Eliminate Depth of Field Confusion: Photographic proof showing that depth of field is independent of focal length... sort of.

While trying to learn what the term depth of field (DOF) meant I came across the webpage http://www.dpreview.com/learn/?/key=depth+of+field. This page explained the term and provided an on-line calculator where you enter the focal length, distance to the object (though it's not explained if this is the distance from the object to the first element on the lens or to the focal plane of the camera), the aperture and it tells you what the depth of field (the distance in front of and behind the focus point over which the image will be in focus) is. It seemed all my questions had been answered.

Then while looking through another page on the same subject I read that "some experts are now thinking that DOF is independent of focal length." This shocked me because I figured people have been taking pictures for so long that all these sorts of questions would have been resolved. Then my brother told me about a site called the Luminous Landscape at http://luminous-landscape.com. On the DOF page of this site the author definitely states that DOF is not a function of focal length and proves it with a series of photographs of a stuffed animal.

After reading through the complex, at least for me, mathematical analysis of DOF on the page at http://normankoren.com/Tutorials/MTF6.html, I think I got an idea of what was going on and how there could be confusion over something that appears to be easily resolved. The problem isn't in the physics or the mathematics that determines DOF, but rather in the semantics of how statements about DOF are worded. I believe Luminous Landscape offers the clearest and most complete clarification: DOF is independent of focal length when the size of the image on the sensor is held constant.

What this means is that DOF is independent of focal length if when you change focal length you also change the distance from the camera to the object by the right amount to keep the image scale constant. By changing both focal length and distance the two changes cancel out each other's effect on DOF. People who claim DOF is dependent on focal length are working under the perfectly valid assumption that the distance remains constant. Their statement about DOF would be: Keeping distance and F stop constant, DOF decreases as the focal length increases.

While the photos of the stuffed animal on the Luminous Landscape site are intended to prove that DOF is not a function of focal length when the image scale is held constant, I didn't find them convincing and decided to test this assumption myself.

Below are two photos I took which I believe makes it obvious that when the image size on the sensor is held constant, the DOF is not effected by changes in focal length.

Shot with a 50mm lens

Shot with a 200mm lens

The top photo is of a grid held at 45 degrees to the plain of the camera lens. The lens was set at 50mm and F11. (Vertical grid lines are 0.20 inches apart.)

I then took a second photo with the lens set to 200mm and F11, but moved the camera back so that the grid was projected onto the sensor at the same size it was in the first photograph. Processing was kept to a minimum and applied to both images equally. It's obvious that the DOF is the same in both even though the upper one was shot at 50mm and the lower at 200mm.

So, which definition is more applicable? I believe it depends on what the person is trying to do at the time. If someone's taking a landscape, they're more likely to switch focal lengths than pick up all their equipment and move to new location. Since they are usually going to stay put while changing focal lengths, the definition that DOF does depend on focal length is going to make more sense. To someone like me, who does a lot of macro work and for a given subject always try to fill the sensor with it by moving in and out, the definition that DOF doesn't depend on focal length will seem more correct. (And more depressing. It means, for example, that when I'm taking pictures of hummingbirds and being careful to fill the frame with the bird, I'll always be limited to the same depth of field: which is only around 4 inches even at F18.)

Another way to reword the statement that DOF is independent of focal length as long as the distance is changed to maintain the same image scale is that the DOF is independent of distance as long as the focal length is changed to keep the image the same size. The two statements are reciprocals of each other.

So, what are the general guidelines for DOF?

1. DOF increases as the aperture decreases. (This is roughly a linear effect: reducing the aperture by two F-stops increases the DOF by a factor of 2.)

(Note: Decreasing the aperture works down to around F18. Beyond that the aperture is so small diffraction effects may blur the image more than the extended DOF helps sharpen it.)

2. DOF increases as the distance is increased if the focal length remains the same. (This is a square relationship: doubling the distance increases the DOF by roughly a factor of 4.)

3. DOF increases as the focal length decreases if the distance to the object is constant. (This is an inverse square relationship: decreasing the focal length by a factor of 2 increases the DOF by roughly 4.)

(The above relationships were obtained from the DOF calculator mentioned earlier on this page. The approximate relationship that DOF is proportional to the distance squared, times the aperture, divided by the square of the focal length is in rough agreement with the analysis on http://normankoren.com/Tutorials/MTF6.html.)

4. DOF is constant if the aperture is constant and the focal length and distance are changed in such a way so that the size of the image of the object projected on the sensor is constant.

 
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