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Copyright – P. J. Smith

But permission is given to distribute this material in unaltered form as long as it is not sold for profit.

MAGNUM EYEPIECES

Having little use for super long eyepieces accepting extremely narrow light cones, I was somewhat taken aback when the topic of a 100 mm efl. eyepiece came up for a 10 inch F:20 refractor.

Initial thoughts

I was always bewitched by wide field low powers, but most design experience has been to cram the longest eyerelief into the shortest efl eyepiece while maintaining maximum apparent field of view.

This usually involves:

1. Possible deep concaves or a thick meniscus lens near the image plane. Eyerelief is thus lengthened but is unnecessary with a 100 mm efl eyepiece. This is fortuitous as the quantity of optical glass increases markedly with eyerelief.

2. Absolute minimum spacings and thicknesses near the eye. The diameters and curvatures of these elements are then kept to a minimum.

3. High index glasses, especially near the eye. This was ruled out on the grounds of the cost for huge chunks of very special glass

 

It was obvious the super wide field types were inappropriate because of the huge size, thickness, and cost of the elements. The act of scaling up a 10 mm Nagler type eyepiece by 10 times is interesting to say the least. 10X10X10 times the volume of optical glass would almost be measured in Tonnes. An act of insanity!

One potential problem was too much eyerelief. Besides being difficult to use without a special eye positioning cup, this increases the diameter and hence thickness of the eyelens elements unnecessarily. Simple geometry dictates that an 80 degree field of view with 100 mm eyerelief makes for a huge eyelens. Yes, you figured right! about 8 inches diameter.

Although some ideas were forming for an El Cheapo version using discarded optics, I could not resist the temptation to scale up a common wide field configuration. Computer time is cheaper than purchasing and pushing glass. A traditional 212 configuration Erfle was chosen because this type has inherently small eyerelief. A decision to use more common glasses was taken although this results in thicker elements and lowered performance.

Yes, it was possible. Field could be 70 degrees. Most of the elements were 30 mm thick and very steep. The field crown element alone was 6 inches wide and 40 mm thick. Spherical aberration of the exit pupil was a problem and to cure this meant considerable changes. The doublet field lens with incredibly deep flint surface was disposed of. It was reversed and moved so a 221 configuration (from eye) resulted. This looked more reasonable to make since the complex doublets were nearer the eye and much smaller. Reducing eyerelief to more normal levels also minimised the sizes of the eye lens components. All very interesting but where was this leading?

Rational approach

At this point, with the initial burst of enthusiasm over, more rational thinking prevailed.

What are the real requirements of an eyepiece of this type?

Firstly, the exit pupil in an F:20 system is 5 mm. Any increase caused by spherical aberration of the exit pupil would push this close to the limit even for very young observers. Although 7-8 mm is often quoted in texts as the pupil diameter of the eye, a more realistic figure for older observers is 5-6 mm.. Rigorous back tracing would be necessary to check pupil aberration for kidney bean degradation. This was done for all the following designs.

It is obvious that F:20 is well matched to a 100 mm efl. eyepiece and F:15 is a sensible limit because of the diameter of the exit pupil.

The following designs are evaluated at F:32, F:16 and F:8. Performance at F:8 is of interest but probably of little consequence.

Performance Criteria

The design criteria are much lower than usual. An Airy disk at F:20 has a semi diameter of 15 microns and the 1 minute semi diameter criterion is also15 microns. If the eyepiece spot radius at the image plane was no more than 15 microns on axis and 75 at the edge, an observer should be very happy with the result.

At 100 mm efl., defocus because of field curvature amounts to 10 mm per dioptre. Thus 5 mm would be quite acceptable and younger observers should handle 10 mm. or more. Certainly it would be a pleasure to reduce field curvature to less than 0.25 dioptres which is a defocus of 2.5 mm.

It takes some time to fully appreciate the opportunities presented by these specifications. They seem incredibly loose but in fact will produce an eyepiece better corrected than some equivalent prestigious commercial designs of shorter focal length.

It would be very easy to run amok with unnecessarily thick large elements. Keeping in mind that performance criteria are quite loose at F:20, and that some poor soul will have to pay for and construct this beast, it is important the designer considers construction problems and keeps both feet firmly anchored to terra firma.

Assessment of an existing simple design

The Huygens eyepiece apparently performs well with large, very long refractors. References occur to working with 45 degrees apparent field in the literature. From my experience of using a Huygens at F:Numbers lower than this I was a little sceptical. As a starting point, lets produce some spots, and field curvature data so we can evaluate the potential of the Huygens eyepiece.

 To allow easy comparison with other designs, the field has been taken to a whopping 72 degrees total. This is not meant to be a serious target. All the following designs are evaluated with graphs to the same scale. The diagram above shows ridiculously thin edges to the field lens but it is intended to be reduced for a narrower field.

If an eyepiece is made from this prescription to, say, 50 degrees apparent field, the element diameters should all be reduced in proportion.

  Dotted lines indicate the 1 min and 5 min criteria used to match performance to the eye. A small relative size of the Airy disk is an indication that higher power eyepieces will be needed for resolution of finer detail.

The results are a surprise. Even at F:8 the image spots of a 100 mm efl Huygens are not too bad but beyond F:16 are excellent. Field curvature, however, is very disturbing and amounts to a defocus of about 17 mm. A young observer could probably use the entire field by refocusing on different zones as needed after initial focus at the edge. Distortion is very evident (not shown).

Unfortunately, the type of curvature is of the worst kind and most users expect better. On the other hand achromatisation inherent in the Huygens design works surprisingly well.

Since the limit is imposed by the very subjective criterion of accommodation of the eye and its comfort, the only way to really evaluate this is by trial. Some could probably tolerate the design pushed to 55 degrees, others might prefer to limit it to 40.

Patterns on curved cardboard could be viewed using a simple lens in an attempt to evaluate your eye's tolerance to field curvature. A simple double convex lens of 100 mm efl has about the same field curvature as this design. If you can tolerate the magnification of a flat sheet without being bothered by the need to accommodate, then the design may be useful. Unfortunately, comparisons really need to be made in dim light with an F:16 cone of rays to be conclusive. A magnifying glass is different to an eyepiece which follows other optical elements.

It would seem that if the right surplus lenses are on hand, this may be worth a trial. Fortunately, planoconvex lenses are common. If only an appropriate field lens is available the eye lens could be scaled from this design and made easily for a trial. Be careful with large condensing lenses. They may not be accurately generated spheres and will probably be useless in this application.

Thoughts on modifying the Huygens

Partly from the previous data and partly from known characteristics of the Huygens eyepiece, some lines of attack become clearer.

Huygens eyepieces have about the worst possible eyerelief. This is great here!

Elements can be kept as small and thin as possible by placing most power near the eye. At 100 mm. efl. this becomes very attractive.

A ready source of high quality coated lenses is objectives from binoculars. If two, from a typical 10 X 50 pair of binoculars are placed close together, the combined efl. is roughly 100 mm.

A field lens must be used to catch all rays from an image plane far wider than the eyelens. If a simple field lens is used the perfect achromatisation of binocular objectives will be compromised.

BUT if the field lens is placed exactly in coincidence with the image plane and used as a collective lens its power and aberrations are of little consequence. This includes achromatic aberration as well. Unfortunately, dust specs will show up very badly especially at F:20.

If the focal length of the collective lens is chosen carefully, aberration of the exit pupil is minimised.

If, after all this, the back focal length (which controls eyerelief) comes out at a reasonable value, the design may be viable.

OK. So let's investigate this concept.

This design is based on a pair of 50X10 binocular objectives that expired. Others are probably similar. Their efl. is 180.4mm each and the plano convex field lens is 193.5.

 Although astigmatism is obvious in the curvature plots, the actual field curvature has been reduced noticeably. I suspect that for systems down to F:16, astigmatism will be acceptable out to 60 degrees total field. It could be worth evaluating performance even to 65 degrees.

Performance on axis is exquisite, far exceeding requirements.

In practice, this eyepiece will probably be set up by obtaining a field lens of almost the same focal length as each binocular objective and manoeuvring its position for best results. As the image plane moves slightly behind to slightly ahead of the field lens, the balance between improved astigmatism and field curvature changes. If you can accept some defocus due to field curvature the astigmatism may be marginally reduced.

A more complex but better solution

A better solution results from the use of a meniscus field lens at the expense of complexity. Unfortunately, the design becomes more critical so the chance of stunning performance from surplus optics is reduced.

This design would be better served by rigorous raytracing from the binocular objectives at hand.

One wonders if the added complexity is worth while, especially as the image plane will show dust on the field lens. The field lens requires a huge slab of glass if taken out to 72 degrees field.

Accessibility to surplus optics will probably be the limiting factor.

Performance is distinctly better right out to 72 degrees total field, even at F:8 although some defocus because of field curvature remains. This amounts to about half a dioptre which should be very comfortable to use. Distortion towards the edge of the field is worse in this design.

A purpose designed eyepiece

A 221 configuration has been investigated with the intention of removing the image plane from the vicinity of the field lens. Dust, scratches, and other imperfections will not now be magnified and obvious. How unpleasant this feature will be depends on usage and personal taste but I can imagine situations where it is very annoying.

 

Very common 'cheap' optical glass has been used as rather large pieces are required. In fact, more investment in optical glass will go into the eyepiece than a moderate sized refractor objective.

The 221 configuration has been chosen to reduce the complexity of the field lens which is 6 inches across and 1.5 inches thick. The image plane is 5 inches across at 72 degrees field.

It would take a rather brave individual to construct a beast like this.

Three radii have been held common to ease construction problems. Any compromise in performance will not be noticed at F:16 or beyond.

 The on axis images are not as small as some of the previous designs but performance is fairly well balanced. It should be a pleasure to use out to the full field of 72 degrees and would work reasonably at F:10 even though this makes little sense because of the excessively large exit pupil.

Element thicknesses could be reduced by using extra elements but this means more light loss and complexity. The flint component closest to the eye is a little thin and delicate but helps to reduce steepness and diameters of all following elements markedly.

If nothing else, this eyepiece would be a guaranteed centre of attention.

Conclusions

 

It is obvious that at F:20 magic things happen to image quality far from the axis. Curvature of field becomes the real limit but with an efl. of 100 mm even this is not the problem we expect.

The best compromise must depend on the type of use, the type of eye, the contents of your optical junk box, and the depth of your pocket.

Although some of this information might be irrelevant or impractical to your needs, I hope it sets the Magnum eyepiece in a clearer perspective. I know that this exercise has done that for me.

Examination of the raytracing data may reveal apparent discrepencies. The size of the field lens, for example, is different in each case. This is due to different distortion in each design.

Anyone contemplating the construction of one of these designs will have to decide on allowable field of view but I suggest 50, 60, 65, and 72 degrees as reasonable limits. Distortion will become noticeable especially for designs 1 and 3.

Since all raytrace information is for an apparent field of 72 degrees, the lens elements can be reduced in proportion to the chosen field. For example, if the option using binocular objectives and planoconvex field lens is restricted to 60 degrees, the field can be reduced to about 50 mm. half diameter.

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