[PDL]

Hi PDL,

while I can see why to avoid FoV, my own post uses it -- for one reason:

DoF for given FoV only depends on aperture (in mm). So, by introducing FoV one effectively eliminates 2 out of 3 variables which cleans up the discussion a lot!

I find it interesting that in the 200 odd years that DoF has been defined that FoV has never once been mentioned in any of the calcualtions.

This is well understood and developed physics - just read the methods used - FoV is not relevant. All this BS is getting in the way, calculate don't speculate.

The Elitist - formerly known as PDL

[falconeye]

I find it interesting that in the 200 odd years that DoF has been defined that FoV has never once been mentioned in any of the calcualtions.

This is well understood and developed physics - just read the methods used - FoV is not relevant. All this BS is getting in the way, calculate don't speculate.

The Elitist - formerly known as PDL

The best known and simplest formula is:
f: lens focal length [mm]
F: lens f-number [number]
c: circle of confusion [mm]
H: The hyperfocal distance [mm]

H ~= f^2/(Fc)


Now, by inserting you get
a: lens aperture [mm] = f/F (read: F=f/a)
d: diagonal sensor/film diameter [mm]
c = d/1730 (the Zeiss formula)

H ~= 1730 a f/d


Now
V: Field of View or FoV = diagonal angle of visible field [angle]
d/f = 2 tan (V/2)

H ~= 865 a / tan(V/2)

implying for a "normal" FoV of 90 degrees:

H(V=90°) ~= 865 a


Of course, the tangens formula isn't used in the calculus as it is difficult to deal with. Even more so if not hyperfocal distance but depth of field is to be computed. However it is very useful to be translated into words:

Depth of Field depends on the "aperture diameter" and "Field of View", only!

So, in a time where people discuss on the internet rather than do math, the Field of View is the required term to clean discussions up.



One comment on PDL's "well understood and developed physics"... I know and I hold a PhD in Theoretical Physics


One comment on Geekybiker vs. baw:

Depth of Field is based on the capabilities of the human eye, not the sensor pixel size. Therefore, Depth of Field does decrease if an image is cropped even though its pixels don't change. This is paradox and one of the causes for the many misunderstandings. To get a hint why this is so: The crop would be magnified more in print and Depth of Field is a holistic property only defined at the image level (e.g., the print).



If somebody wants to know what to do to get all pixels sharp, then he must set the circle of confusion to match the pixel size. The resulting measure isn't called Depth of Field anymore, though!

[Geekybiker]

T
One comment on Geekybiker vs. baw:

Depth of Field is based on the capabilities of the human eye, not the sensor pixel size. Therefore, Depth of Field does decrease if an image is cropped even though its pixels don't change. This is paradox and one of the causes for the many misunderstandings. To get a hint why this is so: The crop would be magnified more in print and Depth of Field is a holistic property only defined at the image level (e.g., the print).

This was discussed at one point, but he insists on some theoretical sensor that would have the same pixel density after the crop and therefore the same magnification in print. :\

At this point I'm arguing from a practical standpoint. I give on the theoretic points. I never have denied any of it. I just wish that they could maybe, just maybe acknowledge that practical application and theory don't always line up.

And again, I get drawn into this. I shouldn't even open this thread anymore.

[pentagor]

Hear,hear.
The nitwit(s) that dreamed up the"crop factor/equivalent focal length" , a marketing ploy I guess, should be evaporated. It has done nothing but sow the seeds of confusion. When I was a 35 mm user ( I started photography in 1969), there was no confusion relating to lens focal lengths re 35mm, MF and LF cameras. I'm certain the concept of equivalent focal lengths was of no consequence to most photogs. My concern these days is that many newbie photogs (digital) really do have a lack of understanding of basic photographic and optical principles.

I have to agree with pixelsaurus and PDL: the focal length is focal length and is measured in mm. Once you get that straight out in your brain, then you are not confused any more, like I was. Just bare in mind, that the FoV will be smaller on a smaller sensor, that's all. No recalculating, or other useless stuff. The important thing is, that you know, what focal length you need for your sensor size.
When I first started with my LBA ( ), I was allways calculating and multiplying with 1.5. I was so confused in fact, that I even thought that an old M lens of 50mm would give me the same image as a DA lens of 33mm - ON THE SAME BODY. That's how confusing this all is. The only difference between new (digital) lenses and old ones in terms of picture size is, that digital lenses in general (not all) have smaller image circle, causing a vignetting on a 35mm format film/sensor.
I think that this crop factor recalculations are simply a product of marketing, targeting the special population of consumers who just seek for a bigger magnification (20 x zoom from the vocabulary of P&S cameras market).

But now we have a crop of cameras using at least 5 formats in DSLR's alone. (ff, 1.3, 1.5, 1.6, 2) Not to mention the whole host of PS cameras that use assorted sensor sizes. Its not like film where there were few formats to compare. There has to be some sort of useful standard to compare the performance of lenses across models. Granted 35mm equivalent isn't ideal. Maybe listing the magnification from normal perspective? Of course that breaks down with interchangeable lenses where the only constant is focal length. Then using some sort of conversion factor is the only way to compare performance.

How would you list lenses such that they are easy to compare across a different platforms?

It depends, what you are comparing. If you are comparing the FoV, then you are right. But as far as I know the comparison of the lenses is grounded on image quality (sharpness, contrast, aberration, distortion etc.) and not on focal length. Even more: if you are making a lens comparison tests, you use one and one body only, to get the credible results. This means, that a crop factor does not play any role in it.
There is maybe only one consideration to take into account: lenses designed for FF or bigger format will not be tested completely on your crop size sensor body, because you are unable to test the corners of the lens/picture.

About DOF: yes, I think the DOF is different on a smaller sensor with the same focal length, aperture and distance to the subject parameters. But I think it does not affect the calculation significantly.

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Last edited by pentagor; 04-09-2008 at 12:02 AM.

[baw]

One comment on Geekybiker vs. baw:

Depth of Field is based on the capabilities of the human eye, not the sensor pixel size. Therefore, Depth of Field does decrease if an image is cropped even though its pixels don't change. This is paradox and one of the causes for the many misunderstandings. To get a hint why this is so: The crop would be magnified more in print and Depth of Field is a holistic property only defined at the image level (e.g., the print).

Seems much of the confusion stems from mixing two types of DOF: theoretical and practical.

Theoretical is straighforward.:
every point in your subject area can be calculated to produce either a dot or a circle on the sensor plane. This is dependant on point distance, focal length and aperture used.
A point on the plane where the lens is focussed will produce a point on the sensor plane.
Points in front or behind the plane of focus will produce a circle (CoC) on the sensor plane.
By choosing a maximum size for this circle you define the DOF for this situation.
Sensor size is not a factor.
(this is a simplification, because the projection on the sensor plane is ao dependant on the shape of the aperture, and towards the edge of the image it will be more like an oval)
So if you use DOF calculators your sensor size is totally irrelevant in the calculation.

Practical.
In the beginning of the discussion I posted:

The whole calculation of DOF is not very relevant imo. It's the DOF in the viewed image that counts, wether on screen or in print.
You might find this article by Harold M. Merklinger interesting. He has a different take on DOF.

Now you can throw in all kind of factors. You could argue that the eyesight of the observer determines the DOF of the viewed image. Also the criteria for DOF changed, because we tend to view images at 100% on a monitor to decide what is sharp and what isn't.

Concluding: if you talk about DOF calculations, sensor size is irrelevant.
If you talk about practical DOF it doesn't really matter how the image is created. The way you view does decide what your DOF is.

[falconeye]

Seems much of the confusion stems from mixing two types of DOF: theoretical and practical.

In my experience, people saying so just haven't understood the theory. Which is ok. Sometimes, it is just too hard to understand some theories... DoF is no difference here.

Theoretical is straighforward.:
By choosing a maximum size for this circle you define the DOF for this situation. Sensor size is not a factor.

Practical.
If you talk about practical DOF it doesn't really matter how the image is created. The way you view does decide what your DOF is.

And now take the Zeiss formula from my posting above:

c = d/1730 (the Zeiss formula)

where c is circle of confusion and d is diagonal sensor size. Therefore, sensor size is a factor and it even got a famous name, the Zeiss factor!

There really is no difference between theoretical and practical DoF. Physicists are no fools.


So, let me repeat myself: DoF (for a given FoV and any sensor size) only depends on aperture in mm and with a larger sensor, you get a full superset of image compositional choices as compared to a smaller sensor.


One more sentence:
When people crop or view at 100% on-screen: This is not called DoF, except if you are also going to create an image from the crop where then you changed the FoV. And of course, crops and this issue have been dealt with at analog times already.

[baw]

In my experience, people saying so just haven't understood the theory. Which is ok. Sometimes, it is just too hard to understand some theories... DoF is no difference here..

Sorry, won't bite.

And now take the Zeiss formula from my posting above:

The Zeiss formula is just a way to arrive at a CoC value, which you can choose according your needs anyway. I sometimes use the DOW method (Day Of Week). In short you add the number of the day of the week to 23 to arrive at the CoC value in µm.
Following your logic the day of the week is now part of the DOF equation.

Have a look at this Wikipedia article.
The last part soms it up nicely:

This article explains that

'Depth of field is insufficient' is the most common complaint to meet the Carl Zeiss service department today,

due to the improvements in lens sharpness and film sharpness since the standards were set. It is perhaps possible that they had earlier reacted to this increase in service calls by tightening up their COC limit for computing lens DOF markings from about 30 µm to about 25 µm, but they did not do so explicitly, nor did they ever state the divisor 1730. David Jacobson reverse engineered what Zeiss had done on one or two cameras, approximately, and put a number to it; later, Warren Young put a name to it, and the Zeiss formula caught on rapidly from there, among web amateurs. It is a perfectly reasonable formula, but does not have the historical basis that its name seems to claim.

[falconeye]

The Zeiss formula is just a way to arrive at a CoC value, which you can choose according your needs anyway.

The CoC value cannot be choosen arbitrarily. It is in the Wikipedia article you mentioned yourself.

Zeiss used d/1730 (as was found out later).

Because the human eye varies you can use you own, but not arbitrarily, i.e., still as a factor to film diameter only.

Maybe, you use d/2000 and call it Ben's factor.


It all doesn't change a single bit in the entire argument, though. I.e., CoC is proportional to sensor size.


You are perfectly allowed to use arbitrary values for CoC (e.g., the pixel size), no problem with me. But you cannot call the resulting measure Depth of Field anymore because this is a scientifically well defined term and every optical physicist will easily prove you wrong.

By using your private definition of DoF you only spread confusion among forum users which I may call "Ben's circle of confusion" then :ugh:

-----------------------------
Let me ease the discussion a bit and change the topic now...

I've seen you are geotagging your photos on BAW Photo Gallery . Some really great shots you have, btw! What do you do to geotag them (which GPS logger, software)? I had a look into Xaiox and GeoSetter.de. Are those any good?

[baw]

By using your private definition of DoF you only spread confusion among forum users which I may call "Ben's circle of confusion" then

I am familiar with this definition of DOF:
"the range of object distances within which objects are imaged with ACCEPTABLE sharpness"

Also have a look here for more definitions, all amounting to the same definition as above.

Since I seem to be so confused, and you seem to have all the answers, would you please explain the difference in sharpness between the early 3mp APS-C sized sensors, and the latest 14mp ones? They obviously both have the same CoC (d/1750), yet the perceived sharpness of the 14mp ones is much better than the 3mp ones. Consequently the DOF is larger for the 14mp ones.

On the above linked Wikipedia page is a link to the Circle of Confusion article. You may want to read that, and then re-read the statements in your last post.

Let me ease the discussion a bit and change the topic now...

In my experience people who say this usually are running out of arguments.

I've seen you are geotagging your photos on BAW Photo Gallery . Some really great shots you have, btw!

Correct and thank you.

What do you do to geotag them (which GPS logger, software)? I had a look into Xaiox and GeoSetter.de. Are those any good?

Since this is way off topic for this thread have a look at this thread.

[falconeye]

the range of object distances within which objects are imaged with ACCEPTABLE sharpness
[...]
Since this is way off topic for this thread have a look at this thread.

Hi again

I think, this is our dilemma. With the meaning you give the word "depth of field", you are correct.

I accept that the term is now used at will in modern net culture. I only wanted to be of help a little bit by getting the term DoF straight for this forum. Being physicist, I thought I could help.

If I may speak for myself one last time, I could never accept such vague a sentence as a "definition". I learned in undergraduate physics that the circle of confusion used for depth of field as scientifically defined is as follows: "The minimum size which can be resolved by the average human eye when having the entire image in view".


As for your interesting 3MP question: You are right again. If a 3MP camera would render razor-sharp pixels (which it doesn't) and you don't crop and don't ever have any close-up look at a detail. It is actually hard or impossible to even see the 2MP of HDTV from a normal viewing distance...

One may want to have all 14.6 Mpixels sharp. Let's just call the thing other than DoF then. That's all I am proposing here.

[ukbluetooth]

Having avidly read this thread for the last hour or so I have to make the following comments.

1) It is really fascinating reading.

2) I was always unhappy about crop factors and equivalent focal lengths. Thanks to this thread I have finally abandoned them. 50mm is 50 mm and is not magically transformed into anything else. Thanks for putting me right.

3) When I focus on the shed from my room at an aperture of say f4.0 an my 50mm prime the acceptable DoF is between the bush immediately in front of it and the tree somewhat further away behind it. Whatever camera I use, what ever sized sensor or film format, it would still be the the same tree and the same bush that would boundary the acceptable DOF. Of course, what would change would be the FoV.

4) If I print the above series of pictures so that the SHED is the same size in all of them, which means that the size of the prints would vary significantly depending on the format of the camera used, then the acceptable DoF of the prints (assuming they were not compromised by pixel or grain resolution) would all be exactly the same. They would NOT be affected by the film/sensor format.

5) If I print all the pictures so that all the PRINTS are the same size i.e the shed looks considerably smaller in some of them, then my PERCEPTION of the DoF would change. I would be more critical of the DoF in the shots taken with the smaller sensor/format than I would be with the larger, simply because these shots (and their concomitant distortions) would be considerably enlarged compared to those from the larger format sensors/films.

This is the perception I have ended up with from following this thread. Is this over-simplistic or is it a good enough working model? Please let me know if it the correct perception or not.

[baw]

Since no one answered you yet I'll give it a shot.
It's hard to judge whether you have the good perception or not.
-3 Acceptable DOF doesn't seem correct, it's acceptable sharpness we talk about.

I'll try to explain my take on the whole DOF thing, might give you some more ideas.

First the definition: Depth of field is defined as the range of object distances within which objects are imaged with acceptable sharpness.
This seems to be generally accepted. See Definitions of Depth of Field
You need a sharpness criterium: Circle of Confusion (CoC). it's the diameter of an unsharply imaged point on the sensor/film plane. You define what you find acceptably sharp by choosing a maximum CoC size.

I feel you should split the whole DOF concept in two parts:
1- the imaging of the object on the image plane
2- the creation and viewing of the resulting image, whether in print or on screen etc.

1) This is the simple part in the process. By assuming a thin, perfect lens that projects the image on a plane that can resolve infinitely small points you can simplify calculations. We need some more assumptions, but this works pretty neat in practice.
Points on the focussed distance will be projected as points. Points in front or behind the focussed plane will be projected as circles. If the circlediameter is equal to or smaller than the choosen max. CoC the point falls within the DOF.
Now you can calculate DOF, using Focussed distance, focal length, aperture and the choosen CoC.
Assuming a certain CoC you can also create the DOF scales on lenses.

2) This is the part where the confusion begins.
First of, I hesitate to talk about DOF in a 2D image. It's sharpness we're discussing, but this is perhaps philosophical.
In this process we work with imperfect lenses, perhaps incapable of resolving anything sharp in the corners.
We use sensors/film of certain dimensions, with a certain resolution.
We use a certain magnification, projecting the image on a medium with certain dimensions, capable of displaying with a certain maximum resolution.
We view with our imperfect eyes, from different distances, under different lighting conditions.
I surely missed some factors that influence all this, but you'll get the idea.

Given the way YOU normally display/view your images, you can decide on a CoC that matches your needs.
It'll give you a "recipe" to create those nice portraits with the blurry backgrounds, or those tack sharp landscapes, using hyperfocal distance (yikes) focussing.

Don't get overly excited in calculating DOF. It's a gradual thing anyway. Points on the focussed distance will be sharpest, others will be less sharp. Points around the boundaries of the DOF will be ALMOST the same sharpness, while one is acceptably sharp and another just isn't.

I again recommand reading this article DOF Revisited. It gives a very usefull way to work with DOF.

[baw]

I think, this is our dilemma. With the meaning you give the word "depth of field", you are correct.

I accept that the term is now used at will in modern net culture. I only wanted to be of help a little bit by getting the term DoF straight for this forum. Being physicist, I thought I could help.

If I may speak for myself one last time, I could never accept such vague a sentence as a "definition". I learned in undergraduate physics that the circle of confusion used for depth of field as scientifically defined is as follows: "The minimum size which can be resolved by the average human eye when having the entire image in view".

The definitions I pointed to are all referenced from books, some of which were published well before the internet became popular, and it seems this definition is generally accepted.

The concept of Depth of Field makes only sense in a 3D object space imo. When capturing that object space on a sensor/film you can talk about DOF, focussed distance, CoC etc.
Once the image is captured, you start a whole new ballgame, of displaying and viewing a 2D representation of your 3D object. I don't think a CoC is relevant here, hence I fail to see what's scientific in your CoC "defintion". It's just a way to arrive at a VALUE for the CoC, just as my DOW method. One thing missing in your definition is viewing distance. The whole image viewed from 1 kilometer away will probably look less sharp then when viewed from 1 meter away.

Regarding the 3mp/14mp paradox: as long as the 3mp sensor can resolve your object acceptably sharp, the 14 mp sensor will have the same DOF, because it's the lens that creates the unsharpness, not the sensor pixels.
(this is assuming everything the same, except sensor resolution)

In my experience, people saying so just haven't understood the theory. Which is ok. Sometimes, it is just too hard to understand some theories... DoF is no difference here.

If I ever was to make a statement like this I would make very sure that I knew what I was talking about.

[ukbluetooth]

Since no one answered you yet I'll give it a shot.
It's hard to judge whether you have the good perception or not.
-3 Acceptable DOF doesn't seem correct, it's acceptable sharpness we talk about.

I'll try to explain my take on the whole DOF thing, might give you some more ideas.

....

Thanks baw for taking the trouble to answer this so succinctly. Yes, I should have said acceptable sharpness.

I think I have a better understanding now. Also having read through the various links I can only conclude that the Zeiss number is highly (in fact totally?) empirical.

Cheers - Gary

[baw]

I think I have a better understanding now. Also having read through the various links I can only conclude that the Zeiss number is highly (in fact totally?) empirical.

Hi Gary
Glad I could be of some help. A pitty this thread got derailed by some misguided posters.
I would have liked to see some arguments pro or contra my position of DOF being applicable only in the imaging stage. This seems obvious from the definition, but.....