Do you know that over 4400 people have scaled Mount Everest? Compare this number with the barely thirty people who have ever successfully captured an analemma of the sun. Do you want to join this elite club? Read on......

So what is the analemma of the Sun? Simply put, if you look at the sun, from the same place on earth, at the exact same time everyday, it’s position will shift slowly over the period of the entire year, slowly tracing out a figure-of-eight shape in the sky.

How does it happen?

Two properties of the earth’s motion combine together to create the analemma. These are,

(a) The earth’s rotational axis is tilted 23.44 degrees with respect to it’s orbital plane and

(b) the earth traces out an elliptical path (called eccentricity) as it orbits the sun.

Over a period of a full year, these two properties combine together, to trace out a figure-of-eight pattern in the sky (providing we observe the sun at the exact same time and from the exact same place).

Step 1: Mathematics Holds the Key

The earth’s tilt and the eccentricity of its orbit give rise to the two factors described below that create an analemma.

Declination of the Sun. As it revolves around the sun, the 23.44 degree tilt of the earth’s axis causes the sun’s position (called declination) to shift north and south of the equator. This movement is extremely significant to life on earth as we know it because it is this property that gives rise to what we call ‘seasons’. Without seasons, life on earth would have been very very different. You can see declination (in degrees) of the sun plotted in the first graph above in red color. Days of the year are on the X axis with January 1st shown as day 0. When the declination is 0, the sun is over the equator and at its extreme values, the sun is over the Tropic of Capricorn (December) and the Tropic of Cancer (June).

The Equation of Time. The earth’s orbit around the sun is not exactly circular, it is slightly elliptical in shape. According to Kepler’s 2nd Law, a planet tracing out an elliptical orbit must travel faster when it is closer to the sun and slower when it is farther away. This difference in a planet’s velocity as it orbits the sun, changes how fast the day progresses. In mathematical terms, we call this The Equation of Time and it gives us the difference between time measured by a sundial and time measured by a modern watch. You can see the Equation of Time plotted in green color. On January 1st (Day 0 on the X Axis), a sun dial would be about 3 minutes behind a modern clock. On November 3rd (Day 307), a sun dial would be about 16 minutes ahead of a modern clock.

Finally, on the bottom graph (in black) we can see the shape of the analemma appears when we plot declination versus Equation of Time.

These graphs can be modeled using fairly straightforward mathematics. I have attached the .m file I created in Octave to plot the graphs, it should run in Matlab as well without modification.

analemma.m
Download

Step 2: Planning and Patience

Proper planning, technical skill, methodical execution and patience are the keys to a successful analemma attempt. Remember, the endeavor takes a full year to complete and each and every exposure with the camera requires a series of very precise steps to get it just right.

Equipment Needed

Camera (DSLR/ Film or Compact) and tripod
1000ND filter or Variable ND Filter
Stopwatch or accurate wristwatch
Computer (to plan the sequence, predict the sun's position and perform post-processing)
Shutter release mechanism (optional but recommended)

Plan the Entire Sequence

First decide how many exposures you would like to capture over the whole year. I have seen analemmas with upto 52 exposures (one per week) on the internet. Remember however, that you will have to manually set up your camera/ filters/ tripod/ timing etc. for every one of these shots, so my advice is not to be over ambitious. I went with a more conservative 26 exposures (one per fortnight) but as you can see from my image, there are significant gaps in the figure-of-eight. This was because of the Indian monsoon clouds obscuring the sun for weeks at a time.

Just so that you don't miss an exposure, set a reminder on your computer or smartphone one day in advance of each exposure. Prepare a calendar. Write it down. Tick off the days as you proceed with the sequence.

Get the Timing Perfect

First, choose a suitable time of day to take each picture. This time will remain fixed throughout the entire sequence. Choose a time so as to make sure the sun is clear of the tree tops / buildings in the winter and also so as not to be too high in the sky during the summer months. If you are in a country that uses Daylight Saving Time, I recommend planning your exposures in GMT so that advancing/ retarding your clock does not affect your instant of exposure.

You can use a program like Stellarium to simulate the sun's position from your location and determine if it will be visible throughout the year at your time of choosing. By noting the elevation & azimuth of the sun, you can estimate whether or not it will be clear of any obstacles in your foreground.

Timing is critical. Since the sun’s disc subtends an angle of only about 0.5 degrees, and moves through the sky at 0.25 degrees per minute, I cannot overemphasize how important it is to get the timing perfect. A timing error of just 15 seconds will cause the sun’s disc to be out of position by 1/8th of its diameter.

Just before setting up for each exposure, synchronize your watch with an internet time service.

Step 3: Camera Details

Camera

You could use just about any camera for your analemma adventure. Ideally it would be better to use a camera with manual exposure settings like a DSLR. According to this compilation of analemma captures, in all of human history, only 6 successful attempts have been made using a SLR camera on a single frame of film.

If you want to try doing it on a single frame of film, you will need to use a camera with a multi-exposure lever (like my Nikon FE shown above). This lever allows the photographer to prep the camera for the next exposure without advancing the film reel. Successive images can thus be captured on one frame of film. Some high-end DSLRs allow you to do this but I'm not sure of there are any that allow more than 5-7 exposures on a single frame.

Focussing Grid

Almost all cameras today come with a focussing grid of some sort. Some even have interchangeable grids for taking precise architectural photos. Take a look at the various types of focussing grids available for my Nikon FE.

For my analemma sequence, I used the Type E grid. Any type of grid/ focus dots/cross hairs will do....you only need them as a reference for alignment of the camera.

Select ONE POINT on your focussing grid. This will remain your camera's reference point throughout the entire sequence.

Step 4: Choosing a Lens

You will need to carefully select the lens that you intend to use as a suitable focal length is mandatory for a task like this. It would be disastrous to have the sun move out of your field of view halfway through your sequence.

Use a program like Stellarium to note down the extremities of the altitude and azimuth of the sun (at your chosen time of exposure) on Jun 21/22 and Dec 21. Now use a compass to estimate the central azimuth line on your foreground of choice. Basically make sure you choose your transit points and foreground so that the COMPLETEanalemma will appear well within the field of view of your camera. Use the diagram and formula above to estimate your camera's Field of View (FOV). Make sure that once your camera is aligned perfectly to your transit points, it will be able to "see" the sun throughout the whole year.

Using the formula from the diagram above, I estimate that using a 28mm (or less) lens on a full frame/ 35 mm film camera will allow a full analemma to be captured.

If you are using a DSLR with a crop factor, don't forget to account for the cropping effect. On my Nikon D40x, the crop factor is 1.5, so I set my kit lens to 18mm which would give me an effective focal length of 27mm.

Step 5: Alignment and Foreground

Camera Alignment

I cannot stress this enough -> Proper alignment is the MOST important factor to get right while photographing an analemma. Half a degree of alignment error (just a nudge of the tripod) would be equivalent to a timing error of no less than 30 seconds. This is why I recommend the alignment be carried out using two permanent foreground structures in line (also called a transit) with each other.

Look at the diagram above to see what I mean. When the two objects are in line, the alignment will be perfect.

The sensitivity of this alignment method is much improved by ensuring that the distance between the camera and the closer object is many times smaller than the distance between the two objects.

When setting up for each shot, you will need to ensure that your focussing grid reference point lines up perfectly with your transit. You need to ensure this for every single exposure in your sequence.

Choosing the Foreground/ Transit Points

The transit points are critical to an accurate imaging sequence. Select your transit points carefully within whatever foreground image you want to overlay over the analemma. I made the mistake of choosing points near some mango trees and you can see from the picture above that the mango tree actually grew tall enough over the year to obscure my transit. Not good. Select you foreground composition and transit points carefully.

Tripod and Shutter Release

Use a good tripod and a shutter release mechanism to prevent camera shake.

Step 6: Exposure Settings

Suppose you have decided to take a sequence of 26 pictures. The exposure settings of 26 of these will be so as to capture only the sun's disc and blacken the entire field of view including the foreground.At each exposure, you need to ensure that your camera captures only the sun’s disc. Your exposure settings should ensure that sky, clouds and trees are blacked out of each of the 26 exposures.

To accomplish this you will need a Neutral Density filter of 1000ND or so. These filters can be quite expensive so I settled for a cheap Chinese variable ND filter like the one shown above. Rotating the outer collar allows you to adjust the filter’s density and black out everything but the sun’s disc from each shot. This done, now make fine adjustments to the exposure with the shutter speed and aperture settings on the camera.

Clouds, haze and other atmospheric disturbances can cause trouble to pre-configured exposure settings. If you are using a digital camera, you have the advantage of being able to take a few practice shots, check the result and fine-tune your exposure settings. A correct exposure should look like the one shown above.......black everywhere except for the sun's disc. Each time you prepare for an exposure, make your settings well before the exact time of your 'final' exposure for the day.

If you are trying this on film, there is no room for trial and error and you need to estimate your exposure perfectly.

Step 7: A Nice Foreground

Once you have completed your entire analemma sequence, its time to capture a foreground image. Any foreground will do, the more iconic, the better.

The only thing to remember is that you should select and photograph the foreground in such a way so that no part of the foreground image obscures the images of the sun that comprise the analemma sequence.

Also make sure that the sun is NOT in the field of view when you capture your foreground.....otherwise you will end up with one additional image of the sun in your frame....not good.

Look at my foreground image above, notice how the car and road occupy just the lower part of the frame leaving plenty of room for the sun's disc images to fill up the sky area.

Step 8: Daily Check of List

Here is a check off list I made during my analemma sequence. It may help you prepare for yours....

I selected 08:05:00 (GMT +5.5) as my exposure time.

Check off List

07:30:00 - Collect all equipment. (Tripod, camera, filters, shutter release)

07:35:00 - Synchronize watch with internet time service

07:40:00 - Set up equipment.

07:45:00 - Complete the alignment of transit points with camera focussing grid

07:50:00 - Test exposure settings on DSLR. Adjust ND filter/ shutter speed/ aperture

07:55:00 - Watch out for nearby clouds that may obscure the sun

08:00:00 - Test shutter release on DSLR

08:03:00 - Advance the multi-exposure lever on 35 mm film camera

08:05:00 - Take the shot with DLSR

08:06:00 - Take the shot with film camera Nikon FE

After completion - Immediately transfer the digital images to your hard drive. Re-name the image into a proper sequence at once so that they don't get mixed up.

Step 9: Post Processing

Once you have captured all the images including the foreground, its time for post-processing.

Your images of the sun should look like the one above......black everywhere except for the disc of the sun.

You now need to merge all of these together (and your final foreground image) using a photo editing software like Photoshop or GIMP. I won't go into the details on how to do this here......merging images is out of the scope of this instructable.

You could start with this instructable on how to use GIMP to merge images. You could even create an animated GIF file showing the path of the sun as it moves through the sky.

If you are doing this on film, there is no post-processing. Re-wind your film reel and send it directly for printing.

Thats it....You're Done!!!! Welcome to the elite group of people who have successfully captured the analemma of the Sun!!!!!!