Sakari Ekko
"EAAE Summerschools" Working Group
Poulalanmaki School (Finland)
Abstract
Sky photographs with all the stars seen by the naked eye can be taken with an ordinary SLR camera and fast film. In addition to camera and film you only need a tripod and cable release; even without tracking decent results are possible. These photographs are a great way to familiarise students with the sky, and combining sky slides with drawings of the mythic constellation figures makes learning faster and more interesting. The idea is to use two slide projectors simultaneously, projecting the slide with drawings on the sky slide.
The students can take the photographs by themselves, and the figure slides can be made in a workshop. The use of a scanner and computer is possible, too.
In this workshop we will make a slide with constellation figures matched for a wide-angle sky slide, and look for deep-sky objects in slides taken with longer focal lengths and tracking. Simple methods for using an ordinary camera for sky photography are briefly discussed.
1. Photographing the sky
1.1. Constellation photography
The longest exposure time for trail-free sky photographs is given by the approximate formula
700s / (focal length in mm x cos d)
where d is the declination of the centre of the field. So, for example with a 50 mm lens and 0° declination the longest exposure time is 14s, but at 60° declination it is doubled to 28s. Any longer exposure will result in elongated star images.
The second factor is the diameter of the lens: the greater the diameter, the dimmer stars will be recorded on the film. The diameter of the lens is
D = focal length / aperture
For example, the diameter of a 50 mm f:2 lens is 50 mm / 2 = 25 mm.
Wide-angle lenses have a smaller diameter for a given aperture than longer lenses and are not as good in recording point objects like stars. The diameter of a 28 mm f:2 lens is 28 mm / 2 = 14 mm, considerably smaller than the diameter of a 50 mm lens at the same aperture.
The third factor is the sensitivity of the film. For this kind of work 400 to 1600 ASA films are best. The faster films are too grainy, the slower ones not fast enough for our simple methods.
These variables can be expressed with the empirical formula:
M = 8.4 + 5 log D + 2 log T - log F + 2.5 log (S/800)
were M is the magnitude of the dimmest star recorded, T the exposure time in minutes, D and F the diameter and the focal length of the objective in centimetres, respectively, and S the speed of the film in ASA.
For example, with a 50 mm f:2 lens, 800 ASA film and one minute exposure it is possible to record stars to the magnitude 9.7, and with an exposure of 14s (without tracking) to about the magnitude 8.5. By using a 28 mm f:2 lens and 1600 ASA film, the magnitude of the dimmest stars recorded without tracking (exposure time 25s) is 8.7, and with a more common 28 mm f:2.8 lens the magnitude limit is 7.9. The results will of course depend on the transparency of the sky, but in any case the number of stars in the photographs will be far greater than seen by the naked eye. Too many stars in constellation slides can even be confusing to the students, and tracking is not really needed for these kind of photographs.
Some constellations occupy a large area of the sky, and wider than normal lenses (about 28 -35 mm) are needed to get the whole constellation in one slide, and slides with many constellations will call for extreme wide-angles (under 24 mm). For geometric and optical reasons wide-angle lenses in particular tend to record the corners of the frame noticeably darker than the middle part, and fewer stars are recorded in the corners. This effect is strongest in photographs taken with extreme wide-angles. Used wide open, wide-angle and normal lenses suffer from lens defects in the corner of the field, recording stars elongated like UFO:s. The cure for this is to stop down the lens, but you lose light, and longer exposures are needed. Stopping down the lens does not help to the corner darkening much, though.
Fig. 1 and table 1 will give you some idea of the sky coverage of different lenses. The scale in mm/degree is also given (see 1.2.).
1.2. Deep-sky photography with an ordinary camera
Photographing deep-sky objects is somewhat different. They are extended objects, and the important factor is the aperture, not the diameter, of the lens. The problem is that the sky background is an extended object too, and by recording dimmer deep sky objects the sky fog caused by light pollution is recorded better too. In any case you will need a dark location as far as possible from the cities and bigger settlements for your sky photography. Most of my sky photographs are taken 50 km north of my home town Turku, and even there the lower part of the southern sky often glows too brightly for deep-sky photography.
To record deep-sky objects you need longer exposures than for the constellations, and tracking is needed. The barn-door tracker in fig. 2 and 3 is easy to make, and used with care is accurate enough for a 200 mm lens at an exposure time of 10 minutes (table 2).
A wedge-shaped hardwood block with the latitude angle for your location makes fastening of the tracker sturdier, and you can leave out the pan-and-tilt head for aligning. By drilling a 8.5 mm hole in the hardwood wedge it is possible to force in the tripod´s 3/8" bolt, thus avoiding the need of a 3/8" tap. If your tripod has an ¼" bolt, use a 5.5 mm bit. Another hardwood wedge for the camera ball head makes the system better balanced.
The longer the focal length and / or exposure, the more accurate polar alignment is needed. 200 mm is the longest practical focal length that can be used with this kind of hand-driven tracker. The succes rate is considerably higher with shorter lenses, though.
The size of most deep-sky objects is very small, and longer than normal lenses are needed to record them other than points of light. In the third column of table 1 is given the diameter of an object with angular size of 1o on film. The size of any object can be calculated using the formula
size of image in mm = angular size of object in degrees x (focal length in mm / 57.3)
Even in photographs taken with 50mm normal lens some of the most extended objects, like the great galaxy in Andromeda (M31), the North America Nebula, the Orion nebula (M42), Rosette Nebula and many others will show their true form.
For example, North America Nebula is about 2o x 1,7o, and in a photograph taken with a 50 mm lens it will be 2 x 0,82 mm x 1,5 x 0,87 mm = 1,6 mm x 1,4 mm. If you project the slide enlarged about 30x (100 cm x 72 cm), the length of the nebula on the screen will be about 50 mm and its shape is clearly seen. With a 200 mm lens the nebula on the screen would be 200 mm long, about one fifth of the picture length.
The picture can be enlarged up to 2x by copying it in a slide copier. The inherently low contrast of nebulous objects is enhanced in copying, too. It is possible to get out details from small objects by photographing their images with a low-power microscope.
With minute-long exposures films suffer from the so-called reciprocity failure: doubling the exposure does not double the effect of light on film, and the colours can be shifted too. A rule-of thumb says, that you have to triple the exposure time to double the effect. When you stop down one stop, you have to double the effect of light by tripling the exposure time to compensate the light loss. For example, an exposure of 2 minutes at f:2 and an exposure of 6 minutes at f:2,8 or 18 minutes at f:4 are approximately equivalent. There is no substitute for aperture in sky photography.
It is very important to keep accurate records on the photographed objects, exposure times etc. The slides are full of stars, and without any record it is very difficult to identify the area of the sky in the picture, and the other data will guide you to better results in the next sky-shooting session.
Remember to ask the film to be left uncut after development. The dark background in the sky slides can fool the cutting machine and it can cut your best slide in half!
2. Making a matched figure slide
2.1. Finding the right scale for the figures
The scale in slides taken with wide-angle lenses is not uniform over the entire picture. The lens records a spherical surface on the film plane, and for geometric reasons the scale will be smaller in the middle of the picture compared to the edges. The shorter the focal length, the more distorted the picture. So, when making matched figures for your constellation slide you have to draw the figures in different scales, depending on where in the picture area they are.
The right scale is best achieved by projecting the slide on the drawing paper using an enlarger or slide projector. The brightest stars are marked on the paper with a pencil as well as the corners of the slide. The marking of the corners is important later: the markings will help you to photograph your drawing in the right overall scale to match the slide.
Using the brightest stars as guides you can then draw the figures directly on the paper or you can make an overhead transparency of the figures drawn all in the same scale and project them on the wall-mounted paper with stars markings, varying the distance of the OHP to get the scale of the drawings right, again using the marked stars as guides. The projected image is then easy to draw on the paper. At this stage it is better to use a pencil instead of a permanent pen, and track the pencil lines with a black felt pen later, when you have the drawing horizontally on a table.
Of course you can make other markings besides mythic figures on your drawing too, like constellation boundaries or star names. Bear in mind, though, that it is difficult to position the two projectors accurately enough to align, say, all the lines connecting the brightest stars of a constellation in star charts.
2.2. Photographing the figure drawing
To project figures on the dark background of a constellation slide you will need a slide with bright lines on a dark background. It is possible to draw with white pen on black paper, but it is easier to use white paper and black pen and photograph the drawing on a black and white negative film, so that the slide will have bright figures on a dark background, as desired.
Common B&W films have a greyish base and too low contrast for this purpose. Copy films have better contrast and a clear base, thus making an ideal slide for our purposes. These films need a more accurate exposure than common films, and the illumination of the drawing must be as even as possible. Do not use a flash mounted on your camera! The light will be reflected back from the middle of the picture and wash out the drawn lines. Outside in open shade the illumination is even, without strong point sources of light. Copy films are often somewhat "colour blind", and require different exposure in tungsten lighting, so the natural sky light is better in this respect, too.
Make sure the film plane of your tripod-mounted camera is as parallel as possible to the drawing, and all the four corner marks fall just outside the viewfinder corners - here temporary tape markings some centimetres inside of the original marks will help. The problem is that the viewfinder of most SLR cameras do not show the entire area recorded on the film, and so the scale will not be very accurate. If the scale of the figure is not exactly the same as in the constellation slide, you can move the other projector until scales match when preparing the show. When making more constellation - figure slide pairs the scale of all the figure slides should be the same, so the projectors can stay in the same position during the show. This is best done by making all the drawings on the same scale and photographing them at the same time, without moving the camera between exposures.
If you have the film developed in a laboratory, do not forget to mention that it is special copying film, and ask for it to be left uncut.
2.3. Mounting and projecting slide pairs
Mounting the slide pairs needs a little fine-tuning to get both slides in the same position in the frame. Some mounts make it possible to adjust the slide, and the correct position is found by trial and error, projecting the slides on the screen with two projectors simultaneously. Fasten the slide in the mount with a tiny piece of document tape, when the right position is found. Tape is not usually recommended for slide mounts, but in most frames the slide can move a little, if it is not fastened, and I have found no harm done by the tape for my slides - but use the document tape, other tapes can spoil the slide.
Try to position all the slides in the same way, if you are going to project them in the same show. This way you do not have to adjust the projectors during the show. And, as I said earlier, avoid details in your drawing needing very accurate positioning. But sometimes it is worth the effort to get Aldebaran as the eye of the Bull or the belt of Orion on its place over Alnilam, Alnitak and Mintaka.
When showing the slides you can cover the lens of the figure slide projector first, then uncover it to show the figures after telling some sky stories. The figure projector´s lens should be covered when changing the constellation slide, too. And you can develop imaginative ways to uncover one figure at a time during your storytelling, or make slides with more and more figures in them, to be added to the sky. These slides are easy to make: cover unwanted parts of your drawing and take the photograph, then uncover a new figure and take another photograph.
3. Using the sky slides to find deep-sky objects
3.1. Making a sky map slide
A slide of a sky map matching the photograph can be made by the same method as the figure slide for a constellation slide in part 2. The sky slide is projected on a star map in the same scale, the corners marked and the map photographed on negative B&W film using the corner marks as guides. Usually it is not possible to get a perfect match between the slide and the map, because the map is projected on the plane in a different way from the photograph. By moving the other projector the part of the picture under scrutiny can be matched with the corresponding part of the map.
3.2. Using an enlarger
The easiest way to look for objects in a sky slide is to project the slide directly on a star map using an enlarger. Once the scale has been adjusted, the objects can be identified. Even tiny dots will reveal their nature when compared with the map. For example, the Ring Nebula in Lyra (M57) is so small, that it seems star-like in all photographs taken with the lenses mentioned in table 1, but it is easy to find in the slide by projection method. The enlarger method is best suited for small student groups, and for the systematic searching for objects in connection with a project. If you have access to a complete darkroom, it is possible to make B&W prints from the sky slides. The prints will be negative, with black stars on a white background. It is easy to mark objects on them with a black felt pen, and the prints can be used in students´ reports.
3.3. Using two slide projectors
With two slide projectors and a matched sky - map slide pair it is possible to reach a bigger audience. By covering the sky slide projector´s beam the markings on the map slide can be seen better. As mentioned earlier, some adjusting of the projectors is needed for different parts of the picture. The downside is the need of a map slide made beforehand.
3.4. Examining the objects
When the objects have been found, they can be studied with a magnifier or low-power microscope. Thus many details not seen even in the projected picture can be found and compared with photographs taken with big telescopes.
Students look for information on the objects in literature or on the Internet, and write an essay about the material. It is always astonishing to find the vast scale in both the distances and sizes of the objects.
4. Conclusion
So, why take so much trouble with sky photography, when the big telescopes make it far better and the material found in books and Internet is free? I have found, that photographs made by me or, better still, the students themselves, show clearly, that the sky is there for everyone to see and explore, it is not the domain of big and expensive instruments and professional astronomers only. The familiar skyline in a constellation photograph will inspire them to look at the sky over them another night. The students will learn constellations and finding objects by star-hopping, and find objects photographed by themselves, and soon they will be very familiar to them. And of course, it is always tempting to find out just what can be done using these simple methods.
5. References
Arnold, H. J. P.: Astrophotography - An Introduction, Sky Publishing 1995 - Basics of astrophotography.
Ballard, Jim: Handbook for Star Trackers, Sky Publishing, 1988 - Everything you need to know of simple barn-door tracking mounts - the book is out of print, sorry.
Covington, Michael: Astrophotography for the Amateur, Cambridge University Press 1985 - A more comprehensive guide than Arnold´s. A new, revised edition available.
Harrington, Philip S.: Star Ware, John Wiley & Sons 1994 - The nuts and bolts of amateur astronomy. Contains short description on barn-door mount and its use. Second, revised edition available.
Martinez, Patrick: Astrophotography II, Willmann-Bell 1987 - If you love formulas, you will find them here.
Reeves, Robert: Wide-Field Astrophotography, Wilmann-Bell 2000 - All about ordinary-camera astrophotography, but Schmidt cameras are discussed, too. Film testing and hypersensitising explained.
Tirion, Wil: Sky Atlas 2000, DeLuxe and Field Editions, Sky Publishing - DeLuxe (or Desk) edition is a good background for projecting sky slides with an enlarger, Field Edition has white stars on black background - you can make a sky map slide using normal positive slide film.