At What Focal Length? (85mm f/1.8 vs 70-200mm f/4L)

I was wondering, at what focal length with the 70-200mm f/4L will I'll be able to recreate the 'light blur' size of the 85mm f/1.8? (Both wide open so bokeh should be rather similar?).I came across this equation online that I wanted to confirm.


It said that if I wanted to recreate the same size 'light blur' I would have to have an equivalent 'blur disk' size which is calculated by Focal Length / Aperture.


So if I wanted to mimic the 85mm @f/1.8 - 85/1.8=47.22


I would have to have roughly 189mm @f/4 - 189/4=47.25


The camera to subject distance was obvious, but does this calculation assume that the subject to background distance remains the same?

I will be interested in seeing some technacal explanation of this. Because I do not see how they could be the same at equal distances since the DOF for the aperature you specified is not the same at equal distances. Because of that the OOF areas will be diffrent.


Also I doubt they would render the same Bokeh. It might be similar but two diffrent lenses will produce Bokeh diffrently due to other factors.

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Originally Posted by TakahiroW4047

I was wondering, at what focal length with the 70-200mm f/4L will I'll be able to recreate the 'light blur' size of the 85mm f/1.8?

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What do you mean by 'light blur'? The size of the disc resulting from an out of focus point source of light? That's going to be dependent on how far outside of the DoF that light source is positioned.


From a DoF standpoint, 127mm f/4 is equivalent to 85mm f/1.8 for the same subject distance - but in that case, the subject framing is obviously going to be different. If you don't care about the framing, the 70-200mm f/4 will result in a thinner DoF than the 85mm f/1.8 (same subject distance) at any focal length longer than 127mm. At a given subject distance, DoF with at 85mm f/1.8 is ~2.5 times deeper than 200mm f/4.


If you want the same subject framing (i.e. you have to back up further from the subject with the 70-200 so the field of view is the same) you cannot achieve the same thin DoF that you get with the 85mm f/1.8 - you'd need a 70-200mm f/1.8 lens for that. Three elements control DoF - aperture, focal length, and subject distance. Since field of view is determined by focal length and subject distance, if you keep the FOV the same as you zoom in, you are changing both focal length (longer meaning shallower DoF) and subject distance (longer meaning deeper DoF) - the two cancel other out, so the only factor influencing DoF is aperture. In other words, you will never be able to recreate the OOF blur of the 85mm f/1.8 with the 70-200mm f/4 if you need to keep the framing the same.


But if tighter framing is acceptable, you can get the same or thinner DoF with the f/4 zoom. In practical terms, that means if you take a head+torso portrait with the 85/1.8, then from the same distance take a head shot with the 70-200mm at 200mm f/4, you'll get more OOF blur with the zoom lens. But of course, if you put the 85mm f/1.8 back on and moved in closer for that head shot, you'd geteven moreOOF blur (which to achieve at 200mm f/4 you'd need to take a portrait of the subject's nose, or something like that).


Note that all of the above refers to the quantity of OOF blur. Strictly speaking, "bokeh" refers to the quality of OOF blur, not how much of it there is (although many people use the term to mean both aspects). Bokeh is determined by the number and shape of the aperture blades, the optical corrections in the lens design, etc.


Hope that makes sense, if not I can try again...


--John

The criteria you give is an under-determined system. That is to say, there is insufficient information with which to answer the question.


To be more precise, for a given subject magnification (i.e, you are able to adjust your camera-to-subject distance such that the subject in focus will appear approximately the same size in the frame in both cases), the diameter of the blur circles depends on the distance between the subject and the background object that is blurred. Your calculation is correct only if the background is at infinity. But if the background is, say, only 5 meters behind the subject, you are going to find the results quite different, and furthermore, the answer will also depend on the chosen subject magnification.


Therefore, there is no single focal length which satisfies your criteria. You must state two additional conditions: desired subject magnification and subject-to-background distance, at which point the focal length at f/4 that results in the same blur circle diameter will be uniquely determined. However, note that a second problem arises even if you can furnish these parameters: for certain smaller magnifications and/or short subject-to-background distances, the required focal length may not exist.

John


I thought his questions was along this line. Bokeh if created perfectly would be cone shaped. As you move further from DOF in to the out of focus area the circle or cross section of the cone would be become larger. For example a wall that is OOF 10

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Originally Posted by neuroanatomist

What do you mean by 'light blur'? The size of the disc resulting from an out of focus point source of light?

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Yes I was referring to the OOF blur size, of say christmas lights or shimmer of light passing through tree leaves, etc. I wanted to avoid saying 'Bokeh', because as you said it describes the quality. I'm trying to achieve the OOF blur size of a 85mm f/1.8 by moving farther back and maintaining the same framing of the subject. I'm hoping to find that sweet spot where the compression of field of view from the longer focal lengths will yield the maximum OOF blur size.

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Originally Posted by neuroanatomist

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Three elements control DoF - aperture, focal length, and subject distance. Since field of view is determined by focal length and subject distance, if you keep the FOV the same as you zoom in, you are changing both focal length (longer meaning shallower DoF) and subject distance (longer meaning deeper DoF) - the two cancel other out, so the only factor influencing DoF is aperture. In other words, you will never be able to recreate the OOF blur of the 85mm f/1.8 with the 70-200mm f/4 if you need to keep the framing the same.

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I guess this applies the best for what I'm trying to figure out.Actually this may simplify things even more. You're saying that since I'm maintaining the same frame of view, the +focal length and +subject distance will cancel each other out. Therefore, you still get the same OOF blur that's maximally possible at f/4. But that still leaves the compression of field of view right? Pardon my elementary drawing [:P] I'm not too worried about the quantity of OOF blur. Please correct me if I have this concept incorrectly!


EDIT: Oops I forgot to add the picture of the subject in the 'final images' haha


[img]/resized-image.ashx/__size/700x0/__key/CommunityServer-Discussions-Components-Files/12/3513.Bokeh-copy.jpg[/img]

The more I think about this. Aperture only affects the volume of light that is allowed in the lens, Shutter speed the duration the light is let in.


The only thing that could change the size of the cones and circles would be the distance to the OOF background, compared to the focus point, distance to the camera and size of the lens. Wouldn

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Originally Posted by wickerprints

Your calculation is correct only if the background is at infinity.

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Would the "infinity" distance be the "Hyperfocal Distance" listed with the DoF calculator? Assuming I did the subject distance calculation right to keep the same frame of view...


85mm f/1.8 @ 30ft from subject: Subject to Background: 700.5ft


190mm f/4 @ 67ft from subject: Subject to Background: 1559ft


*(190/85) * 30 = 67 is this right?

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Originally Posted by HDNiteHawk

Via Wikipedia: Cone of Confusion



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Defocused object points are imaged asblur spotsrather than points; the greater the distance an object is from the plane of focus, the greater the size of the blur spot. Such a blur spot has the same shape as the lens aperture

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From what I've experimented so far, longer the subject to background distance creates larger diameter OOF blur. But typically the subject to background distance is significantly long enough, that the subject to camera distance typically has greater impact on the OOF for me. I think the ratio of 'camera to subject to 'subject to background' is the greatest determinator of OOF rather than the distance?

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Originally Posted by TakahiroW4047

From what I've experimented so far, longer the subject to background distance creates larger diameter OOF blur. But typically the subject to background distance is significantly long enough, that the subject to camera distance typically has greater impact on the OOF for me. I think the ratio of 'camera to subject to 'subject to background' is the greatest determinator of OOF rather than the distance?

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I am responding to the posts in the hopes of actualy learning somthing here, rather than saying I have any insight.


It looks like to me the closer the subject, the ratio of how far it is to the background compared to the distance from subject to camera is going to have the biggest impact. As you get closer and the background further away the circles become larger and overlap creating more blur.

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Originally Posted by TakahiroW4047

Would the "infinity" distance be the "Hyperfocal Distance" listed with the DoF calculator? Assuming I did the subject distance calculation right to keep the same frame of view...

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No. What I mean is that the size of the blur circle is proportional to the entrance pupil diameter only when the background is infinitely far away. Recall that the entrance pupil diameter obeys the relationship D = F/N, where F is the focal length and N is the f-number. Thus your calculation of 85/1.8 and 190/4 are actually calculations of the entrance pupil diameter. When you focus on a subject not infinitely far away, then any object not in the plane of focus will cast a blur circle (or circle of confusion) on the image plane. The size of this image circle may or may not be small enough for you to consider the result "acceptably sharp," which is why we construct a convenient abstraction called "depth of field." The DOF basically answers the question of the range of object distances over which the resulting blur circles are smaller than some predetermined upper limit, which is our criterion for what is acceptably sharp.


For example, using a particular camera and with a certain amount of sensor-to-print enlargement in mind, I might say that my definition of "acceptably sharp" is if the circle of confusion is less than 0.03 mm in diameter. Then an object not in the plane of focus may still appear acceptably sharp if it is close enough to the plane of focus to project a blur circle smaller than this limit. But if it is far enough away, it will project a blur circle large enough for me to discern, and thus that object will no longer be acceptably sharp.


Now, back to your question. If your subject is at some fixed finite distance from you, and you focus on it, then background objects behind it will cast blur circles on the image plane whose size increases with subject-to-background distance. But this increase tends towards a maximum limit, in the sense that even an object at infinity will cast a blur circle of some finite size. That is to say, objects at infinity do not become infinitely blurred. How large is this maximum blur circle? The answer is, it is proportional to the diameter of the entrance pupil, with the precise proportion being related to the subject magnification.


Therefore, for the same subject magnification, a background object infinitely far away (not the hyperfocal distance, but actually AT infinity, in the sense that light rays entering the lens from that object are parallel), will cast the same size blur circle if you use an 85/1.8 or a 190/4 lens.


But as I noted previously, this is not going to remain true if the background object is NOT infinitely far away.

Let me label the diagram you posted with the terminology I am using. We call the distance from the point "Camera" to the point "Subject" the subject distance, which we might label S. The distance from "Subject" to "Lights" is the subject-to-background distance, or B. We will use the traditional F for for focal length and N for f-number. Finally, not directly shown in your diagram is the subject magnification M, which is the ratio of the size of the subject on the image plane, to the size of the subject in the object plane. In other words, M is simply the size of the subject in focus on the sensor divided by the size of the same subject in real life.


When you say that you want to maintain the same "frame of view," what you are actually meaning is that you wish for M to remain the same. For a pair of different focal lengths as you have drawn in your diagram, what this requires is a change in S, which you have also drawn. You have also shown that because F relates to angle of view, changing S also changes the relative size of the blur circle at S+B.


But as you have correctly surmised, by stopping down in the lower diagram, you are able to decrease the size of the blur circle to match those in the upper diagram. Alternatively, you have also correctly inferred that, if the f-numbers of the upper and lower diagrams are fixed at, say, f/1.8 and f/4, then there is a relationship between the focal lengths that would result in the same degree of background blur.


However, what my previous posts have explained is that this relationship would only hold true for a SPECIFIC subject distance S and a SPECIFIC subject-to-background distance B. If you changed either of these, then the focal length required in the lower diagram to match the degree of blur in the upper diagram will also change. Even worse, there are certain combinations of S and B for which NO focal length in the lower diagram will give you the same degree of blur.

Fortunately, I have created this nifty tool to illustrate the relationship between focal length, f-number, magnification, subject-to-background distance, and blur circle diameter. Below, we assume a fixed magnification M = 1/30. For the focal lengths being compared, the subject distance is automatically calculated so as to achieve this value of M. Then the value of B is logarithmically plotted on the horizontal axis, and the blur circle diameter in the image plane is plotted on the vertical. We have two hypothetical lenses, an 85/1.8 and a 189/4. This chart demonstrates the principle we previously discussed, in that for a background at infinity, the blur circles for both lenses are the same size (about 1.56mm). But as you can also clearly see, when a background object is not infinitely far away, the blur circle it projects on the image plane will not be the same in both cases--the longer lens' blur circle is smaller at each value of B. it should also be noted that, for any lens at f/4, 188.88mm is the shortest focal length that will yield this behavior; any shorter, and the blur circle will ALWAYS be smaller than 85/1.8, even at infinity, no matter the magnification chosen.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/5381.coc06.gif[/img]


Next, we show another comparison, the same 85/1.8 against a 300/4, for the same subject magnification (M = 1/30). Note the red curve is unchanged (only the vertical scale has changed), but now the 300mm lens shows that at a subject-to-background separation of about 8.5 meters, the two lenses will have the same blur circle diameter. Beyond that, the 300/4 renders objects much more blurry.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/5700.coc07.gif[/img]


Finally, we see how changing the subject magnification also affects the degree of blur. Here, we have chosen a relatively large value of M = 1/5, again between the 85/1.8 and 300/4. Notice that the shape of the curves appears to have shifted to the left, but also the vertical scale has increased greatly, so that the blur circles are MUCH larger than in the M = 1/30 case. In this scenario, the crossover occurs around 1.6 meters.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/3007.coc08.gif[/img]


I hope these diagrams help. It is my intent to make this interactive tool freely available for use by the general public in the near future.

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Originally Posted by wickerprints

Fortunately, I have created this nifty tool to illustrate the relationship between focal length, f-number, magnification, subject-to-background distance, and blur circle diameter.

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Now I have to ask this, and this questions is for the OP as well: Why? What would a scenario be that aperson would need to know the blur circle of two diffrent lens and try and match them to the same size?

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Originally Posted by wickerprints

It is my intent to make this interactive tool freely available for use by the general public in the near future.

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Great work! I'd love a copy, when it's ready for sharing. Looks like it'll run on my Mac. [H]

Wow! Thanks for the amazing explanation to go along with your extremely clever tool!!


So would a high-level generalization be that if your subject is close to the background then the most blur will come from aperture butif the subject is far from the background then most blur will come from iris size?

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Originally Posted by HDNitehawk

Now I have to ask this, and this questions is for the OP as well: Why? What would a scenario be that aperson would need to know the blur circle of two diffrent lens and try and match them to the same size?
<div style="clear: both;"]</div>

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To be clear, I did not create this tool in specific response to the OP's question. It has existed for some time now, because I was initially interested in exploring the question of which lenses will give me the greatest amount of background blur for a given set of conditions; and as you can see, the answer is not as straightforward as you may be initially led to believe. In fact, there are certain cases where, say, a 50/1.2 will give more background blur than an 85/1.8 but only up to a certain subject-background separation. I was not specifically interested in the point at which two lenses will yield the same blur circle diameter--but this tool happens to be easily adapted to show this.


Developing this tool has helped me to weigh my future lens purchases. It took about an hour of programming and debugging in Mathematica 7, then a few more hours of tweaking to make it look pretty. I plan to put it in a standardized notebook format with appropriate annotations, to prepare it for publication via the Wolfram Demonstrations Project.

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Originally Posted by wickerprints

To be clear, I did not create this tool in specific response to the OP's question.

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Darn! I would have been so honored! [;)]


Thank you so much for the elaborate explanation! I think I understand what your are trying to say but I'll be re-reading this multiple times for sure.


For those who were wondering. I was not trying to get the exact same OOF as the 85mm f/1.8, but just seeing if the lens itself was capable of creating OOF that was equivalent to or better than the 85mm f/1.8. As explained by wickerprints, the answer wasn't as simple as I had hoped for, but I now know that if used correctly I could basically substitute (to a degree) the 85mm f/1.8 (which I don't have) with the 70-200mm f/4L (which I do have)


Just trying to save myself ~$350 by utilizing my current gear to it's fullest [:D]

Thanks for the great diagrams, wickerprints, very informative.