VNP: Analemma

VNP: Analemma of Kolozsvár/Cluj-Napoca, Transylvania

I am the first photographer to take a picture of an analemma in Transylvania.

The phenomenon itself, the celestial path of the Sun during a year is quite easy to understand yet it is a challenge to photograph it, even in the digital era, being a project spanning over a long time. And I did it, well, a bit differently.

This article is a summary of the last solar year, also with the intention to possibly serve as a guide for those future photographers who might take the challenge.

What is the Analemma?

In astronomy, an analemma (/ˌænəˈlɛmə/; from Greek ἀνάλημμα “pedestal of a sundial”) is a curve representing the changing angular offset of a the Sun in our case from its mean position on the celestial sphere as viewed from Earth in our case. The term is used when the observed body appears, as seen from the viewing body, to move in a way that is repeated at regular intervals, such as once a year or once a day. The analemma is then a closed curve, which does not change – as wikipedia says.

In the context of this photographical challenge, the analemma is a figure 8 trail left on the sky by the Sun when imaged from a fixed geographical point at a fixed time of the day. The size and exact shape of the analemma seen from Earth is determined by the axial tilt of our home planet (~23.5 grades), the constant rotational period of it and the almost circular yet still elliptic orbit we go on around the Sun. The length of the shape is given by the tilt, while its width by this tilt and the acceleration and deceleration of the orbital motion resulting in deviation from the mean solar day.

As a photo challenge

Arrows show the direction of the movement.

Arrows show the direction of the movement. See the full resolution version.

From a scientific point of view, photographing an analemma yields no value anymore. But it is a great challenge for enthusiasts even in the digital era. Though the challenge must have been somewhat greater in the film era.

In theory one can photograph an analemma by mounting a camera very firmly, with a sufficiently wide angle lens and taking a picture every 86400 seconds. Without changing any settings. And without the camera being moved even in the slightest amount. One would also need some kind of a filter for the Sun to present its disk in place of a patch of overexposure. Overlaying these individual frames taken over the course of a whole year results in the figure 8 analemma.

In other words: a series of white dots or maybe indiscernable dots fused into the curve and a pitch black background – now where is the aesthetical value in that. One would need a background picture over which to superimpose the analemma – and as far as I looked it up, photographers did this in three ways depending on the purpose, taste and mental constitution of the maker.

  1. Photoshopped background. Well, it sure looks good but I find this method the much too easy way. I think it is ill-advised.
  2. Using the original background although it might not be a pictoresque one. I find this method sincere, somewhat humble and yielding accuracy. I have to admit, I’ve seen analemma pictures composed with a high level of creativity making an everyday background very pleasant.
  3. Chosing an iconic location and background, meticulously planning all the details. I find this approach inherently aesthetic, the most elegant and, needless to say, the most demanding way to do it. So this is the path I’ve chosen for my analemma.

 

Previous analemmas

The first analemma was photographed by Dennis di Cicco in the US in 1978-1979. Closer to me I’d like to mention two pictures: the first Hungarian one made by Tamás LADÁNYI in 2010 and the first one made in Romania by a Bulgarian student studying in Bucharest in 2005. This least one has an added stronghold depicting a partial solar eclipse, however I find the background very sloppy and the Romanian language article is erroneous in the labeling of the curve (last check July 20th 2013).

Kolozsvár’s Analemma – getting ready

As I wrote, I chose maybe the hardest and most demanding way to accomplish this task – to get the most elegant result. So I decided to choose a location from where the iconic pictures of Kolozsvár/Cluj-Napoca are taken, a familiar and known point of view, possibly seen by everyone spending a longer time in the city. I cannot think of the Treasure City without it’s old church in the center, so I needed to include the Saint Michael’s Catholic Church in the field of view. Having these in mind I used two freely available softwares to aid me in choosing the best location and the best time of the day: Stellarium and Google Earth.

Azimuth: Google Earth

Azimuth: Google Earth

Altitude: Stellarium

Altitude: Stellarium

The camera

The camera having the flipping filter

Budget: well, I didn’t want to buy a new camera for the project and I was lucky for already having a Fuji HS20EXR with a 24mm (equivalent) lens which provides a broad field of view, enough for a considerable landscape, the analemma and the sky. Using a piece of Baader solar film, pieces of cardboard and duct tape I made a flipping filter for the camera so I was able to image both the correctly exposed disk of the Sun and the landscape (for reference) on a single frame.

Having all these in mind, I chose the location shown above and UTC 7:30 as the time of the day. Initially I thought of a two weeks interval for the project to not interfere at all with my daytime job.

Evidently I had no way to permanently mount the camera on site so I was ready (at least thought to be ready) to make the final fitting using a PC. This bit turned out to be by far the hardest part of the project. And another thing: using only freely available softwares/software libraries.

During the project I periodically synchronized my cell phone used as the timer mainly before each field work with the internet time given by atomic clocks.

On August 3rd 2012 I took the first picture which became the master frame, having it printed and carrying it with me for reference every time I took the picture of the day. Also in August, a few days later on a beautiful afternoon when the Sun was well out of the field of view and the sky was stunningly blue, I took the background picture.

Sketch: the view from my site

Sketch: the view from my site. Nope, this is not the backround picture :P

Difficulties

The weather in November (ANM/Radio Cluj)

The weather in November (src: ANM/Radio Cluj)

In total I climbed up to the site about sixty times, being unlucky only two times because of the clouds obscuring the Sun unexpactedly.

Ideally I would have taken each photo with the given interval and the exact same settings (ISO, infinite focus, exposure, F, resolution etc). However the weather turned unfavorable and I had to adapt. The most frustating was November when between 8th and 30th no photo could be made – I felt the project might be in danger.

Combining errors

Combining errors

The second problem arised from the first one. After November I decided to go out and take the picture whenever I could. And these short intervals, on the order of days, even consecutive days, showed the grave errors in the rather naive combining method I imagined would compensate the differences in the orientation of the camera (a few grades of pitch, roll, yaw impossible to set by the eye being on site, using an electronic view finder). The second method I came up with, corrected the deviations near the reference points but proved to be more and more inaccurate when the Sun started to get away from the ground (in the spring). The third, most complex approach gave the right outcome.

Combining the individual frames: by eye, on a plane, on the surface of a sphere

I tried to elliminate pitch-roll-yaw by trying to set up the camera and tripod the exact same way each and every time, using the printed reference photo. I thought that a simple offset of a few dozens of pixels and a slight rotation of a few grades, done with a mouse, would do it just fine. I was wrong.

The second approach was a more accurate one, using my own rather basic program to mark reference points (distinctive features on the churches and the position of the Sun) and offsetting and rotating the cartesian coordinates of the given pixel locations (x,y). I was still hoping I can avoid the painful calibration process of a compact camera with unknown lens structure and firmware behaviour. This method worked well while the Sun stayed close to the ground, but as it got higher and higher during the spring, errors started to add up and I was forced to come up with a new method or face total failure.

Reference points

Reference points

Pozition of the Sun marked

Pozition of the Sun marked

Red curve: the pixel-distance of reference points changes as their placement in the field of view changes. Due to both the rectilinear projection and the distortion of the lens

Red curve: the pixel-distance of reference points changes as their placement in the field of view changes. Due to both the rectilinear projection and the distortion of the lens

Failed approach: using cartesian and polar coordinates

Failed approach: using cartesian and polar coordinates

For the third approach I shifted the paradigm. Instead of using the pixels’ cartesian coordinates I considered the virtual sphere sorrounding the camera and the angular distances of the objects – buildings and the Sun. In fact these are the basics of taking panorama photos, but this is not obvious since the purpose was to image the very same field of view and the resulting photos were very-very close approximations of this – but not close enough.

The theory is easy – most theories are easy compared to the field work needed to fulfill them. Each and every picture has the same point of origin (give or take a few centimeters), I was very careful about this, while the buildings were far away (hundreds of meters). So each and every picture imaged the same virtual sphere with slight differences in pitch, roll or yaw, combined. Consider the center of each image the pole of the sphere, and one gets the reference points’ and the Sun’s position in terms of right ascension and declination relative to the center of the image. Angular separation of the buildings does not change, since nothing moves, so the angular separation of the Sun and the buildings can be used to transpose the Sun from the field image to the bakcground. Without being worried anymore about the pitch-roll-yaw of the camera as far as it rotates around its entrance pupil – and it does due to the very large distances involved and the same position of the tripod.

But – there is always a but. I had no idea how the Fuji lens and firmware projected and produced the final JPEG output file. A few calibration photos made it obvious that the lens looks rectilinear but has a mustache distortion at the used focal length, enough to cause trouble. I tried to find the right equation of the distortion (assuming it was something concentric) using Hugin and pictures of modern buildings. I failed. I tried the checkerboard method too – failed. I contacted the manufacturer (tracking code: 92JPDX0) asking for technical details about how the spherical coordinates got translated into pixel locations at given settings – I mean who else to know it other than the manufacturer. To my grave disappointment, after clarifying some tehnical details about my project, I was given absolutely no reply.

Sketch: rectilinear projection

Sketch: rectilinear projection

Nasty distortions

Nasty distortions

Lines of the building are no lines

Lines of the building are no lines

Checkmate?

Checkmate?

So after multiple failures I managed to determine the distortion of the lens by empirical method: I printed a long tape having graduated for a fairly large radius and took pictures of it with the camera placed in the middle. It’s harder than it sounds, I must admit. For start, I had to use the settings specific to analemma frames, so I needed some spotlights in my otherwise normal living room having nothing in common with a photo studio. A few photos set up like this allowed me to deduce the graduation of the field of view of the camera at the given settings. By interpolating the values of this table, I got the algorhythm to determine the declination of each pixel relative to the image center – right ascension being already known.

The formula to determine the angular separation of two points identified by ra and dec is known, available on the internet, and is used for both astronomical and geographical purposes.

I don’t realy like the improvisations made, but they proved to provide fairly good accuracy, the maximum errors being about one or two solar diameters when the furthest from the reference points (the summer solstice). With this setup the Sun’s diameter varied between ~30 pixels in the image center and ~45 pixels on the margins of the image file 5760 pixels in diagonal, yielding an error of at most 30-60 pixels on the final result but negligeable when closer to the reference points.

Before we forget: although I tried to achieve the best scientific accuracy and image fidelity I could, the main purpose of this project was aesthetical. It is to be noted that the inaccuracy still in the process does not affect the final outcome which does not include all the solar disks pictured nor the exact dates attached to the solar disks.

The graduated tape

The graduated tape

A documented PHP bug found in the imageellipse function. Implemented my own :P

A documented PHP bug found in the imageellipse function. Implemented my own :P

Declinations on the virtual sphere

Declinations on the virtual sphere

Angular distances between reference objects from testframe to testframe: experiment stressed well beyond the requirements of the analemma-project

Angular distances between reference objects from testframe to testframe: experiment stressed well beyond the requirements of the analemma-project

Errors adding up far from the reference points

Errors adding up far from the reference points

The error becomes insignificant when looking at the big picture

The error becomes insignificant when looking at the big picture

Software

Hóban

Writing in the snow.

As I said I used only free and/or my own softwares. Mainly PHP/GD running in XAMPP, with a dom-css-javascript based GUI handled by an internet browser.

Final words

Firstly I would like to share some pictures made during the project. Mainly in the winter the low Sun and the otherwise frustrating clouds provided breath-taking views. Other photos are about the process of making the analemma.

Photographing the Sun became a routin so I created some other photos depicting the rising Sun moving along the sky showing the latitude it is on. I included these pictures too.

And I would like to thank to István SZÖLLŐSI, mathematician for the long discussion we had about the math principles behind the project and to E.SZ. for the support during the frustrating periods of the analemma making.

 

The background image

The background image

Just breathtaking…

Just breathtaking…

…

Winter timelapse

Winter timelapse

Equinox timelapse

Equinox timelapse

Summer timelapse

Summer timelapse

 Be humble!

 Be humble!

… 

… 

… 

… 

View with the master camera set up

View with the master camera set up

 It’s an airplane :)

 It’s an airplane :)

Autumn with a squirrel

Autumn with a squirrel

Winter with frost.

Winter with frost.

Spring with a bee

Spring with a bee

Summer with a cat

Summer with a cat

 

 

 

 

 

 

a social media teaser (in Hungarian)

a social media teaser (in Hungarian)

Nocturnal view

Nocturnal view

 

 

Photographing the photographing of the photographing event

Photographing the photographing of the photographing event

 

 

 

 

 

 

 

 

 

 

This happened too

This happened too

 

 

This also happened

This also happened

And a failed day

And a failed day

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Me, winter

Me, winter

Summer

Summer

Analemma

Analemma

The Analemma Story in a video

About the author

VÁRADI NAGY Pál

VÁRADI NAGY Pál

My name is Pál VÁRADI NAGY, I’m a radio person, writer, amateur astronomer and hobby programmer living in Kolozsvár/Cluj-Napoca, Romania, EU. I have a BA in Hungarian and Finnish language and literature and a basic certificate about my programming skills. As a daytime job I work for the Romanian Radio Broadcasting Company, for the regional public radio, Radio Cluj. I present news, create programmes related to public life.

I am a Hungarian national, citizen of Romania. For those unfamiliar with the meaning of this phrase: Hungarian people define nationality not by citizenship as most countries/people do, but by culture, since Hungarian nationals are scattered in many now independent countries of the former Greater Hungary. During the past century, borders moved, not people, meaning Hungarian nationals living in Romania are not immigrants. In a nutshell, you do offend me by calling me a Romanian without specifying my nationality.

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