I truly, truly don’t understand why this continues to be source of debate. It’s not about Cannikon vs. Fuji. At the end of the day, it’s not even really about FF vs. APS-C. There is nothing inherent to the size of the sensor that directly affects DoF per se. It’s really about the interaction of lens focal lengths, aperture diameter, and the resulting f-number.
If you have two lenses of different focal lengths, but the same aperture diameter, than of course the f-number is going to be different. You will get the same DoF because the aperture diameter is the same, but you will use a different f-number to do it.
Conversely, if you have two lenses of different focal lengths, but the same f-number, than the aperture diameter will be different. In this case, you will get a different DoF because the aperture diameter is different even though the f-number is the same. Again, it’s because you have two different lenses of two different focal lengths.
All of the above is true even if we’re talking about two lenses of different focal lengths used on the same body with with same sensor so this isn’t really a FF vs. APS-C thing at the end of the day. It comes into discussions of FF vs. APS-C because we use lenses of different focal lengths to achieve the same FoV when comparing FF to APS-C. So naturally, when we’re using lenses of different focal lengths to get the same FoV then we have to use different f-numbers to get the same aperture diameter and the same DoF.
Remember, it’s aperture diameter that determines DoF, not the f-number which is ratio of focal length to aperture diameter.
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Chris Lee
I apologize if this seems pedantic to most, but I realize there are a lot of people reading these forums that may be learning the hobby as they go so I’ll just add something that might seem obvious to most, but is essential to understanding what I wrote above.
The f-number is not the absolute aperture, rather it’s relative to the focal length and the aperture diameter. To be specific, the f-number is the focal length of the lens divided by aperture diameter.
So again, if we’re talking about two lenses of two different focal lengths, but with the same aperture diameter, then the f-number to achieve that aperture diameter will be different between the two lenses. That’s just how f-numbers work.
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Chris Lee
There are two concepts in play. From the equations from optics for a simple lens one has first "hyperfocual distance: which is the the minimal distance of focus beyond which all objects out to infinity are in focus. It is a function of the only the lens only
H=(f^2)/(N*c) +f where N is the f-number and c is the circle of confusion. Since f/N is the diameter of the aperture, A this can be rewritten as H=A*f/c +f. There is no reference to focal distance which is or magnification.
The object size determines the lateral magnification and as a proportion of the sensor size (which determines the proportion of the of the image size to sensor size) which in turns determines the distance one has to stand from the object for a given field of view.
M= hi/h0 = -di/d0 (minus because the image appears behind the lens and objet in front of the lens. The focal length equation is given by 1/f = 1/di +1/d0.
The DOF is not calculated by Dn = (H-f)*s/(H+s-2f), Df=s*(H-f)/(H-s) where Dn is distance of near focus and Df is distance of far focus and s is focal distance. The DOF around s is
DOF= Dn-Df.
Equations for depth of field and hyperfocal distance calculations.
www.dofmaster.com
The two concepts that go into the DOF is the hyperfocal distance which is totally independent of FOV, sensor size, etc and dependent on ln the focal length and aperture or focal length and f-number.
The second is the magnification which which brings in FOV and sensor size into play. The confusion arises when the distinction is not made between these two independent factors with most of the confusion causes by the sophomoric explanations you find online in the guise of equivalence between sensor sizes. Even more confusion in these explanations is while the lateral magnification is determined by sensor size for a given object size and proportion of the focal plane to the focal plane size or field of view, the axial magnification ( the relative magnification difference of two objects at different distant down the lens axis in the image ) is highly dependent on the absolute focal length - independent of the sensor size. So the same "normal lens" on a different lenses will give a different perspective in the lens axis dimension.
Lateral magnification is given by hi/h0 = M = -di/d0. This is where the sensor comes in say you want a 2 meter tall object (tall person) to take up 75% of the height of the sensor. Since the height varies - the lateral magnification goes goes down as the sensor height goes up. The lens equation 1/di + 1/d0 =1/f gives the relationship that allows one to calculate the distance for various formats that give same same height given f is a multiple of the "normal lens for the sensor size). That is the lateral magnification is different for the Same FOV for different sensor sizes for a "normal" lens on that sensor.
EG for a 2 meter tall person taking up 3.4's of the height on an Fuji APS-C XTrans the magnification is 8.5d-3, on a FF and the magnification is 9d-3 for a 35 mm or FF, 22.5d-3 for a 6x7 and 111d-3 for a 4x5. That is the final image on the sensor for a 2 meter high object will take up the same proportion of the height of the sensor with these magnification factors. This allows one to determine that a 35 mm on an Fuji APS-C is approximately equivalent to a 54 on a FF since you get the same FOV from the same point. This says for perspective in thpe image focal plane, the lateral or transversal perspective is the same for a 35 on an Fuji X-APSC and a 54 on a full frame or the approximate 1.5 crop factor.
All well and good. That gives the perspective in the image focal plane. What what about magnification in the direction perpendicular to the image focal plane, i.e. the axial axis fo the lens. This is known as the axial or longitudinal magnification. It measures the rate of change of the image distance as a function of the object distance. It is given by
Maz=(M^2)/f where M is the lateral calculated above. Given the image distance is related to the image size by hi/h0 = - si/s0. For a longer lens independent of format the axial magnification is smaller than for a shorter focal length independent of sensor size. That is a object behind the image focal plane with a 35 mm lens appears to be further back (shorter) than the same image shot with a 55 mm lens. That is the reason that telephotos tend to flatten the image and wide angle lenses tend to destroy in the axis of the lens - the big nose effect with portraits taken with short lenses. This is independent of sensor size.
For our 33 mm normal on the Fuji APS-C the Maz = 1.04d-6. for a 90 mm (normal) on a 6x7 the axial magnification is 5.625d-6. So the image appears different in the axial direction ( background appears closer for longer lenses ) although it is equivalent in the focal plane FOV. The difference between an APS-C say 28 on a APS-C and 43 on a FF is small 1.2d-6 vs. 1.8d-6 it is there.
The "theory of equivalence" only goes so far and DOF and FOV are about it. For hyperocal distance and axial perspective focal length and f-number (for hyperfocal ) are the only variables. However, different sensor sizes do have different rendering of the same image even if the FOV is the same. The difference is slight between the APS-C and FF but gets larger as the sensor size grows.
For example in this image taken by a my Mamiya RB67 with a 127 mm lens the waterfall would appear further back from the rock (image focal plane) if it were taken on an Fuji X APS-C lens with the equivalent focal length which would be 40 from the same spot.
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Truman
www.pbase.com/tprevatt
