Diffraction effects and magnification

[rjlittlefield]

Then surely as far as diffraction is concerned the effect of extension tubes on apparent aperture must be balanced by another effect in the lens plus dioptre system giving the same magnification and that indeed the light loss would be the same ?

That is correct. The calculations get ugly and it is easy to make mistakes, but when everything is properly accounted for, all of the competing effects balance out except for absorption in the glass and reflections at the lens surfaces.

The simplest way I know to think about this is "same light, same image". In more words:

The DOF, diffraction blurring, and relative exposure of an image are determined entirely by which light rays get through the lens to be focused on the sensor. Those rays are selected by the aperture to form an entrance cone. Any two lens systems that are set to give the same magnification and the same entrance cone will give the same DOF, the same diffraction blur, and the same relative exposure. This is because both lens systems are delivering the same light to the same area on the sensor. Since the "effective f-number" is really a measure of cone angles, it will be the same for both systems also.

I will walk through a single example only.

<math mode on>

Consider:

Case A. 100 mm thin lens set at f/8 and extended from infinity focus by 200 mm to give 2:1 at an effective f-number of f/24.

Case B. 100 mm thin lens at infinity focus, front-ended by another 50-mm lens to also give 2:1.

Question: What nominal f-number settings are required in Case B to give the same DOF, diffraction blurring, and exposure time as Case A?

Solution: Consider the entrance cone. Case A has an aperture with a diameter of 100/8 = 12.5 mm, sitting 150 mm away from the subject. Case B has the aperture sitting only 50 mm away from the subject. To have the same entrance cone, the aperture in case B must be only 12.5*(50/150) = 4.17 mm in diameter.

If a 4.17 mm aperture is achieved by stopping down the rear lens, then the nominal setting will be 4.17/100 = "f/24". Hence a nominal setting of f/24 on the rear lens also produces effective f/24 even though we're operating at 2:1. One way to understand this is that adding the front lens reduces the lens-to-subject distance by exactly enough to compensate for the magnification.

If a 4.17 mm aperture is achieved by stopping down the front lens, then the nominal setting will be 4.17/50 = "f/12". This reflects the general principle that the effective f-number from the standpoint of the camera is always equal to the effective f-number from the standpoint of the subject , multiplied by the magnification (f/12 * 2X = f/24).

<math mode off>

Personally I find it a lot easier to just think in terms of that little mantra: "same light, same image".

I was amazed to learn that a 1.4x teleconverter gives exactly the same image as a 1.5 crop sensor (minus the compromise from extra glass). DOF, shutter speed and noise level (after compensating with ISO) are exactly the same.

"Sensor size doesn't matter" is another surprising result that is also predicted by that simple mantra, "same light, same image". As long as both sensors can actually capture the same light with the same quantum efficiency (a matter of apertures and sensor technology), it doesn't matter whether that light is spread out across a large sensor or a small one. The advantages of a larger sensor are 1) more flexibility to work with larger apertures (giving less DOF but potentially higher resolution, and capturing more light in the same time), and 2) ability to capture more light in total, leading to less image noise if brighter light or more time is available. Smaller sensors have the advantage of working with shorter lenses, which can be used to give shorter working distances leading to more intimate perspectives and better operation of auto-focus. For available light photography when stopped down for maximum DOF and with a restricted shutter speed, neither sensor has the advantage.

The archives contain several long and chaotic discussions regarding apertures and sensor sizes. The most recent is HERE. An earlier one is HERE. The earliest one I participated in (December 2005) is HERE. The basic relationships were well established in December 2005 and have not changed since. But I'm still wrestling with how to explain them quickly and effectively.

--Rik

[LordV]

Thanks again for the reply Rik. Sounds like you have similar holistic reasoning that I often use but it's not easy then to explain it to someone else.

Brian V.