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F/ number in relation to the sensor size

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It is known that the aperture number have an unequal effect with different sensor sizes. For example, if the lens is f/2.8 on a APC-S sensor, it gives much more isolation of the subject than a f/2.8 lens on a 1 inch sensor. The depth of field will be much more for the 1 inch sensor.

I wonder if there is any equation to tell the equivalent f/stops for each sensor, say, similar to the crop factor for the focal lengths of lenses on different sensor sizes. For example, can we say that f/8 on FF sensor equals f/2.8 on 1 inch sensor? which f/number can give the same DOF for each sensor size measured with FF as a standard?
 
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Equivalent f/stop = Full frame f/stop / crop factor.

So, with a Micro 4/3rds camera with a crop factor of 2, you'd divide the FF f/stop by 2.
 
And for a 1"-type sensor, the crop factor is 2.7. So f/4 on a FF is equivalent to 4 / 2.7 = about 1.5 on a 1".
 
But please note that this only works if both cameras are in the same position, with the same focus distance, and when they are using equivalent lenses with the same angle of view.

Also, many lenses change their focal length when focused rather closely; this is called focus breathing, and so this may change the results, consequently, the aperture values will also change. Please be aware that the equivalence equations are only a first approximation to reality.
 
Mark Scott Abeln said:
And for a 1"-type sensor, the crop factor is 2.7. So f/4 on a FF is equivalent to 4 / 2.7 = about 1.5 on a 1".
Click to expand...
This was somewhat confusing on my first read as we usually encounter the approximation being argued in the reverse direction on the frequent equivancy threads. (We are used to your f/1.5 on 1" sensor gives equivalent dof to f/4 on full frame sensor rather than the f/4 on your full frame gives dof equivalent to f/1.5 on 1" sensor). Got it now.

D
 
Derma pro said:
I wonder if there is any equation to tell the equivalent f/stops for each sensor
Click to expand...
Well, that's what crop factor is for. First, find the crop factor of one format compared to another, and than multiply or divide by it, depending on which way you want to go.

Simple.

Take MFT vs FF, for simplicity's sake. Crop factor is 2, so f/4 eq f/8, f/2.8 eq f/5.6 and so on. So if you want to find out what's the equivalent of 1" sensor and f/2.8 combo on APS-C, just multiply by the crop factor of 1" in relation to APS-C.
 
Mark Scott Abeln said:
But please note that this only works if both cameras are in the same position, with the same focus distance, and when they are using equivalent lenses with the same angle of view.

Also, many lenses change their focal length when focused rather closely; this is called focus breathing, and so this may change the results, consequently, the aperture values will also change. Please be aware that the equivalence equations are only a first approximation to reality.
Click to expand...
 
Astrotripper said:
Derma pro said:
I wonder if there is any equation to tell the equivalent f/stops for each sensor
Click to expand...
Well, that's what crop factor is for. First, find the crop factor of one format compared to another, and than multiply or divide by it, depending on which way you want to go.

Simple.

Take MFT vs FF, for simplicity's sake. Crop factor is 2, so f/4 eq f/8, f/2.8 eq f/5.6 and so on. So if you want to find out what's the equivalent of 1" sensor and f/2.8 combo on APS-C, just multiply by the crop factor of 1" in relation to APS-C.
Click to expand...
Thanks for the explanation

this shows that certain work can not probably be done by smaller sensor cameras because if f/1.8 is needed for FF, anyone using 1" sensor will need f/0.7 lens (with other conditions put in mind), and that lens either will not exist or will be very expensive even more expensive than the equivalent f/1.4 on FF.
 
Derma pro said:
this shows that certain work can not probably be done by smaller sensor cameras
Click to expand...
And vice versa. There's always a right tool for the job.
 
Derma pro said:
It is known that the aperture number have an unequal effect with different sensor sizes. For example, if the lens is f/2.8 on a APC-S sensor, it gives much more isolation of the subject than a f/2.8 lens on a 1 inch sensor. The depth of field will be much more for the 1 inch sensor.

I wonder if there is any equation to tell the equivalent f/stops for each sensor, say, similar to the crop factor for the focal lengths of lenses on different sensor sizes. For example, can we say that f/8 on FF sensor equals f/2.8 on 1 inch sensor? which f/number can give the same DOF for each sensor size measured with FF as a standard?
Click to expand...
The Equivalence Ratio (more commonly called the "crop factor") is the ratio of the sensor diagonals. For example, the Equivalence Ratio is 2.7 between FF and 1", 2 between FF and mFT, 1.5 between FF and DX, and 1.33 between DX and mFT, etc., etc., etc.

So, with that in mind (and apologies for not including 1" in the mix below):

Equivalence in 10 Bullets:

Neither the focal length nor the f-ratio of a lens change as a function of sensor (for example, a 50mm f/1.4 lens is a 50mm f/1.4 lens, regardless of the sensor behind the lens). However, the effect of both the focal length and the f-ratio on the visual properties of the photo very much depend on the sensor, and scale in direct proportion to the size of the sensor:

25mm f/1.4 on mFT (4/3) is equivalent to 31mm f/1.8 on 1.6x (Canon APS-C), 33mm f/1.9 on 1.5x (APS-C for everyone else), and 50mm f/2.8 on FF (FX), where "equivalent to" means:
  • The photos all have the same diagonal angle of view (25mm x 2 = 31mm x 1.6 = 33mm x 1.5 = 50mm) and aperture diameter (25mm / 1.4 = 31mm / 1.8 = 33mm / 1.9 = 50mm / 2.8 = 18mm).
  • The photos all have the same perspective when taken from the same position.
  • The photos all have the same DOF (as well as diffraction softening) when they are taken from the same position with the same focal point and have the same display size.
  • The photos all have the same motion blur for the same shutter speed (regardless of pixel count).
  • The same total amount of light falls on the sensor for the same DOF and shutter speed.
  • The same total light falling on the larger sensor will result in a lower exposure than the smaller sensor (the same total light over a larger area results in a lower density of light on the sensor).
  • The larger sensor system will use a concomitantly higher ISO setting for a given brightness of the LCD playback and/or OOC (out-of-the-camera) jpg due to the lower exposure.
  • The same total light will result in the same noise for equally efficient sensors (regardless of pixel count and regardless of the ISO setting).
  • If the 25mm lens at f/1.4 is 2x as sharp as the 50mm lens at f/2.8, 1.33x as sharp as the 33mm lens at f/1.8, 1.25x as sharp as the 31mm at f/1.8, the sensors have the same pixel count, and the AA filter introduces the same blur, then all systems will also resolve the same detail.
  • Other elements of IQ, such as bokeh, color, distortion, etc., as well as elements of operation, such as AF speed/accuracy, size, weight, etc., are not covered in this use of the term "equivalent".
 
Equivalence is a false idea. If you factor in depth-of-field, then exposure changes and vice versa. You cannot and will not get the same results from different sensor or film sizes.
 
Derma pro said:
It is known that the aperture number have an unequal effect with different sensor sizes. For example, if the lens is f/2.8 on a APC-S sensor, it gives much more isolation of the subject than a f/2.8 lens on a 1 inch sensor. The depth of field will be much more for the 1 inch sensor.

I wonder if there is any equation to tell the equivalent f/stops for each sensor, say, similar to the crop factor for the focal lengths of lenses on different sensor sizes. For example, can we say that f/8 on FF sensor equals f/2.8 on 1 inch sensor? which f/number can give the same DOF for each sensor size measured with FF as a standard?
Click to expand...
Great Bustard is the most technically accurate source for the mathematically inclined.

As a simplification, if you're not math inclined, just assume that the ratio of the F-numbers is the inverse of the ratio of crop factors, as you've surmised in your post.

For instance, if you have a FF (crop factor of 1) vs. a 1" (crop factor of 2.73), then if you have F/8 on the FF, the equivalent F-number on a 1" is F/(8/2.73) or about F/3 (more accurately F/2.93).
 
lumigraphics said:
Equivalence is a false idea. If you factor in depth-of-field, then exposure changes and vice versa. You cannot and will not get the same results from different sensor or film sizes.
Click to expand...
Interesting comment ... can you illustrate/define where and why it is "false". I do not find any false ideas.

--
Charles Darwin: "ignorance more frequently begets confidence than does knowledge."
tony
http://www.tphoto.ca
 
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lumigraphics said:
Equivalence is a false idea. If you factor in depth-of-field, then exposure changes and vice versa. You cannot and will not get the same results from different sensor or film sizes.
Click to expand...
There is nothing false about Equivalence. Equivalent photos do not have the same exposure, just as equivalent photos do not have the same focal length or same relative aperture. What equivalent photos have in common is the same perspective, the same [diagonal] angle of view, the same DOF, the same exposure time, and the same total amount of light projected on the sensor.
 
lumigraphics said:
Equivalence is a false idea. If you factor in depth-of-field, then exposure changes and vice versa. You cannot and will not get the same results from different sensor or film sizes.
Click to expand...
Equivalence gives you the:
  • Same angle of view;
  • The same depth of field;
  • The same diffraction blurring;
  • The same shutter speed; and,
  • The same total photon shot noise.
To a first approximation, you get two equivalent photos. Differences include:
  • Optical aberrations;
  • Read noise; and,
  • Processing unique to a camera model.
Not to mention having to deal with a tiny unergonomic camera/heavy unweildy camera.
 
Great Bustard said:
lumigraphics said:
Equivalence is a false idea. If you factor in depth-of-field, then exposure changes and vice versa. You cannot and will not get the same results from different sensor or film sizes.
Click to expand...
There is nothing false about Equivalence. Equivalent photos do not have the same exposure, just as equivalent photos do not have the same focal length or same relative aperture. What equivalent photos have in common is the same perspective, the same [diagonal] angle of view, the same DOF, the same exposure time, and the same total amount of light projected on the sensor.
Click to expand...
Equivalent photos do not have the same exposure? What? How are they equivalent?

If I need f2.8 on one camera to get the same DOF as f/5.6 on a different camera, my shutter speed or ISO sensitivity has to change. Don't you think that changing shutter speed makes a difference?
 
Are you shooting video and filming the same take from different angles using cametas with different size sensors?
 
lumigraphics said:
Equivalent photos do not have the same exposure? What? How are they equivalent?

If I need f2.8 on one camera to get the same DOF as f/5.6 on a different camera, my shutter speed or ISO sensitivity has to change. Don't you think that changing shutter speed makes a difference?
Click to expand...
You raise the ISO on the larger sensor camera or lower the ISO on the smaller camera so that the total amount of light that falls on both sensors is the same. This equalizes the photon shot noise on both.

The iPhone has a small base ISO which is one reason why that tiny camera produces unexpectedly high quality photos.
 
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