A reader(ABW) has asked me to comment on a recent posting on the PetaPixel website concerning the creation by photographer “Michael “Nick” Nichols”, under the auspices of the National Geographic Society, of a giant image of the second largest Sequoia in the Sequoia National Forest, “The President.”.  I was all set to do so, when another reader (CJHinsch) responded so elegantly to my New Year’s Resolution post, expressing my desire to learn to photograph trees, and further pointed me to the work of James  Balog.  Mr. Hinsch really hits the nail on the head.  The real issue is not the marvel of how this is done technically, but the marvel of the tree itself, and that’s a very personal thing.  So more discussion on all of this needs to happen.

As far as the tree mosaics are concerned, the technical need for this type of image is the recognition of two points:  First, if you try to photograph a tree from its base, or suspended in another tree, or even from the air you are going to wind up with a pretty distorted image or a very tiny one from far away.  Second, that’s not how the eye works.  We see the tree in its entirety, then focus in on a few leaves, see them in fine detail, perhaps even notice a caterpillar.  Finally, we focus back and in our minds eye imagine that we have seen the whole tree at the caterpillar level of detail.  So if your desire is to reproduce the human experience “tree” in it’s full scale entirety, this is what you need to do.

Recognize that trees are not the only subjects that call out for this type of treatment. This happens whenever we are confronted by a subject that is physically larger than our lens can handle, unless, of course, we step way way back and lose all detail.  It should also be said removal of distortion is not always the artistic intent.  In the case of the tree images the goal is presenting a sharp and highly resolved undistorted image.  But there are other cases, making a 360 degree image of a landscape, where the distortion is intentional as a means of adding drama.  Moving frame by frame perpendicular to an image removes distortion.  Rotating around the axis of your tripod actually introduces a so called “spherical distortion.”

Doing a mosaic is conceptually pretty straight forward and is illustrated in Figure 1.  Imagine that I want to photograph something that is way too large to fit in my field of view, here the letters ABCDEFGHIJKLM.  In fact, my camera can only photograph five letters at a time.  What I do is take four overlapping images.  Then I reconstruct them by overlapping the images.

Now in the age of digital photography, this is an automated process.  Your Iphone or IPad will do it for you (have apps.) as will Photoshop.  When photography was a purely analog, this was a laborious and painstaking process.  But could be very effectively done, as witnessed by Ansel Adams’ giant landscapes for the Wells Fargo Bank.  It still is pretty laborious as the Sequoia project illustrates.  The desire is to keep things perfectly flat so as to minimize distortion and the need for corrected algorithms. In the case of the tree image the camera is moved up down and sidewards snapping multiple images on a hoist and framework.  The advantages of creating an image this way is that it is flat and undistorted and it has a much higher level of detail than could be accomplished with a single image.  In fact the major limitation in practice tends to be how big and at what resolution can you print.

That’s it technically, but like I said there’s a whole lot more to consider from a aesthetic and emotional viewpoint.

Figure 1 – the “Golden Rectangle,” from the Wikicommons and in the public domain

As I indicated the “golden rule of thirds” is an approximation of the “golden proportion” aka the “golden ratio.”  The “golden proportion” comes from the ancient Greeks, so it must be cool and mystical.  But what exactly is it?

It is a special rectangle as shown in Figure 1.  The rectangle has a height, which we will call a and a width, which we will call a+b.  Now honestly that is true of all rectangles.  Since as long as the rectangle isn’t a square, the width is always a bit larger than the height.  So we might as well call that amount b.  But the “golden rectangle” has the special property that

(a+b)/a = a/b =ϕ

I know that a lot of you don’t like equations, but forget the equation.  All that I am saying is that for this particular rectangle, when I divide it as shown, I create a second rectangle only on its side, and that the width divided by the height is the same for both rectangles.  This ratio is so important that we’ve given it a name, really a symbol, the Greek letter ϕ, which happens to equal 1.6180339887, approximately.  “Approximately?”  Mr. Spock.”  “I try to be precise, Captain.”

Figure 2 – The ratio of the width to the height of the Parthenon is the golden ratio phi. Original image from the Wikicommons and is by Eusebius (Guillaume Piolle)(own work).

Now before we go off on any tangents, take a look at Figure 1 again.  You see that the line b is almost a third of a+b.  Remember the “golden rule of thirds.”  If you do a little calculation you realize that instead of being 1/3 which is approximately 0.33, the fraction is actually approximately 0.38.  And it is this division of the image that we are really supposed according to the Greeks, or the imagined Greeks, to be striving for n order to attain both geometric and aesthetic perfection.

So now take a look a Figure 2, which shows the Parthenon in Athens, what did the architects Temple of the Goddess Athena choose the ratio of the width to the height to be.  Yes, you guessed it ϕ!  Perfection in the Goddess is here symbolized by perfection in the geometry of the building.

Figure 3 – The Fibonnaci spiral from the Wikicommons by Dicklyon and in the public domain.

Finally, recognize that one of the key points of the construction in Figure 1, is that the placement of a line a distance a from the start of the width create a second and rotated “golden rectangle.  This construction can be done on paper with a simple drawing compass.  This process can be repeated over and over an infinite number of times each step creating a smaller and smaller “golden rectangle.”  If you look at Figure 3, you can see how this process defines a spiral, called the Fibonnaci spiral (for the mathematicians I apologize for not going into the subtle differences between the Fibonnacci spiral and the Golden spiral.”).  This is very cool!  And cooler still is the fact that this spiral is the basis for a large numbers of forms in the animal world including the ram’s horn and the spiral of ancient ammonites as well as the modern chambered Nautilus.  We find all of these to be objects of great beauty.  So therein lies the basis of the concept that this ratio is fundamental to the concept of beauty and to be emulated in the division of an image.

In my last blog I talked about the resolution of the human eye.  That is all fine and dandy, but it is very important to remember that the eye does not function like a CCD or CMOS-based digital camera.  It does not snap pictures that it then stores intact in the brain.  The eye is part, an important extension, of the brain, and the brain is an image processing device that stores images in its own peculiar way, connects and combines them with other images, and connects them all with emotions.  When looking at a scene or photograph the eye doesn’t even stand still.  Rather it scans the scene picking out important recognition points.

Now I’m not an expert on this topic.  So I’m not going to dig myself in more deeply for risk of being inaccurate.  I just want to emphasize a few significant points.

• First, when talking about the eye and brain, it’s important to recognize that you’re dealing with physiological and ultimately psychological optics, not just plain vanilla physical optics.  There’s even different set of units to describe physical and physiological optics.
• Second, the brain connects an images and ultimately evokes emotion.  In a very real sense we feel an image.
• Third, all of the aesthetic tricks of photography, the golden rule of thirds, the dynamicsm within an image, foreground/background flip, etc. are the result of what’s going on in the brain during image perception.

Of course, the eye, the brain, and all of the rules of physiological and psychological optics are ultimately determined by the physics and chemistry of the eye and brain.  But, and perhaps most importantly, without the brain and the way it processes there could be no photography, since it is the brain that accepts a flat image of a three dimensional world, even  images devoid of color, and enables it to evoke the same emotions as the original scene.*  It is the eye/brain that enables us to look at a photograph and say: “How beautiful!” – not just to say but to feel it.

*At the recommendation of a reader, I have been reading Timothy Egan’s biography of Edward Curtis, “Short Nights of the Shadow Catcher.  Egan records that in “December of 1904 Curtis rented out a large hall in Seattle and mesmerized the audience with hand-colored lantern slides and moving pictures of Indians of the Southwest.  The film prompted members of the audience to jump from their seats in fear.”

In our discussion of camera resolution we never asked what the resolution of the human eye is?  This is an important question, since ultimately, when we look at a photograph, regardless of how it is presented to us, we are looking at it with the human eye.

Doing the same kind of analysis that we have done to determine the diffraction limit of a camera lens, it can be shown. The human eye has an angular resolution for green visible light of about 1.2 arc minutes.  An arc minute is 1/60th of a degree.  Those pesky Babylonians, with their base 60. are at it again! Physicists prefer a different unit of measure, called the radian.  There are 2 π radians in 360 degrees; so 1.2 arc minutes is about 2.1 milliradians.  The value of using radians is that the spatial resolution is just the distance away from what you are looking at times the angular resolution in radians.

So say you are reading a book or looking at a photograph 12 inches in front of your face, then you resolution is going to be 12 inches X 2.1/1000 = 0.0252 inches.  Remember that this is in line pairs.  There are about 40 line pairs per inch – or 80 lines (or dots) per inch.  This is kissing close to the 72 dots per inch standard that Adobe Photoshop and historically topography use.

Similarly, as I write this, I’m looking from about 18 inches at a 15 inch laptop screen.  So in that case my eye’s resolution is going to be 18 inches X 2.1/1000 = 0.0378 inches or 26.5 line pairs per inch which is 53 dots per inch.  Across my 15 inch screen that’s 794 dots.  If I decide that I’m going to peer in, putting my nose to the screen at about nine inches, I’m going to need twice as many dots per inch or 1,588.  That’s pretty close to the 1366 that my screen is set at.

We’ve seen these numbers before.  But now we realize that the requirements in dots per inch for computer displays and digital prints of various sizes ultimately are defined by the resolution of the human eye.  And hidden in all of this is another important point that the print or display resolution required is defined by how far away you are viewing it.