Does effective f-number reduce image brightness at close focus?

Asked 10/23/2013

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I’ve read that when a lens is focused very close, the effective f-number becomes higher than the marked f-number, especially at macro magnifications. If a lens is set to f/2 at its closest focus, does the image on the sensor become dimmer than it would be at infinity focus? In other words, as you move from close focus to infinity while keeping the same marked aperture, does image brightness increase because the effective f-number decreases?

Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0

Photography Stack Exchange contributor

12y ago

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The common f-number we use in photography embodies the assumption that the magnification is much less than 1. When you're taking a picture of a mountain 3 miles wide and that will be imaged 30 mm wide on the sensor, the magnification is so small that the common f-number approximation is quite valid.

However, this breaks down as magnification approaches 1, and fails dramatically above 1. The "real" amount of light you get is described by the f-number times 1 / (1 + M)2. M is the magnification, which is the linear dimension of the actual object divided by the linear dimension of its image on the image plane. As you can see, this correction factor is close enough to 1 as long as the magnification stays well below 1. At exactly 1:1 magnification, note that this factor is 1/4, which means you are two f-stops down.

So how close to macro is close enough so that you have to consider this effect? We can work the equation backwards and see what magnification results in the minimum factor we care about. Let's say anything less than a 1/4 f-stop is slop so that we don't care. 1/4 f-stop means the equation must result in 2-1/4 = .841, which results in M of .095, or a reduction factor of 11. So as long as you aren't closer than 11:1, you can pretty much ignore this effect. For a "35mm" frame, which is 36x24 mm in size, this means you are fine as long as the subject is 400x270mm, or about 16x11 inches.

Of course any thru the lens metering will see the light actually delivered thru the lens and automatically compensate for this effect. Since just about every camera has that nowadays, your pictures will still be properly exposed, but you might notice the increasingly worse tradeoff between f-stop and shutter speed as you get more into macro range.

Originally by user7603. Source · Licensed CC BY-SA 4.0

user7603

12y ago

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Yes—at close focus, especially in macro work, the sensor receives less light than the marked f-number suggests.

The usual f-number assumes magnification is very small, which is true for most normal-distance photography. As magnification increases, that approximation becomes less accurate. In macro ranges, the effective aperture becomes “slower,” so the image on the sensor is dimmer for the same marked f-number and shutter speed.

A common correction is that light transmission scales by about 1 / (1 + M)^2, where M is magnification. At 1:1 magnification, that means only 1/4 as much light reaches the sensor compared with the low-magnification assumption—about a 2-stop loss.

So, yes: if you go from closest focus toward infinity at the same marked aperture, image brightness at the sensor increases because the effective f-number decreases back toward the nominal value. In everyday non-macro shooting this effect is usually negligible, but in macro it matters a lot.

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