How to explain that m4/3 can't achieve certain DOF pics from FF

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My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.





HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)


Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
 
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My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.

HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)

Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
Your argument is based on a faulty assumption, that DOF does not change depending on sensor size/crop. This is patently incorrect. DOF is dependent on a number of factors, including sensor size/magnification, output size, and viewing distance. Other things that change DOF: cropping an image (assuming fixed output), printing an image at different sizes (assuming fixed viewing distance) and viewing an image from different distances (assuming fixed output size).

This is because DOF is calculated by measuring the circle of confusion relative to a physical space. If the circle of confusion is small enough, the the image will appear to be in focus. As the circle of confusion grows, it appears to be out of focus. You literally can not calculate DOF without knowing the sensor size, output size and viewing distance (most DOF calculators have fixed assumptions for some of these parameters).

To your example of a 50/1.4 on both FF and M43 from the same distance, you suggest that the DOF will be the same. This is false. The magnification has changed with the smaller sensor camera, thus the out of focus areas/circles of confusion are enlarged, and the cropped image has perceptively narrower DOF. Try it with any DOF calculator:

FF 50/1.4 5 feet: focal plane is 0.25 feet wide

43 50/1.4 5 feet: focal plane is 0.125 feet wide

Now, if you were to say, the sensor does not alter the way a lens let's in photons, you would be entirely correct. An 50/1.4 is an 50/1.4 no matter what camera you attach it too. That is because these numbers are physical measurements that can be absolutely calculated. However, the focal length and aperture ratio are far from the only factors that determine DOF.

If you want to achieve the same DOF for a given FOV on both M43 and FF, you need to use an aperture two stops wider, or more accurately, you need to use a lens that has the exact same aperture opening (not aperture ratio). For example, 45/1.8 = 25mm, while 90/3.6 = 25mm, so yes, a 45/1.8 on a 43 sensors does provide essentially the same DOF as a 90/3.6 on a FF sensor, all other things being equal.

Another faulty assumption is that you can back up to achieve the same FOV. This is once again incorrect. No matter where you are, your lens (for a given sensor size) will provide the exact same FOV. Moving does not change the FOV, it simply changes how much is visible through the lens. Importantly, moving forwards or backwards also changes perspective, which means now the images you're comparing are not comparable.
 
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Try this site and put 45mm f1.8 using Olympus m4/3 and 90 f3.6 full frame camera (I used a Leica M9). You get the same depth of field and would have pretty the same(ish) angle of view. All lenses are different so it will not be an exact science. You can get the same dof with m4/3 as full frame and with telephoto lenses it is possible but as you move to wide angle forget it as m4/3 doesn't have many f0.7 or so lenses to buy and imagine the size and cost of them!

 
Your friends claim that 45mm f1.8 is the same as 90mm f3.6 on FF explains about 90% of the equation. The rest is irrelevant in the real world.

If you want a 90 second explanation from me:

The smaller the sensor, the shorter the actual focal length for the same framing and shooting position. THe shorter the focal length, the smaller the actual aperture diameter at the same f/ratio. The smaller the actual diameter of the aperture the smaller the blur circles.

But if you just double both due to the 2x crop factor, as above, 45mm f1.8 and 90mm f3.6 will be near identical. You have the same framing from the same shooting position. They also have the same size aperture diameter which means the same size blur circles. So pretty much like I said, your friend's explanation works fine.
 
My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.

HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)

Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
I am going toPredict that this thread is going to devolve into our next equivalency argument.
 
My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.

HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)

Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
I am going toPredict that this thread is going to devolve into our next equivalency argument.
 
One can spend hours fiddling with a DOF calculator making endless comparisons. One eventually discovers at the extremes the differences between formats are scant millimeters and not worth stressing over, provided one has access to exotic, fast lenses.

The rest is better expended at the Albuquerque hot air balloon festival.

Cheers,

Rick
 
What your friend may not be considering is that f 0.6 and f 0.7 lenses don't exist for m43 - and those would be the ones to align with f 1.2 and f 1.4 on FF

In the other direction most cell phone pictures have deep DOF mostly due to the small sensor.
 
My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.

HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)

Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
Your argument is based on a faulty assumption, that DOF does not change depending on sensor size/crop. This is patently incorrect. DOF is dependent on a number of factors, including sensor size/magnification, output size, and viewing distance. Other things that change DOF: cropping an image (assuming fixed output), printing an image at different sizes (assuming fixed viewing distance) and viewing an image from different distances (assuming fixed output size).

This is because DOF is calculated by measuring the circle of confusion relative to a physical space. If the circle of confusion is small enough, the the image will appear to be in focus. As the circle of confusion grows, it appears to be out of focus. You literally can not calculate DOF without knowing the sensor size, output size and viewing distance (most DOF calculators have fixed assumptions for some of these parameters).

To your example of a 50/1.4 on both FF and M43 from the same distance, you suggest that the DOF will be the same. This is false. The magnification has changed with the smaller sensor camera, thus the out of focus areas/circles of confusion are enlarged, and the cropped image has perceptively narrower DOF. Try it with any DOF calculator:

FF 50/1.4 5 feet: focal plane is 0.25 feet wide

43 50/1.4 5 feet: focal plane is 0.125 feet wide

Now, if you were to say, the sensor does not alter the way a lens let's in photons, you would be entirely correct. An 50/1.4 is an 50/1.4 no matter what camera you attach it too. That is because these numbers are physical measurements that can be absolutely calculated. However, the focal length and aperture ratio are far from the only factors that determine DOF.

If you want to achieve the same DOF for a given FOV on both M43 and FF, you need to use an aperture two stops wider,
Unless DOF is already infinite.

The issue where this often gets taken further is to say that the FF camera needs to be stopped down two stops....and that is not always the case (and more often than not isn't for me)....it depends if you really need an "equivalent" photo.....lots of the time, you can change the shutter speed instead....especially with a static subject like a parked car in the day time.
or more accurately, you need to use a lens that has the exact same aperture opening (not aperture ratio). For example, 45/1.8 = 25mm, while 90/3.6 = 25mm, so yes, a 45/1.8 on a 43 sensors does provide essentially the same DOF as a 90/3.6 on a FF sensor, all other things being equal.

Another faulty assumption is that you can back up to achieve the same FOV. This is once again incorrect. No matter where you are, your lens (for a given sensor size) will provide the exact same FOV. Moving does not change the FOV, it simply changes how much is visible through the lens. Importantly, moving forwards or backwards also changes perspective, which means now the images you're comparing are not comparable.
Best idea is for the OP and friend to not try and shoot the exact same shot and just use their own gear for the shot they each want.

Enjoy the difference (that's why I have both FF and M4/3).
 
Its true.it's not dependent on sensor size but on apperture size and distance to subject. The formula for the dof conferms this. There is no variable for sensor size.

If you take a tripod and place a 50 f1.4 and take a panorama you can accieve the same fob and blur as full frame + 50 f1.4 with any sensor (though smaller sesors would require a lot of photos to study together)
 
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My friend does not think there is any difference between m4/3 and FF. He just cites "crop equivalent" calculation to say you can get the same photo with a different lens. If I show a photo of an entire car with shallow DOF, he will reply with, "45mm f1/.8 on m4/3 is the same as 90mm f/3.6 on FF"

Here is how I tried to explain:

ME: DOF is a function of focal length, distance, and aperture. The most effective thing to do is simply walk outside and try to take a shot of a car with a blurred background. Try it with the 20mm f/1.8 If the FF camera is doing that shot at f/1.8 and you are at same aperture, you will not be able to FIT the car into the m4/3 frame. You will need to back up, and get less blurring of background.

HIM: DOF is a function of not only aperture, but also sensor size. In terms of DOF, a 45 1.8 on an M43 sensor is equivalent to a 90mm 3.6 on a FF sensor. Therefore, the DOF issue you are saying can only be accomplished with FF sensor can be resolved by using a smaller sensor with a 2x aperture. While this is tough to do, the limitation is only because of lens availability on the M43 system. However, this is also coming around with the recent development of the Voightlander 42.5 .95, and others like it.

ME: DOF is not a function of sensor size. DOF is a function of focal length, distance, and aperture. The lens has no idea what sensor is behind it. It simply captures an image, even with no sensor at all. If you screwed your lens onto a different camera, the DOF doesn't not magically change. It is a static image projected by the glass. The sensor size only determines how much of that fixed picture you will capture. DOF is an indirect function of sensor size, b/c it affects how close or far away you must stand, to capture the equiv. field of view.

If you stuck a 50mm f/1.4 lens onto FF and m4/3, you'd have the same image, but a different crop factor. The m4/3 has a 2x crop sensor. If you wanted the same field of view as the FF, you'd have to either:
1) Back up.
2) Use a lens with much lower focal length (wide angle)
3) Use a faster lens (let's just agree you aren't going lower than f/1.4)

Now, picture the car photo.The FF camera is not using 90mm 3.6. It's using 80mm f/1.8. If you stuck that lens onto your m4/3, you'd get the identical image, but basically be seeing HALF the car. So, to get the same field of view on m4/3, you'd have to back way the F up, or use a lens with much lower focal length. There goes your shallow DOF. Yes, you can get the equivalent field of view, but it's a totally different DOF.

Sensor size affects where you stand, and what focal length you can use.To fit an entire car, you simply will not get the same DOF as a FF.Try to photograph an entire car with your 20mm f/1.8 and see what sort of bokeh effect you get.You simply can not get close enough to the car, to get the same DOF, since it will not fit in the crop frame.
Your argument is based on a faulty assumption, that DOF does not change depending on sensor size/crop. This is patently incorrect. DOF is dependent on a number of factors, including sensor size/magnification, output size, and viewing distance. Other things that change DOF: cropping an image (assuming fixed output), printing an image at different sizes (assuming fixed viewing distance) and viewing an image from different distances (assuming fixed output size).

This is because DOF is calculated by measuring the circle of confusion relative to a physical space. If the circle of confusion is small enough, the the image will appear to be in focus. As the circle of confusion grows, it appears to be out of focus. You literally can not calculate DOF without knowing the sensor size, output size and viewing distance (most DOF calculators have fixed assumptions for some of these parameters).

To your example of a 50/1.4 on both FF and M43 from the same distance, you suggest that the DOF will be the same. This is false. The magnification has changed with the smaller sensor camera, thus the out of focus areas/circles of confusion are enlarged, and the cropped image has perceptively narrower DOF. Try it with any DOF calculator:

FF 50/1.4 5 feet: focal plane is 0.25 feet wide

43 50/1.4 5 feet: focal plane is 0.125 feet wide

Now, if you were to say, the sensor does not alter the way a lens let's in photons, you would be entirely correct. An 50/1.4 is an 50/1.4 no matter what camera you attach it too. That is because these numbers are physical measurements that can be absolutely calculated. However, the focal length and aperture ratio are far from the only factors that determine DOF.

If you want to achieve the same DOF for a given FOV on both M43 and FF, you need to use an aperture two stops wider,
Unless DOF is already infinite.

The issue where this often gets taken further is to say that the FF camera needs to be stopped down two stops....and that is not always the case (and more often than not isn't for me)....it depends if you really need an "equivalent" photo.....lots of the time, you can change the shutter speed instead....especially with a static subject like a parked car in the day time.
Right, I was assuming the focal plane would be shallow enough, or that the goal would be shallow DOF for purposes of subject isolation (as per the OP's example of a car with a blurry background). Of course, if you're shooting a distant subject you may have everything in the frame in focus at different nominal apertures. At a certain distance, you no longer need to stop down to get more in focus. What distance this is depends on the lens and sensor size you're using.
or more accurately, you need to use a lens that has the exact same aperture opening (not aperture ratio). For example, 45/1.8 = 25mm, while 90/3.6 = 25mm, so yes, a 45/1.8 on a 43 sensors does provide essentially the same DOF as a 90/3.6 on a FF sensor, all other things being equal.

Another faulty assumption is that you can back up to achieve the same FOV. This is once again incorrect. No matter where you are, your lens (for a given sensor size) will provide the exact same FOV. Moving does not change the FOV, it simply changes how much is visible through the lens. Importantly, moving forwards or backwards also changes perspective, which means now the images you're comparing are not comparable.
Best idea is for the OP and friend to not try and shoot the exact same shot and just use their own gear for the shot they each want.

Enjoy the difference (that's why I have both FF and M4/3).
 
Its true.it's not dependent on sensor size but on apperture size and distance to subject. The formula for the dof conferms this. There is no variable for sensor size.
Any DOF calculator worth using certainly does have sensor size as a variable. A really good DOF calculator will let you change magnification/output size and viewing distance as well (I found one at one point but can't seem to find the link again). If you've found a DOF formula that does not take into account sensor/film size, chances are it was created specifically for one format, probably 35mm, and will not apply to others.

Here are a couple decent ones:

http://www.dofmaster.com/dofjs.html

http://www.cambridgeincolour.com/tutorials/dof-calculator.htm
If you take a tripod and place a 50 f1.4 and take a panorama you can accieve the same fob and blur as full frame + 50 f1.4 with any sensor (though smaller sesors would require a lot of photos to study together)
Only if you view the resulting stitched panorama at the same magnification. Let's say the panorama is 10x wider than a single frame, this means you would have to print it 10x wider for the DOF to be the same. Printed at the same physical width, the DOF will be very different (unless of course, as noted above, everything is in focus in both shots).

If viewing at 100% on a computer screen the DOF will also be the same. But few would compare photos in this manner. 100% of a full resolution pano means you're missing the forest for the tress.
 
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