EFL - MYTH OR MATH -

[Bill McCrystyn]

Some people are really bothered by the term Effective Focal Length. The math and concept of a DX sensor size and the term "crop factor" assigned to it by the manufacturers has been drummed into my head until late at night I see little circles that fit into big circles that make the big circle little but at the same time even though different remain larger. It's enough to make you nuts.

I call this one of the great circles of confusion. It is one of those things that depend on how you look at it and in the end, both are right.

The premise is that - IF - your end need is to produce a usable image at say 16x20 then "Effective Focal Length" is going to help you do that at a price less than your car. My math has less to do with the realities of pixel density and more to do with the reality of dollar cost vs. print size.

The focal length remains the exact same of any lens but the "angle of view" is reduced to the same as that of a lens of 1.5 or 1.6 times greater focal length on that of a 35mm format camera. Thus it is called "Effective Focal Length".

The truth is, that to get a usable size subject image at the same print size as that had by a 400mm lens used with a DX camera will take a 600mm lens on an FX body. Some will say that you can crop the FX frame to result in the same image size as you got with the DX in the first place. It is also argued that the cropped FX IQ will not be noticeably better, if at all, at that size. The end truth is at 16x20, most certainly at 12x18 no one without a loop at 3 inches will be able to tell the difference.

Unless you have an American Express Gold card, 3 sherpas and an *** to carry it all (no pun intended) - it will remain indeed a very "Effective Focal Lenght".

[John Chardine]

I agree it is a bit confusing Bill. Just a small point re. terminology. Effective focal length is the real focal length of the lens, regardless of the sensor or film size you put behind it. If you include the crop factor in the focal length calculation then you have Equivalent focal length, with the modern convention that you are speaking about equivalent to 35 mm film or a full frame sensor.

[Bill McCrystyn]

Good point John! Much more correct. Why is it I haven't heard that corrected/used before? Effective in one sense - Equivalent in proper context and actuality, hence the nomenclature in my EXIF. NO wonder that "effective" business drove you guys crazy. :)

Thanks for the clarity John.

[Roger Clark]

Hi Bill,
I think of the problem this way:

35mm equivalent focal length and crop factor is simply a crutch to illustrate field of view coverage for a given lens+camera. It has nothing to do with pixels on the subject.

To determine if you have enough pixels on the subject, you need "plate scale" or pixels per subject height. For example, if you want a nice bird image printed large, you want as many pixels as you can get on the bird. The way to do that is to increase focal length up to the point that the bird fills the frame. How many pixels you then actually get depends on how small the pixels are on the sensor.

Example: 30D versus 5D Mark II, and a 500 mm f/4 lens, imaging a bird. The bird is the same size (same number of pixels) from each camera because the pixel spacing is the same for each camera. The 5DII image will have more space around the bird because of the larger sensor.

So for field of view, use 35mm equivalent focal lengths, but for subject size you need plate scale, or pixel pitch (e.g. microns/pixel).

Plate scale, by the way originated in the early days of photography when film was glass plates.

[Bill McCrystyn]

Thanks Roger. Another example of this would be a D300/12mp and a D700/12mp haveing the same number/quantity of sensors but different sizes, FX over DX, giving none the less a different field of view for the lens.

I hate to open another can of worms that sounds like it is above my math head, but - plate scale?

[Roger Clark]

quote=Bill McCrystyn;224996]
I hate to open another can of worms that sounds like it is above my math head, but - plate scale?[/quote]

Plate scale is the size of the subject in the focal plane. Not that you would do these calculations for a bird, but you might (or maybe the photographer mathematician would). Astronomers use it all the time. Let's say you are headed to a lake with an island in the middle that is 20 meters away from the shore where you photograph. If the birds have a 1-meter wing span and you want them full frame with their wings open, how big will it be with a 500 mm lens in your full-frame camera? 1 meter at a distance of 20 meters is an angular size, A, of:

A = 2 * arctan(1/2 * object_size/distance) = 2 arctan (.5/20) = 2.86 degrees.

A full frame sensor is 24x36 mm and a 500 mm lens has a field of view with that camera of:

Av = 2 * arctan (0.5 * 24/500) = 2.74 degrees.
Ah = 2 * arctan (0.5 * 36/500) = 4.12 degrees.

So the bird easily fits in the frame. If you had 6000 pixels in the long dimension, and the bird's wings span 2.86/4.12 = 69% of the long dimension, that comes out to 0.69 * 6000 = 4140 pixels.

You could crop the final image to the size of the bird, which would be no different than if the camera's sensor was smaller, but the size of the bird would be the same (assuming the pixel spacing were the same).

Another way to look at this is to fill the full frame camera with the bird's wingspan, you would need 1/0.69 = 1.45 times the 500 mm focal length, so adding a 1.4x TC would be very close. So without ever visiting the site, you could arrive with a 500 mm lens with the 1.4x TC attached and not have to wait for a bird to open its wings to figure out what focal length was needed.

[Bill McCrystyn]

Quote Roger:
"So without ever visiting the site, you could arrive with a 500 mm lens with the 1.4x TC attached and not have to wait for a bird to open its wings to figure out what focal length was needed".

Thanks Roger. Now I know why I arrive with 200-400VR and a 1.4X. :D Lets see, that's the "equivalent" to a 420mm - 840mm zoom.

[Roger Clark]

Thanks Roger. Now I know why I arrive with 200-400VR and a 1.4X. :D Lets see, that's the "equivalent" to a 420mm - 840mm zoom.

Only in field of view equivalent, not pixels on subject. The term would be more correctly stated:

200-400. That's 420-840 in 35mm field of view equivalent.

People drop the "field of view" part and then believe it is equivalent in other way when it is not.

[Bill McCrystyn]

I am with you 100%. I believe my next to last paragraph, the original point of the matter, is the economies are valid and can only be enjoyed using the field of view advantage of the smaller sensor with the 35mm lens format. Would you agree?

[James Shadle]

"field of view" yes Roger!

When I used my Pentax 6x7 or Speed Graphic 4x5 no one wanted to know the "effective focal length".

Angle or field of view was standard measurement.

[Bill McCrystyn]

James I would agree with you as well. The difference is, people here are trying to get the biggest bang for the buck comparing two DSLR systems, FX and DX. If your end need does not require you to go beyond a 16x20 print the economies of the DX system are obvious and only brought about by the difference in the "field of view" as compared to a 35mm lens and FX system.

[Roger Clark]

I am with you 100%. I believe my next to last paragraph, the original point of the matter, is the economies are valid and can only be enjoyed using the field of view advantage of the smaller sensor with the 35mm lens format. Would you agree?

Bill,
I'm not sure I understand (but then I am very jet lagged at the moment). Why does the smaller sensor have a "field of view advantage?" It would seem to me the advantage goes to the camera with the larger field of view. If you really mean the number of pixels on a subject, then it is the camera with the smaller pixels, which could be either camera. If you consider only field of view, you can crop any image in post processing and declare that a longer focal length 35 mm equivalent (and I have seen that done).

[Roger Clark]

James,

I agree. But with different format film cameras we always use the same sensor (film) in each camera. The problem has changed with digital and the many pixel sizes those sensors come in. It is the pixel size that people forget/ignore/or don't know that creates major confusion. It doesn't help that camera manufacturers rarely tell us pixel size and seem go go out of their way to hide it in many cases by using obscure vacuum tube technology
specifications.

Roger

[Bill McCrystyn]

Sorry James and Robert. In post #11 I made a big mistake leaving out the word "does not require you to go beyond 16x20." You guys are sharper with jet lag than I am in the morning fresh.

Correct me if I'm wrong but my understanding is the field of view is a reference to the "area" a sensor sees as regard the lens in front of it. The smaller the sensor size the less that is captured by it in optical or area image terms. My point has nothing to do with pixel density or size inparticular. While there is no doubt you can crop down an FX image to the size of a DX size image so that it will print the same area and subject size at the same IQ, the expense of the larger FX system is lost or wasted if you will. It's a simple matter of economy. After that Genuine Fractals is a good way of tighting up a 12mp DX at 16x20 if needed after cropping.

Don't get me wrong, the big guns are great. I get that I am being perceived as scraping FX systems. For many works and sizes above 16X20 there is no other way to go and the new 21mp and 24 mp images are at or near medium format quality. Most inspiring, but at 16x20 or less, really not necessary from an expense standpoint.

[Arthur Morris]

Wow, am I glad that I am technically challenged. I tried very hard to follow the comments above but quickly got a headache. All that I have ever done is bought a lens, taken a walk and made some images, and then decided if they were any good or not. None-the-less, I do appreciate Roger's expertise.