A Subject for Yet Another Cloudy Night

Pittsburgh is on its way to about the tenth day in a row where the dusk brings a bank of clouds and haze from the west. So I'm going to talk about field of view, image size, focal length and image size and a cool photo-related astronomy service. Anyway, we'll start with a horribly dry and boring technical discussion having to do with optics.

Focal Length and Focal Ratio

The focal length of a simple telescope the distance the light must travel before it comes to a single point of focus in the optical system. In lens-based systems this is a property of the main objective lens. Light enters the system through the front of the lens and comes to focus somewhere in back of the lens. The distance from the focal point to the center of the lens is the focal length. Similarly with mirror-based systems the light hits the front of the mirror and then comes to focus somewhere in front of it.

The focal ratio of a simple telescope is the ratio of the focal length of the scope to the size of its aperture. So, if your Newtonian telescope has an 8 inch mirror and a 80 inch focal length, then its focal ratio is 80/8 = 10. For some reason we write this "F10" to make sure everyone understands what is going on.

Many telescopes are made up of multiple lenses, multiple mirrors, or some combination of both. My Celestron C8, for example, uses an optically neutral lens, a concave mirror and a convex mirror. The concave mirror is around F2. The convex mirror has a "negative" focal ratio of F5. I'm not sure how this is computed, since convex mirrors don't focus the light at all. In any case, this arrangement stretches the effective focal length of the primary resulting in an F10 telescope.

Why Do We Care?

The short answer is: the focal length of the telescope determines, to a large extent, the apparent size of the objects that you look at with that telescope. The general rule is this: longer focal lengths make things bigger.

If you are using your eyeballs to look through the telescope, you can't just look into the back end of the scope and see an image. You actually need a second lens to put the image on your eyeball. This lens, or set of lenses is called an eyepiece. Eyepieces come in various sizes and shapes, and since they are lenses, they have focal lengths. In general eyepieces with long focal lengths are for looking at large fields of view at low power. On the other hand, eyepieces with short focal lengths are for looking at small fields of view at high power. In other words, the final object size in your field of view is determined by a combination of the characteristics of the telescope and that of the eyepiece.

This turns out to be handy. You can carry a bunch of different eyepieces around with you and pick which one to use based on how big the object is that you want to look at. This is how things worked for hundreds of years, until someone invented cameras.

Cameras are different

Here's an unexpected annoyance when you switch from using eyepieces to using a camera: the camera always sees the same field of view. The field of view of the camera is completely determined by two measurements:

1. The effective focal length of the telescope.

2. The size of the sensor in the camera. Ok, so you might be using film, so the film size would matter instead of the sensor size. But chances are you are not, so let's forget about that.

Since the size of the sensor in most cameras is fixed, if you want to change the size of the field of view covered by your pictures, the only thing you can do is manipulate the effective focal length of the telescope. Another way to put this is that the only way to change the scale of the objects in your pictures is to change the focal length of the telescope. If you want to take a picture of something really small, you want a long focal length. If you want to take a picture of something really large, you want a short focal length.

At first this seems sort of inconvenient. Carrying multiple telescopes around is a lot harder than carrying a small bag of eyepieces. Luckily, those clever optical designers have again come to our rescue. It turns out that you can buy any number of special lenses that attach to the end of a telescope and manipulate the effective focal ratio.

Some lenses flatten the light cone and therefore stretch the focal length. We call these barlow lenses. On the other side of the coin, focal reducers make the light cone steeper and make the effective focal length shorter. Thus, as a general rule Barlows make things bigger, and focal reducers make things smaller.

Focal Reduction is Your Friend

For Mallincam use, it turns out that we are generally more interested in shorter focal lengths than longer. There are several reasons for this:

1. The chip in the Mallincam is small. In addition, the camera's strengths lie in capturing images of deep sky objects, which tend to be more extended in size than (say) double stars or planets. Therefore, generally the case that you are trying to fit relatively large objects on to the relatively small chip, so reducing the image scale is a good thing. Now, this is not always true. If you are hunting tiny planetary nebulas, you'll need to be working at a relatively long focal length.

2. Short focal lengths usually mean smaller F-ratios. From our lessons in photography we will all remember that smaller F-ratios mean shorter exposures. This is true in astrophotography too, at least for the extended deep sky objects that we tend to use the Mallincam for. Shorter exposures are always a good thing.

3. In addition to shortening exposure times, short focal lengths mean that you can get away with sloppier tracking in your telescope mount. This is because you are effectively working at a lower level of magnification, so tracking errors will not be as evident.

So Now What?

There is no lack of advice on how to combine various focal reducers with the Mallincam. Just consider this PDF file with dozens of different combinations. The available hardware for this can be summarized in the following list:

1. Reducers that attach to the back of your telescope using the standard Schmidt-Cassegrain threads. These tend to be designed specifically for SCTs, but who knows, maybe they can work elsewhere. Celestron, Meade, Antares and others all make an .63x reducer that hooks up this way. Meade also makes a .33x reducer that is designed only to be used with small CCD cameras. Conveniently, the Mallincam is just such a camera. I have a Celestron .63x which I also use with my eyepieces.

2. Reducers that attach as eyepiece filters. The best example of this is the Antares .5x reducer. There are a few others. But I have this one so I'll talk about it.

3. Special reducers made specifically for the Mallincam that thread on the front. These can be hard to come by. I have an MFR-5, which is a two piece device which I will talk about in a bit. Rock Mallin has also made an MFR-3 which was a single lens. The use of this lens is covered in the PDF I linked to above.

4. If you use Celestron telescopes, you can look into the Hyperstar system. This device lets you run your SCT at around F2, which is pretty cool. This works particularly well for larger apertures. For smaller scopes, the image scale gets to be too small to be useful.

5. Finally, various optical companies make custom reducers/field correctors just for their telescopes, usually refractors. You can find these devices made by Vixen, Astro-Physics, Televue, Borg and others. I don't have any of these (maybe soon!).

For my purposes below, I'll cover some experiments that I have done with devices that fall into the first three buckets above, since I actually own them.

Computing Effective Focal Length

This turns out to be harder than you think. You would naively hope that when you buy a focal reducer, somewhere on the box it would say something like "when you attach this to your telescope, it will cut the focal length in half." Unfortunately, it's not that simple. The effective focal length your telescope with the focal reducer added depends on the optical qualities of the reducer and on the spacing between the reducing lens and your eyeball, or the CCD in the camera. The Celestron/Meade/Antares "F6.3" reducer is specified as being a .63x reducer, but this is only actually true if the spacing is just right. If you are closer to the lens than the assumed distance (around 90-100mm, I think), then the final reduction is a bit smaller. If you are further away, then you get more reduction.

This effect is why you see so much traffic on the Mallincam groups about putting "spacers" between the camera and the focal reducer. Note that while you can get some mileage out of changing the spacing, if you get too far outside of the optimal range you will experience various optical maladies, the most obvious of which will be light fall-off in the corners of your picture. The more you push the reduction the worse this gets, since the steeper light cone will inevitably can only cover a smaller image area. This is why reducers like the Meade .33x can only be used with small chip CCDs. Put anything bigger behind it and you get dark corners.

In addition, you may have trouble focusing your telescope and you may find that the image at the edges of the field of view are distorted in strange ways. These issues all reflect the fact that the focal reducer is working against the laws of physics and trying to get you a free lunch.

Now, there are some optical formulas that let you plug in the focal length of the focal reducer and the spacing and compute the effective focal reduction. However, these are of limited use for two reasons:

1. Focal lengths tend not to be specified, and measuring the spacing is hard.

2. The formulas go out the window if you use multi-lens systems. This is because you can manipulate the spacing in multiple places and wen you do that who knows how the reduction factors combine. The MFR-5 has this problem since you can put spacers between the two lenses or just after them. You can also end up confused if you combine the Celestron .63x reducer with another lens.

A better way to figure out what your effective focal length is is to just use the camera to take a picture and then compute the field of view of the picture. If you know the field of view covered by the picture and you know the size of the CCD you used to take the shot, then you can solve for the effective focal length. Now, you might ask, how do you compute the field of view covered by a picture? Here the Internet comes to the rescue. All you do is this:

1. Join Flickr.

2. Joint the astrometry Flickr group.

3. Take your screen gran and add it to the group's pool.

4. Wait.

If your shot is clean enough, the bot that watches the pool will grab it and compare it against a huge database of star and object positions. Usually it will then tell you what part of the sky you took a picture of and the size of the field of view covered by your photo. I have a few examples here in my Flickr page. This one is the best:

Note the comment from the Astrometry bot. It tells you the coordinates of the center of the photo, the size of the field, and even all of the interesting objects in the picture, in case you didn't know. This is fantastic. Anyway, I take the field of view and then use Skytools 3 to match it with the right effective focal length. Skytools has an engine that will show you the field covered by your camera at a given focal length, so you can just plug values into that until you get something that matches. If you don't have Skytools there are any number of other package that do this, including some handy web pages.

Using this scheme, I have tested the following configurations of focal reducing lenses, and computed the efective focal length for each one:

1. The Antares 1.25" .5x reducer. This one is designed to be used with around 50-60mm of extension. I did not have quite that much, so in my pictures the effective F-ratio (with my C8) is about F5.5 instead of F5.

2. The MFR-5 with a 5mm spacer between the lenses. This gives you F5.

3. The MFR-5 with a 10mm spacer behind the entire assembly. This gives you F3.5 or so. This combination also produced obvious vignetting.

4. Finally, the Celestron .63x combined with the front lens of the MFR5 the standard 1.25" diagonal. This also gave me around F3.5. I used this odd combination because I fit in my diagonal without bottoming out on the mirror. Since I switched to the GEM I stopped using the diagonal so this is not that critical anymore. Still, it's a nice combination.

The next test I plan to run if I ever get a clear night is to combine the .63x reducer with the Antares. I expect to get to around F3.5 or hopefully a bit less. I might also try the Meade .33x focal reducer.

In my telescope, I find that F3.5 is nice because everything is a bit brighter, but the image scale at F5 has been better for the smaller galaxies that you tend to look at in the Spring. Your mileage will vary according to the aperture of your telescope and the quality of your mount.

I will note here that my measurements of the MFR-5 do not match what appears on the various Mallincam web sites, in the Internet forums and in the camera's documentation. I have no insight into why what I found was different, but my numbers are consistent and I'm fairly confident that they are right.

Summary

1. Focal length determines field of view and therefore image scale in the camera. For the Mallincam, shorter focal lengths tend to give you a better image scale.

2. Shorter focal lengths also reduce your focal ratio and therefore your exposure times.

3. Focal reducers can do their job well, but only under certain constraints, like spacing and the size of the final image circle.

4. With an 8 inch SCT telescope, working at F5 to F3.5 is a good range of focal lengths. Any shorter and stuff gets too small. If you need to go wider, it's probably wiser to get a wider field telescope.

Late Night with the Mallincam

If there is one thing that I have learned in my now medium-long lifetime it's that in Western Pennsylvania you cannot count on clear skies lasting. So when the clouds parted last Friday night at 11:15pm, I had a short quandry. On the one hand, it was 11:15pm and I should be in bed. On the other hand, it might be the last window of clear sky for another month. April to this point had been nothing but gray skies, cold, and rain. After considering this for about 45 seconds, I started to set up the telescope.

As this was my second time out with the new mount and as the first time had gone pretty well (got set up and aligned in about 20 minutes) this time things went less smoothly. To make this work well, you need script and a list. And I forgot a few parts of the script. Here is how you set up.

First, we need short tangent on what we want the mount to do for us when we are done. By convention we keep track of the position of every cataloged astronomical object that we deal with using something called the equatorial coordinate system. This coordinate system is similar to the one we use on the Earth, with the longitude and latitude, except it that it's projected on the sky. The east/west coordinate, similar to longitude, is called Right Ascension or RA. I don't know why. RA is measured like time, in hours, minutes, seconds and so on. This turns out to be convenient because you are often interested in the time at which objects are visible or not. If you know the time of year and the RA of the object, you can compute whether or not you should be able to see it.

The North/South coordinate, similar to Latitude is called Declination, or DEC. This coordinate is measured in the familiar degrees, minutes, seconds, and so on.

Our equatorial mount, unsurprisingly, has two axes that go by these same names. The right ascension axis is also called the polar axis of the mount.

The eventual goal of the setup is to align two things. First, we want to align the polar axis of the mount with the polar axis of the Earth. This alignment is called polar alignment and allows the mount to track objects in the sky while only driving the telescope along one axis.

Second, we want to give the mount's computer an accurate picture of what is where in the sky so it can point the telescope automatically. I call this star alignment to distinguish it from polar alignment. When we are done, we should be able to tell the mount to point the telescope anywhere we want in the sky, and it can do some quick calculations to figure out exactly how to run the motors to pull that off. Then we sit back and watch the object come into the field of the eyepiece, or camera. So, here we go.

1. Take the mount outside. Point the right ascension axis of the mount roughly north.

2. Attach the counterweight on the counterweight thingy.

3. Go back inside and grab the telescope. Attach the telescope to the mount using the quick release dovetail arrangement.

4. Balance the scope and the counterweight along the right ascension axis. To do this on my mount, you release the clutch on the RA axis. This lets you turn the mount by hand rather than with the motors. Now turn the mount until the shaft is horizontal and gently let go. If the telescope drops, move the counterweight further away from the telescope and try again. If the counterweight drops, move it closer to the telescope and try again. Iterate until the whole system is balanced.

5. Now balance the telescope along the declination axis. Tighten the RA clutch. Carefully loosen the DEC clutch turn the telescope until it is horizontal. Slooowly let go and see how the tube moves. With the Celestron telescopes you can then move the scope backward and forward in the quick release saddle until it balances.

6. Now turn the mount until the little index marks line up. When you are done doing this the scope is in its "zero" position and should be pointing North. If it's dark enough you can look in the finder scope and maybe see Polaris. Resist the urge to center Polaris in the finder. This will do you no good because the axis of the finder is not what you want to point at Polaris. I shoud know, I wasted my time doing this.

7. Instead what you want to do is look through a hollow in the RA axis and put Polaris into that hole. Then you know the polar axis is looking roughly at Polaris, which is more useful. To do this, loosen the DEC clutch and turn the tube to 90 degrees from where it was. You should now be able to look through the hole and see sky.

Get down on your knees and push the mount around and peer into this hole and see if you can see Polaris. It might take a few tries before you can see anything, depending on how dark it is. If you can't see it, use the following odd scheme to find it. First, you will note two long bolts with handles on them on the front and the back of the mount. These adjust altitude. They do not do it very well. In particular, it's hard to smoothly lower the altitude. So, on the theory that you are pointed too high, loosen the front lever and push the mount so it falls down a few degrees in altitude. Then, using the back lever raise the mount again and hopefully you'll see Polaris enter the field. If not, you might be off to the side a bit. Shove the mount sideways one way or another and try again until you get Polaris in the hole. The field of view through this hole is pretty wide so this isn't too hard.

8. Also on the front of the mount you will notice two knobs that push the mount side to side. If Polaris is not centered side to side in the hole, use these knobs to move it around. To move the mount you loosen one knob and then tighten the other one. I don't remember how things are oriented so you will just have to try yourself until you figure it out.

Starting with Polaris roughly in this hole turns out to be important. In my short experience, if you are too far off the star alignment which I will describe next never ends up working.

9. Now turn the scope back to the zero position and plug in the power cord. Answer all the questions about time and date and such that the hand controller will ask you and start the two star alignment. Tell the mount to move the scope to the first star it suggests. If you can't find that star or its blocked, hit the undo key to try other stars until you get one you like. The mount will point the telescope at the star you picked and then you will use the arrow keys on the hand control to center the star in your finder then the eyepiece. The Celestron manual tells you to always make sure the final movements of the stars are driven by the Up and Right arrow keys. This minimizes the resulting backlash in the gears. I have no reason to doubt the manual on this point, so be careful about that.

The mount will then let you repeat this process on a second star. You will notice that by default both of these stars will be chosen from the western part of the sky. After you are done, the hand controller will ask you if you want to add "calibration" stars, all of which will be chosen from the eastern part of the sky. You can add up to four of these stars. Keep adding them until the pointing gets very accurate.

There are two important things to know about this procedure:

First, the east/west breakdown is important for mounts like the CG-5. The CG-5 is what we call a "German Equatorial Mount", or GEM. The geometry of the GEM is such that you have to be aware of the relative position of the telescope and an imaginary line called the meridian. The meridian is the line that runs North/South and splits the sky in half East/West. If you have set up your mount correctly, the middle of the tripod sits right on top of the meridian, and in a GEM this means that the scope is on one side of this line and the counterweight is on the other. The thing you have to remember is that GEMs have a hard time tracking past the meridian because when you go too far either the scope or the counterweight shaft will run into the mount. Bad news.

To get around this problem GEMs flip the scope around whenever they cross the meridian. You want to be able to do this and maintain pointing accuracy, so the Celestron software does allows you to do extra calibration to make sure this works right.

The second thing to remember about star alignment is not to try to do it when there are thin clouds around. This makes it easy to guess wrong and align on the wrong stars, or stars you cannot see. Then no matter how many stars you align to, the pointing never gets any better. If you notice this happening, the best thing to do is to reboot the mount and start over. I ended up in this situation at about 11:45pm. By then the sky had really cleared, so I buckled down and tried again. I turned the mount off, made sure that I got Polaris into that damned hole, and started again. Ten minutes later I was ready to move on.

10. Having fine tuned your star alignment, you can now engage a nifty little piece of software that is unique to the Celestron controllers. It is called "all star" polar alignment. Pick one of the stars that you used for the final calibration as long as it is not too close to either due North or zenith. Hit the Align button on the hand controller and navigate to the Polar Align menu and then choose Align Mount and hit Enter. The mount will think a bit and then move the telescope to point at the star you just picked. Use the hand control to center it just like you did before. When you are done, you tell the hand controller to start the Polar alignment. The telescope will think a bit and then move to another spot in the sky. This is where the alignment star would be the mount were in fact polar aligned. Now you get to get down on the ground again and use those knobs and levers from before to push the mount around in azimuth and altitude until the star is centered in your eyepiece. When you are done hit the Align button and you are done.

By this time your knees and shoulders should be a bit sore, but your mount will be well aligned for both pointing and tracking. I managed to get to this state by about 12:15am. So then I yawned and went in and got my camera.

While the CG-5 mount is bigger, heavier and more complicated than my old 8SE mount, it does have its advantages. First, I have found that the tripod is much more solid, so the telescope does not shake and shimmy when I'm trying to focus. Second, it's a lot easier to use the camera because I can stick it into the back of the telescope without worrying about it hitting the base of the forks. On the other hand, there are some things you want to be careful about.

If you do not firmly attach your eyepiece to the telescope, you may find that the mount can make it fall out as it turns and twists the telescope at all strange angles. This is bad. You may also find that the various cables that stick our from various ports in the mount and lodge themselves between the motor housings. I've had this happen twice now and I'm not sure why, but it does make the mount upset. Try to avoid this.

Luckily, on this night, with the time nearing 12:30am, I had none of these issues and was able to happily go to my first target, the galaxy NGC 2903. There are two things to note here. First, you can see the cool spiral arms of the galaxy. Second, even with about a minute of exposure, the mount is still tracking pretty well. I have found in general that a minute works well. Two minutes is a bit too long.

Second target of the night was the "Hockey Stick" galaxy, NGC 4656. This is a pretty dim object, I was happy to get a good view of it.

I then cruised through the galaxy clusters in Virgo and Coma Berenices. There was M64, M84, M86, M87, and M91. For two hours, everything I asked for hit right on the camera and the mount tracked with relative smoothness. I was using the camera with a .5x focal reducer, which means that the effective focal length of the telescope was 1000mm instead of 2000mm. This means that the field of view of the camera is roughly 20 by 15 arc minutes, which is pretty darned small. Overall I remain impressed by the ability of a 25 cent embedded processor to accurately point a 15 pound telescope with this level of accuracy.

Somewhere around M87 I noticed the pictures looked funny, with ugly bloated stars. I didn't think about it too hard until I tried to look at M101 and it was all blurry. So, I turned the telescope to the globular cluster M3 and tried my best to refocus.

Having gotten closer, I went back to M101 and got the surprise of the night. Most of the objects I had looked at had been small with bright cores but not much in the way of larger scale detail. M101 was different. The arms spread out over the field of view with dim hints of dust lanes and other grand details.

I finally shut down for the night at 2:45, sleepy but pretty happy. I was also hopeful that with a bit more practice I'd be able to tease even more out of these objects sitting above me in the sky. Who would have thought you could see this much with relatively little work in your backyard.