Is f2.8 the same as f2.8?

[Bill W]

this thread jogged a memory from nearly a year ago....this may help, then again, it may not.


http://community.the-digital-picture.com/forums/t/1212.aspx

[Daniel Browning]

Is f/2.8 the same as f/2.8?

If you only look at the unimportant issues and things that don't really matter to the end result (photograph), then yes, they are the same.


However, if you care more about factors that actually affect photography and the final picture, then no, they are not the same at all.

While I'm pretty sure I understand the conversion to 35mm equivalent, I haven't heard much about the f range.

I'm not surprised that you haven't heard about how the crop factor applies to f-number, because most photographers think it doesn't apply, even though, in reality, it does.

It highlights the curious state of general knowledge in photography with regards to the central focus of attention. On some subjects, the entire focus is on the end result. In others, it is on the means.

The reason you have heard a lot about the 35mm-equivalent focal length is because it relates to angle of view. The angle of view is the end result. Photographers want a certain angle of view (say, 40 degrees), and they don't really care what actual number is required to get it (whether 7mm on a digicam or 80mm on a Medium Format), they just want the final angle of view.

Only a novice would first choose his focal length (e.g. 7mm), then let the angle of view be dictated by the choice of camera format (e.g. fisheye on full frame vs. telephoto on digicam). Rather, the normal photographer chooses the angle of view that he wants, and then picks the focal length to get that angle of view on the given format.

In other words, photographers know that focal length scales with format size as it pertains to important factors in photography: angle of view (and perspective, if you instead scale field of view).

The situation is reversed for f-number. Instead of focusing on end-results, photographers tend to focus on the f-number itself. For example, a common misconception is that smaller formats have a "deep DOF" advantage, because they have deeper DOF at the same f-number (the myth is that there is less diffraction, more DOF, and/or less noise -- when in fact none are true). In reality, the diffraction and noise scale in perfect proportion with the DOF, so there is no such advantage.

In other words, most photographers have no clue that f-number scales with format size as it pertains to important factors in photography: DOF, diffraction, noise, lens weight, etc. This leads to the situation that most of the information out there about sensor sizes is incorrect.

This misunderstanding causes many to think that f/2.8 on a digicam would give you the same picture as f/2.8 on a DSLR. Since the obvious reality is that it does not, a variety of incorrect explanations have been proposed, from more advanced technology in DSLRS (actually, DSLRS are practically stone-age compared to modern mobile phones) to better electronics. But the most prevalent explanation is that the dumb camera designers ruined all the the digicams by making the pixels so small; which is of course totally wrong and completely backwards.

f2.8 at 28mm sounds pretty fast for such a small lens, and f5.7 at 560mm sounds great, but is that true?

Unfortunately, no, it's not true. The f-number scales exactly the same way as the focal length. That 100mm f/5.7 digicam is equivalent to 560mm f/32 on a 35mm DSLR for DOF, diffraction, and noise. That means ISO 100 on the digicam is equivalent to ISO 1600 on the DSLR (taking into account typical 1-stop ISO calibration difference).

The only way it is the same as f/5.7 on a DSLR is in regards to exposure -- but noise, DOF, and diffraction are all far more important than exposure (since you can still get the desired brightness with ISO).

While I'm sure the picture quality is very different, is the ability of the P&S lens to gather light, really the same as that on a "real" camera?

Yes and no. If you focus on the part that doesn't matter, "light per area", then they are the exact same. But if you focus on the part that is actually important, "total light", then they are very different.

Here's another way to think of it. The *real* focal length and f-number of that digicam is 100mm f/5.7. If you put a 100mm f/5.7 lens on your DSLR, and then threw away 90% of your sensor by cropping down to the same angle of view, you would get the similar results to the digicam. As long as you have the same pixel size, digital cropping gives you the exact same result as using a smaller sensor.

I keep think there should be something like a "35mm equivalent" for this information as well?

There is. Simply apply the crop factor to f-number and ISO as well as focal length. (For ISO, you need to square the crop factor before multiplying it.)


No matter what body you put a lens on, the focal length always stays
the same. 100mm is always 100mm, no matter if you use it on a 1.0X, 1.3X,
1.6X, or 7.0X body (such as the Canon XL-H1, which has a 1/3" sensor
and EF lens mount). That is why I think the term "effective focal
length" is very misleading -- it is much more clear to say "equivalent
angle of view". For example, these are correct:

• 100mm on a 5.6X digicam has the same focal length as 100mm on full frame.
• 100mm on a 1.6X DSLR has the same focal length as 100mm on full frame.
• 100mm on a 5.6X digicam has the same angle of view as 560mm on full frame.

Same thing applies to f-number. No matter what body you put the lens
on, the f-number is always the same. However, just as "angle of view"
changes between format sizes, many factors affected by f-number change
as well: total light gathered, noise, dynamic range, diffraction, depth
of field, and more. Of course, some of these are affected by the sensor
as well. But in the case where the sensors in both cameras have the
same performance per area, such as the case of the 5D2 and 7D, then
things become very simple:

• f/5.7 on a 5.6X digicam has the same f-number as f/5.7 on full frame.
• f/5.7 on a 5.6X digicam has the same exposure as f/5.7 on full frame.
• f/5.7 on a 5.6X digicam has the same amount of light per area as f/5.7 on full frame.
• f/5.7 on a 5.6X digicam has the same depth of field as f/32 on full frame.
• f/5.7 on a 5.6X digicam has the same diffraction as f/32 on full frame.
• f/5.7 on a 5.6X digicam has the same total amount of light as f/32 on full frame.
• f/5.7 on a 5.6X digicam has the same noise as f/32 on full frame.

Most people just stop at "exposure". They only consider what happens
when you use the same ISO and same f-number on both cameras, in order
to get the same exposure. But it's important to also consider that the
larger sensor allows you to use a different exposure (i.e. higher ISO
and less exposure) and still get the same (or better) results. After
all, it's the results that matter.


I've done some demonstrations of this equivalence here:


http://thebrownings.name/images/2009-10-5d2-equivalence/


Here is a 1.6X image taken at 70mm f/4 ISO 640.





Compare that with the following image which is 111mm f/6.3 ISO 1600:





They have the same noise, diffraction, and depth of field, despite
being at two completely different f-numbers and ISO settings. That
shows that f-number scales with format size for all the important
factors in photography.

[Bill W]

I was wondering when you'd jump in Daniel....now where's George Slusher?

[ShutterbugJohan]

I was wondering when you'd jump in Daniel....now where's George Slusher?
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I've been wondering that too... I don't think that he's been online much since his camera and a bunch of his lenses were stolen (see his profile for a list). I hope he's back soon.

[LJ2b2c]

Thanks for the education. I'll have to read this a few more times, but I think you hit the nail on the head as to what I was looking for.

[Colin500]

Although I didn't ask the original question: Thanks for this excellent explanation, with so many example calculations that it's impossible not to "get" it!


It clears up some things that I had been wondering about while considering whether to upgrade to a 7DmkII or a 5DmkIII (from my current 500D/T1i) ... and since it confirms my suspicions about crop factors, apertures, and iso-numbers, I'm starting to lean much more towards the 5DmkIII.


Regards, Colin