Focal length & 1.x crop factor

[andrew_carlson]

I've read and searched bunches on the 1.6x crop factor of the Canon

20D and other DSLR cameras but then I just had an interesting thought.

This may take awhile to articulate here please bear with me.

 

I have a canon EOS 20D camera with a known 1.6x crop factor. We know

that if I have a 100mm lens the relative focal length of that lens on

my 20D is 160mm, on a standard EOS film body it would be 100mm. So

far ok, this hasn't really impacted me through what I see in the

viewfinder yet.

 

I recently read a book by Chris Weston that explained that Aperture or

f-stop is a divisor of your focal length. (I hope I have that right I

could be confused) So my 100mm lens at say f/1 would be wide open

equal to the focal length. That same lens at f/2 would have an

aperture opening of 1/2 of 100mm and so forth so f/4 is 1/4 of my

focal length. This is fine I get this and it makes sense to me. (if

I have it right - er, um if I'm wrong then it doesn't make sense to me.)

 

The way I think about it is f/1 would be 100% light reaching the

sensor. f/2 would be 50% light reaching the sensor, f/4 would be 25%

light. f/2.8 is something like 35.7%. Yet aperture size has a direct

relationship to depth of field.

 

So the relative focal length of that lens on my 20D being 160mm isn't

my aperture also affected by the 1.6x crop factor? Isn't depth of

field also being affected? I would think that my depth of field would

be 1.6x deeper (how ever wide you measure depth of field is this why

some recommend shooting rulers lengthwise?) Is this over technical or

wouldn't 2.8 be affected by 1.6 and really become (approximately)

f/4.2? (1.6 x 2.8 = ~1.4 + 2.8 = 4.2) ((Not exact I'm guestimating))

 

This is just an interesting concept, I've never really given the 1.6x

crop much thought. Most posts just describe the affects on focal

length in regards to telephoto vs. wide angle, but I've never seen

anything beyond that. I must admit I've probably taken the 1.6x

factor for granted up till now.

[ellis_vener_photography]

<I>So the relative focal length of that lens on my 20D being 160mm isn't my aperture also

affected by the 1.6x crop factor?</I><P>No. Because the focal length of the lens is still

100mm that chas nothing to do withthe size of the format.<P>

<I>So the relative focal length of that lens on my 20D being 160mm isn't my aperture also

affected by the 1.6x crop factor?</I><P>No and ofr the same reason. However if you

compared an image made on a 24x36mm format camera with a 160mm lens to an image

made on your 20D with your 100mm lens (assumption; the camera to subject distance

doesn't change) you will see more depth of focus in the image made on the 20D even if

the framing & composition is identical.

[photobyalan.com]

The short answer is no. <p>

 

The size of the imager has <i>absolutely no effect whatsoever on f-stop or depth of field</i>.<p>

 

Here is where you have gone wrong:<p>

 

1. Focal length is an <i>absolute</i>. It does not change no matter what size imaging chip or film is behind it, and the basic characteristics of that focal length do not change. The only thing that changes with the size of the sensor is how much of the image circle you're using. Because of this, the f-stop values of a lens are also absolute values that cannot change. The focal length stays the same, the actual aperture at whatever stop is set is the same, therefore the ratio of the two (the f-number) must be the same.<p>

 

2. Exposure is (Lumens x time). The shutter controls the time and the lens controls the Lumens. Since Lumens is a measure of light per area (1 Lumen=1 footcandle per square foot), it matters not one bit how much of the area you use.<p>

 

3. Depth of field is controlled by three factors: The actual focal legth of the lens, the distance from subject to imaging plane, and the aperture of the lens. That's all. The size of the imager makes no difference for depth of field. The reason many people say digital cameras have more depth of field is because lenses of shorter focal length are frequently used on digital cameras to achieve the same framing and perspective as one would get with a 35mm camera. It's the shorter focal length that's in play in that case, not the camera's smaller sensor. If you put a 100mm lens on a digital camera, take a photo, and switch that same lens to a film camera without moving closer to or farther away from your subject, the depth of field will remain the same. Some people may argue about this, saying that the size of the sensor makes a difference. <i>Prove it</i>.<p>

The "1.6x factor" is very misunderstood. The only effect it has is in the framing of a subject at a given distance. A larger sensor uses more of the image circle projected by the lens, therefore it would show more area around the subject (a wider view). A smaller sensor uses less of the image circle and will show a tighter view of the subject. That's all. All the principles and laws of optics remain unchanged.

[andrew_carlson]

Alan - GREAT explanation....thanks - as I stated this was just a curiosity and I started playing out the popular misunderstandings in my mind and just followed them to conclusion.

<p>

<I>

The "1.6x factor" is very misunderstood. The only effect it has is in the framing of a subject at a given distance. A larger sensor uses more of the image circle projected by the lens, therefore it would show more area around the subject (a wider view). A smaller sensor uses less of the image circle and will show a tighter view of the subject. That's all. All the principles and laws of optics remain unchanged. <p>

</I><B> This is exactly the way I always wanted to interpret the 1.6x crop factor. Yet everything I had read on it confused the matter.</B>

<p>

This is excellent stuff! Thanks.

[mark u]

Alan's explanation is fine except for one item - depth of field. Depth of field is determined as he says by aperture, focal length and focus distance, but also by the acceptable circle of confusion size (and pupil magnification factor, but that only really matters in macro work). The point here is that when you enlarge the image captured by the sensor or film, you magnify the blur of anything that is even slightly out of focus too. The more you enlarge, the more visible that is at any given viewing distance. If you take a given lens and use it at a given focus distance and aperture, the physical blur at the film or sensor is the same regardless of the size of the capture medium. However, if you use a smaller sensor or (equivalently) crop the image, you probably end up enlarging it a greater amount - which will reduce the apparent depth of field at any given viewing distance of the print.

 

The size of acceptable circle of confusion in a print (and by inverse magnification on the film/sensor) is subjective - it depends on the acuity of your vision and your personal taste, as well as the distance from which you typically view the print. Ultimately, it's about what your eye sees.

 

I can recommend reading the following for an excellent discussion of depth of field:

 

http://www.vanwalree.com/optics/dof.html

 

About the only feature not discussed in that otherwise excellent article is the inescapable physics of diffraction, which of itself produces a blur circle whose size increases the smaller the physical aperture on the lens. In practical terms, diffraction limitations depend on your circle of confusion criterion in a non diffraction limited case - when the diffraction disk starts to become larger than the CoC, it makes the image appear less sharp. The size of the diffraction disk depends solely on the aperture mutiplied by the wavelength of light being imaged. Unless your sight is poor, I'd expect you would find an image taken with your 20D at f/22 would be noticeably less sharp than one taken at f/11.

[photobyalan.com]

Mark,

 

I stand by my earlier statement.

 

If you stood at the same spot and took identical photographs with a 35mm camera and an APS C digital camera, you would need to use a shorter focal length on the APS camera. This would increase the depth of field sufficiently to make any COC difference meaningless.

 

If however, you changed lenses, then you would have to move away from your subject to get the same framing (although not the same perspective) with the digital camera, again increasing DOF.

 

The third possiblity would be that you did not change lenses and did not change your position. That would mean you would need to crop the 35mm image to compensate for the field of view of the two cameras. In effect, you would be working with an APS C-sized piece of film, which you would then be enlarging an identical amount when compared with the digital sensor. Same focal length. Same subject distance. Same aperture. Same enlargement amount. Same depth of field.

[mark u]

Alan - I think you should review carefully what you actually wrote.

 

`Then you should say what you mean,' the March Hare went on.

 

`I do,' Alice hastily replied; `at least--at least I mean what I say--that's the same thing, you know.'

 

(Mad Hatter's Tea Party, Alice in Wonderland)

[ilkka_nissila]

Practical shots taken with small-sensor cameras have more depth of field than large-sensor cameras given that the framing is the same. Whether you consider this to be due to the difference in focal lengths used to get the same shots, or due to the different magnifications involved (since the smaller sensor requires lower FL to magnify the image to fit the size of the sensor), is just a game of words.

[mark u]

<p>For the avoidance of doubt and confusion:</p>

 

<p><em>Depth of field is controlled by three factors: The actual

focal legth of the lens, the distance from subject to imaging

plane, and the aperture of the lens. That's all. </em></p>

 

<p>No, it's five factors - including the chosen circle of

confusion which is related to the size of the image as captured

and the intended magnification of the image for viewing, and the

pupil magnification factor, although the latter only matters at

short focus distances in practical terms. See equation 9 <a

href="http://www.vanwalree.com/optics/dofderivation.html#eq8">here</a></p>

 

<p><em>The size of the imager makes no difference for depth of

field. </em></p>

 

<p>This is only true if you assume that 1 square mm of capture

will be enlarged by the same amount when viewed, regardless of

the size of the imager - an unlikely scenario.</p>

 

<p><em>The reason many people say digital cameras have more depth

of field is because lenses of shorter focal length are frequently

used on digital cameras to achieve the same framing and

perspective as one would get with a 35mm camera. It's the shorter

focal length that's in play in that case, </em></p>

 

<p>True</p>

 

<p><em>not the camera's smaller sensor. </em></p>

 

<p>The sensor size is also in play.</p>

 

<p><em>If you put a 100mm lens on a digital camera, take a photo,

and switch that same lens to a film camera without moving closer

to or farther away from your subject, the depth of field will

remain the same. Some people may argue about this, saying that

the size of the sensor makes a difference. Prove it.</em></p>

 

<p>This is completely wrong. Here are some results using Julian

Loke's DoF calculator (which assumes a constant pupil

magnification factor of 1 - which can be seriously erroneous with

a macro lens at close focus, but otherwise is a reasonable

assumption: a macro lens may also change its effective focal

length significantly at close focus, fuirther complicating

matters), available at <a

href="http://members.rogers.com/jul.loke/jlcalc.html">http://members.rogers.com/jul.loke/jlcalc.html</a></p>

 

<p>Settings: Frame format <strong>35mm</strong>; Focal length <strong>100mm</strong>;

Working Distance <strong>5m</strong>; CoC <strong>0.025mm</strong></p>

 

<p>At say <strong>f/4</strong> Near DoF point: <strong>4.766m</strong>;

Far DoF point <strong>5.263m</strong>; Total DoF: <strong>0.497m</strong></p>

 

<p>At say <strong>f/16</strong> Near DoF point <strong>4.178m</strong>;

Far DoF point: <strong>6.250m</strong>; Total DoF: <strong>2.072m</strong></p>

 

<p>Settings: Frame format <strong>EOS D30</strong>; Focal length <strong>100mm</strong>;

Working Distance <strong>5m</strong>; CoC <strong>0.015mm</strong></p>

 

<p>At <strong>f/4</strong> Near DoF point: <strong>4.857m</strong>;

Far DoF point: <strong>5.155m</strong>; Total DoF: <strong>0.298mm</strong></p>

 

<p>At <strong>f/16</strong> Near DoF point <strong>4.473m</strong>;

Far DoF point: <strong>5.682m</strong>; Total DoF: <strong>1.209m</strong></p>

 

<p>Of course, if you take a crop of the 35mm image that has about

40% of the area of the capture and enlarge that to the same print

size as the entire "D30" image, they will exhibit

similar DoF characteristics when viewed under similar conditions

- but that isn't what Alan originally said. To avoid confusion,

it is necessary to be very precise about the conditions you are

comparing. I expect Alan knew what he meant, but he didn't say it.</p>

 

<p>It's worth having a play with Julian's calculator which has

handy adjustments for teleconverters, extension tubes and closeup

lenses, and also reports on effective apertures, hyperfocal

distances and field of view at the focus distance in terms of

both angles and physical dimensions for a variety of DSLR and

film sizes.</p>

[photobyalan.com]

Agreed, my second post was much more accurate than my first. <p>

 

<b>In theory</b>, sensor size has an effect on depth of field. However, in the real world, there is no such effect, for the reasons I stated in my second post. If you want to compare apples to oranges, you can certainly prove that the size of the sensor affects DOF. The truth is, you simply cannot produce the same photograph with two different formats without changing focal lengths or cropping the larger format. In the first case, there is a direct effect on DOF. In the second case, there is an effect on circle of confusion. Either variable effectively couteracts any perceived effect of a different imager size.<p>

 

Look, if you don't believe me, maybe you'll believe <a href=http://www.photo.net/learn/optics/dofdigital/>Bob Atkins</a>.

[kelly_flanigan1]

In the 1950's and early 1960's; it was common to use LTM and Exakta lens; on 16mm and 8mm movie cameras. There were a mess of XXX to C mount adapters; and also C mount to D mount adapters. A tighter circle of confusion was used for the smaller formats; as outlined in the 1940's Kodak lens books. I never remember the term "crop factor" used then; when a 5cm lens was used on a 16mm or 8mm camera. Maybe folks then understood geometry better then; and were more use to dealing with angles and DOF tables. Many folks had 16mm and regular 8mm movie cameras; and used the same c mount lenses on either body; using the D mount adapter for the 8mm body. The movie camera bodies had a sliding viewfinder tab; that one could set to the focal length of lens in usage. One learned a 25mm lens had less coverage on a 16mm camera; versus an 8mm camera as being second nature.

[kelly_flanigan1]

One learned a 25mm lens had <b>MORE</b> angular coverage on a 16mm camera; versus an 8mm camera as being second nature.

[hakon_soreide]

Strange how people are able to argue over subjects of depth of field, focal length and circle of confusion calculation. Basically, any arguments over these subjects are due to people using different variables in the same equations, and that is again usually due to the fact that the <i>acceptable</I> circle of confusion (keyword italicised) is a subjective figure, however much some might feel it's a fixed number for all pictures in a given format.<p>

I don't know who said it first, but a "circle of confusion" could also be defined as a group of photographers sitting around a table discussing this very subject.<p>

Anyway, when it comes to the original question, the term 1.6x <i>crop</I> says it all, really. That's what it is: a cropping of the image circle.<p> It might be worth noting, however, that as the smaller sensor or film size uses the centre of the image circle where a lens tends to be sharper than at the very edges (a variable that's different for all lenses), there might be more latitude when accepting a certain circle of confusion.<p>

Anyway, however fun hair-splitting is, in the end it's all about the photos people take, and however interesting or enjoyable they might be to look at whether it be just for the photographer sitting on his own peering at slides on his light table all evening, or if they are displayed in an art gallery. I think photographers (myself included) who spend any time arguing over such subjects should rather spend that time taking pictures.<p>

<a href="http://www.hakonsoreide.com/Photos">www.hakonsoreide.com</a>

[andrew_carlson]

Well Said Hakon.