# Luminous Landscape Forum

## Equipment & Techniques => Cameras, Lenses and Shooting gear => Topic started by: 01af on March 05, 2008, 12:56:42 pm

Title: Circle of confusion
Post by: 01af on March 05, 2008, 12:56:42 pm
Circle of Confusion n (abbr.: COC) A group of photographers desperately trying to understand --> DOF.

This article is intended as a continuation of a thread (http://luminous-landscape.com/forum/index.php?showtopic=23361) in the Beginner's Questions (http://luminous-landscape.com/forum/index.php?showforum=41) subforum which asked about field of view and magnification but quickly was carried away with questions about DOF and COC. Warning: This article contains a lot of math. If you don't like formulas then please read on elsewhere.

My contentious hypothesis is this: When taking an image from the same point of view with different format cameras, using equivalent focal lengths (i. e. same angle of view) and equivalent apertures (i. e. same depth-of-field) then the images still won't be identical. Instead, the transition from perceived sharpness within DOF range to blur outside DOF range will be different---that is, smoother for the larger-format image. At close distance, this effect will be more pronounced that at or near infinity.

To discuss this hypothesis, I'd like to introduce a few formula symbols:

f = focal length
g = subject-to-lens distance
b = lens-to-image distance
d = focus distance
k = aperture number
z = diameter of the circle of confusion
q = quotient of the linear sizes of two frame formats

The simple thin-lens equation thus becomes:

[1] 1/f = 1/g + 1/b

The focus distance is the distance from subject to image:

[2] d = g + b

Please note that [2] ignores the fact that real lenses are not "thin"; it assumes the nodal planes' distance to be zero.

Now we need two functions g = G(f, d) and b = B(f, d) which calculate g and b from f and d so that f, d, g, and b will meet both [1] and [2].

[3] g = G(f, d) = d/2 + sqrt(d*d/4 - d*f)
[4] b = B(f, d) = d/2 - sqrt(d*d/4 - d*f)

As you can see, for d > 4*f, these are the two real solutions to a quadratic equation. They hold for magnifications below 1:1; for larger magnifications, simply swap b and g. Please note that lenses cannot create images at focus distances shorter than 4*f.

In the thread mentioned above, some contributors have digged out a formula from the Internet which calculates the diameter z of the circle of confusion of an object at a distance d for a lens with focal length f, focused to the distance d[span style=\'font-size:8pt;line-height:100%\']o[/span]:

[5] z = (f * f * |d - d[span style=\'font-size:8pt;line-height:100%\']o[/span]|) / (k * d * (d[span style=\'font-size:8pt;line-height:100%\']o[/span] - f))

Common wisdom suggests that if one frame format is larger than another by a linear factor q then you'd get the larger format's equivalent focal length by multiplying the smaller format's focal length by q:

[6] f[span style=\'font-size:8pt;line-height:100%\']_lf[/span] = q * f[span style=\'font-size:8pt;line-height:100%\']_sf[/span]

(Here, "_sf" is supposed to mean small format; "_lf" means large format.) Common wisdom also suggests the same method to calculate equivalent aperture numbers:

[7] k[span style=\'font-size:8pt;line-height:100%\']_lf[/span] = q * k[span style=\'font-size:8pt;line-height:100%\']_sf[/span]

However [5] suggests a slightly different formula for calculating equivalent aperture numbers. Obviously, [7] only holds for focus distances near infinity; at shorter distances it will become increasingly inaccurate. So the modified formula for equivalent aperture numbers, depending on focus distance d, becomes:

[8] k[span style=\'font-size:8pt;line-height:100%\']_lf[/span] = q * [(d - f[span style=\'font-size:8pt;line-height:100%\']_sf[/span]) / (d - f[span style=\'font-size:8pt;line-height:100%\']_lf[/span])] * k[span style=\'font-size:8pt;line-height:100%\']_sf[/span]

For d approaching infinity, the factor in brackets [] will approach 1, and thus [8] will approach [7].

Using [6] to calculate equivalent focal lengths, and [8] to calculate equivalent aperture numbers, [5] suggests that the COC curves of all frame formats will match exactly across all possible object distances d, thus rendering exactly the same image. Some contributors in the above-mentioned thread used this as an argument against my hypothesis stated above.

However [5] is not accurate; it holds for long focus distances only. At shorter focus distances it will become increasingly inaccurate. It ignores the fact that at shorter focus distances, the lens-to-image distance is not equal to the focal length anymore. By the way, the same flaw affects [6] because angle of view is not determined by focal length f but by lens-to-image distance b! In other words, the equivalent focal length depends on focus distance; the well-known rule to multiply with the form factor holds at infinite focus distance only.

So we need a new, improved formula to calculate the larger format's focal length f[span style=\'font-size:8pt;line-height:100%\']_lf[/span] equivalent to the smaller format's focal length f[span style=\'font-size:8pt;line-height:100%\']_sf[/span] for the form factor q at focus distance d. Using [4], we get:

[9] f[span style=\'font-size:8pt;line-height:100%\']_lf[/span] = q*q * f[span style=\'font-size:8pt;line-height:100%\']_sf[/span] - (q*q - q) * B(f[span style=\'font-size:8pt;line-height:100%\']_sf[/span], d)

Compare this to [6] and note how complicated things are getting when taking the effects of shorter focus distances into account properly! Further note that [9] will be acurate only if you know your lens' actual focal length at focusing distance d---for lenses employing internal, front-part, or rear-part focusing, this cannot be taken for granted.

Finally, to improve upon [5], I developed the following formula, to calculate the diameter of the circle of confusion z for an object at distance d for a lens with focal length f, focused to d[span style=\'font-size:8pt;line-height:100%\']o[/span] (for B, refer to [4]):

[10] z = (f / k) * |1 - (B(f, d[span style=\'font-size:8pt;line-height:100%\']o[/span]) / B(f, d))|

When using [10] rather than [5], and when using [9] to calculate equivalent focal lengths, then we'll find that for different frame formats the run of the COC curve across all possible object distances d will be different, and more different at shorter focus distances d[span style=\'font-size:8pt;line-height:100%\']o[/span]. Surprisingly, the growth of the COC diameter outside the DOF range is slower for the larger format! While this seems counter-intuitve, it does make sense because a COC growing at a slower rate in the blurred area beyond DOF will make for a smoother transition from perceived sharpness to blur---just as my hypothesis suggests. To evaluate [5] and [10], I used this function plotter (http://www.mathe-fa.de/en).

So [10] provides strong evidence that my hypothesis actually is true.

-- Olaf

P.S. Unfortunately, I have not found an exact formula to calculate equivalent aperture numbers. While [8] is better than [6], it still is based on the over-simplified formula [5] and thus not really accurate. To find equivalent aperture numbers, so far I resorted to trial-and-error, trying various values until DOF matches, using the function plotter.
Title: Circle of confusion
Post by: Ray on March 06, 2008, 10:42:30 pm
Quote
My contentious hypothesis is this: When taking an image from the same point of view with different format cameras, using equivalent focal lengths (i. e. same angle of view) and equivalent apertures (i. e. same depth-of-field) then the images still won't be identical. Instead, the transition from perceived sharpness within DOF range to blur outside DOF range will be different---that is, smoother for the larger-format image. At close distance, this effect will be more pronounced that at or near infinity.

With all due respect, O1af, we're into a situation here that is very analogous to that apocryphal story of the group of philosophers in ancient Greece who sat around all night arguing about the number of teeth a horse has. Each philosopher made reference to different authoritative sources, which he claimed was more credible and/or carried more weight than other sources of opinion on this matter to which his colleagues referred.

Eventually one member of the group, as dawn was breaking, suggested that everyone walk over to the nearst farmer's field where a horse was grazing and count the teeth. That member of the group was me in a previous incarnation. I was there. (Just kidding   ).

Now your authoritative sources are mathematical formulae. How accurate and reliable such formulas are is anyone's guess. I'm no mathematician but I believe that the mathematical calculations used in the design of many modern products are so complex that, without the aid of a computer, such calculations would be impractical. They would take the lifetime of one or several mathematicians.

In the previous thread where this discussion started, it was suggested that one could test this DoF issue using the same camera as both large format and small format by cropping the larger image to the same dimensions as the smaller format, then downsampling the large format image to the same file size as the cropped image.

Such methodolgy would be seriously flawed with respect to all subtle DoF changes. That which is OoF to a barely perceptible degree in the full resolution large image, would appear as completely in focus in the downsampled version. That which is clearly OoF in the full rez large format image would appear as OoF to a barely perceptible degree in the downsampled image, and so on. Similar results would apply if the cropped image were uprezzed to the same size as the uncropped image.

A fundamental condition for the claim that there can be an exact replication of DoF characteristics amongst different formats, is that system resolution must be the same. System resolution is mostly dependent upon sensor pixel count and lens quality. It would be interesting to cary out some tests comparing the Canon G9 with the 'yet to be released' 450D with the current 5D. They are all around the 12mp mark so it's just a matter of choosing the appropriate lenses which will deliver equal system resolution at the appropriate  f stop. Off the top of my head, F2.8 on the G9 should be equivalent to F8 on the 450D which should be equivalent to F13 on the 5D.

Before carrying out such a comparison, the system resolution of each camera should be checked at those equivalent f stops. If the G9 proves to be sharper at F2.8 than the 5D at F13, then one has to try F3.2 or F3.5 on the G9 with F16 on the 5D, whatever. Learning from my own mistakes, I would say, if you get this right from the beginning (ie. equal system resolution) and you ensure that focussing is spot on (another problem) then we can have some credible results on this issue.

Oops! I didn't mean to leave out our MF contributors. We should include the Phase P21. So it's G9 at f2.8, 450D at f8, 5D at f13 and P21 at f22. Focals lengths of whatever gives the exact FoV. Nope! Sorry! We'll have to exclude the P21. It has a higher system resolution so the 'look' is bound to be different.
Title: Circle of confusion
Post by: jani on March 07, 2008, 05:22:48 am
Quote
Oops! I didn't mean to leave out our MF contributors. We should include the Phase P21. So it's G9 at f2.8, 450D at f8, 5D at f13 and P21 at f22. Focals lengths of whatever gives the exact FoV. Nope! Sorry! We'll have to exclude the P21. It has a higher system resolution so the 'look' is bound to be different.
The H10, then. It has a slightly lower number of pixels; 10.6 Mpx.

Apart from that, I'm just stunned at the volume of text in this thread, and refuse to read it until I've had a chance to do something fun and entertaining instead.
Title: Circle of confusion
Post by: Paul Kay on March 07, 2008, 06:40:46 am
Throw in different lenses with different design requirements, different treatment of aberrations, etc., etc., as well interactions between the image formed and the sensors and you have a far more complex situation which would require far more maths.

We live in a real world (difficult to believe sometimes I know) so I just go out and takes some pictures to see what I like equipment/lenswise when I get the chance (my local camera shop is very helpful!). Whilst there may be photographers (working in scientific areas perhaps) who have genuine technical reasons for determining such differences they will be few and far between and are probably able to test any equipment which fulfills their other, almost certainly narrow, parameters.
Title: Circle of confusion
Post by: Rob C on March 07, 2008, 06:57:59 am
Quote
The H10, then. It has a slightly lower number of pixels; 10.6 Mpx.

Apart from that, I'm just stunned at the volume of text in this thread, and refuse to read it until I've had a chance to do something fun and entertaining instead.
[a href=\"index.php?act=findpost&pid=179747\"][{POST_SNAPBACK}][/a]

Jani

You don´t of course, have to read the thread. However, I do take your point and find that it touches very closely on my own views about the new photography.

I have sometimes mentioned that, had photography back in the late 50s/early 60s been as it is today, I might well never have thought of taking it up as a way of life, of earning the daily bread through it, etc.

My feelings are that the old film days were relatively simple and intuitive; that all one really needed was some reasonable equipment and premises and that was it; success depended on your talent and business acumen or lack of it. Today´s photography comes in at much higher levels of investment and I wonder where aspiring young snappers find the dough to get into the game. But that´s only a financial consideration. More disturbing, for me, is the huge shift from the artistic side of it to the technical. I spend much time at the computer these days, and I suppose I can make PS give me most of what I seek from it, but whilst admitting that I can exercise much more local control within precise areas of a print, I cannot escape the suspicion that the fine-tuning is killing the spirit of the thing. It becomes very difficult to call a halt to yet another layer of tweaking, something which might not really do anything for the image but only for the technician´s ego. I do because I can.

This current thread exemplifies the problem: there is this hugely disproportionate attention to optical theory which, in the old days, occupied the minds of a few clubistas and never the day-to-day work of the pro. If you used 35mm you bought the best you could afford, ditto within 120 and then upwards if your work required it. You used what was provided by the makers and mostly it worked very well. Nowadays, it seems it doesn´t work so very well at all. From camera faults at delivery to lenses that fall apart or just don´t work, it seems no price level is a guarantee.

Why are we here? It might well be nothing more than the fact that digital is new, within the history of the business, and that there is no time for the science to expand within the time-frame allowed film to get it right; it might be that the introduction of digital has been far stronger in its effects on the camera industry than those who introduced it ever imagined it would be. In other words, today we expect and NEED digital to be as immediately developed as was film technology but over a period of many years.

So much for the hardware. The other side of the thing is that today´s photographer is expected to be able to do what was once done by specialists in process houses after lengthy apprenticeships. It doesn´t ring real. Many are left floundering or having to employ specialist staff who know more about that side of life than the photographer does, business not always increasing enough to justify the new overheads. Quite apart, of course, from the point that those new duties might never actually appeal to the person who does love doing the photography.

Flux. Not a happy state in which to exist.

Or, to return to your post, Jani, perhaps this site is really not a lot more than a gigantic camera club and such discussions are to be expected, just as they would have been in amateur circles as described earlier.

Ciao - Rob C
Title: Circle of confusion
Post by: 01af on March 07, 2008, 11:26:05 am
Quote
... we're into a situation here that is very analogous to that apocryphal story of the group of philosophers in ancient Greece who sat around all night arguing about the number of teeth a horse has.[a href=\"index.php?act=findpost&pid=179704\"][{POST_SNAPBACK}][/a]
No, it's not. Sure we could walk over to that horse and simply take a look into its mouth. But the better part of your own post then explains why looking into the mouth won't be too helpful. It is so difficult to find the truly equivalent focal lengths and apertures, to get the focus precisely right, and to tell frame-size-induced effects from other effects that may come just from using different pieces of equipment. So if two (or more) test shot revealed differences, we still wouldn't know what to accredit them to.

That's the reason why I sat down and developed my formula. The original over-simplified COC formula ([5] in my post above) suggests there were no frame-size-induced effects. I wanted to know if that really is the case or just a bogus consequence of the simplification. Now my improved COC formula [10] proves that frame-size-induced effects do exist. That was my point. It does not say anything about how significant those effects tend to be in real life.

Of course, everybody is entitled to consider this problem as significant to real-world photography as counting the angels on a pin's head. Basically, I do. I don't carry tables of those formulas with me in my bag when I'm out. It just was fun juggling with the thin-lens equation and the theorem of intersecting lines, and to find out how far this would carry.

The most interesting corollary that turned up was the formula for equivalent focal lengths [9]---I never was aware this was so dependent on focus distance! So I learned something interesting (albeit only slightly useful for everyday shooting), and it was fun. I thought the one or the other of you might find it interesting, too. Don't take it too seriously. And Rob, don't think it had anything to do with digital or modern times---it hasn't.

-- Olaf
Title: Circle of confusion
Post by: marcmccalmont on March 07, 2008, 03:16:19 pm
I just finished a flight with a new pilot that was a bit confused with equal time points and points of no return. With 20 years of flying he had not been exposed to long haul over water flights. I started the discussion by deriving a simple formula " if I have a 100 mile trip and I'm traveling at a rate of 50mph our trip will take 100/50 hrs". If we want the midpoint (Equal Time Point) take the distance and divide it with the rate plus the rate (100/ 50+50). That's all it took, deriving a formula simply and everything made sense. I feel that sometimes a simple formula does help understanding a concept.
Marc
Title: Circle of confusion
Post by: Ray on March 07, 2008, 09:18:03 pm
Quote
No, it's not. Sure we could walk over to that horse and simply take a look into its mouth. But the better part of your own post then explains why looking into the mouth won't be too helpful. It is so difficult to find the truly equivalent focal lengths and apertures, to get the focus precisely right, and to tell frame-size-induced effects from other effects that may come just from using different pieces of equipment. So if two (or more) test shot revealed differences, we still wouldn't know what to accredit them to.

Olaf,
Well, of course I disagree   . One set of practical tests is not likely to be conclusive. The matter is more complicated than counting horses' teeth. There are other variables which may affect the results to a noticeable degree.

In such circumstances it is necessary to do a number of tests using different lenses at various f stops and various focussing distances in order to see if a trend emerges. But the one crucial factor that is necessary to get right in all tests in order for them to be valid, is absolutely accurate focussing on the same spot with all formats being compared. This in my view is the major methodology challenge that has to be overcome when attempting such tests.

Furthermore, the reason why focussing becomes such a challenge in these circumstances is because we are not trying to get a good (or extensive) DoF as landscape shooters often aim for, but a relatively shallow DoF.

I'm amazed that my miscalibrated 17-55/2.8 lens still shows the misfocussing when autofocussed at a point several hundred metres away (at 50mm FL), basically at or close to infinity. But the misfocussing is only apparent at f2.8 and to a lesser extent at f4. By f5.6 there is virtually no observable difference between the autofocussed and manually focussed shots.

Without LiveView and the 10x magnification of the image that's possible on the LCD screen, I would not be able to detect such differences without engaging in a lot of tedious manual focus bracketing then selecting the sharpest image on the monitor.

Whenever I compare my lenses for sharpness and resolution, I always include a line chart in the test target, not so I can see the number of lines resolved (which seems to vary very little in any case) but because I can be sure I'm focussed properly as a result of the clarity of aberrations.

All lenses suffer from some degree of chromatic aberration at full aperture, which is the aperture used when focussing. These imperfections in the lens are the clue to accurate focussing. When you see a blaze of chromatic aberration on the line chart, where the lines are sufficiently close-spaced, you know that focussing is spot on.

Without the aid of LiveView on all formats, I feel it would be necessary to place a line chart (downloaded from Norman Koren's site for example) somewhere in the scene at an appropriate distance as a focus point. The size of the chart and the spacing of the lines would have to be right for this blazing swirl of chromatic aberration to appear.

I sometimes wish I could capture such colorful aberrations, but they are either beyond the resolving power of the sensor or blocked by the AA filter.

Quote
That's the reason why I sat down and developed my formula. The original over-simplified COC formula ([5] in my post above) suggests there were no frame-size-induced effects. I wanted to know if that really is the case or just a bogus consequence of the simplification. Now my improved COC formula [10] proves that frame-size-induced effects do exist. That was my point. It does not say anything about how significant those effects tend to be in real life.

This might be an interesting exercise for you or anyone interested in the maths and physics of optics, but the rest of us, including myself, wouldn't have a clue as to how approximate such formulas are in the context of the myriad of complex calculations that are used in the design of any good lens.

Quote
Of course, everybody is entitled to consider this problem as significant to real-world photography as counting the angles on a pin's head. Basically, I do. I don't carry tables of those formulas with me in my bag when I'm out. It just was fun juggling with the thin-lens equation and the theorem of intersecting lines, and to find out how far this would carry.

The most interesting corollary that turned up was the formula for equivalent focal lengths [9]---I never was aware this was so dependent on focus distance! So I learned something interesting (albeit only slightly useful for everyday shooting), and it was fun. I thought the one or the other of you might find it interesting, too. Don't take it too seriously. And Rob, don't think it had anything to do with digital or modern times---it hasn't.

If it's fun and you learn something, that's all that counts. However, sometimes one just has to do the experimental, practical stuff in order to find out how relevant such differences (as implied in some mathematical formulae) really are.
Title: Circle of confusion
Post by: Morgan_Moore on March 07, 2008, 11:47:59 pm
If anyone is still reading a couple of notes..

I tried doing a TEST (http://81.5.138.214/smmcom/format_test/index.html)

That some may find interesting

This subject IMO is worth understanding.

I have been of the opinion that APS sensor cameras create rubbish looking images (for my purposes) - basically they have an inability to isolate the subject from the background

Over time I have a member of the 'sensor size is all' school of thought (for portraits) leading me to purchase an Hassy H and 22mp Digiback

Well at the time (four years ago)  that was one of the only digicams that could provide a decent DPS magazine resolution and enabled me to coax some clients from tranny to dig and won me some clients

Nowadays with 22mp available from DSLRs the onlly real difference between the systems is 'the look'

But testing the D3 against the H1 the look seems, considering the wider apertures avaialble on the DSLR, fairly minimally different

However there are tests I intend to perform that may show differences at smaller apertures

Anyway - to photographers considering what system to buy into and understanding of DOF, look or whatever is important because the price of systems is so radically different ie one pays big bucks for big sensors

So I would argue that knowing what one is buying is important..

SMM
Title: Circle of confusion
Post by: Ray on March 08, 2008, 05:25:36 am
Quote
I have been of the opinion that APS sensor cameras create rubbish looking images (for my purposes) - basically they have an inability to isolate the subject from the background
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That's not surprising, Morgan. Comparing an APS dslr with a DB is like comparing 35mm film with 6x9cm format. With Nikon the multiplier is about 2.28 but with Canon it's about 2.4.

Just out of curiosity, I checked the Photodo MTF charts of a few lenses to see how a good MF lens compares with a good 35mm lens at the corresponding f stop and focal length after applying the multiplier.

The resolution/sharpness differences are not by any means subtle. 35mm lenses simply cannot compete. The following charts tell the story. I compared the Mamiya 150 N F4.5 with the Canon 50 F1.8 and Canon 85 F1.8.

Using the Mamiya at full aperture should be equivalent to using a Canon 60mm lens at F1.8 from the same position. There is no Canon 60mm lens available with an aperture that wide. The closest is the 50/1.8.

The 3 pairs of red lines on the charts, from top to bottom, represent contrast at 10, 20 and 40 lp/mm. Not only are both the Canon 50/1.8 and 85/1.5 significantly worse than the Mamiya at full aperture, they actually need to be significantly better. There's a huge gulf in lens performance here.

I blocked out the far right of the charts so the distances from the centre to the corners correspond with the sensor sizes we are talking about.

[attachment=5498:attachment]
Title: Circle of confusion
Post by: Morgan_Moore on March 08, 2008, 06:36:17 am
Of course there are other reasons why larger format cameras have advantages

For example dust on the sensor tends to occupy a smaller percentage of the image

the physical ability to access sensors on MFDBs means thier sensors can be easily cleaned

The lenses have less LPI and still resolve higher

Some MF cameras have decent flash synch speeds and low ISO if you want it

etc

Of course dslrs win on weight cost, high ISO, AF performance, IS etc

These factors would however appear IMO to be off topic

SMM
Title: Circle of confusion
Post by: Ray on March 08, 2008, 08:57:37 am
Quote
The lenses have less LPI and still resolve higher
[a href=\"index.php?act=findpost&pid=179977\"][{POST_SNAPBACK}][/a]

I don't believe this is the case at apertures where resolution is mainly limited by diffraction. An MF lens at F22 will inevitably deliver less lp/mm to the DB sensor than a 35mm lens at F14 for FF 35mm and F9 for the Canon cropped format.
However, at these f stops, if the different formats have the same pixel count, resolution and DoF characteristics should be very similar.

The differences are likely to be more obvious at wider equivalent apertures of F5.6, F3.5 and F2.2, or F4.5, F3.2 and F1.8, or F2.8, F1.8 and F1 etc. At such apertures the MF lens is likely to be higher resolving, as shown in the MTF charts in my previous post. Some of these new Digitar and Rodenstock lenses designed for the cropped MF format of the DB seem to be higher resolving than most 35mm lenses, according to the charts that I've seen.
Title: Circle of confusion
Post by: Morgan_Moore on March 08, 2008, 10:38:51 am
Quote
I don't believe this is the case at apertures where resolution is mainly limited by diffraction. An MF lens at F22 will inevitably deliver less lp/mm to the DB sensor than a 35mm lens at F14 for FF 35mm and F9 for the Canon cropped format.
However, at these f stops, if the different formats have the same pixel count, resolution and DoF characteristics should be very similar.

The differences are likely to be more obvious at wider equivalent apertures of F5.6, F3.5 and F2.2, or F4.5, F3.2 and F1.8, or F2.8, F1.8 and F1 etc. At such apertures the MF lens is likely to be higher resolving, as shown in the MTF charts in my previous post. Some of these new Digitar and Rodenstock lenses designed for the cropped MF format of the DB seem to be higher resolving than most 35mm lenses, according to the charts that I've seen.
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I mean that less LPI are required for a larger chip to have an equal or greater resoution than a smaler chip

diffraction can of course become an issue when trying to acheive DOF with a large sesnor

S
Title: Circle of confusion
Post by: Ray on March 08, 2008, 06:42:44 pm
Quote
I mean that less LPI are required for a larger chip to have an equal or greater resoution than a smaler chip

diffraction can of course become an issue when trying to acheive DOF with a large sesnor

S
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Yes, that's true both in theory and presumably in practice. It is possible to get better results on a higher resolving, bigger format DB using an old-fashioned MF lens which by 35mm standards may be very average.

The interesting thing about diffraction effects is that they seem to be roughly proportional to format size when using equivalent f stops that are in the diffraction limited zone. Therefore, providing the formats being compared have equal pixel count, the only DoF disadvantage for the larger format is in the range of aperture settings available on the lens.

Comparing a P21 with an 1Ds3 cropped to the 4:3 aspect ratio (which results in a pretty close pixel count match), F32 with the P21 should produce the same DoF as F22 with the 1Ds3. Both images will be a bit soft at such apertures. If too soft, then compare F22 with the P21 and F16 with the 1Ds3.

The difference in resolving power of lenses at diffraction limited apertures is about 1.4x per stop. Ie. a lens at f22 has 1.4x greater resolving power than the same lens at F32 and the 35mm format needs almost exactly that same degree of extra resolving power, so providing the sensors of both formats have equal pixel count, everything balances out.

The quality differences between these two formats should begin to emerge at apertures wider than F11. Lens resolution simply isn't 1.4x greater at f5.6 than it is at F8, nor 1.4x greater at F4 than at F5.6, unless one is comparing high quality lenses with very low quality lenses.

Perhaps this is something you'd like to test in practice   .

Basically, I'm saying that the DoF disadvantage of the larger format is a myth. The disadvantage is purely one of shutter speed and high-ISO image quality. When comparing an Oly 4/3rds system with a Canon DSLR, the DSLR might appear to have a shutter speed disadvantage for an equivalent DoF, but fortunately Canon DSLRs have lower noise and produce sharper images at high ISOs so one can always raise ISO to get the same shutter speed without seriously compromising image quality.

Apparently, this is not an option on the DB where high ISO settings produce results that are no better (perhaps worse) than underexposure at base ISO.
Title: Circle of confusion
Post by: schrodingerscat on March 08, 2008, 10:14:35 pm
Hopefully this is relevant and not too obvious.

Long ago I ran across an article that explained DOF/focal length in relation to magnification. The example they used was a wide angle lens and telephoto both at the same f stop. They cropped a frame from the wide angle to the same area of view as the telephoto, and they both had the same DOF. One of those ah-Ha! moments.

Since this seems to be a rather learned bunch(numbers make my eyes roll into the back of my head after about 30 seconds), I'm hoping for some insight into something I've been pondering.

dSLR lenses use the FF counterpart values for focal length and aperture. It's up to the user to use the crop factor to convert the focal length to the appropriate value for his camera. Does the crop factor also influence the aperture value as well, and the DOF with it, as the size of the lens opening(f stop) would also change in relation to the size of the sensor?

In regards to DOF, is f8 still f8 on a Rebel, 40D, 1D, and 1Ds? I can see where this would be moot in regards to exposure, but since sensor size influences focal length, and thereby magnification, would it also factor into aperture size and DOF as well?

With film, you pretty much purchased the lens for the camera, which determined the format, and not many people tried to hybridize. Now you can buy a lens and possibly install it on one of four formats.

My main concern for this is working with hyperfocal distance.

Thanks for your indulgence.
Title: Circle of confusion
Post by: Ray on March 09, 2008, 01:13:02 am
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Does the crop factor also influence the aperture value as well, and the DOF with it, as the size of the lens opening(f stop) would also change in relation to the size of the sensor?
[a href=\"index.php?act=findpost&pid=180124\"][{POST_SNAPBACK}][/a]

We have to distinguish here between aperture value in terms of f stop description and aperture value in terms of physical diameter.

For the same FoV, shooting from the same position, both the focal length and the f stop number should be increased in proportion to the increase in the diagonal of the sensor (or in proportion to either side if we're comparing sensors of the same aspect ratio).

This is to ensure that the physical diameter of the aperture in both cases remains unchanged so that the CoCs on both sensors remain the same relative to the sensor size, which is a necessary condition for DoF to remain the same.

With the longer focal length, with the larger format, the CoCs will be magnified to a greater degree, but will remain the same as a proportion of sensor size.

The physical diameter of the lens aperture is given by the basic formula FL/F Stop.

A 50mm lens on a 40D at F5.6 is equivalent to an 80mm lens on a 5D at approximately F9, with respect to FoV and DoF.

The physical aperture diameter in both cases is 50/5.6 = 8.9mm for the 40D and 80/9 = 8.89mm for the 5D.
Title: Circle of confusion
Post by: Morgan_Moore on March 09, 2008, 01:25:52 am
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Hopefully this is relevant and not too obvious.

Long ago I ran across an article that explained DOF/focal length in relation to magnification. The example they used was a wide angle lens and telephoto both at the same f stop. They cropped a frame from the wide angle to the same area of view as the telephoto, and they both had the same DOF. One of those ah-Ha! moments.

Since this seems to be a rather learned bunch(numbers make my eyes roll into the back of my head after about 30 seconds), I'm hoping for some insight into something I've been pondering.

dSLR lenses use the FF counterpart values for focal length and aperture. It's up to the user to use the crop factor to convert the focal length to the appropriate value for his camera. Does the crop factor also influence the aperture value as well, and the DOF with it, as the size of the lens opening(f stop) would also change in relation to the size of the sensor?

In regards to DOF, is f8 still f8 on a Rebel, 40D, 1D, and 1Ds? I can see where this would be moot in regards to exposure, but since sensor size influences focal length, and thereby magnification, would it also factor into aperture size and DOF as well?

With film, you pretty much purchased the lens for the camera, which determined the format, and not many people tried to hybridize. Now you can buy a lens and possibly install it on one of four formats.

My main concern for this is working with hyperfocal distance.

Thanks for your indulgence.
[a href=\"index.php?act=findpost&pid=180124\"][{POST_SNAPBACK}][/a]

Think about this and it may answer your question..

If you shoot a pic on a FF camera with a certain lens and aperture and crop that image in PS down to 'crop sensor' size the DOF doesnt magically change - you just get less of the image

-------------------

To Ray - you have lost me now - I hope this board is here to make information open accessable and worth thinking about by photographers looking to learn- not apparent from this thread

Anyway it is my opinion that getting big DOF is easy with small cameras - too easy for portratiure and very helpful for interior shots
Title: Circle of confusion
Post by: Ray on March 09, 2008, 04:40:04 am
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To Ray - you have lost me now - I hope this board is here to make information open accessable and worth thinking about by photographers looking to learn- not apparent from this thread
[a href=\"index.php?act=findpost&pid=180163\"][{POST_SNAPBACK}][/a]

Morgan,
Since you are a user of larger format cameras, I thought the DoF/diffraction issue would be intuitive.

Wasn't it Ansel Adams who set the trend for using F64 with large format, 8x10" field cameras? Some large format lenses stop down to F128. There's no DoF disadvantage with large format provided the lens has the larger F stop settings. But there is the restriction of having to use slow shutter speeds and therefore stationary subjects. The fact that resolution falls off as one stops down applies to all formats. Just as F32 is a bit soft with DBs, F22 is a bit soft with FF 35mm and F14 is a bit soft with the cropped format 35mm. F8 is also very soft on P&S cameras.

However, if you use the lens at its sharpest aperture, I think there is an obvious trend for the larger format camera to deliver a shallower DoF at that optimum aperture, as well as a higher resolution image.
Title: Circle of confusion
Post by: Morgan_Moore on March 09, 2008, 05:34:17 am
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Morgan,
Since you are a user of larger format cameras, I thought the DoF/diffraction issue would be intuitive.

Wasn't it Ansel Adams who set the trend for using F64 with large format, 8x10" field cameras? Some large format lenses stop down to F128. There's no DoF disadvantage with large format provided the lens has the larger F stop settings. But there is the restriction of having to use slow shutter speeds and therefore stationary subjects. The fact that resolution falls off as one stops down applies to all formats. Just as F32 is a bit soft with DBs, F22 is a bit soft with FF 35mm and F14 is a bit soft with the cropped format 35mm. F8 is also very soft on P&S cameras.

However, if you use the lens at its sharpest aperture, I think there is an obvious trend for the larger format camera to deliver a shallower DoF at that optimum aperture, as well as a higher resolution image.
[a href=\"index.php?act=findpost&pid=180171\"][{POST_SNAPBACK}][/a]

We agree

BUT with a real world 50ISO back you can need a lot of shutter time and/or some very bright flashguns to get F22

Ovbviously if the subject is large or moving this can create real world difficulties

I can shoot an interior (quick and dirty but pretty well) with a SB28 and a D3 HANDHELD, while the Hassy always need elinchroms and a tripod with the setup time and budetary impications

S
Title: Circle of confusion
Post by: 01af on March 09, 2008, 11:17:36 am
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Well, of course I disagree ...[a href=\"index.php?act=findpost&pid=179925\"][{POST_SNAPBACK}][/a]
Umm---first you say you disagree ... and then you just repeat what I said, only in greater detail. Where's the dissent?

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This is to ensure that the physical diameter of the aperture in both cases remains unchanged so that the CoCs on both sensors remain the same relative to the sensor size, which is a necessary condition for DoF to remain the same.[a href=\"index.php?act=findpost&pid=180159\"][{POST_SNAPBACK}][/a]
Sigh ...

That condition will keep FOV and DOF constant across varying frame formats at infinite focus distance only. And even then---same FOV and DOF still does not mean same out-of-focus rendition.

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Anyway it is my opinion that getting big DOF is easy with small cameras---too easy for portraiture and very helpful for interior shots.[a href=\"index.php?act=findpost&pid=180163\"][{POST_SNAPBACK}][/a]
Your opinion!? Actually that's a matter of fact. However, getting sufficiently narrow DOF for portraits to look good still is easy enough with cameras of APS-C or Four-Thirds formats.

-- Olaf
Title: Circle of confusion
Post by: witz on March 09, 2008, 12:01:33 pm
The way I see it is.... but I reserve the right to be wrong!

the larger the format... the more angle of view you have at a given distance ( D ) and focal length ( L ). The DOF ( F )  is determined by the F and is the same on any format at the same D & L.

see attached for a basic reference.

The advantage of smaller formats is that lens' can be made "faster" ( bigger F.. ie f1.2 ) because the image circle can be smaller and the distance between lens and film/sensor is shorter... therefore allowing one to use wider lens' at faster F's. And obviously a 1ds3 is easier to run about and shoot with.

The advantage of larger formats is that the cost of resolution is much cheaper ( except for extreme wide angle )... it's amazing to me that the canon 14mm 2.8 has about the same "field of view" as the infamous Hypergon for 8X10... at around 115º!

I went through a stint back in the late 80's where I ran around shooting "real world" type images in san francisco with a speed graphic 4X5 and an SA 65mm lens ( recessed board of coarse )... It was fun.... but I had to shoot hyper-focal to guaranty a high success rate of good images.  but now with the 1ds3 I'm convinced that my options are much better for more situations. I just love the 35mm f1.4.... as much as I loved my 50 2.8 on my old hassy 2000fcw.
Title: Circle of confusion
Post by: Morgan_Moore on March 09, 2008, 02:23:58 pm
Yoiur attached image

Could you choose a wider lens on the Canon, open it up and recreate the big chip look - that is the question

I think in this case (f2) you couldnt because the lens speeds are not there, but this is a practical limitation

Is there a theoretical limitation too ?

S
Title: Circle of confusion
Post by: 01af on March 09, 2008, 02:43:54 pm
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The DOF ( F )  is determined by the F ...[a href=\"index.php?act=findpost&pid=180224\"][{POST_SNAPBACK}][/a]
F is determined by F?

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... and is the same on any format at the same D & L.[a href=\"index.php?act=findpost&pid=180224\"][{POST_SNAPBACK}][/a]
No, it's not. At the same distance and focal length (and same aperture, of course), DOF generally is smaller with smaller frame formats.

-- Olaf
Title: Circle of confusion
Post by: witz on March 09, 2008, 02:58:09 pm
well... digging around I found this...

"Whenever the depth of field is compared between lenses, formats, or whatever, a complete framework must be sketched within which the comparison takes place. If not, the comparison is meaningless."

http://www.vanwalree.com/optics/dof.html (http://www.vanwalree.com/optics/dof.html)

it makes my eye's hurt reading it.... They are probably correct. hehe.

looks like every lens has it's own qualities of DOF.... and the math can't be generalized.
Title: Circle of confusion
Post by: 01af on March 09, 2008, 04:43:38 pm
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Looks like every lens has its own qualities of DOF... and the math can't be generalized.[a href=\"index.php?act=findpost&pid=180246\"][{POST_SNAPBACK}][/a]
Well ... yes and no. The math generalizes and idealizes, otherwise the formulas would become *WAAAY* more complex than they are. So when analyzing formulas, we effectively are looking at "ideal" lenses, i. e. lenses with no aberrations. In reality, such lenses don't exist, so the idealzied math doesn't perfectly reflect all the the actual properties of the lenses in our bags. Still it's not pointless; it does provide a framework which outlines the basic properties, behaviours, effects, and limitations of the optical laws and thus describes the lenses and their images properly, within limits.

-- Olaf
Title: Circle of confusion
Post by: Ray on March 09, 2008, 08:46:22 pm
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Umm---first you say you disagree ... and then you just repeat what I said, only in greater detail. Where's the dissent?

Olaf,
The dissent is in relation to your claim that the 'counting horses teeth' analogy is not a meaningful analogy because it's a simpler process.

I think it's a perfect analogy. When we were all there at the farmer's field in the early hours of the morning about 5,500 years ago, having had some difficulty in catching the horse which seemed a bit shy, there was some doubt as to whether the filly was in possession of a full set of teeth. The counting was made difficult by the horse shaking it's head and struggling to get away, although I must say that Plato and some of his burly students did a pretty good job holding that head still and keeping the mouth open. Aristophanes did his best holding the lantern, but when the torch was brought too close to the horse it really struggled, so we were never really sure just how many teeth that horse really had.

Nevertheless, the group decided that the count was 38 and that the matter was resolved. I protested that we couldn't draw any firm conclusions from this single, rather ambiguous result and that we should count the teeth of a few more horses. I conjectured that perhaps not all breeds of horse have the same number of teeth. The horse whose teeth we counted was a filly. Perhaps a fully grown horse has a greater number of teeth, or perhaps a stallion has a different number of teeth than a mare.

Socrates, who was older and wiser than the rest of us, agreed with me. However, the rest of the group seemed to have lost its enthusiasm for this entire process of gathering data, perhaps understandably because at least one of us was almost seriously injured by a kick from that filly.

I got the impression that most of us would rather sit in a confortable chair and speculate on such matters, and gather mathematical formulas and other opinions to support our preconceptions, instead of engaging in the dangerous activity of gathering real data.
Title: Circle of confusion
Post by: witz on March 09, 2008, 09:01:51 pm
There are some odd horses out there though.... for instance, when I used to shoot jewelry with 4X5 I'd reverse my 210mm and it would have an odd effect on DOF... there was more room in front than in back rather than the normal more infocus behind than in front usual. So I'd imagine that different lens designs will be different? I'd guess that maybe iris blades will effect the bukeh as well?

but... that 110mm of mine on both MFDB and FF35 gave the same result of DOF.... but different FOV.

Fun topic! as I'm an addict to SDOF and always have been. One of the first questions I ask an art director is " do you want it all in focus or do you want it artsy"?
Title: Circle of confusion
Post by: Ray on March 09, 2008, 09:31:46 pm
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well... digging around I found this...

"Whenever the depth of field is compared between lenses, formats, or whatever, a complete framework must be sketched within which the comparison takes place. If not, the comparison is meaningless."
http://www.vanwalree.com/optics/dof.html (http://www.vanwalree.com/optics/dof.html)

it makes my eye's hurt reading it.... They are probably correct. hehe.

looks like every lens has it's own qualities of DOF.... and the math can't be generalized.
[a href=\"index.php?act=findpost&pid=180246\"][{POST_SNAPBACK}][/a]

The article you refer to might appear to be confusing in relation to the narrow topic we are discussing here. It covers situations of different perspective, same f stop with different focal lengths, same magnification of main subject with different focal lengths on the same camera from different distances ( ie. different perspective).

The bone of contention in this thread, is a very specific one. Namely, having done apparently the right thing in adjusting focal length and f stop number in proportion to sensor size, and having ensured that the lenses on both formats are roughly comparable in quality, and having ensured that the sensors of the different formats have roughly the same pixel count and therefore the same resolving power, and having ensured that the shooting position (perspective) is unchanged in all comparisons, are there any significant differences in perception of DoF amongst the different formats in same size images or prints?B]
Title: Circle of confusion
Post by: AJSJones on March 09, 2008, 11:25:15 pm
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Think about this and it may answer your question..

If you shoot a pic on a FF camera with a certain lens and aperture and crop that image in PS down to 'crop sensor' size the DOF doesnt magically change - you just get less of the image

[a href=\"index.php?act=findpost&pid=180163\"][{POST_SNAPBACK}][/a]
This may be off topic by now, but it wasn't commented on
The following is a version of that that I would agree with:

If you shoot a pic on a FF camera with a certain lens and aperture and make two 8x12 prints and crop the second print down in proportion to 'crop sensor' size (e.g. down to 5x7.5 for a 1.6 sensor) and view them from the same distance the DOF doesnt magically change - you just get less of the original print to look at.

Correspondingly, if you make an 8x12 after cropping in PS and view them from the same distance, the DoF will be different, due to the different degree of enlargement, no magic required
Title: Circle of confusion
Post by: Ray on March 09, 2008, 11:56:48 pm
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This may be off topic by now, but it wasn't commented on
The following is a version of that that I would agree with:

If you shoot a pic on a FF camera with a certain lens and aperture and make two 8x12 prints and crop the second print down in proportion to 'crop sensor' size (e.g. down to 5x7.5 for a 1.6 sensor) and view them from the same distance the DOF doesnt magically change - you just get less of the original print to look at.
[a href=\"index.php?act=findpost&pid=180329\"][{POST_SNAPBACK}][/a]

Put even more simply, cropping is cropping, whether it's done by the camera or in Photoshop. But, as you admit, that's not the issue we're discussing here.
Title: Circle of confusion
Post by: Morgan_Moore on March 10, 2008, 02:21:36 am
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Put even more simply, cropping is cropping, whether it's done by the camera or in Photoshop. But, as you admit, that's not the issue we're discussing here.
[a href=\"index.php?act=findpost&pid=180333\"][{POST_SNAPBACK}][/a]

Im not sure I'm with this

A crop of a FF image is the same as a Crop camera used with the same lens (etc) from the same point

How is it not one of the factors in the issue being discussed?

S
Title: Circle of confusion
Post by: 01af on March 10, 2008, 06:58:02 am
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The dissent is in relation to your claim that the 'counting horses teeth' analogy is not a meaningful analogy because it's a simpler process.[a href=\"index.php?act=findpost&pid=180308\"][{POST_SNAPBACK}][/a]
Since I never made any claim like that, I still cannot see any dissent.

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I think it's a perfect analogy.[a href=\"index.php?act=findpost&pid=180308\"][{POST_SNAPBACK}][/a]
Well, not perfect ... but pretty good indeed. It would be perfect if, in addition to all the  hassles of taking a deep look into a struggling horse's mouth, there were objects to be found in horses' mouths than would easily get confused with teeth. So even if, against all odds, you managed to come up with a count of tooth-like objects, you'd still be unsure how many of them actually were teeth.

And if counting several horses' teeth and finding different numbers, you'd still not know if some horses had simply lost some of their teeth, or if you miscounted in some cases (and if so, in which?), or if the difference was due to age, sex, or breed.

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... so we were never really sure just how many teeth that horse really had.[a href=\"index.php?act=findpost&pid=180308\"][{POST_SNAPBACK}][/a]
Exactly.

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I got the impression that most of us would rather sit in a confortable chair and speculate on such matters, and gather mathematical formulas and other opinions to support our preconceptions, instead of engaging in the dangerous activity of gathering real data.[a href=\"index.php?act=findpost&pid=180308\"][{POST_SNAPBACK}][/a]
But gathering mathematical formulas isn't the same as disregard for real data! To the contrary---both strategies complement one another. Actually, my endeavour to improve that COC formula was triggered by the evidence found in empirical data.

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... when I used to shoot jewelry with 4 × 5" I'd reverse my 210 mm and it would have an odd effect on DOF. There was more room in front than in back ...[a href=\"index.php?act=findpost&pid=180311\"][{POST_SNAPBACK}][/a]
That's impossible. Obviously your plane of focus wasn't where you thought it should be. Umm ... did you focus at full aperture and then stopped down for the shot? Most likely, your 210 mm lens has some aperture-related focus shift (not uncommon).

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But ... that 110 mm of mine on both medium-format digital back and 35-mm format gave the same result of DOF ... but different FOV.[a href=\"index.php?act=findpost&pid=180311\"][{POST_SNAPBACK}][/a]
And different (relative) magnification, too. So DOF isn't comparable.

-- Olaf
Title: Circle of confusion
Post by: 01af on March 10, 2008, 07:36:30 am
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The article you refer to might appear to be confusing in relation to the narrow topic we are discussing here.[a href=\"index.php?act=findpost&pid=180321\"][{POST_SNAPBACK}][/a]
Exactly. The article referred to by "witzke"---which is very good by the way---covers DOF in great width. The topic we are discussing here is only one tiny aspect of all that ... it's an aspect the article covers with just one casual remark. About three quarters into the article, a few paragraphs above Fig. 9, it says:

The smaller format employed at an F-number N yields the same DOF as the larger format at an F-number of R × N. Please note that this rule of thumb is just a rule of thumb, not a mathematically exact relationship. It should only be applied at intermediate and long object distances, because at close range the equivalence breaks down.

Here, we are discussing how exactly that equivalence is breaking down, and how that rule of thumb might be replaced by a mathmatically exact relationship.

-- Olaf
Title: Circle of confusion
Post by: Ray on March 10, 2008, 09:20:36 am
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The smaller format employed at an F-number N yields the same DOF as the larger format at an F-number of R × N. Please note that this rule of thumb is just a rule of thumb, not a mathematically exact relationship. It should only be applied at intermediate and long object distances, because at close range the equivalence breaks down.

Here, we are discussing how exactly that equivalence is breaking down, and how that rule of thumb might be replaced by a mathmatically exact relationship.

-- Olaf
[a href=\"index.php?act=findpost&pid=180389\"][{POST_SNAPBACK}][/a]

Shouldn't we first gather some evidence demonstrating that the equivalence actually is breaking down and to what extent it is breaking down. I never noticed this breaking down of the rule of thumb at the close range of my own tests, so how close is close? Macro?
Title: Circle of confusion
Post by: AJSJones on March 10, 2008, 02:32:48 pm
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Put even more simply, cropping is cropping, whether it's done by the camera or in Photoshop. But, as you admit, that's not the issue we're discussing here.
[a href=\"index.php?act=findpost&pid=180333\"][{POST_SNAPBACK}][/a]
I guess my point was that it does matter whether you crop before you enlarge or after you enlarge, vis-a-vis the DoF, because the CoC gets enlarged in the former case but not the latter.  Whether that affects the transition from in focus to OOF, as I understood the scope of the original post, I haven't the faintest
Title: Circle of confusion
Post by: Ray on March 10, 2008, 06:55:07 pm
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I guess my point was that it does matter whether you crop before you enlarge or after you enlarge, vis-a-vis the DoF, because the CoC gets enlarged in the former case but not the latter.  Whether that affects the transition from in focus to OOF, as I understood the scope of the original post, I haven't the faintest
[a href=\"index.php?act=findpost&pid=180446\"][{POST_SNAPBACK}][/a]

It's understood that perceptions of DoF change with print size and viewing distance. If you enlarge a crop of an 8x10 enlargement back to 8x10 size, then the result is effectively a crop of an A3+ size, with respect to the original FoV and image.
Title: Circle of confusion
Post by: AJSJones on March 10, 2008, 07:49:09 pm
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It's understood that perceptions of DoF change with print size and viewing distance. If you enlarge a crop of an 8x10 enlargement back to 8x10 size, then the result is effectively a crop of an A3+ size, with respect to the original FoV and image.
[a href=\"index.php?act=findpost&pid=180494\"][{POST_SNAPBACK}][/a]

Agreed - which is why the comment  from Sam

"If you shoot a pic on a FF camera with a certain lens and aperture and crop that image in PS down to 'crop sensor' size the DOF doesnt magically change - you just get less of the image"

looked possibly incorrectly "understood" without the necessary qualifiers...