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Reprints of articles, or complete issues of the CONSTELLATION, are available by contacting the Editor at the address listed below, and portions may be reproduced without permission, provided explicit acknowledgement is made and a copy of that publication is sent to the Editor. The contents of this publication, and its format (published hard copy or electronic) are copyright ©2001 BMAA, Inc.

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Field Curvature: Occurs when the focal surface is other than a plane.

Distortion: Systematic variation in image scale across the focal plane.

Field curvature and distortion are special among the aberrations specified by Seidel in that star images may be formed perfectly when these aberrations are present (although not necessarily at the focal plane). In the case of pure field curvature a curved piece of film or refocus of the instrument will correct for the aberration. With distortion the stars may be perfect but are displaced relative to their correct locations.

The cause of field curvature is easy to imagine. Just consider where "one focal length" is situated from the center of the objective and one finds a curved field- NOT the ideal plane used in lens design. There is, in fact, no focal plane. If the difference in focal position differs at the edge and center then the image suffers. Of course this simple example becomes more complex when real objectives are considered. See Illustration 1.

Fields can be curved toward the objective (positive) or outward (negative) or inward in one plane and outward in another. When the surfaces do not coincide (tangential and saggital) then astigmatism is present (see CONSTELLATION: March 2001, April 2001). See Illustration 2.

Field curvature is generally of little concern to the user, at least in visual application. When we consider wide-angle photography, particularly with medium format cameras, the image degradation may be considerable if the field and plane are different. In such situations then field flatteners may help, or one can curve the film (as in the Schmidt).

Use of a Barlow lens may flatten the field, but as they are used to increase the effective focal length (and consequently decreased field of view) their application is limited. Keep in mind the eyepiece has a curved field of it's own and may augment or negate the field of the objective. Ultimately field curvature and distortion are a function of eyepiece and objective, and some telescope designs take both eyepiece and objective into consideration.

Distortion is a strange bird. Here the star's relative placement to each other suffers while the individual image is diffraction limiited.

There are two types of distortion. In pincushion distortion (positive distortion) the sides of a rectangle are curved inward, while with barrel distortion (negative) the sides are curved outward. See Illustration 3, 4 and 5 for a demonstration of what distortion does to the star field. Individual star images remain unaltered while their relative placements are changed. In the presence of distortion astrometrics becomes problematic.

Illustration 1: All points at "one focal length" from the center of a lens form a curved surface (sphere) that touches the focal plane at only one point! Refocus at 70% of the way out from the center of the field of view, a curved piece of film, or other corrective optical elements help to control field curvature.

Illustration 2: Most curved fields are rather complex. Here the positive curve is that found in a fast Newtonian while the negative curve is that of the writer's slow Gregorian.

Illustration 3: Starting with this image of M3 (15 second unguided exposure, 7in Maksutov-Cassegrain, F/16), showing little distortion, Illustrations 4 and 5 are modified with an art-work program to demonstrate pincushion and barrel distortion.

Illustration 4: Carefully distorted image of M3 to demonstrate pincushion distortion.

Illustration 5: Distorted by artwork program this image of M3 shows barrel distortion.

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Having taken a month off from this column I find myself with no real idea for a subject, (however) during the last several months we've had some interesting celestial phenomena and whatnot.

Mars has made its closest approach since '99. This opposition was much more favorable than the last as the Earth was closer to Mars by a good bit. Due to the strongly elliptical orbital path of Mars our distance at opposition can vary from about 56 or so to 34 million miles, causing the disk of the planet to vary from 13 seconds diameter at an aphelic opposition to about 25 seconds at a perihelic. One of these is due in 2003. The current maximum size of Mars was about 20 seconds of arc, or about the size of the globe of Saturn at it's opposition.

Aphelion refers to the furthest point a planet is from the sun in it's orbit (ap= away or far, helion= sun), while perihelion refers to the closest the planet gets in it's orbit.

Since we 'catch up' to Mars about every 26 months, the point of closest approach can vary over the mentioned distance.

This opposition, at 20 seconds of arc maximum, was fairly favorable. Much detail could be seen as the apparent size of the planet grew over the last few months. However, a planet wide dust storm has eradicated all but some glimpses of major features. During the night of July 14 several of us were at Van Sant airport. Even in Bruce Colliers' 18" there was little to see on the disk. The night was very turbulent, which didn't help either. Prior to July, I had been surprised at the ease of some features, even in a 3" refractor. I won't get into that here, as the purpose of the column is to get some input on what others saw. Those who didn't look will probably have little input.

If you haven't even checked Mars, you missed a fine show for several months. Still, the planet is large enough for about 2 more months to get out and take a look.

Some of our members were conversing on the 'flares' sometimes visible on Mars. I personally have never seen one, but the evidence is somewhat overwhelming in favor of their existence. Perhaps some member will take the time to look into the reports and do a 10 minute talk on the subject. And, God forbid, write something for this column.

Alan P has reported some faint aurora in June in the early morning hours. As far as I know, he is the only one in the club who has seen anything other than the awesome March 31 display. The reason he saw the aurora and we didn't? He was outside.

Just this Tuesday, the 17th, there was a daytime occultation of Venus by the moon. Sadly, Achmet was clouded out completely. I had taken a 3" refractor to work and asked the boss for some time during the afternoon. Perhaps someone else was luckier?

I have always wanted to do some asteroid hunting. Not for new ones, just the known brighter ones at good approaches. For all the time I have spent under the stars, I've seen exactly 3 asteroids (Ceres, Juno, and I forget the other). How did I know I had seen them? I actually made a small chart and compared it the next night. The motion is obvious.

One of these days I'm going to follow a few bright variables. All these years and never even checked Algol.

So there is still lots I have to do.

The sun has shown tremendous variance in spot visibility. It seems like every day the Zurich and Wolf numbers change dramatically. There have been some naked eye spots (I use Baader film as a sunscreen) visible at various times over the last two months.

The Zurich and Wolf numbers refer to the numbers of visible spots and groups of spots. See spaceweather.com and related links for detailed explanations, or read a generalized astro book. These usually mention at least some of the solar phenomena.

The largest solar blast ever recorded took place in April, an X22 event. If the particles blasted off the sun had been aimed at Earth their would have been colossal aurora, power line surges causing tremendous damage to the grids, and serious exposure problems for astronauts, not to mention the satellites themselves.

When a stream of particles hits the Earth, the atmosphere also expands and causes increased drag on the satellites. This causes every imaginable problem for the controllers on the ground.

Cell phone, short wave, and possibly most radio, would have been shut down for several hours due to atmospheric and ionospheric effects.

During the mid to late days of July there will be, and have been, several lovely planetary and lunar groupings in the morning sky. We have Jupiter, Saturn, Venus and Mercury all up early.

Comet Linear was and is a fine sight, easily seen with slightest optical aid in Pegasus. I easily saw the comet July 15th from just outside Trenton at 10:30p with 7X50 binocs. Later that week, at the airport as mentioned earlier, the comet was just at the limit of naked eye vision after midnight or so. I managed to get some half decent photos, but the comet just shows as a greenish (????) glow. It seemed to be about a full degree in diameter in the binocs.

Some simple astrophoto notes. I have had very good luck with Fuji 800 film, exposed with a standard 35mm camera with 50mm f/2.2 lens, using a tripod and cable release to prevent vibrations. A 15 second shot will show stars to the naked eye limit, and the results are surprisingly fun to show off. Longer shots can be made nearer the polar regions, up to about 30 seconds before trailing makes it's appearance.

Try it sometime. No, you won't frighten Bruce Collier or Brad Miller with your photographic abilities, but the fun is there. Give it a try. At least you can spend some time under the stars. Who knows? You may catch something very interesting. A meteor, or a nice starfield, or perhaps something you've never seen before.

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The Forum is available for any BMAA member to express club-related information. This month is e-mail regarding the recent 'fireball':

On Monday evening at approximately 6:20 Eastern Daylight Time (22:20 UT July 23) a very bright bolide was seen by reportedly a thousand people on the East Coast of the United States from Virginia to New York State while the Sun was still about 20 degrees above the horizon. Judging from various reports, the object could easily have been magnitude -10 or brighter.

BMAA member Wayne Adams witnessed the event while driving west on Woodhaven road, just north of Philadelphia. The fireball was bright enough to distract him from driving. He said that he could easily see different colors coming from the head of the bolide. There was no smoke trail seen or sonic boom heard at his location. He said that it traveled from northeast to southwest, and disappeared over the horizon which was a building. He was later interviewed and broadcast on the air by local news radio station KYW.

According to other news sources, a sonic boom was heard, windows shattered, and fragments were retrieved in Lycoming County, Pennsylvania. Another source reported that the object was "the size of a jeep", however the jury is still out as far as reports from the general public are concerned until a full investigation is completed.

It should be noted that this event was NOT the result of a "meteor shower" as some of the media have labeled it. Meteor showers are associated with leftover material from now-extinct comets, and generally do not contain larger than pebble-sized fragments of non-icy material. The next true meteor shower is the Delta Aquarids, which peak on July 28 with a maximum Zenith Hourly Rate of 20.

- Clear skies, Alan Pasicznyk

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No, I didn't see it. At 6:20 on Monday night I was in the supermarket buying cat food or something. But today I did interview an eyewitness--my boss' son--who saw it while driving home.

He said it was about 30 degrees above the horizon and red and yellow sparks were "coming out the back". It was visible for at least 10 seconds. He didn't think it was a celestial object because it moved so slowly above the trees. His first thought was that somebody had shot off a bottle rocket, and he didn't think any more of it until he saw the news on TV that night. He didn't hear any sound because he was in a closed car with the radio on.

As for media coverage, a coworker said he had seen a report on TV that showed burn marks on leaves in a cornfield somewhere. Evidently part of the meteor exploded above ground and hot particles scorched the leaves. The field was being searched for debris.

He said an anchor on a later news show said "a corn field had been reduced to ashes." These are the same people who are scaring the beejeezus out of everybody about global warming.

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This series has described the five third order aberrations: spherical aberration , coma, astigmatism, field curvature, and distortion. Seidel described these aberrations in the language of mathematics. While the math looks complicated it demands no more than algebra. The value of the approach is:

1) Accuracy: when the field of view is narrow (sound like a telescope?), the technique is sufficient for most design application.

2) Simplicity: the analysis can easily be carried out on a calculator, let alone a computer.

3) Comparisons of design variables are readily made on the basis of a small set of numbers.

4) Each optic element can be examined in turn for contribution to image formation.

This technique is the second step in telescope design, following the paraxial calculation. The paraxial calculation is sometimes called the "first order" calculation and yields the focal length of the telescope and placement of the elements. The paraxial calculation does NOT give an indication of the magnitude of aberrations. The next step in design traditionally has been the meriodonal calculation, which does give an exact solution of aberration in a single plane (meridional or tangential) and precedes the Seidel calculation. However, one step more complicated and much more complete is the Seidel calculation. While the Seidel calculation is generally sufficient under most circumstances, the use of computers has made analysis via skew ray trace readily possible. In fact, one tends to skip the intermediate steps (meridional and Seidel). The skew ray trace is an exact analysis and is immediately interpretable in the form of a spot diagram. Programs available include Zemax, Optix, Atmos, etc. Optix is a free download.

The Seidel calculation is properly called the Seidel sum because of number 4, above. The calculation can be carried out with each optical element in turn so as to reveal the source of image aberration, and then summed to yield the final aberration.

Each of the image aberrations are treated as separate entities- something that does NOT occur in nature, However, human beings are good at classifying and categorizing phenomena, making analysis and discussion much easier. The skew ray trace, being exact, shows all of the aberrations (third order).

There are other aberrations in addition top those addressed in "Meet The Aberrators". Chief among them is chromatic aberration. Chromatic aberration is NOT addressed by Seidel, and will be discussed in the next issue of Constellation. Also, there are 5th, 7th and 9th (and higher!) order aberrations. Each successive order adds less to image degradation.

ABERRATOR continues to be a great tool for display of image aberrations. While the math behind the program is much more complex than Seidel (Seidel and ray trace ignore the wave nature of light), each aberration can be viewed separately and then combined at the users will.

Illustration 1: Mars as seen as the sum of Sediel aberrations and atmospheric disturbance. You can explore the relative contributions to image quality of third order aberrations and turbulence using ABERRATOR. This image produced by the author with a 7in Maksutov-Cassegrain and Pictor 416XTE camera on a night of poor seeing.

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