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September 07, 2010, 01:38:48 AM
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Author Topic: FX/DX depth of field  (Read 27813 times)
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« Reply #40 on: December 08, 2007, 04:56:10 PM »

I have a  setup with FX 1:10 and DX 1:15 in progress right now. The data needs to be verified so I might run it again if time (and weather) permits. Besides that, I have FX/DX comparisons for shooting distances 50 and 750 m loaded onto the network but some more processing to do before can be published. The tentative analysis is that FX and DX at the same FOV differs in DOF but not by the equivalent of 1 stop.

The simple equations come into trouble for several reasons, one of them is that the lens isn't an ideal "thin lens", the other (following from the previous) is that the pupil factor isn't taken into consideration. Pupillary magnification enter the extended equations for DOF.
I would be most interesting test. One thing I like most about your lens tests is you have comments how a lens work different distances.
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« Reply #41 on: December 08, 2007, 06:01:12 PM »

Interesting thing with this setup of D300 vs D3 at similar picture-angles is that the "real-world" gets mapped almost identical to the sensors, as both cameras have almost the same number of pixels ((see, I don't use the word "exactly" any more, only "almost" and "similar" Wink)).
So you can think of the D300 just as a 1.5:1 scaled down version (a "lens+sensor-shrink") of the D3 (if the apertures are equal on both lenses).
But as subjects still have the same absolute distance to both cameras,  everything is now "relatively" 1.5 times further away from the D300 (in comparison to the D3)
That should lead to approx. 2.25x the dof with the D300 than with the D3 if you're pixel-peeping (meaning: circle of confusion = 1 pixel)
or 1.5x the dof if you're accepting larger airy disks.

Don't fret! This is just a challenge for me to try to predict the outcome of Björn's experiment Cool
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« Reply #42 on: December 09, 2007, 07:52:43 PM »

No, field of view is different from angle of view and or actual picture angle. FOV is the dimension of the field that is encompassed by the picture angle as manifested with a given format of the captured image. So say FOV is 100 m when a shot is taken using a lens with picture angle of 100  degrees (or any other value). This means the image captures a field 100 m wide when the shot is taken at a given distance with a lens having a given  picture angle. These are of course interconnected quantities based upon geometry and the projection formula of the lens, but one should not use an angular measure (picture angle) when the concept really is a spatial dimension.

We can propose better semantics, but I think it should be pointed out that FOV is frequently -- usually, even -- described as an angle, and that usage is synonymous with AOV.  And I'm not talking about neophytes; FOV is commonly expressed this way in the imaging business and in scholarly work.

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« Reply #43 on: December 09, 2007, 07:54:48 PM »

Repeating an error does not make it more correct. It only muddles the issue.


FOV is a distance and AOV is an angular measure.
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« Reply #44 on: December 09, 2007, 09:06:46 PM »

Is this right ??

IF
a = AOV
w = FOV
d = distance from lens to subject
THEN
tan(a/2) = .5w/d
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« Reply #45 on: December 09, 2007, 09:30:01 PM »

approximately Grin Grin Grin
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« Reply #46 on: December 09, 2007, 09:30:32 PM »

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« Reply #47 on: December 10, 2007, 12:50:32 AM »

relativity.....I never knew anything but the "crop factor" really.
Should I get a D3, I'll have to get used to my lenses giving me
an entirely new and perhaps unsettling FoV.
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« Reply #48 on: December 10, 2007, 01:27:25 AM »

Noct writes:
Quote
The magnification M of a subject at distance v with a focal length f is: M = f / (v-f)
So for another sensor format with relative cropfactor X (e.g. 1.5 for FX/DX),
the magnification of the subject has to change to M*X
(otherwise the subject will not have the same relative dimensions to the frame size);
M*X = f2 / (v - f2)
X = f2/f * (v-f) / (v-f2)
It can be easily seen that f2/f is not equal to X, except for large v.

When Noct wrote that "the magnification of the subject has to change to M*X,
shouldn't he also add that the distance has to change too ??

Magnification cannot change unless distance changes, right ?
(....still assuming we are in the World of Perfect Lenses which is probably co-located with B&H in Manhattan....)

So the equation becomes something like X = f2/f1 * (v1 - f1)/(v2 - f2).
As distance v1 grows larger, so does distance v2 and therefore in the large f1 = f2 X = f2/f1
....and therefore what ? Not sure if that is relevant or the limit exists.

For all practical purposes distances v1 and v2 are "large enough" with respect to focal length anyway.

I think I'm getting confused all over again.....
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« Reply #49 on: December 10, 2007, 08:14:52 AM »

It will always be easier to arrange a real-world experiment, instead of trying to untangle model parameters and their interelationship. To add to the  complexity, DOF as being modelled is a geometric concept and manifests itself as a distance measure. DOF thus becomes a one-dimensional non-linear function of  {CoC. focal length, aperture, [primary and secondary] magnification, [pupillary magnification]}, meaning that when a combination of the parameter values is plugged into the model, a single DOF value results.

My testing so far has lead me to believe that we need to add the constraint that "simple DOF" is only on-axis of the optical system. Thus, what we do observe is that the perceived (NOT modelled) DOF is 3-D and that field curvature (and spherical abberation) leads to DOF follows a curved shape in space. So there is no single-value DOF.

In the very first DOF comparison pictures I posted in this thread, the curvature of field is immediately obvious. One can, probably correctly, argue that the curvature results from strong spherical abberation of the lens. So not only did the field curve, sharpness off-axis deteriorated as well and makes the exact delination of DOF more difficult. When I conducted yesterday's experiment, I shot at a distance of 54 m with two well-corrected lenses (200/2 VR and AFS 300/2.8 ). I would normally not consider curvature of field to be an issue for either of the two at that distance, but nevertheless, what I could observe was a 3-D DOF distribution that made comparion with the DOF models difficult. Very obvious also was that DOF was asymmetrically distributed with almost no frontal DOF and many times more rear DOF than expected (the model says about 50/50 distribution around the target at that distance). What troubled me the msot was that both lenses showed a very similar behaviour. So obviously this is not exceptions to a rule. Could this result from the lens design being IF (internal focusing)? I have no idea.

To exacerbate the situation, the NikonGar gallery rejected the uploading of my test pictures, claiming the exceeded the maximum size set by site configuration, whilst they in fact were smaller. After having informed Dallas about the calamities, I decided to call it a day. M;y books and accounting need to cater for today's deadline of VAT return anyway.
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« Reply #50 on: December 10, 2007, 10:32:34 AM »

My testing so far has lead me to believe that we need to add the constraint that "simple DOF" is only on-axis of the optical system. Thus, what we do observe is that the perceived (NOT modelled) DOF is 3-D and that field curvature (and spherical abberation) leads to DOF follows a curved shape in space. So there is no single-value DOF.


I can imagine, but I think first to start with a fundamental "basic". Afterwards looking to the differences by lens characteristics.

When I conducted yesterday's experiment, I shot at a distance of 54 m with two well-corrected lenses (200/2 VR and AFS 300/2.8 ). I would normally not consider curvature of field to be an issue for either of the two at that distance, but nevertheless, what I could observe was a 3-D DOF distribution that made comparion with the DOF models difficult. Very obvious also was that DOF was asymmetrically distributed with almost no frontal DOF and many times more rear DOF than expected (the model says about 50/50 distribution around the target at that distance). What troubled me the most was that both lenses showed a very similar behaviour. So obviously this is not exceptions to a rule. Could this result from the lens design being IF (internal focusing)? I have no idea.


You didn't write which method you where using for focussing.
It can also be a difference from the autofocus by the system (not calibrated in perfect way), or manual focus on screen in view finder, and the plane of the sensor. A difference that you could "believe" there is a difference to distribution of the front and rear DOF than expected, could be the result of a wrong focus. To avoid differences between manual focus in view finder / autofocus / sensor plane, at least use the method to focus by LiveView and enlarge the image far out.

To test the course of DOF, maybe use a subject like metail nails raised up on a board with fixed distances, or printed text on flat glued plate, photographed oblique.

(As for controlling the result after practical test, the DOF calculator of Paul van Walree do include values for pupillary magnification --> if set within the options "Field of interest" as several other bonus interests can be chosen). http://www.vanwalree.com/optics/vwdof.html
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« Reply #51 on: December 10, 2007, 10:51:16 AM »

LiveView was used for critical focusing on both lenses. Maximum magnification.
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« Reply #52 on: December 10, 2007, 12:24:01 PM »

Very obvious also was that DOF was asymmetrically distributed with almost no frontal DOF and many times more rear DOF than expected (the model says about 50/50 distribution around the target at that distance).


Speaking of asymmetrical distribution, check this out: http://www.diglloyd.com/diglloyd/blog-images/2007/12/04/_DSC-092x.html
At f/2 the DOF is shallower in the middle of the frame, but there is virtually no difference to f/2.8 at the edges and corners! This is probably an effect of the aperture (or other shadowing things in the lens) getting "lens shaped" instead of circular - and thus smaller - with greater angle. More vignetting = greater DOF in the corners?
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« Reply #53 on: December 10, 2007, 12:57:31 PM »

Quite interesting.
Never thought about before, but if you know it is quite obviously.
Lens wide open, the shape of the opening at corners is more like two "half moons"
as result by looking (shading) to the "tube" of a lens inside.
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« Reply #54 on: December 10, 2007, 01:42:12 PM »

So, I finally managed to upload the test files to our server. Good job, Dallas.

Now, to the field experiment. I'm shooting a horse pen surrounded by an electric fence. My focus is on the birch trunk in the middle. Precise focus was achieved using LiveView on the D3, at maximum enlargement of the LCD. I double-checked by taking a picture and examining it again. After the critical focus was achieved, the focus collars were taped down, and focus rechecked once more to ensure nothing had moved.

I shot the 300/2.8 AFS on the D3, at f/2.8,  ISO 200, and the 200/2VR on D2X, also ISO 200, both cameras using mirror lock-up and a cable release. NEFs processed i Capture NX. No sharpening applied. After the initial evaluation of the images, I returned to the site and using a surveyor's rod, measured the relative psoition of key elements I had found on the shots. Although I aimed to shoot the fence at 45 degrees, closer examination showed it to run in a slight zig-zag manner so I felt it necessary to do actual field measurements.

Shooting distance was 54 m (zero point: the tree trunk).

First, the overviews

D3:



D2x:



Note: the control points are marked with relative distance to the zero point, + indicating a greater (rear) distance, - the corresponding frontal position.

One will appreciate that there is servere foreshortening of the apparent perspective at this distance.

I did not aim to achieve perfect colour match between these images, so they are slighlt different despite being shot with only a minute apart.


Now, to the details. The positions refer to the poles of the fence unless otherwise noted. D2X/200 to the left and D3/300 to the right on all A/B comparisons.

This is the comparison at the +7.5 m point, 100% crop no sharpening.

It can be seen that both systems are quite similar, with the D2X being ever so slightly softer. The background blur is different too, one should expect the D2X /200 to provide the smaller blur, but the opposite is seen. Note that DOF concerns what's in focus, not what's out of focus. But the different blur sizes do indicate which lens will increase DOF the most by stopping further down.

After having poured over the 100% crops for a while, I'd say this point is close to the rear DOF extension. Possibly one could add 0.5 m to it, but no much more.




Moving closer to the reference point, here is the +3.6m comparison. Again 100% crop and no sharpening.



Obviously, both systems are well within the zone of high sharpness here.


Now, here is the -1.2m comparison. It includes the birch tree that was the zero point (in the background) and it is apparent the focus there is positioned correctly. Both DX and FX shows a severe loss of sharpness and the pole at -1.2 no longer is in critical sharpness. Details of grass at the ground level confirms that we now have reached the front of the DOF.




The final point is -4.2m in front of the birch tree. Here, we very evidently are way outside the DOF region.



Running across in a slanted direction in the background  is the transition zone between sharp and unsharp. The transition is much better defined here in the front than we saw for the rear section. This can be seen to be ever so slightly more forward in the FX shot.

**************** so much for the actual field data **************

The test shots show that DOF is very, but not quite, similar between DX/200 @ f/2 and FX:300 at f/2.8. The difference there is may be more of an academic value. So if we adjust the hypothesis of "one stop advantage" to read "more than 0, but less than 1 stop advantage", that should cover the observed facts. The demarkation lines between sharp/unsharp are not  prominent enough when the distance is this great to allow us to assign an accurate DOF estimate. So the best guess would be around  9 m in the setup I used.  Scrutiny of the originals show also that there is curvature in the DOF intersection with the ground, thus one can see that the details of the grass becomes blurred at the same distance from the camera that the poles are well defined (the poles were better aligned to the optical axis).

We can, however, say that DOF is very asymmetrical in its distribution, in this case, at most 1.5 m in front and at least 7.5 m to the rear. 

So, how does this compare to the DOF models? This is where the CoC criteria enter the fray. I've run several DOF calculators and they all agree of a value around 5.5 m, a little more for the DX format (contrary to observation). We observe nearly twice that value. What is more striking is that the models all insist on DOF being quite distributed quite symmetric around the target, which very obviously is not the conclusion one draws on the basis of these test shots. I've tried to use the full set of parameters including pupillary magnification, but the model estimates are pretty much the same. So at least this discrepancy illustrates that the modelled DOF (based upon geometry) need not have a direct counterpart in the perceived DOF.

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« Reply #55 on: December 10, 2007, 03:21:11 PM »

Very interesting! One thing that I think should be considered is the characteristics of the bokeh for the given lenses. Even at the exact same CoC, DOF can appear to be different in depth. If the CoC has an even distribution of luminosity, DOF will appear shorter than if CoC is a bit "gaussic". Here's a little simulator that shows the phenomenon: http://www.flarg.com/bokeh.html Click the different distribution functions under the pic.
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« Reply #56 on: December 10, 2007, 03:40:58 PM »

DOF is only meaningful for the in-focus section of the image, bokeh applies to the out-of-focus rendition. So influences of bokeh cannot possibly be encompassed by the DOF concept.
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« Reply #57 on: December 10, 2007, 04:02:42 PM »

DOF is only meaningful for the in-focus section of the image, bokeh applies to the out-of-focus rendition. So influences of bokeh cannot possibly be encompassed by the DOF concept.

And exactly where does the border of DOF go? I thought this whole test was to examine the differences in "size of out-of-focus blur" between the sensor sizes? The CoC is only infinitely small in the absolute plane of focus (which is infinitely shallow), so I'd say bokeh does affect perceived DOF.

Edit: Of course the CoC is never infinitely small in a real lens though. Roll Eyes
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« Reply #58 on: December 10, 2007, 04:12:06 PM »

Read more of the DOF theories using the links provided by Leon earlier. The topic of diofferentation DOF vs OOF is covered amply there.
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« Reply #59 on: December 10, 2007, 04:23:00 PM »

Read more of the DOF theories using the links provided by Leon earlier. The topic of diofferentation DOF vs OOF is covered amply there.

I already have.

"Depth of field is defined as the range of object distances within which objects are imaged with acceptable sharpness."

...says it all. I cannot see how the distribution of luminosity of the CoC could not change perceived DOF.
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