. To say the details of the image you see improves with aperture size isn't something we hear with camera photography much, but why? Does this not apply to camera lenses? And if not why not? A prime lens is not much different than a telescope, in fact they are nearly identical. Even using a telescope tube assembly attached to a camera is called prime scoping.

So what gives here? They physics behind it will have to be sorted out, which is why I hope this thread attracts those of you who can do so. As I understand it, larger aperture would possibly reduce affects of diffraction (but at a point diffraction may already be un-noticeable?), and it would add more light for better SNR. But if a photo is already at base ISO with proper exposure, more light won't help SNR right? So for an increase in detail, it must be either diffraction reduction or something else.

This brings up another question, is the severity of diffraction based on the F stop or the diameter of the front element (of lens or scope)? To me this is all important information. A lot of these AP guys are very serious into their stuff, I find it hard to accept that they are just wrong. I have met some serious AP buffs and they put any photographer I know to shame when it comes to enthusiasm.

So the question, does front element diameter (in refractors) impact detail and resolving power, or is something else going on here, either they are wrong or misunderstood? I know there are other factors that will affect detail, like quality of glass and aberrations, so lets understand that we are speaking about even playing fields with those. If all else is equal, ie if quantity of light isn't a factor with ISO ect, will a larger aperture offer more detail?

Resolution, DOF, and diffraction all go hand-in-hand:

As the DOF deepens, more of the image is rendered sharply, both because more of the image is within the DOF, and because the aberrations of the lens lessens as the aperture gets smaller -- up to a point. Depending on the sensor pixel size and display size of an image, the effects of diffraction softening will begin to degrade the sharpness of the image more than the deeper DOF and lesser aberrations increase the sharpness. However, the point diffraction softening outweighs a deeper DOF and lesser aberrations depends tremendously upon the scene and the lens sharpness. It is common to read about "diffraction limited apertures", but these are based on a "perfect" lens and images where the whole of the scene lies within the DOF. In other words, it is quite common to achieve a sharper and more detailed image that is past the "diffraction limited" aperture due to the deeper DOF including more of the scene.

So, for an aberration free lens where the entire scene is within the DOF wide open, then the highest resolution would be obtained wide open.  Of course, lenses are not aberration free nor do we often take photos of scenes where DOF is a non-issue.

The other issue is noise.  The wider the aperture, the more light that falls on the sensor for a given exposure time, and thus the less the noise, which is especially pertinent for scenes with motion in them where a faster exposure time is needed to mitigate the effects of motion blur which is one of the, if not the, most destructive attributes with regards to resolution.

Thus, the highest resolution is achieved by balancing DOF, lens aberrations, diffraction, motion blur, and noise, and this will only very rarely occur at the widest aperture in photography.

Easy ways to improve your viewing.

## STOPPING DOWN A TELESCOPE

Increased clarity, along with a longer focal ratio, decreased brightness and the ability to use the best part of your mirror is some of the advantages of Stopping Down a Telescope.

The technique is particularly useful on larger reflecting and refracting telescopes about 8" (reflecting) and 6" (refracting) and above.

Cut out a cardboard or similar disk about the same diameter as your tube. This will be placed over the end of the telescope (where the light goes in). From the disk, cut holes in the places where only the mirror sees (no obstruction). eg. between secondary mirror arms, around the secondary mirror, or even if your focuser sticks in too far creating an obstruction. Keep the cornering of the circles neat. Oblongs are ok. Each hole is now your mirror without the obstruction of the secondary mirror, arms and maybe focuser which steal resolution. Your new size mirror changes the focal ratio of the telescope to a longer one making it great for Moon, planets and Transits - as long as the subject is bright enough for you now, smaller mirror. Using circles in the disk makes it easier to work out your new focal ratio etc. Circles also allow you to choose what part of the mirror is used by rotating the disk.

## Astronomy 110 Laboratory: Course Outline

One evening meeting per week, involving a combination of short lecture, laboratory work, use of astronomical computer software, and field trips for astronomical observations. There will be one daytime meeting to view the Sun, and one or more nighttime field trips to a dark site to view the Milky Way and faint objects. Enrollment will be limited to 24 students per section.

Flexibility is necessary in conducting this course. At any given time only some planets and other objects are visible. Moreover, observing may be impossible during bad weather when it's cloudy, laboratory exercises or work with astronomical computer software will be substituted for astronomical viewing. From time to time, additional viewing sessions may be scheduled to take advantage of unique astronomical events such as eclipses, meteor showers, occultations, etc.

Warning: this section is still in development, and some parts may be added or change in the future. This warning will be deleted after all additions and changes have been introduced.

### OVERVIEW OF THE PROGRAM

-1. Organization. Release form. Transportation to and from Kapiolani Park. Procedures, general information, grading system. Books required and recommended. An astronomical reflecting telescope: description, assembly, first use. Questionnaires. The five-minute astronomy talk. Burning questions. Visit to the computer laboratory and first contact with the computers.

0. Starting point: primitive man and primitive thinking. Hypothetical ideas about the first rational thinkers. Starting assumptions: we need to postulate the existence of (1) an objective reality, accessible to all observers, and of (2) natural laws without exceptions. Reason alone is not enough: the case of Aristotle. Experimental control: the example of Galileo. The modern scientific method and the ideas of Karl Popper. Distinguishing science from pseudo-science.

Practical activities: observation and orientation. The celestial sphere, cardinal points, other basic features. Coordinate systems. Measuring time. Time zones. Universal time. Julian dates.

1. First step: sphericity and rotation of the Earth. Experimental evidence: Eratosthenes, Foucault's pendulum. Day and night: the Earth as a dark body. The Sun is hot, but the Earth is not. The Moon and its importance as a second example of dark body. Lunar phases and lunar sphericity. Testing a model: explanation of lunar phases as a function of position relative to the Sun.

Practical activities: getting familiar with maps of the sky. The brightest stars in the sky, the most easily recognizable constellations. Mapping the positions of the Moon for different phases. Angles and their units: degrees and radians. Measuring angular distances.

2. Second step: physical size, angular size, and their relation with distance. The size of the Earth. Parallax and the distance to the Moon. Size of the Moon. Are the Sun and Moon at the same distance from us? The argument by Aristarchus as a test to be decided by observation. Lunar eclipses and verification of sizes and distances.

Practical activities: using the astronomical ephemeris to test intervals betweeen lunar phases. Star brightnesses and the magnitude system. Variable stars: locating Delta Cephei. Graphs and functions: how to plot a variable quantity as a function of another. Plots as a function of time: periods and phases.

3. Third step: a first idea of the size of the Sun. What moves around what? The planets and their complicated apparent motions. Demonstration of the comparative simplicity of the heliocentric system. Prediction: phases of Venus. Galileo and his telescopic discoveries. Confirmation of the heliocentric system. Kepler's laws. Determination of distances within the inner Solar system by radar. Distances to the Sun and to all planets in the solar system using Kepler's third law. Sizes of the Sun and planets.

Practical activities: mapping the motions of planets across the constellations. The apparent size of the Moon, and Kepler's laws. Visual or binocular observations of Delta Cephei. Laboratory activity: study of a simple telescope.

4. Fourth step: Gravitation. From "all things fall down" to the concept of central attraction from a spherical body. Newton's contribution: the apple and the Moon obey the same law. Newton's universal gravitation law. Determination of G, the constant of gravitation, and of the mass of the Earth. Confirmation using Kepler's third law. Masses of the planets and of the Sun. Regularities in the Solar system and their probable origin.

Practical activities: telescopic observations of planets and asteroids from Kapiolani Park.

5. Fifth step: stars as faraway suns. An argument based on observations of occultations of stars by the Moon. Huygens's experiment and his first distance estimate. Distance measurements: stellar parallaxes. Color-mag diagrams. Apparent and intrinsic brightness. Stellar luminosities. Main sequence. The Pleiades: a typical star cluster. Cluster diagrams. Cluster distances. Cepheid variable stars, period-luminosity relation and its calibration. Globular clusters and their distribution. The Milky Way as a stellar system (Galaxy) and the location of the Sun.

Laboratory activity: parallax in the lab. Extra activity: observations of the Sun, to be performed near noontime at a date to be agreed upon.

6. Sixth step: galaxies. Cepheids in Andromeda's galaxy. A universe of galaxies. Wave model of light. Rainbows: the spectrum of our Sun. Spectroscopes and spectrographs. Spectra of stars, nebulae and galaxies. The Doppler effect and its uses. Binary star systems and stellar mass determinations. Redshifts of distant galaxies. Hubble and the expansion of the universe. Looking back in time. The big-bang model and the steady-state universe.

Laboratory activity: spectra in the lab.

7. Structure of matter. Natural forces. Quantum model of light: photons. Interactions between matter and radiation. Interpretation of stellar spectra. Chemical composition of stars. Stellar populations, metallicity. The age of Earth and how to keep the Sun shining for so long. The source of the Sun's energy. Star formation and stellar evolution. Supernovae and black holes. The origin of chemical elements. Chemical history of our Galaxy.

Practical activities: deep sky telescopic observations from Sandy Beach.

8. How old is the universe? Olbers's paradox: why is it dark at night? The model of a homogeneous, infinite and eternal universe, and its refutation.

Practical activities: deep sky telescopic observations from Sandy Beach.

9. Big-bang model: predictions and observational verification. The microwave background radiation. A sketch of the history of the universe. Again the Doppler effect: dark matter and its role in the formation of galaxies. Supermassive blackholes in nuclei of galaxies. Quasars. Extragalactic supernovae and the acceleration of the universal expansion. Unsolved problems.

Practical activities: final telescopic observations from Kapiolani Park.

10. Back to Earth. The Apollo program and lunar rocks. The impact theory of lunar formation. Comparative planetology: Venus, Earth and Mars. The greenhouse effect. Meteorites, craters and dinosaurs. A comet collision with Jupiter. Search for asteroids that might impact our Earth. Other cosmic dangers. Long-term survival strategies.

No practical activities. The End.

### MORE DETAILED DESCRIPTIONS OF PRACTICAL ACTIVITIES

The activities that can actually be undertaken change from semester to semester, depending on the visibility of astronomical objects. In Fall 2007 we will not be able to include all the exercises listed here (for example, we will not have a chance to see Venus or Saturn), but I have not deleted them because they may be again possible in the future, and because some students might be interested in some extra reading. Note that some sections have not been updated and remain as they were in 2005. My thanks to Josh Barnes, who provided most of the older material, and to Mike Nassir.

1. The Sky
1. Orientation: compass points, rising and setting of astronomical objects [outdoor].
2. Constellations: recognizing landmarks in the sky [outdoor].
3. Phases of the Moon: relation between position and phase of the Moon [outdoor].
1. A Simple Telescope: study formation of inverted images, predict and measure magnification [indoor].
2. Using Astronomical Telescopes: finding objects, tracking, choice of magnification [outdoor].
3. Advantages of Aperture: count stars visible after stopping down to different apertures examine resolution of close binary stars [outdoor].
1. The size of our planet: watch a sunset at the beach and measure the Earth's radius [outdoor].
2. Viewing Mars: in November 2005, Mars comes close to the Earth, providing an opportunity for detailed observations [outdoor].
3. Viewing the Moon: small telescopes reveal an enormous amount of detail on the surface of the Moon [outdoor].
4. A Lunar Occultation: watch the Moon cover a star, to place limits on the star's angular diameter [outdoor].
5. Deep Sky Objects: study appearance of double stars, star clusters, nebulae, and galaxies [outdoor].
6. Light Curves of Variable Stars: naked-eye observations of Delta Cephei can yield its period, and hence its luminosity [outdoor].
7. Observing rainbows: you have to do this on your own, because we cannot predict where and when will a rainbow appear! [outdoor].
8. Lunar eclipse: if you are sleepless on Sunday night (October 16), stay awake two hours into Monday 17 and you will see a partial lunar eclipse [outdoor].
9. Viewing Venus: watch Venus getting bigger and bigger, and changing phases like the Moon [outdoor].

1. Motions of Venus and Mars: observations of these two planets reveal consequences of our own motion around the Sun [outdoor].
2. Shape of the Moon's Orbit: the

1. Parallax in the Lab: use cross-staff to estimate distances by triangulation [indoor].
2. Distance to the Moon: coordinated observation from two points yields estimate of lunar distance [outdoor].
3. Inverse-Square Law: verify relationship between distance and apparent brightness [indoor].
1. Spectra in the Lab: each element has a unique fingerprint'' of spectral lines [indoor].
2. Solar Spectrum: observe absorption lines in Sun's spectrum [outdoor].
3. Viewing Stellar Spectra: the spectra of stars reveal stellar temperatures and compositions [outdoor].

It is not possible to give a detailed week-by-week schedule for this course. Things are not likely to happen exactly as listed in the "overview of the program". We will have a range of activities prepared for each meeting thus we can take advantage of clear weather, and work indoors when the weather is bad. Some topics can be completed in a week or two, but others entail observations spread over longer periods. In particular, repeated observations are necessary to follow the motion of planets and asteroids (for example Mars in 4.a), study the shape of the Moon's orbit (4.b), and measure the light curves of variable stars (3.f).

## Stopping down a telescope to reduce brightness by 5 magnitudes - Astronomy

In the early 1990s I built what must have been one of the earliest automatic focusing devices for a CCD camera 1 with the help of software written by David Briggs. My favourite method of focusing any telescope however, is to watch the monitor while making very small adjustments until very suddenly, the faintest stars ‘pop’ into view. I prefer to judge for myself if the images are sharp enough rather than let software decide for me.

Some of the amazing images published today are usually taken with either large detectors, short focal lengths, small pixels or a combination of any of the three. When these images are scaled to fit on a single computer screen they can look absolutely stunning. However when enlarged to a scale representing a more modest camera and pixel size, e.g. 10mm detector and 12 microns pixels, they often appear soft or fluffy especially after intensive processing. The easiest way to make images appear sharp is to reduce them in size enlarging lets you see the truth.

Achieving good focus has been a major interest of mine dating back to the days of photography, so when a friend of mine was having trouble getting sharp star images I was very keen to help. I worked with this person at Southampton University and knew that he was an absolute perfectionist, so his poor star images must have been driving him mad! His problem was that he only had one eye and that was awaiting a cataract operation. For him, software and hardware for auto-focusing were out of the question.

There are various focus testing mask designs on the Internet and some are available commercially. Their main drawback, especially for anyone with impaired vision, is they usually rely on the user’s ability to judge when one object bisects or aligns perfectly with another, and in my view the results can be rather ambiguous. The test I suggested was very easy, virtually zero cost and most importantly, unambiguous it is very obvious when perfect focus is achieved. I call it ‘The Diffraction Focus Test.’

In principle it consists of placing a rod or batten, either round, square or rectangular, metal or wood, across the main entrance of an optical system in such a way that it creates a diffraction spike to appear parallel to the edge of the CCD in the resulting image. The width of the rod is not critical as good results have been achieved with both ¼" (6mm) and 1¼" (32mm) on the 14" (350mm) f/6 SCT setup shown in Figure 1. The resulting diffraction spikes can be made thicker or thinner by adjusting the exposure. The only requirement is that the sides of the rod or dowel are parallel.

Diffraction spikes will appear at 90º to the orientation of the rod and should be approximately aligned with a row of pixels in order to avoid pixellation. Contrast stretched exposures of 2 to 5 seconds are usually adequate for a bright star which should be at a high altitude. When experimentation has determined the correct exposures for a suitable diffraction spike length and width, the software can be set for continuous update. It is advisable to take several exposures after each adjustment to allow time for the telescope to settle.

When far from focus there will be two well-separated parallel diffraction spikes on each side of the star. Even when very close to focus there will still be two diffraction spikes (Figure 2). Only when perfectly focused will the image show a solitary spike (Figure 3). My images were binned 2x2, effectively producing 12.9 micron pixels, but the images look as small as in many cameras with much smaller pixels.

Although primarily intended for telescopes of moderate focal length and aperture, i.e. upwards of 6" (150mm) aperture and 40" (1 metre) focal length, the test can also be applied to the longer focal length DSLR camera lenses, i.e. >200mm. It is especially useful for those lenses that can focus beyond the infinity setting. It should be mentioned however, that DSLR cameras will need to be set to manual focus and, if possible, manual aperture priority in order to get enough light, and longer exposures to gain adequate brightness in the spikes.

The full aperture setting will produce more light but more importantly, avoid confusion due to the many additional spikes caused by iris diaphragms when stopping down. The shutter should be triggered with delayed action to eliminate camera shake which can cause fake parallel secondary spikes.

As the spike length is very much shorter with short focal lengths and small aperture lenses, the required exposures will have to be longer. This might result in the star overwhelming the diffraction spikes making them hard to see. All resulting test shots will need to be zoomed in the viewfinder.

For critical focusing of a telescope the test leaves little to be desired the apparatus costs virtually nothing and can be made in a couple of minutes from a piece of steel rod held in place by masking tape and spring clips. Perfect focus can be achieved very quickly and positively leaving no room for uncertainty. Please give this simple test a try if only as a useful confidence check of your usual method.

Ron Arbour - While my main interest is searching for and discovering supernovae, I also enjoy designing and constructing telescopes and ancillary equipment to achieve maximum performance.

Article originally published in the JBAA 126, 1, 2016

[Readers may be interested to explore the BAA's Instruments and Imaging Section, or to look at images of observatories and equipment BAA members have uploaded to the BAA Members Pages.]

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### A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by John Baars » Wed Jun 24, 2020 8:34 pm

Everybody knows it. A 150mm Achromat is a widefield telescope with terrible CA . Certainly not suited for observing Jupiter.

When I was doing a bit of deep sky the other night with my 150 mm f/ 5 Achromat, Jupiter popped up above the far away buildings and trees. Could you resist that? I certainly couldn't. So I aimed for Jupiter.

A Jupiter with a few belts and a pronounced blue rim around it was presented to me. Still. I was not really impressed by the blue color.
But then, I remembered that the manufacturer had made an lockable 11cm central hole in the cap for. occasional planet observing??
It turns the original f/ 5 instrument in a 110mm f/ 6.8 one.
Even as a rather spoiled planetary observer with a 120mm APO I thought it turned out to be okay. Good enough to show when no Reflector or Apo is at hand. Of course I 'll allow all disagreements

I did not make a sketch. Instead I took an old sketch and tried to turn it with Paint into an impression which came near to it.

Here is the original sketch, with a 4.7 inch APO "

There still is a little problem though. Being so low near the horizon Atmospheric Dispersion kicks in. As an example I tried to make an impression of that too. So. to all occasional observers and beginners: if Jupiter looks like this, it is not your telescope, eyepiece or diagonal, it is the atmosphere! Don't worry, within several years the planet Jupiter and Saturn will be much higher up, and much of these colored rims will be vanished by then. Experienced observers use a atmospheric dispersion corrector to eliminate these colors.

( experienced planetary observers will note I made a mistake. And I am not going to tell which one )

Telescopes in Schiedam in frequency of use : * SW 150mm Achromat F/5, * grabngo: SW 102 Maksutov F/13,
* SW Evostar 120ED F/7.5, * OMC140 Maksutov F/14.3, * Vixen 102ED F/9, on Vixen GPDX.

Most used Eyepieces : * Panoptic 24, * Leica ASPH zoom, * Zeiss barlow, * Pentax XO5.

Most often used binoculars : * AusJena 10X50 Jenoptem, * Swarovski Habicht 7X42, * Celestron Skymaster 15X70,
* Kasai 2.3X40, * Swift Observation 20X80.

Rijswijk Observatory Foundation telescopes : * Astro-Physics Starfire 130 f/8 on NEQ6, * 6 inch Newton on GP, * C8
on NEQ6, * Meade 14 inch SCT on EQ8, * Lunt.

### Re: A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by Bigzmey » Wed Jun 24, 2020 9:32 pm

### Re: A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by helicon » Wed Jun 24, 2020 10:06 pm

### Re: A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by Makuser » Thu Jun 25, 2020 12:00 am

### Re: A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by John Baars » Thu Jun 25, 2020 3:23 pm

I figured out that a Baader Moon & Skyglow filter might come in handy to enhance contrasts a little. Natural colors remain better intact than with colored filters.

About the atmospheric dispersion. Even the Sun has to do with it. A perfect example:

Note that the blue/ green rays are at top. Same with Jupiter.
But I forgot in the sketch South was up. so the colors are okay, but the image of Jupiter itself should be reversed 180 degrees.

Telescopes in Schiedam in frequency of use : * SW 150mm Achromat F/5, * grabngo: SW 102 Maksutov F/13,
* SW Evostar 120ED F/7.5, * OMC140 Maksutov F/14.3, * Vixen 102ED F/9, on Vixen GPDX.

Most used Eyepieces : * Panoptic 24, * Leica ASPH zoom, * Zeiss barlow, * Pentax XO5.

Most often used binoculars : * AusJena 10X50 Jenoptem, * Swarovski Habicht 7X42, * Celestron Skymaster 15X70,
* Kasai 2.3X40, * Swift Observation 20X80.

Rijswijk Observatory Foundation telescopes : * Astro-Physics Starfire 130 f/8 on NEQ6, * 6 inch Newton on GP, * C8
on NEQ6, * Meade 14 inch SCT on EQ8, * Lunt.

### Re: A 150mm f/5 Achromat stopped down on Jupiter, just for fun.

Post by John Baars » Tue Jul 07, 2020 10:54 am

I observed Jupiter and Saturn at full aperture the other night. The first post was about CA . This post is about details.

At full aperture I still could see more details than stopped down to 110mm , even though the CA is bigger.
Jupiter is quite yellow, with blue rims. Nevertheless it shows at least as much big details as a 90mm - 95 mm refractor, maybe a bit more, but. with obvious contrast loss. Subtle details, like the swirl of a festoon, were seen but ever so dim. On the other hand I could easily magnify to 180X, without mouches volantes, which would normally be seen at that magnification and a 90mm instrument, thanks to the larger exitpupil. This helped a lot on the + side.

To compensate fore the yellow color I added a Baader Moon & Skyglow filter. It bleaches the yellow color, but contrast too.
So in the end I preferred the full aperture .

I had been so busy with it that I totally forgot to use the ADC! Quite stupid Normally it would add some more subtle details.

Telescopes in Schiedam in frequency of use : * SW 150mm Achromat F/5, * grabngo: SW 102 Maksutov F/13,
* SW Evostar 120ED F/7.5, * OMC140 Maksutov F/14.3, * Vixen 102ED F/9, on Vixen GPDX.

Most used Eyepieces : * Panoptic 24, * Leica ASPH zoom, * Zeiss barlow, * Pentax XO5.

Most often used binoculars : * AusJena 10X50 Jenoptem, * Swarovski Habicht 7X42, * Celestron Skymaster 15X70,
* Kasai 2.3X40, * Swift Observation 20X80.

Rijswijk Observatory Foundation telescopes : * Astro-Physics Starfire 130 f/8 on NEQ6, * 6 inch Newton on GP, * C8
on NEQ6, * Meade 14 inch SCT on EQ8, * Lunt.

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