How to Calculate Crop Factor, F-Stops, and Equivalent Lenses

[kshapero]

see this atricle:

http://www.seriouscompacts.com/f42/how-calculate-crop-factor-f-stops-equivalent-lenses-google-11338/

 

[Nikon Bob]

Well, I don't know I always thought the F-Stop value was the same no matter the sensor size and that is not the impression you would get from the article. He was possibly referring to the idea that a small sensored camera at f1.8 has the equivalent DOF of that a 35mm camera has at f4.9. After reading that I did not read the rest.

Bob

 

[jonasv]

I was wondering about something similar just a few days ago.

The old compacts had zooms like a 45-135 mm equivalent, f/2 - f/6.3

The newer ones, raving about wide-angles, often have lenses closer to 24-100 mm equivalent, f/2 - f/5.6.

In the 'normal' range (35-50mm), used for a lot of snaps, the maximum aperture has thus decreased as lenses progressed! (From f/2 to f/2.8-f/4-ish)

To be completely honest, I did not read the article and don't know if that's what this is about, but I did want to share my insight 😛
Edit: I see the article is actually about something slightly different. What Nikon Bob said.

 

[kshapero]

I have read stuff like this before. Basically he is saying, for example, if you have an M4/3 sensor with a lens at f2.0, then you really(as it pertains to DOF) have a lens that is f3.5. So do not expect bokeh to look like a true f2. I think I got it.

 

[kshapero]

BTW, I think this is an important issue for digi photogs and I am surprised so few have piped in. Unless I am wrong about this whole thing in which I invite being corrected.

 

[splitimageview]

Yep. It's simply a way to normalize comparisons between various sensor sizes, since smaller sensors have more inherent DOF.

 

[Jamie123]

I have read stuff like this before. Basically he is saying, for example, if you have an M4/3 sensor with a lens at f2.0, then you really(as it pertains to DOF) have a lens that is f3.5. So do not expect bokeh to look like a true f2. I think I got it.

No, it's still a 'true' f2 lens. If you have a 20mm f2 lens on a M4/3 camera then it will have the same DoF as any other 20mm f2 lens at a given plane of focus. It should be obvious that even if the crop factor is 2x it is not going to have the DoF of a 40mm f2 lens because that's not what it is. While it might be practical to speak of crop factors in relation to sensor sizes, I think it's quite silly to start doing the same in regards to aperture as you are then only talking about DoF, not about the amount of light the lens lets in.

 

[dct]

No, it's still a 'true' f2 lens. If you have a 20mm f2 lens on a M4/3 camera then it will have the same DoF as any other 20mm f2 lens at a given plane of focus. It should be obvious that even if the crop factor is 2x it is not going to have the DoF of a 40mm f2 lens because that's not what it is. While it might be practical to speak of crop factors in relation to sensor sizes, I think it's quite silly to start doing the same in regards to aperture as you are then only talking about DoF, not about the amount of light the lens lets in.

All depends... The article should be more specific what exactly it tries to normalize. You are right, if we only look at the light values we receive on a sensor or film pane (given through the aperture value by the shutter time), it doesn't depend from the dimensions of the sensor. I suppose the mentioned article doesn't consider this point of view because if you are discussing light values there is no normalization needed: It belongs only to lenses.
Normalization of lens information is interesting comparing different sensor sizes regarding some compository aspects: FoV and DoF. What the article misses to correctly mention is the third value in such a reflection: Distance to the object. (deliberately I don't throw in the changing angles of view stepping away, which is also a compository change)

- Field of View
The fact that the FoV angle of the recorded image changes swapping a lens from a FF body to a cropped one is simple to understand. (to keep it simple we often use the term "equivalent focal lenght" which is not strictly correct, but it gives a good indication how the FoV of the same lens would look like on a different sensor).

- Depth of focus Field
The discussion and formulas around F-stop normalization is also correct if the author would mention that you typicall step further away to obtain the same FoV like with a FF body. In this case you are changing another variable: The distance and consequently also the DoF using the same nominal aperture on the lens. In his formulas he seems to assume this compository aspect without mentioning it. (I suppose this is why some posts are upset on the topic of "equivalent aperture").
With this 2nd normalized value the author tries to give an indication how the aperture has to be changed to get the same DoF using the same FoV (with different distance to the object!) on a cropped sensor.
Or how wider the DoF is, using a smaller lens on a smaller sensor at the same distance and settings as a FF lens.

 

[shimokita]

It might be useful to also refer to the camera review and table that is referenced in the OP link.

http://www.dpreview.com/previews/sony-dsc-rx100

As a reference in the context of the original camera review it makes sense, if in fact digi-cam users are interested in DOF.

Casey

 

[Nikon Bob]

I still think the article was poorly worded and would add confusion for the average digicam user. Some digicam users care about DOF and that is why I mainly use a D700. When I do use my P&S digicam it usually is wide open or stopped down very little because it has huge DOF at virtually any f stop. The majority of digicam users could give a hoot about DOF, they just want an image. If you mentioned DOF you would just get the deer caught in the headlights look.

Bob

 

[Monochrom]

Hi, remember dof depends on focal length, and fov depens in the relation between focal length and sensor size.

If you want the dof and fov of a 50mm lens on a little sensor you´ll have to go very large on aperture....but the issue here is that no camera maker has any lens that can dof like a f1.4 50mm lens on a little sensor...

For larger sensors you may use a simple formula, crop factor x focal length. for instance 1.5 x 50 = 75....There are no many sensor sizes....since apsc is x1.5....micro 4/3 is x2 and the sony rx100 is about 2.7.....below that sizes you enter the land of hyperfocal...because all those cameras have lenses of tiny focal length...not even the vario-summicron of the lx3 can achieve small dof....

Really doesn´t matter at all, since small sensors are always in focus since their fixed or zoom lenses have ultra small focal lengths....6mm 7mm etc...

So DOF is dead plain to know...just go to dof master and use it in real focal length and 35mm format...set your apereture...and voilà...

To make an example....the leica x1...has (large) apsc sensor plus a 24mm lens with 2.8 max aperture....The fov is 35mm....

When you set the x1 at 5.6 and focus at 10 feet you almost get dof from 5 up to 90 feet....in real terms thats hyperfocal...also you get that unbearable wide angle lens distortion of field....when objects in different perspective seem to be more far in comparison with you´re eyesight...or normal lenses...

So, if you want samll dof get any 135 format camera and go shooting...even a moderate fasta lens of 2.8 will give you a nice shallow dof...and the quality of the image will be the best in comparison with any little sensor camera...

cheers!

 

[kshapero]

It might be useful to also refer to the camera review and table that is referenced in the OP link.

http://www.dpreview.com/previews/sony-dsc-rx100

As a reference in the context of the original camera review it makes sense, if in fact digi-cam users are interested in DOF.

Casey

I think this chart is poorly done because it doesn't show the full frame factor.