Presented at the 1988
Riverside Telescope Makers Conference by:

Jeffrey R. Charles
Owner and Chief Engineer of

© Copyright 1988, 1997 Jeffrey R. Charles. All Rights Reserved.



This article is mainly for those who have only a small telescope, and is intended to show you just what can be done with such an instrument. Even if you also have a larger instrument it is good to know what your old observing buddy can do since its portability will likely allow you to take it along when you travel. Besides, using a small telescope is just plain fun! All photos shown here were taken with a 4" aperture or smaller instrument. We will cover the full spectrum of available subjects, from terrestrial and lunar to planets and deep-sky objects. As will be seen, small telescopes are capable of producing good photos of deep-sky objects, even at relatively large image scales, with today's fast color films. Since finances may be a factor for many, a minimum of accessory equipment will be stressed for each application.

Wide field photography with camera lenses will not be covered here, since this is a subject in itself which has been well covered in other papers by myself and other authors and speakers. It is, however, appropriate to suggest that an inexpensive tool used by wide field astrophotographers may be applicable for use with small unmounted telescopes. This is the Haig or "Barn Door" mounting. If robust and well made, these mounts can provide a sidereal drive for your telescope that is more precise than that provided by many commercial telescope mountings! David Charles (my brother) has some pretty convincing results taken with lenses of up to 600 mm focal length on such a mounting. Many are probably familiar with Tom Fangrow's innovative "Hiss" mounting for his 13" telescope, which is also based on the "barn door" principle, having a hinge for its polar axis.

In addition to "opening the door" to wide field photography, such a mounting will allow you to photograph planets and many deep-sky objects, not to mention how handy it will be for high power visual observation! As with any mounting, you will need an off-axis guider or a separate guide scope to get a good deep-sky photo. Think about this: If its axis of rotation can be pointed toward the celestial pole, you can use just about anything that turns for an equatorial mounting! A fan... a record player... a swivel chair... a bicycle... Many of today's commonplace items are based on ideas once considered crazy by most people.

Return to Beginning of Document


Even without an equatorial mounting, many small telescopes can be used to photograph a wide variety of subjects. Starting close to home, they work nicely for photographing birds and other wildlife. If your telescope focuses close, you can get pictures of creatures that look like they came from another planet by photographing insects! Moving along to more distant subjects, you can try prime focus photography of the moon. Once you have a collection of lunar phase photos, there are always the added attractions of conjunctions, occultations, and the partial phases of a Lunar eclipse. If you have a 2x teleconverter for your camera or can use a Barlow lens photographically on your telescope, you can get a larger image. Most 2" and larger telescopes will produce a really good photo of the moon with this arrangement. If you have a glass or mylar solar filter which can be used in front of your telescope, you can also photograph the sun. With sunspot maximum coming up, the sun will be an increasingly interesting subject. If you are fortunate enough to go see a total solar eclipse, the subject will more than speak for itself!

For even larger images, you can use the afocal method (where you point your camera and lens with aperture set "wide open" into your eyepiece) or conventional axial eyepiece projection. Either of these methods can be used for lunar close ups and sunspot photography.

The afocal method is particularly effective with small telescopes because it requires a minimum of equipment (no camera adapter is needed and you can use any camera with manually adjustable shutter speeds, even if it is not an SLR!) Focusing and calculation of your focal length are also easier for afocal photography. To focus, use a monocular or binocular of 7 to 10 power as a magnifier. This is to compensate for the accommodating effects of your eye when looking in an eyepiece (when using your telescope visually, especially at low power, you may have noticed that the image remains sharp when the focus is adjusted slightly). Look at the stars through your binoculars and adjust the focus until the stars in the center of the field look sharp.

Locate and center your subject in your telescope eyepiece, then point your binocular into the telescope eyepiece and focus only the telescope until the image looks sharpest. This will perfectly adjust the focus for any camera lens with its focus set at infinity, and thus eliminate the need for the laborious and imprecise task of focusing the image in your camera finder! For best results, the subject should be centered in the eyepiece at the time the picture is taken. To ensure this, position the center of your subject at the edge of your eyepiece field that is opposite of the direction of drift and time how long it takes to move to the center. The camera lens should be well within 1" of the eyepiece and be centered over and squared on with it. The camera lens focal length should be between 35 mm and 105 mm. A black cardboard disc around the eyepiece will help eliminate stray light.

To calculate your focal length, just multiply your camera lens focal length by the power of your telescope. If you are not using the afocal method, you can use the moon as a reference to roughly determine your telescope's effective focal length. For every 110 mm of focal length the moon will be about 1 mm in diameter. The dimensions of the 35 mm format are 24 x 36 mm. Check to see how many moons it will take to go across your focusing screen. If you have a larger image scale, see how many picture widths it will take to cover the moon. To get your f/ratio, divide the focal length by your telescope's aperture. Remember not to mix inch and millimeter values in your computation! The exposure times for different solar system objects can be estimated by knowing their relative distances from the Sun and using the inverse square law. For example, Jupiter is about 5x farther from the Sun than the Earth, so it will need about 25x (5x5) more exposure than a terrestrial subject of the same reflectance.

You can also photograph many of the planets without an equatorial mounting. Venus is so bright that its phases can be photographed without tracking it at all, even with f ratios as slow as f/100 on faster films! Mars and Jupiter require longer exposures, but can still be photographed provided you track them during your exposure. For short exposures, the fact that you need only track an object for the duration of your exposure is an important thing to remember. This is because many means can be used to properly move a telescope for a short period of time. If your telescope has an alt-azimuth mount (or you can attach it to a good camera tripod) here is some good news; when a planet is on the meridian and not too near the zenith, you only have to move your telescope in azimuth to track it! One way tracking can be accomplished is by rolling your finger along a solidly mounted object that is placed near your eyepiece in such a way that your finger pushes the eyepiece slowly to the side as it moves. This method works quite well for exposures up to about 4 seconds. If you are using the afocal method, the edge of your camera lens will work nicely for your finger drive surface.

The pictures of Jupiter shown at the end of this article, which clearly show cloud belts, were taken in 1982 with this method using a 4" refractor telescope at f/50 on Kodachrome 64 film (1 to 6 second exposure times; afocal with a 100x eyepiece and 50 mm camera lens). This particular image is used because it was y first attempt at this type of photography. Just think what could be done with faster film! Bright double stars such as Alberio can also be photographed using this method. If you feel adventuresome, try improvising on this procedure for the longer exposure times required to photograph Saturn. A simple suggestion would be attaching a short section of plastic pipe to the front of your camera lens that has a screw through its side which can be turned against the side of your telescope's eyepiece (see illustration at end of article). This concept could be applied to move your camera body and telescope when taking prime focus pictures of a total lunar eclipse, etc.

Return to Beginning of Document


As we have seen, a wide variety of subjects can be photographed without a drive or equatorial mounting by making the telescope "think" it is equatorially mounted for a short period of time. An equatorial mount and clock drive will greatly simplify your photography of the previous objects, since tracking can be important even for exposures of only a few seconds. Total solar and lunar eclipses, close-ups of the moon and planets, and deep-sky photography can all benefit from an equatorial mounting.

Even if you have an equatorial mount, you may want to try some of the previous methods of photography. For some people, a good part of the fun in astrophotography is the challenge of pushing the envelope to achieve impressive results with modest equipment, which means that it is possible to simplify a task so much that it ceases to be fun! Those of us who have on occasion lacked the financial means to start with a large or fancy telescope are thus given the privilege of being in a position where we must sharpen our creative skills to achieve our astrophotographic ends, and this is marvelous! My first telescope was a 90-230 mm zoom lens with some of the optics from an 8 mm movie projector lens mounted in a film can for an eyepiece. This was improved upon 2 years later in 1976 when I obtained an inexpensive 400 mm lens (dubbed a "girl watcher" lens by the manufacturer). In 1979 I purchased a used 800 mm f/8 Soligor "stovepipe" lens and used my 50 mm lens for an eyepiece to make it an R.F.T., then bought a Celestron 90 spotting scope from a friend for my planetary telescope. The 4" refractor used for the "finger guided" Jupiter shots was built from commercial parts and irrigation pipe in 1980.

Even with an equatorial mounting, afocal photography is one of the best methods for planetary photography because of the previously mentioned ease of focusing, etc. Here it is best to position the eyepiece so it will move directly toward or away from your camera lens as the telescope tracks. You can orient your camera tripod so the camera can be repeatedly swung toward and away from your eyepiece by tilting the tripod over slightly so that only one leg leaves the ground. This will allow you to check the centering of your subject without severely disturbing the alignment of your camera. If your telescope has been outside for less than 30 minutes, or if the temperature is changing rapidly, you should check the focus every several minutes.

Deep sky objects (nebulae) are very dim and thus require much longer exposure times. Here an equatorial mounting (not necessarily in a traditional embodiment) is required, as is some means for guiding your photograph. Guiding is necessary to correct for tracking errors caused by atmospheric refraction and imperfections in the telescope drive over the long exposure times required (over an hour in some cases). Guiding is accomplished by referencing your subject or an object fixed in relation to it (such as a nearby star) to a reticle in an eyepiece which is fixed in relation to your film. This reticle eyepiece can be used in an off-axis guider or in a separate guide scope which is rigidly mounted on the same mounting as your main telescope. To work well, a guide scope should have a focal length at least as long as the main telescope, though its aperture need not be as large. Some means of interrupting your exposure without losing the view of your guide star is desirable.

An off-axis guider is typically recommended for catadioptric telescopes such as the Celestron C90, 4" Meade 2045, Questar 3.5", larger Cassegrain instruments, and 3" or larger refractors. A separate guide scope or the Lumicon low profile off-axis guider is useful with a Newtonian telescope. Beamsplitters can also be useful, but they can introduce ghost images and increase the required exposure time. Therefore, their use is best limited to applications other than deep-sky photography.

The deep sky pictures in this article are those I took through a Questar 3.5" f/16 instrument, but don't let the fact that the Questar is a high priced instrument discourage you. The fine resolution the Questar is noted for is not apparent at this image scale because the grain of most films and the guiding tolerance allowed by most good astrophotographers are over 3 times larger than the diameter of the airy disc. Further, the Questar's f/ratio is a full stop slower than most other catadioptric instruments and so requires a 2x longer exposure. It is therefore accurate to say that with the same effort, equally good deep sky results can be expected from many other telescopes of the same aperture. Why do I still take some of my deep sky photos with a Questar 3.5" and its slower f ratio even though I now own a larger telescope? Because it's fun!

Return to Beginning of Document


Since most guiding systems do not include adequate instructions for those who have not taken guided astrophotos yet, here is a suggested procedure for off-axis guided photography. If you have a large telescope or are using a separate guide scope (which is easier than off-axis guiding in many respects) you may still find some of the following information useful. This information has been adapted from instruction manuals I wrote for the patented (or Patent Pending in 1988 and subsequently patented) Versacorp DiaGuider, VersaGuider, and VersAgonal, which include guiding systems that are among the easiest to use available. The DiaGuider and VersAgonal are designed as photo-visual accessories which can make astrophotography comparatively simple.

1. Accurately polar align your telescope and start its clock drive.

2. Locate subject in low power (20 mm F.L. or longer) eyepiece. If you are using a diagonal mirror attachment, look for guide stars below and to the sides of your subject. If not using a diagonal, look above and to the sides. Note rotary position of diagonal (if used) and location of prospective guide star(s) with respect to subject. The area searched should be considerably outside the edge of the field of a .965" O.D. eyepiece and slightly outside the edge of a l.25" O.D. eyepiece field. If you are using a diagonal, refer to the part of the field toward your telescope as the top. Also note the appearance of your subject, star patterns, etc. in your finder scope so you can find your way back to your subject after the next few steps.

3. Attach guider with reticle eyepiece installed to scope, then attach camera and counterweight.

4. Locate a bright star within a few degrees of your subject and focus its image in your camera, then move telescope back to your subject. If your camera does not have a clear centered aerial focusing screen, focus the star on the plain matte part of your standard screen, just to the right or left of its central spot. DO NOT adjust your telescope's focus control after you have focused the star image in your camera.

Comments: When you later locate the guide star in your reticle eyepiece, the orientation of the top of the guider as seen from the rear should be a "mirror image" (with the "mirror" horizontal) of the orientation of the star to your subject; i.e. if the guide star is at the 5 o'clock position below your subject, the top of the guider should point toward the one o'clock position as seen from the rear. For this application, the part of the eyepiece field toward the front of the telescope is always considered to be the top, and the previous orientation of your diagonal is always considered to be the 12 o'clock position for the guider. If you were not using a diagonal, simply rotate the guider so that its top points the same direction as the guide star was from your subject in your low power eyepiece.

If your subject is too dim to see in your camera finder, it is desirable to parfocalize your eyepiece and camera by positioning your eyepiece in your diagonal in such a way that the assembly can be interchanged with your camera and used without refocusing. You may instead be able to mount or simply hold a low power eyepiece behind your guider body (with the camera removed) to see your photographic field. Better yet, some telescopes and accessory systems, such as the Questar 3.5" or Versacorp accessories such as the DiaGuider or VersAgonal (a little plug there!) offer the convenience of simultaneous attachment of a camera and low power eyepiece.

If the subject and guide star are bright enough to see in your camera finder, you can orient your guider so the guide star will be easier to see in your guiding eyepiece: With your subject centered, rotate your camera so the long dimension of your picture is vertical with respect to the guider, then look for a guide star near the bottom edge of your finder (the side toward the bottom of the guider). Keeping the subject centered, rotate the guider with your camera until the star is positioned at the middle of the bottom edge of your camera finder. If your camera has a right angle finder, center the star on the top edge. The shadow of the guiding prism may prevent you from positioning the star at the edge of your camera finder. If so, slightly move your telescope to move the star image toward the edge until it dims considerably.

5. Turn on your illuminated reticle eyepiece and set the brightness so the reticle lines are as dim as you can easily see. Focus the top part of the eyepiece until the reticle lines look sharp. Using one of the above procedures, position the star so you can bring it into your reticle eyepiece field. Once the star is in your eyepiece field, loosen the guider's eyepiece holder lock screw and pull the reticle eyepiece up until the star is in focus, then lock in place. To save time in the future, you can mark the barrel of your eyepiece so you can roughly position it for proper focus without using a star.

6. If a guide star is not visible when you look in your reticle eyepiece, then rotate your guider slowly until a guide star is found and roughly centered from side to side. Move your telescope slightly to position it vertically. If your guider has radial adjustment (as do Lumicon and Versacorp guiding systems) use this feature instead of moving your telescope. This will allow you to keep your subject centered.

7. Loosen the guider's eyepiece holder lock screw and rotate reticle eyepiece so reticle lines are roughly parallel with motion of star when scope is moved in R.A. or declination, then lock in place.

The telescope can be moved slightly to center your guide star, but too much motion (enough to move the star more than about 1/4 of your reticle eyepiece field) will noticeably de-center your subject. If the guider is rotated sideways to acquire a guide star, the telescope motions used to move the star image will be reversed, i.e. R.A. will move the image up and down (if down is considered to be toward the back of the guider) and declination will move the image from side to side.

If more than one star is available for guiding, use the one that will allow you to assume the most comfortable guiding position. If you have a 1.25" Barlow lens, you may want to attach it at this point. A Barlow will allow you to guide more accurately.

8. With the star centered, move your head slightly from side to side while still looking at the guide star. If the star seems to move from side to side in relation to the reticle, adjust the focus by slightly moving your reticle eyepiece up or down until no motion is seen. This is to ensure that the plane of best focus is coincident with your reticle so there will not be any parallax which could cause you to make false guiding corrections! Once focused, check to see that all lock screws, etc. on your guider are tight.

9. Rotate camera to desired angle for picture composition.

10. Attach a locking cable release to your camera, set speed to "B", and wind the shutter. If your camera has a "T" setting, a cable release may not be required.

11. Be sure you are in a comfortable guiding position, taking into account where the eyepiece will have moved to by the end of your exposure. Also check to see that you are not in a position where you could accidentally bump or touch your camera or reticle eyepiece during your exposure.

12. Stand up, stretch out, and check the sky for picture killing airplanes. If you are out alone, get your Walkman ready. If you are in a group, show some friends about where you will be photographing and see if they will check the area for airplanes and bright satellites every now and then.

13. Center guide star.

14. Open the camera shutter. (Then open your guider's manual shutter if it has one)

15. Guide your photograph carefully! If you are using a conventional 12 mm double line illuminated reticle eyepiece, you will need to guide to an accuracy of less than 1/4 (1/2 if you are using a guiding Barlow) of the width of the reticle's central box to get a really good picture. (The required guiding accuracy can at least twice this critical if you are using a CCD imager.) If there are bright stars in your picture, a guiding error of only one second duration could cause these stars to appear streaked or elongated.

Some guiding systems (such as those offered by Versacorp and Questar) permit you to interrupt your exposure while still permitting you to see your guide star. This feature will permit you to take a break during your exposure if necessary, or to break a long exposure up into a number of shorter guiding sessions.

16. Close camera shutter.

17. Finally, stick with your predetermined exposure time. As I have guided photos, thoughts have come into my mind like: "It looked so bright in the eyepiece, the picture will surely be ACCEPTABLE (so much for a GOOD picture!) with a shorter exposure... and I'm cold, so the emulsion is cooled, right?" Wrong! Don't give in, go the distance, and you will be glad you did! Remember, an underexposed photo is a spoiled photo!

If you make guiding errors well into your first exposures or discover that your polar alignment is slightly off because of frequent declination adjustments in the same direction, continue to guide the rest of your exposure anyway. Even though the star images may be streaked, you will still be rewarded with a good image of your subject and begin to discover the acceptable amount of guiding error for your applications.

Good luck, and may all your star images be round!

Return to Beginning of Document

(Telecompressors, Barlow Lenses, Filters, etc.)

Telecompressors for film photography, the pros and cons. If you are using a Cassegrain telescope, you can use a telecompressor to permit a shorter exposure time and cover a wider field in your picture. With a 0.7x telecompressor, your exposure time will be about 55% as long as for a prime focus exposure. Some telecompressors will work at 0.5x, but most will only shorten your exposure time to about 30% of the prime focus exposure due to the fact that most of them can severely vignette your picture, producing reduced off-axis illumination. Remember that the image of your subject will be smaller when a telecompressor is used. Some telecompressors reduce the quality of the off-axis image, resulting in enlarged and asymmetrical star images. All photographic procedure steps are basically the same as for prime focus photography.

The 55% and 30% exposure figures given above (rather than the 50% and 25% figures you might expect) tend to be true in practice, particularly with hypered film, because of its lower reciprocity failure.

Following the initial publication of this paper, the Celestron f/6.3 reducer/corrector has become widely available. A few years after that, Meade introduced a telecompressor system which appears to be similar. These telecompressor optics represent some of the most monumental optical improvements "recently" implemented by manufacturers of commercial Schmidt-Cassegrain telescopes. Since the introduction of low priced commercial Schmidt-Cassegrains, amateur astronomers have typically had to rely on small independent accessory manufacturers to provide the innovative accessories which make photographic use of their telescopes practical and convenient.

Barlow lenses and photographic teleconverters will give you a larger image, but they will increase your exposure time. Some Barlow Lenses (particularly some stronger ones having short tubes) can introduce a substantial amount of field curvature.

Eyepiece projection can produce an even longer focal lengths for still larger images, but only with a corresponding increase in exposure time and the criticality of accurate tracking. It is important to realize that wide field eyepieces offer little or no advantage when it comes to eyepiece projection imaging. In fact, many simpler designs such as the Plossl, Brandon, Orthoscopic, can actually produce better images than many wide field eyepieces. I even found that some Kellner eyepieces (such as the older 18 mm Celestron unit) have worked remarkably well.

While it does not work particularly well for deep-sky astrophotography, let's not forget the usefulness of the Afocal method! This is where your camera and lens are simply pointed into the eyepiece. Depending on the optics you have, the afocal method may yield even better results than eyepiece projection!

Photography with filters:

The rest of this section is Under Construction.

Copyright 3/1988 by Jeffrey R. Charles All Rights Reserved.

Return to Beginning of Document

Optimum Use of AutoGuiders

The rest of this section is Under Construction.

Return to Beginning of Document

Other Techniques

Issues to Consider Before Taking Astrophotos:

Equipment: Astrophotography Techniques: After You Take Your Astrophotos:

The rest of this section is Under Construction.

Return to Beginning of Document

Astrophotography Exposure Guide


OBJECT:                   ISO:                      f/RATIO:

                           25:   - -   f/1.4  f/2.8  f/5.6  f/11   f/22   f/45
                          100:   f/1.4  f/2.8  f/5.6  f/11   f/22   f/45   f/90
                          400:   f/2.8  f/5.6  f/11   f/22   f/45   f/90   f/180
                         1600:   f/5.6  f/11   f/22   f/45   f/90   f/180  f/360

SOLAR SYSTEM OBJECTS:                  TIME IN SECONDS  (or as specified)

Sun - With Most Solar Filters    1/4000 1/1000 1/250  1/60   1/15   1/4    1
Total Solar Ecl. - Prominences    - -   1/4000 1/1000 1/250  1/60   1/15   1/4
"  No Filter  "  Inner Corona    1/2000 1/500  1/125  1/30   1/8    1/2    2
"             "  Outer Corona    1/125  1/30   1/8    1/2    2      8      30
Crescent Moon - Earthshine       1      4      15     1m     4m     15m    - -
"           "   <30 Hours Old    1/125..or  Underexpose Twilight Sky 1 f/Stop
"           " 30-60 Hours Old    1/500..or  Underexpose Twilight Sky 1 f/Stop
"           " 20-35% Illum.      1/2000 1/500  1/125  1/30   1/8    1/2    2
1/2 Moon                         1/4000 1/1000 1/250  1/60   1/15   1/4    1
Sunlit Earth, Full Moon           - -   1/2000 1/500  1/125  1/30   1/8    1/2
Terminator of <50% Illum. Moon   1/500  1/125  1/30   1/8    1/2    2      8
Moon 4' from Terminator          1/2000 1/500  1/125  1/30   1/8    1/2    2
Partial Lunar Eclipse 0-30% Ecl. 1/4000 1/1000 1/250  1/60   1/15   1/4    1
"  (+/- 1 f/stop)  "  30-80%     1/1000 1/250  1/60   1/15   1/4    1      4
"  (+/- 1 f/stop)  "  80-95%     1/250  1/60   1/15   1/4    1      4      15
"  (+/- 1 f/stop)  "  95-99%     1/60   1/15   1/4    1      4      15     1m
Total Lunar Ecl. (+/- 3 f/stops) 4      15     1m     4m     15m    - -    - -
Mercury and Venus                1/2000 1/1000 1/500  1/250  1/60   1/15   1/4
Mars                             1/250  1/125  1/60   1/30   1/8    1/2    2
Jupiter                          1/60   1/30   1/15   1/8    1/2    2      8
Jupiter and 4 Moons              1/2    1      2      4      15     1m     4m
Saturn                           1/8    1/4    1/2    1      4      15     1m
Uranus  (or 6th Mag. Star)       4      4      4      4      15     1m     4m
Neptune (& Saturn's Moon Titan)  15     15     15     15     1m     4m     15m
Naked Eye Comet Nucleus          6m     25m    100m   - -    Tail = Same as M42

DEEP SKY OBJECTS:                      TIME IN MINUTES  (or as specified)

12th Mag. Star (20 cm Aperture)  10     20     40     80     - -
Open & Globular star cluster      8     30     2h     - -    - -
Brighter nebulae, i.e. M42       15     60     4h     - -    - -
Most objects, i.e. M20, M51      22     90     - -    - -    - -
Very Dim, i.e. Veil Nebula       30     2h     - -    - -    - -

*  Double exposure if object is only 8-14 degrees above horizon.
*  Quadruple (4x) exposure if 5-8 degrees high, or for thin clouds.
*  If ISO is higher, decrease exposure time by same proportion, i.e. if
   ISO is doubled (or if film is hypered) reduce exposure time by 1/2.
*  Keep a record of your own exposure data, it will save film!
*  Use the f/11 exposure data if you are using an f/10 SCT.

Small  planetary images will show little detail.    Mercury    Illustration:
Therefore, planetary exposures shown in the left    Venus        Not Shown
three columns will overexpose the image to  make    Mars
it more visible in the picture.  A focal length     Jupiter
of at least 5,000 mm is recommended for detail.     Saturn
Image sizes @ 18,000 mm FL are shown at right:                 24 x 36mm Format

Useful Angle Ratios:  1 deg = 1:57.3   1 min = 1:3,438   1 sec = 1:206,265
                      .573 degrees, or 34.38', or 34'22.7 sec = 1:100
For each 100mm of focal length, the Moon's image will be about 1mm in diameter.
To calculate your f/ratio, divide the focal length by your telescope's aperture.

f/number counter; double the exposure time for each successively larger number:
Each number, or f/stop is a multiple of the square root of 2, or about 1.4142.

1  l.4  2  2.8  4  5.6  8  11  16  22  32  45  64  90  128  180  256  360  512

       Copyright  3/1988  by Jeffrey R. Charles     All Rights Reserved.

Return to Beginning of Document

Future Images:

* Black and white image published with this paper in 1988 RTMC Proceedings.

Return to Beginning of Document

References & Additional Information

Return to Beginning of Document

Need creative solutions for your engineering, motion picture, or other project? Jeffrey R. Charles performs systems engineering, conceptual design, and technical writing for a variety of applications. In addition, Jeff can provide science consulting in regard to total solar eclipse phenomena, and engineering consulting for optical instrumentation. Please direct inquiries to Jeffrey R. Charles or click here for more information.

Return to Beginning of Document

Go to EclipseChaser Home Page / Technical Articles, Papers, & Images

Go to EclipseChaser Home Page

Go to Versacorp Home Page / Articles & Papers

Go to Versacorp Home Page

© Copyright 1991, 1997, Jeffrey R. Charles, All Rights Reserved. Any form of reproduction or posting of any part of this document at a web site other than "" without including this notice and without the prior express written consent of Jeffrey R. Charles is strictly prohibited.

This material is the intellectual property of Jeffrey R. Charles. Commercial use (such as in a publication, program, broadcast, or motion picture) of data or other material in this paper or of related material by the same author (whether said material was obtained directly or indirectly) without the prior express written and signed consent of Jeffrey R. Charles is strictly prohibited.

Mail to: Jeffrey R. Charles (

Document Created: March, 1988
Document Converted to HTML: 27 Sept. 1997
Document Last Modified: 27 Sept. 1997
Links Last Modified: 18 Mar. 1998