LX200 Maximum Field of View Calculations

       

Subject: LX200 Maximun Field of View?

From: Doc G

Robert Preston wrote:
> I bit yet another additional bullet and treated myself to a 2" diagonal and
> a Panoptic 35mm to go with my 8" f/10. It was prompted by my first exposure (in
> several years) to a fairly dark sky site not too far from home base in
> Pittsburgh. The dark sky is still totally unbelievably gorgeous!
>
> So, naturally, I'd like to see broad expanses of the summer Milky Way regions
> and as large a view as possible of deep sky nebulae. The question
> is, would the addition of a focal reducer to an f10 be worthwhile at this
> point (in combo with the Panoptic 35) ? At what size does the f10 field begin
> to vignette, and how bad is it when it does, and like that. Eventually
> I intend to do some (film) photography of wide star fields, so that's also
> a consideration, in addition to my current visual emphasis.

RP asks about maximum field. I wrote a brief note on this topic which is attached.

Field of View - Basic Optics

I am sure most MAPUG members already know what I am about to say. However, there are some who seem to be confused about Field of View and the relation of it to Eyepiece Power, the Eyepiece field of view and the use of so called field reducers. I present here a way of thinking about these issues that I hope will be useful.

The actual field of view of the sky is determined only by the focal length of the telescope and the diameter of the most restrictive field stop in the optical system. The field stop is usually at or near the real aerial image position in the system. For a telescope this is just outside the back plate of the telescope at a position called the back focus focal plane.

The ultimate field stop is the hole in the back plane of the telescope. The practical field stop is that of the eyepiece. The size of this field stop is limited by the diameter of the eyepiece tube. On a given telescope a 2 inch eyepiece has greater maximum field of view of the sky than a 1 1/4 inch because it can intercept more of the real aerial image that the telescope objective produces.

The purpose of the eyepiece is similar to that of a fancy magnifying glass. It enables the human eye to inspect the real aerial image in fine detail. The focal length of the eyepiece determines the magnifying power of the whole system. A so called wide field eyepiece is designed in such a way that for a given focal length of the eyepiece the field stop can be made larger. The field stop can never be larger than the diameter of the eyepiece tube. (obviously) The larger diameter field stop of the wide field eyepiece actually intercepts a larger portion of the real aerial image and thus gives a view of a larger circle of the sky. It also gives what is called a larger apparent field of view. This is the size of the circle seen when one looks into the eyepiece.

Now what this has to do with using field reducers is as follows. The field reducer is placed inside the focal point of the real aerial image and not too far from it. Thus the reducer becomes the effective field stop and limits the size of the actual field of view of the sky.

The reducer actually moves the real aerial image forward and reduces its size. This means that the field of view as observable by the eyepiece is confined to the size of the now reduced real aerial image even if the field stop of the eyepiece is much larger. So the actual field of view of the sky is still limited by the focal length of the telescope and the diameter, in this case, that of the focal reducer.

Thus if you can see a certain amount of sky with an eyepiece with a field stop 2 inches in diameter, you will be able to see the nearly the same amount of sky with the 2 inch diameter field reducer. The real arial image will simply be smaller by the amount of field reduction. This is the purpose of the field reducer. It reduces the image size in order fit more of it on the imager chip.

There is no point of having an optical element close to the opening in the rear of the telescope that is much larger than that opening. You can't squeeze ten pounds of image through a five pound hole.

Similarly, once the field of view is limited by a field stop, no matter where it is in the optical path, you can't view more of the sky. That is why people who make field reducers say that their reducer will only cover a more limited field size than the original image. Note that when the most limiting field stop is not exactly at the focal point of the real aerial image, the will appear out of focus. The intensity will fall off rather than being cut off abruptly. This effect is called vignetting.

When you think about it, the name field reducer is not very precise. It should be called an image reducer. The reducer only gives an apparent shortening of the focal length and increase in the speed of the telescope because it concentrates the image, makes it smaller, as a shorter focal length would do, and at the same time puts the same amount of light energy in the smaller image making it brighter (of lower f number). The actual amount of energy you intercept from the object (star) is limited only by the size of the objective.

I hope this discussion helps when thinking about viewing the image that the objective creates at the eyepiece end of the telescope. Again, I apologize for the wordiness but I can't help trying to be clear and precise. (among professors this is known as verbal overkill)

Subject: Field of View Definition --part 1 of 2 

From: Doc G

OK!! Let us get the terminology straight. There are two meanings to Field Of View.

One is the actual angular field of view against the sky. This is determined only by the focal length of the telescope and the diameter of the field stop in the eyepiece. The field stop can be no larger that the eyepiece tube and is generally smaller by a few mm. The Meade 40 mm and 55 mm have as large an actual field of view as you can get with a 2" eyepiece tube.

If you mean apparent field of view, then this is determined only by the eyepiece. The apparent field of view depends on the diameter of the field stop and the optical design of the eyepiece.

So what you want is an eyepiece with a field stop as large as possible and a design that gives you a comfortable apparent field of view. There is, in my opinion, no point in having a so called super wide eyepiece if you have to move your eye around too much to see the entire field. A 40 mm Plossl which has a field stop that is as large as possible, generally 46 mm, will give you as wide a field of view as possible.

Your 12" f/10 has a focal length of 120"(3000 mm) and will give an actual field of view that is smaller than the 10" f/10 which has a focal length of 100" (2500 mm). That is with the same eyepiece that has a maximum diameter field stop. What you ask for in your post is impossible if you mean actual field of view.

You can see some eyepiece designs and their fields of view on my web site (see MAPUG-Astronomy.net homepage) under the optical attachments section.

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Subject: Field of View Definition --part 2 of 2  

From: Robert Preston <rbrtprstnearthlink.net>

>....... If the apparent field is large, the true
> filed also is comparatively larger than an eyepiece of less apparent field.
>
>.....If you are looking for a bigger true
> field, then you need to lower the focal length of the telescope. And the only
> way to do that is by using a focal reducer >
> Michael J. Cook

Michael, thanks for the info. I'd offer the opinion that your summary statement that "the ONLY (my caps) way to ...is by using a focal reducer" is rather confusing, since you also (correctly) pointed out that an eyepiece with larger apparent field gives a larger true field, other things being equal.

The original message was asking about the maximum possible field in a given scope (a 12" f/10 SCT), and there are limiting factors other than the apparent field and the magnification. You can see that the telescope tube itself blocks light beyond a certain angle of sky from hitting the primary mirror, and that gives one limit to the maximum true field (no matter how much you reduce the mag or raise the apparent field of the eyepiece). But I think there's a minimum magnification set either by the maximum pupil opening of the eye, or by the secondary beginning to be visible as an obstruction. I don't have the formula for calculating that limit, myself, but I'm pretty sure that you can exceed the limit with combinations of focal reducers and/or long focal length eyepieces. Perhaps another 'pugger knows the real field limits of your 12" f/10. Then, knowing that limit, you can buy either long f.l. eyepieces or wide-field eyepieces or a focal reducer or some combination of those, just so the calculated true field (which equals the apparent field divided by magnification, as Michael stated) is less than or equal to the maximal true field for your 12" f/10 SCT.

We shouldn't assume that a large actual field is the main item of interest here. I find that wide angle views (i.e., apparent fields larger than the typical 50 degrees of ordinary eyepieces) are esthetically much more pleasing, less like looking at the sky through a too-small porthole. I bought a 35mm Panoptic (70 deg. apparent) rather than a 56 mm Plossl that had about the same true field for just that esthetic reason. Other people more interested in astrophotography might prefer a focal reducer to a longer f.l. eyepiece, since the reducer would benefit both visual and photographic use of the scope.

Subject: Max FOV with f/6.3 Focal Reducer  

From: John Mahony <jmmahonyhotmail.com>

George Goodman wrote:
> I want to get an f-6.3 focal reducer for my 12-inch, in order to obtain a larger
> field of view. I primarily use the Televue 27mm Panoptic, and a Meade 56mm
> Plossel. I know I can't use the 56 with the reducer because of vignetting.
> But the 27 should be fine. My question is, When I use the reducer with the
> Panoptic, will I get the 56 percent increase (or any good increase) at the
> expense of just bringing the view to what it was with the 56mm PlosseL?
>
> In other words, will the 27mm view as far as magnification, stay the same,
> just with more field of view? Or should I just continue using the 56? I really
> would like to have the mag. of the 27mm along with an increased field. I'm a
> little confused about how that works.

With the 56mm Plossl, you have an apparent field of about 50Â, and a magnification of 3000/56=54X, so the true FOV is about 50/54=0.93Â The 27mm with the reducer will give an effective EP focal length of 27/0.63=43mm, so the magnification is 3000/43=70X. The apparent FOV stays the same, about 67Â for a Panoptic. So the true field is 67/70=0.96Â. So the true FOV is very similar, but it will appear larger, in a wider apparent field.

That large of an apparent field in a 12" will cause some vignetting, except if you use an Eyeopener type adapter with the 56mm. With the 27mm and reducer, that won't help because the reducer's lens is only about the size of the standard rear port anyway. But if you haven't noticed the vignetting in the 56mm (when used without an Eyeopener), you probably won't notice it in the 27mm with the reducer.

For a given scope, exit pupil depends only on the EP focal length. The apparent field of view is not involved. A 56mm EP would give an exit pupil of 56/10=5.6mm on an f/10 scope. A 27mm EP with reducer would give a 27/6.3= 4.1mm exit pupil. 5.6 is borderline- it depends on your eye. But 4.1 should be fine.