Physics and Focal Planes

Studio7Four

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Due to some recent discussions in another thread I’ve decided to share some fundamental physics on how lenses work, particularly with regards to sharpest focus. Hopefully a little tutorial will help you understand why your camera does what it does (or, more accurately, why your camera isn’t doing what you think it should be able to do).

Many of you have heard the phrase “focal plane”. That is because lenses work on the principal that the light from one plane refocuses on a parallel plane. For the light to be focusing on your detector plane (whether it is a digital sensor or a film frame), it started in the same plane. Here is a sketch of a simple lens (more complex lenses behave essentially the same way, they’re just better at reducing aberrations):
TPF_FocusSketchA.jpg


(In case you trust what you find online more than my simple sketch, check here: File:Lens3.svg - Wikipedia, the free encyclopedia)

As you can see, light which leaves one point on the focal plane – at any angle which passes through the lens – will come back together at a common point on the detector plane. This is the physics of focus.

Note that there are no dimesions in this sketch. By definition a plane extends forever in two dimensions (in this sketch, up/down and in/out of the screen). With a suitably large lens and a suitably large sensor, incredibly large subjects can be captured. But more relevantly, it means that the small portion of that image plane which is your detector is focusing the light from a single plane. Whether you’re using a full-frame or a crop sensor digital camera, or 35mm or a medium- or large-format film camera, if you’re focusing on a plane, that light came from a parallel plane.
 
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Studio7Four

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Here’s an interesting illustration of the effects of parallel planes. By definition, parallel planes are the same distance from each other – go straight out from one to the other and you’ve gone the same distance. All paths marked ‘A’ in this sketch are the same length. They all start on the detector plane and end at equivalent points on the subject plane.

TPF_FocusPlaneOffsetSketch.jpg


This also means that, if you don’t go straight out, you will have gone further before you reach the other plane. If you focus your camera straight ahead (towards ‘A’) then turn it towards ‘B’, whatever you are now pointing at is further away than you’ve focused.

Why is this relevant? This is why “focus and recompose” can leave your image out of ideal focus.

TPF_RecomposeSketch.jpg


Let’s say you want to compose your final image so that your subject (‘S’) is not centered in your frame. You turn towards ‘S’, set the focus at distance ‘D’, then turn back forward. Your camera is still focused at distance ‘D’, so anything on the plane parallel to your sensor will be in focus. You can see that your subject is now not on that plane – it is in fact at a distance ‘d’ from your sensor plane. Your subject will not be in ideal focus – whether it is in acceptable focus depends on your settings (I’m sure someone has the depth of focus calculator link handy and will post it here before I’ve bothered to take the time to track it down).
(Edit: Found it! http://www.dofmaster.com/dofjs.html)
 
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Studio7Four

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Let’s go back to the first sketch, but this time let’s put an actual object in it.

TPF_FocusSketchB.jpg


You’ll see that the image on your detector is smaller than the original object (and inverted, but that’s irrelevant). That shouldn’t be a surprise, as we all know the real size of things that fit on our small sensors. Now, let’s take this sketch, keep the camera the same distance from that same tree, and move the lens to the right.

TPF_FocusSketchC.jpg


In this simplified example, the line from the bottom of the tree still passes through the center of the lens to the same point on the detector. But the line from the top of the tree, which still also passes through the center of the lens, is now at a different angle, so the point at which it hits your detector is different. In this case, since we’ve moved the lens to the right, that line has gotten steeper, and now hits further down on the detector – the image of the tree has gotten bigger. Generally speaking, that is why most zoom lenses get longer as you zoom in.
 
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Studio7Four

Studio7Four

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Okay, one last one for now...

There are a few applications for tilt/shift lenses; one of these is to extend the depth of focus. As you can find in other threads, there is a range over which an image is in acceptable focus, and it is not equal about the plane of sharpest focus. Let’s say that you wanted to shoot a gently sloping hill of wildflowers. With a standard lens, perpendicular to the detector, your range of acceptable focus looks something like this (parallel planes in front of and behind the plane of sharpest focus):

TPF_TiltLensSketch1.jpg


By using a tilt/shift lens (tilting, not shifting) you can change the angle of the detector relative to the lens. This then changes the angle of the plane of sharpest focus. The planes of acceptable focus are at the same distances, but because they are now angled the range of acceptable focus – along the hill – looks like this:

TPF_TiltLensSketch2.jpg


You are now able to capture more of the wildflowers in acceptable focus!
 

Dao

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For focus and recompose. It also depends on if how far the subject shift in the frame and how far away the subject from the camera.
First, if the subject is far away, let say 50 feet away, and focus and recompose shift distance is 2 feet. At that time, the difference between distance D and distance d is insignificant.
 

Helen B

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Okay, one last one for now...


By using a tilt/shift lens (tilting, not shifting) you can change the angle of the detector relative to the lens. This then changes the angle of the plane of sharpest focus. The planes of acceptable focus are at the same distances, but because they are now angled the range of acceptable focus – along the hill – looks like this:

TPF_TiltLensSketch2.jpg


You are now able to capture more of the wildflowers in acceptable focus!

A good basic explanation, but the tilt is going the wrong way - the image plane, the subject plane and the nodal plane (I'm making the two nodal planes singular for ease of explanation) should all meet at a single line (call it a point if you wish).

Regards,
Helen
 

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