Lens Conversion for Different Sensor Sizes

A lot of photographers know the rule for converting focal lengths between different sensor sizes to maintain the same framing. For example, a 50mm on a aps-c camera would have the same framing as a 80mm on a full-frame camera, and we do this by multiplying/dividing by the crop factor.

However, not many people discuss the aperture of the lens to maintain the same amount of depth of field, or bokeh. I heard some ways online but it seemed pretty vague and not based on actual calculations. I thought it would be convenient to have a way to calculate the aperture we need to use to maintain the same framing AND bokeh in a shot, so I calculated a pretty simple formula. Check it out on my blog post I wrote up!

http://www.yutowatanab​e.com …rsion-for-aperture-bokeh/

I had a look at your blog post, and I do like it, but it may be too complex for many. I do have a few suggestions, and I'll post them here if that is ok with you.

The aperture factor and crop factor are the same, and I guess most people know that already anyway. I'd suggest you add an introductory paragraph, where you say as much, explain that this is a little less than 1 2/3 of an f-stop (for Canon APS-C, and a bit more than 1 1/2 stop for Nikon APS-C, at 1.5X). Note: it is almost 1 /2/3 of an f-stop, not 1 1/3 as you indicate in your blog, see below.

I would then continue to indicate that the calculations follow next.

Since FL and sensor size are both expressed in mm, I am wondering why you use a value converted to metres. Not necessary if you ask me, and also confusing to many, and making this more complex than may be necessary.

As to bokeh, this is a quality you cannot express as having an amount, as you seem to say a few times ("amount of bokeh", "bokeh amount"), because it is a subjective quality. You can say "great bokeh", "ugly bokeh", "smooth bokeh", "swirly bokeh", but it is not quantifiable. It looks to me like you mean amount or size of the Dof zone or OOF zone, and in order to avoid confusing people, you may want to consider using that. What you are doing is calculate the aperture to be used an a camera with an APS-C sensor to get the same DOF as with an FF equivalent lens on a FF sensor camera for a certain aperture on the latter.

You are making 1 mistake, BTW, namely converting the "aperture factor" to a logarithm of sqrt(2). The aperture factor is in stops already, namely 1.6 stops, or close to 1 2/3 of a stop. It is expressed in N, numerical aperture, which is the relative diameter of the lens opening derived from an area, hence converted already.

You can check this with any aperture calculator. Take f.e. 80 mm on FF, focusing distance 5 m, CoC is 0.30 mm, DoF is 1.29 m. For an equivalent FL on an APS-C 1.6x crop, 50 mm on APS-C IOW, CoC is 0.0195 mm, DoF is 1.24 m at F/3.2. 1.24 m is slightly less than 1.29 m, even if close enough for normal use, so clearly on APS-C this is almost 1 2/3 of an f-stop larger than an equivalent lens on FF.

BTW, since the "aperture factor" is a constant, I wouldn't bother with the graph.

HTH, kind regards, Wim

Hey wimg, thanks for your response. I'm definitely not an expert field, so I appreciate the constructive criticism.

I used meters instead of mm because... that's just the standard thing to do in physics a lot of the times, I guess. You're right, I could've used mm and made everyone's lives easier but.. I didn't, haha.

Bokeh is a subjective quality - you can have smooth bokeh, swirly bokeh, donut-shaped bokeh, etc, but the essential "amount" of bokeh is given by the size of the CoC. As the diameter of the CoC approaches 0, we see the image in focus.

The amount of DoF is the same thing, but I just took a different approach. Essentially the DoF calculators have a formula that calculates the diameter of the CoC as a function of distance, and finds the distance at which the CoC is the same size as a pre-determined size for each specific sensor size. That pre-determined size is the point where people would say the image is out of focus.

I don't think i'm making a mistake by converting the aperture factor to a log of sqrt(2). For instance, if the aperture factor were 1.4, then you would multiply f/2.8 to f/4. This difference is 1 stop, not 1.4 stops as it would be with your calculation.

I checked my calculations with an DoF calculator, as you suggested. I used this one
http://www.dofmaster.c​om/dofjs.html
My baseline was a 7D at 50mm, d=5m, f/2.8. total DoF was 1.08m
For a 5D at 80mm, d=5m, at f/4.5 (1 1/4 stops darker) the total dof was 1.05 meters
For a 5D at 80mm, d=5m, at f/4.8 (1 1/2 stops darker) the toal dof was 1.11 meters

Therefore, they two sensor formats achieve the same dof somewhere in between 1 1/4 stops and 1/2 stops. My hypothesis of 1 1/3 fits those requirements.

I graphed the aperture factor simply because that's how I got the answer, and I thought it would be a logical process for others too. Looking at the graph before that, it's not obvious that the factor is a constant instead of depending on the size of the CoC, so the graph makes it clear.

Please tell me what you think!\

Reevo wrote in post #13508757
Hey wimg, thanks for your response. I'm definitely not an expert field, so I appreciate the constructive criticism.

I used meters instead of mm because... that's just the standard thing to do in physics a lot of the times, I guess. You're right, I could've used mm and made everyone's lives easier but.. I didn't, haha.

No, bokeh is a characterisic, not a quantifiable parameter. Sharpness as in what is in DoF is - and that is what you are really calculating by calculating DoF, not bokeh.

Actually where it is still just in fcous, based on the acuity of the human eye, at a certain print size and certain viewing distance. Slightly different approach .

I mentioned 1 2/3 of a stop. This is a stops factor really, so honestly, if you use the correct CoCs in the calculation, namely 0.030 mm for FF and 0.0195 mm for APS-C, you do get 1.6 stops difference. I guess I shouldn't have called it factor. It is the number of stops difference.

I checked my calculations with an DoF calculator, as you suggested. I used this one
http://www.dofmaster.c​om/dofjs.html
My baseline was a 7D at 50mm, d=5m, f/2.8. total DoF was 1.08m
For a 5D at 80mm, d=5m, at f/4.5 (1 1/4 stops darker) the total dof was 1.05 meters
For a 5D at 80mm, d=5m, at f/4.8 (1 1/2 stops darker) the toal dof was 1.11 meters

A tiny difference in CoC used makes a big difference in the DoF calculation. Since DofMaster doesn't give you the option to influence the CoC, I suggest you use this one, which has a few more options and allows one to fill in the exact CoC required: http://eosdoc.com/jlca​lc/.

I used this calculator to come up with my figures.
By default it uses a rather small CoC for FF however, so you will have to adjust that to 0.030 mm, and set CoC for APS-C to 0.0195 mm, because it uses a rounded 0.02, which also makes DoF for APS-C even bigger than it is.

I respectfully disagree. This is what most people seem to believe, but it is not correct.

I think that in this case, a picture is not worth a thousand words , but maybe that is just me.

Kind regards, Wim

Okay fine, maybe bad wording on my part. The quantifiable quantity, sharpness, is what determines the amount of bokeh. So we can calculate sharpness by using the diameter of CoC, and therefore the amount of bokeh is also proportional to that. You can definitely say that a photo has "less" or "more" bokeh, so I think it's quantifiable in this way.

dofmaster uses 0.030 mm for FF and 0.0195 mm for APS-C as the size for the sizes of the max size of circle of confusion we perceive to be in focus, which is what you used as well. This is understandable because they are just proportional to the sensor sizes. It's the same thing I do in my calculations by determining "Ceff" instead of "C".

Well I just used eosdoc, and a few examples showed that the difference was around 1 1/2 stops. so, we're both within 1/6 of a stop... does that make us happy?! haha.

It is a multiplication factor - I just divided one by the other. If it actually is a 1.6 stops difference, the factor should be sqrt(2)^(1.6)=1.74 instead of 1.6. What if the f-stop difference was 0 stops (meaning that the two cameras we are comparing are both full-frame)? then the multiplication factor should be sqrt(2)^(0)=1, which makes sense. By your logic, if you get 0 stops of difference, the multiplication factor is also 0!

Well, unless someone else wants to chime in, I guess we could agree to disagree, haha.

Reevo wrote in post #13509202
Okay fine, maybe bad wording on my part. The quantifiable quantity, sharpness, is what determines the amount of bokeh. So we can calculate sharpness by using the diameter of CoC, and therefore the amount of bokeh is also proportional to that. You can definitely say that a photo has "less" or "more" bokeh, so I think it's quantifiable in this way.

There is no such thing as an "amount of bokeh". There is no such thing as "less bokeh" or "more bokeh".

The term "bokeh" simply refers to the non-quantifiable aesthetic qualities of background blur and not how much or how little background blur there is in an image.

Reevo wrote in post #13509202
Okay fine, maybe bad wording on my part. The quantifiable quantity, sharpness, is what determines the amount of bokeh. So we can calculate sharpness by using the diameter of CoC, and therefore the amount of bokeh is also proportional to that. You can definitely say that a photo has "less" or "more" bokeh, so I think it's quantifiable in this way.

No, you can't. The quantifiable characteristic sharpness defines DoF, and where the transition is from sharp to unsharp, at either end of the DoF plane. It doesn't determine bokeh at all. It only indicates from which points you could have good or bad bokeh. Not the amount. No tless or more.

"Usually, the chief concern of lens designers is the best possible image quality of the plane of sharp focus. The rendering of out-of-focus (OOF) image parts does not enjoy a large weight in the overall design compromise of a normal photographic lens. However, the OOF blur characteristics mattered to certain Japanese photographers who introduced the term "bokeh" to the photographic society to describe the aesthetic quality of the blur. In the absence of a single English word with the same meaning, there seems no reason not to adopt the Japanese term. The internet abounds with lens qualifications like "good bokeh" and "bad bokeh" but strictly speaking this use of the word should be discouraged. Owing to the subjective implications of some unquantifiable aesthetic value, it would be more appropriate to speak of pleasant or unpleasant bokeh, respectively."
http://toothwalker.org​/optics/bokeh.html

Highlight by me.

Please read what I said: I already mentioned it was a poor choice of words. That number indicates the number of f-stops required to get to the same DoF. It is 1.6, and therefore 1.6 stops. BTW, if calculated correctly, it even is 1.61 or 1.62, depending on which Canon APS-C camera you use, so even closer to 1 2/3 of a stop.

I don't know what you did, but my guess is you didn't change the CoC for FF to 0.030 mm, but left it at 0.025mm

Some screendumps. First 80 mm FF at F/5.6, CoC 0.030 mm, focusing distance 5 m, DoF is 1.29 m.

HTTP response: 401 | MIME changed to 'text/html'

HTTP response: 401 | MIME changed to 'text/html'

HTTP response: 401 | MIME changed to 'text/html'

You're talking to the wrong guy because... I am, a Japanese photographer, muhahahaha. and it's totally normal for people to say もっとボケてる or こっちのほうがボケてる, which means that you can compare the amount of bokeh. I'm sorry but I don't think you can argue with me about this when you can't even read those characters (assuming that you can't speak japanese).

But I'm saying that it isn't a poor choice of words. All I did in the original equation was divide two and found the multiplication factor between the two graphs, not how many stops they were different. aperture factor is exactly the words I would use to describe that quantity.

I took a look at the results you got using eosdoc. So, I was right, the difference is in between 1 1/3 stops and 1 2/3 stops, and close to 1 1/2 stops. I took a linearization approximation of using the two points you provided (4/3, 1.36) and (5/3, 1.24) and y=1.29 when x=1.52778. So by this linearization, the difference is 1 1/2 stops. I guess you were a tad closer than my hypothesis.

Except this is kind of going off topic. I just wanted to mathematically derive that quantity instead of plugging in some numbers into a dof calculator. I think my calculation of 1 1/3 stops is pretty close to the real value of 1 1/2 stops, so I guess it's okay. 11% error? not bad, I'd say.

Good lord,I'm going back to my point and shoot gear, lol

Reevo wrote in post #13510806
You're talking to the wrong guy because... I am, a Japanese photographer, muhahahaha. and it's totally normal for people to say もっとボケてる or こっちのほうがボケてる, which means that you can compare the amount of bokeh. I'm sorry but I don't think you can argue with me about this when you can't even read those characters (assuming that you can't speak japanese).

What you may not realize is the the word "bokeh" is now an English word which is a derivative of a Japanese word and may have a different meaning from the original Japanese word (or phrase). In photographic English lingo, "bokeh" is not a direct substitute for "background blur".

Reevo wrote in post #13510806
You're talking to the wrong guy because... I am, a Japanese photographer, muhahahaha. and it's totally normal for people to say もっとボケてる or こっちのほうがボケてる, which means that you can compare the amount of bokeh. I'm sorry but I don't think you can argue with me about this when you can't even read those characters (assuming that you can't speak japanese).
.

You have raised an intriguing point. Within the photographic community outside of Japan, proper discussion of 'bokeh' is that it is a quality, and is not quantified.

This article was one of the first to discuss the concept of bokeh to the Western world
http://www.trenholm.or​g/hmmerk/ATVB.pdf

Another early article (not found on the internet) by Oren Grad has been described as stating:

In May/June 1997 Photo Techniques, Oren Grad’s article goes on to describe some vague and subjective bokeh terms:

* The overall look of the image may be described as sofuto (soft) or katai (hard)

* As the bokeh becomes less clean it may be described as hanzatsu (complex) or as kuzureru (breaking up or loosing shape).

Also noted in the article are some, overall judgmental terms summing up a lens’ bokeh: kirei (pretty, beautiful, clean); sunao (gentle, well behaved); yoi (good); konomashii (nice, likeable); odayaka (gentle); shzen (natural) or even “kani no yoi bokeh " - bokeh that gives a good feeling; or when the reviewer is being critical, as the absence of such qualities.

And the article by Mike Johnston popularized the term in the Western community Here is his discussion of some subjective ratings which he applied to certain lenses. http://theonlinephotog​rapher.typepad.com/fil​es/bokehrankings5.pdf.
None of the early articles mentioned had any attempt to quantify bokeh! So it interesting to hear one Japanese claim that they do quantify it.

Even Zeiss mentions the 'bokeh -- the quality of blurriness', and then also the 'quantity of blurriness'
http://www.zeiss.com …/$File/CLN35_Bo​keh_en.pdf


Makes me wonder just how long you have been in photography, to see if you are like most Western abusers and quantifiers of the term 'bokeh'...relative newcomers since the digital age of photography, and the misuse comes regardless of one's language.

Yeah, I suppose elsewhere the term is used a bit differently.

bokeh is a noun, verb, and adjective in Japanese.

the noun just refers to the blurry part of the image.
the verb means "to make blurry"
the adjective essentially means "blurry".

Well, here's the wikipedia article for bokeh in Japanese
http://ja.wikipedia.or​g/wiki/ボケ_(写真)

"F値が小さいほどボケの量も大きくなるが、解​放絞りではレンズの収差も出やすくなるので、少​し絞って撮影する場合も多い。"

It says, "as you lower the f-stop the amount of bokeh increases, but aberration tends to occurs when lenses are used wide open, so most of the times people stop down the lenses".

So while bokeh is not directly quantifiable, you could definitely say one photo has more bokeh than the other. You can indirectly quantify the amount of bokeh by using the diameter of CoC.

the quality of bokeh is called ぼけ味 (bokeh-aji).

Reevo wrote in post #13510806
You're talking to the wrong guy because... I am, a Japanese photographer, muhahahaha. and it's totally normal for people to say もっとボケてる or こっちのほうがボケてる, which means that you can compare the amount of bokeh. I'm sorry but I don't think you can argue with me about this when you can't even read those characters (assuming that you can't speak japanese)....

I ran those two phrases through Google Translate. もっとボケてる translates as "more ditzy", and こっちのほうがボケてる came through as "Koch is more ditzy" (perhaps quite apropos in U.S. current events, but I'm not sure how it relates to photography!)

From here on out, I move that we describe the aesthetic quality of out-of-focus blur as being more or less 'ditzy'!

To me it sounds like those writers Wilt mentioned could have misused the word while introducing it to the western world which in turn very happily accepted that catchy word in their vocabulary for the lack of a better word to describe the quality of OOF blur. Now that it has assumed the widely accepted meaning to describe quality instead of quantity, I am going to stick to it. The point of the original post wasn't to discuss the meaning of the word, was it?

Veemac wrote in post #13511992
From here on out, I move that we describe the aesthetic quality of out-of-focus blur as being more or less 'ditzy'!

My 70-200 MkII is way more ditzy than my other lenses.


Although I am no mathematician, I do like to learn about different DOF and how the different the different sensored cameras behave at same focal lengths. All I read was blah blah bunch of numbers, 1.6 stops different at 50mm. That's good info.