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Lens Separation in Stereo Photography

By David Lee

Obtaining a Consistent Amount of Deviation

If one chooses to obtain a consistent amount of deviation on the film from one image to the next there are mathematical principles that will help. The formula seems like a complicated matter, but by the end of this paper I will explain how to simplify it so that one can easily use it in practical situations. There are five parts to the formula:

1. Depth Factor – many stereo photographers call this the 1/30th rule, but I have chosen to call it the Depth Factor because you could choose to make it more or less than 1/30.
2.

3. Near Point Factor – This is simply the distance to the near point of the scene.
4.

5. Far Point Factor – This factor is calculated by using a formula incorporating the near and far point distances. When the far point distance is ¥ , the factor is "1".
6.

7. Lens Factor – The focal length of the camera lens compared with the focal length of the viewing lens. When these are the same the factor is "1".
8.

9. Separation – The four previous factors multiplied together will give a separation for the 2 cameras (or lenses) that will result in a predictable deviation.

Depth Factor

The Depth Factor is based on the amount of deviation (a measure of the difference of the distance between the far points and the near points of a stereo pair) that looks good in a stereo pair. You can see how much deviation you like in a typical stereo pair by:

1. Using a normal focal length lens, carefully set up a scene in which you accurately measure the distance to the near point (for example, 10 feet), and where the far point is at least 100 times farther than the near point.
2.

3. Make a series of exposures with slightly varying separations (for example, vary separation from 1 inch to 8 inches with 1 inch increments).
4.

5. View the images in the viewer you would normally use (or slide projection) and note which separation you prefer.
6.

7. Divide the separation for the image you prefer into the near point distance (10 feet in this case). The resulting dividend will be the denominator for the Depth Factor (with "1" as the numerator).

The most commonly used Depth Factor among stereo photographers is 1/30, hence the 1/30th rule. The 1/30th rule in practice means you measure the distance to the near point of the scene and then divide by 30. I am aware of people using from 1/20 th to 1/60th the near point distance as a depth factor.

Near Point Factor

You simply measure the distance to the near point. Sometimes you can do this by using the distance scale on your camera. When you deal with distances over about 20 yards then you must estimate the distance in some other way. You can get either optical or laser range finders and topographic maps are sometimes helpful for really long distances

Far Point Factor

It is usually more difficult to estimate the distance to the far point since it is often very far away. Fortunately this is not really a problem because all you really need is a broad estimation of how far it is compared to the near point.

Lens Factor

When the camera lens and the viewing lens are (approximately) the same focal length, then the lens factor has a value of "1", and so does not change the separation. When the camera lenses are shorter than the viewing lens then the deviation (amount of depth) is reduced for the same separation. When the camera lenses are longer than the viewing lens then the deviation is magnified for the same separation. Therefore, to get the target deviation it is necessary to multiply the camera separation by a factor proportional to the change in focal length of the camera lens. In other words, if the camera lens is half the length of the viewing lens then you must multiply the calculated separation by 2. If the camera lens is twice the length of the viewing lens then you must multiply the calculated separation by ½.

The Complete Formula

Here is the complete formula: Further Analysis of the Far Point Factor

I am sure that most people would look at the Far Point Factor like it was a foreign language and give up on it before they started. In fact, I wouldn’t even use it myself while out in the field. Fortunately, when we actually examine the formula it has a pattern that simplifies things greatly:

1. Note that as the far point distance becomes greater compared to the near point, the Far Point Factor approaches the value of "1". If you use 10’ for the near point and 1000’ for the far point then this part of the formula yields "1.01". If you use 10’ and 10,000’, then the result is "1.001". So when the far point distance is large compared to the near point distance, then this factor becomes a non-factor.
2.

3. We can examine what happens when the far point is not a lot greater than the near point. For instance, if we use 10’ for the near point and 20’ for the far point, the math works out to a factor of 2. As it turns out, whenever the far point is exactly twice as far as the near point, you get a factor of 2. If the far point is three times farther than the near point then the factor is 1.5. Here is a list of factors for far points that are at varying distances compared with the near points:
4. a) If the far point is 2 times the near point, the Far Point Factor is 2

b) If the far point is 3 times the near point, the Far Point Factor is 1.5

c) If the far point is 4 times the near point, the Far Point Factor is 1.3

d) If the far point is 5 times the near point, the Far Point Factor is 1.25

e) If the far point is 6 times the near point, the Far Point Factor is 1.2

f) We start to reach diminishing returns and we can assume the factor is 1.

5. What about using even more separation when the scene is even shallower than twice the near point distance? My practical answer to this situation is that if you start making a shallow scene appear to have the depth of a scene with infinity, then it will look pretty weird. As a result I do not use any values greater than 2 for this factor.

Too Much or Too Little Camera Separation

If there is too little deviation then the image will have little depth and will look flat. How flat is too flat is a matter of opinion. An experienced stereo photographer may have a pretty good idea whether an image might look better with more depth, but for the most part it is probably better to have too little rather than too much depth. If there is way too much depth then the image may be un-fusable, but before it becomes un-fusable it may just cause eyestrain, which may be more noticeable to some than to others. When I bracket camera separations I usually find that the most pleasing separation is not the widest that I can fuse. I won’t even necessarily feel that it is a strain, but that it just does not have as smooth a look as one with less depth. A deviation of 1/30 the focal length of the viewing lens usually looks good to me, although I can easily fuse 3 times that much deviation. I have found that many novices using twin cameras have the habit of getting more deviation than they would otherwise chose if they were to view an alternate pair with less deviation. I think that bracketing camera separation is a good idea for people who are just starting out so they can compare how images look when they have more or less depth. I would suggest using your best guess as your initial separation, and then using twice as much and half as much, just like bracketing exposure in one stop intervals.

Accuracy of Calculation

When we talk about accuracy of exposure we may say we need to be within one half stop to result in an optimum slide (for instance). We can look at depth in the same way. If one had a series of pairs the depth of which varied by 5% from one to the next, there would not be one pair that was so superior to the rest that the viewer would say, "This one is the only one that works and the others are wrong." Instead the viewer would be more likely to say, "These 3 work the best and the ones with less depth look pretty good, but they become gradually too flat, while the ones on the other side look pretty good but they become gradually too deep and are less smooth than the others." If asked to pick out the best depth, it is likely that several viewers would choose different amounts of depth or that an individual might say that he/she saw advantages and disadvantages for several of them but that no one stood out as clearly superior. In my experience making lots of images with varying depth, I have concluded that a range of one stop of depth (the greater depth having twice as much depth as the narrower one) is pretty acceptable. Another way of looking at it is to say that if there were an optimal separation, then a factor of one half stop of depth in either direction would look good. If this hypothetical separation were 1/30th the distance to the near point, then the acceptable range would be from 1/40th to 1/20th the distance to the near point. So when we are aiming for a good lens separation we do not have to be perfect, but if we get within an acceptable range then the depth will look good. We must remember that no single lens separation will seem preferable to every viewer. Don’t get either too obsessive or too sloppy about determining camera separation.

Practical Situations

I will try to give a few practical tips to those who are still trying to figure out what to do:

1. Regarding composition, some sources say to use foreground subjects such as plants, people, or branches to give depth in scenes that would not have much otherwise. My experience indicates exactly the opposite. That is, get rid of all foreground objects, including the ground, that do not add to the impact of the scene, and increase the camera separation accordingly. The higher up you get the better it works. I have an 8-foot tripod that I use occasionally.
2.

3. For moderate hyper-stereos a tripod with a sturdy bar is preferable, although they can be made with a single camera handheld. I use a 2-foot bar, but up to 3 feet is not too cumbersome. When the cameras are at full separation I brace them by attaching cord from the ends of the bar to rings on the tripod legs. A level is always helpful. Do not underestimate the depth impact of a moderate hyper-stereo.
4.

5. For longer hyper-stereos:
1.

2. I always take 2 tripods in the car and often hike with them.
3.

4. Be on the look-out for good places to make hyper-stereos from. These should preferably be from a high position with no foreground obstructions with enough level space to have the cameras perpendicular to the lens axes. Good prospects include bridges, dams, across rivers, tall buildings, tops of hills and mountains.
5.

6. After you set up the second camera and level it, sight along its back and it should line with up with the first camera. If it doesn’t you can move the positions around until both camera backs line up with each other and are level. If you cannot find this position then one camera may be closer to the scene than the other which may affect the view-ability of the image, but you may as well take it anyway so you can see the effect.
7.

8. It helps to have an assistant to release the second shutter. If you toss a rock in the air and both release the shutter at the time it hits you can get remarkably close to synchronization.

Cheat Sheet

Measure or estimate the near point distance.

Times 1/30 (4" per 10’ or 1’ per 10 yards or 50 yards per mile)

Times far point factor (pick one):

1. 1 - if far point = ¥
2.

3. 2 - if far point is < or = twice the near point
4.

5. 1.5 - if far point is > twice the near point, but < ¥

Times _____ (put your lens factor here)

Separation = Depth Fac. x Near Point Fac. x Far Point Fac. x Lens Fac.

Separation = ________ x ____________ x ___________ x _______

Example: near point = 10’, far point = 30’, normal lens

Separation = 1/30 x 10’ x 1.5 x 1 = 6"

An Even Easier Way to Remember Things

Knowledge of very few principles may result in excellent depth in the vast majority of cases.

1. Use a stereo camera for people and other close subjects.
2.

3. Use a separation of 1/30th (4 inches for every 10 feet, 1 foot for every 10 yards) the distance to the near point of the scene when the far point is at ¥ .
4.

5. If the far point is distinctly closer than ¥ then add 50% more separation.
6.

7. When using wide lenses (say twice as wide as normal), use twice as much separation.
8.

9. When using long lenses (say twice as long as normal), use half as much separation.

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