Focal length

Firstly thank you for taking the time to comment. I always appreciate getting challenged as it helps me think through angles I’d perhaps not quite ironed out.

Now, you’ll notice that I’ve used the term “relative framing” quite often above.  I say this, because the angle of view, when altered by way of crop factor when used on different sensor sizes, cannot be directly replicated when using the same focal length.  For example, you’ll have a different amount of the scene in view in the background depending on the originating angle of view, but can relatively frame a subject to match at the focal point.  You can (assuming you have enough physical room) accomplish this at the focal point regardless of how far away that focal point is, but you’ll always have a difference in the angle itself.  To achieve the same angle of view from a fixed location between a full frame and micro 4/3 sensor, you would need to either double the focal length on the full frame, or halve the focal length on the micro 4/3 camera.  At this point, because the physical focal length is the variable, it will affect the DOF by increasing it for the smaller format, and decreasing it in relation by way of the larger format.

Focal length vs aperturetelescope

Much like a 50mm lens being a 50mm lens regardless of the size sensor it focuses light onto, an f/1.8 lens is an f/1.8 lens as well, period.  It doesn’t matter what size sensor it projects an image onto, a lens’ physical attributes are unchanged and the focal length is a physical measurement as is the aperture in relation to that physical measurement by way of a mathematical ratio.  That being said, there’s not really any need to understand the math involved to grasp that the aperture of a lens can be a powerful, creative tool as well as a huge aid in effectively capturing certain images.

You’d get the same depth of field effect when cropping the picture from the full framer down to the size of what the MFT camera would have captured with the same lens and the same lens settings. So I don’t really see the point of this comparison.

I’m curious as to how you’ve come to the conclusion that two pictures, taken from different locations are principally incomparable. If by “principally incomparable” you mean spacially inconsistent in relative terms, sure, but in no way would I say that means they’re principally incomparable. What I wanted to illustrate was the conception of depth of field and framing. When discussing the differences in FOV over various formats, many of us tend to reference this FOV in terms of the 135mm format, and to help illustrate this, it helps many of us who haven’t quite wrapped our heads around the math, to use this as a basis for comparison. Like I’ve said, focal length and aperture are physical measurements and do not vary. What vary’s is how these measurements interact with different formats in relation to each other. How subjects may relate to each other in frame spacially, outside of the actual horizontal slice of area in focus (DOF) was not really a concern in this discussion to me.

F-stop andfocal length

I do want to educate my audience, but I’m not quite sure what you mean by “debunk the zooming with your feet myth.” I’m not aware of that in terms of myth. You can “zoom with your feet” with any camera, with any lens, at any aperture and with any number of other variables, so I’m confused by your statement, but certainly elude to the idea of altering one’s distance, and what happens to your DOF, and angle/field of view if and when you do. I didn’t call it “zooming with your feet” per se, but I think that we’re able to surmise that is what varying your physical distance to mean.

I’m traveling for a little while but I’ll try to more accurately document my math and try to get some visual test shots as well.

Here is a mathematical breakdown where the ONLY variable changed is the sensor size. (we will say a full frame/135mm format using a 400mm lens at f/2.8 and a micro 4/3 camera using a 400mm lens at f/2.8, with a fixed location, focusing on a fixed subject, let’s say 100 feet away.

From a fixed location, using a singular focal length, regardless of the size of the sensor, if all is equal, so too will the depth of field be, or area in acceptable focus.  If shooting on a smaller format (sensor) you will gain the crop factor as well, which if using the focal length example above, a 50mm f/2 lens will operate with a field of view like a 100mm lens while on a 2x crop micro 4/3 format camera, with the depth of field of a 50mm f/2 lens on a full frame camera from that fixed location.

By using the wall as an example, I was only referring to EXPOSURE, and how a lens’ aperture will not affect the light let through from an exposure standpoint, not angle/field of view. This is why I broke the article up into two separate portions, DOF and EXPOSURE, as there are misconceptions in both areas in relation to lenses, apertures and formats.

If I were shooting birds, and wanted a nicely defocused background, and knew I would be doing so from a set, fixed location and had a 400mm f/2.8 lens available to me let’s say, (let’s assume that the 2x or 1.5/1.6x crop factors and the subsequent AOV would be preferable from that fixed location, or I’d be cropping into the image to match that anyway) I would more easily achieve that shallow DOF/defocused background by using a smaller sensor vs. using a full frame sensor and cropping after the fact. If I were, however able to decrease the distance to match the angle of view by way of the crop/smaller sensors while using a full frame, then of course, the DOF would be shallower still by way of the decrease of physical distance. The reasons to compare different formats from a fixed location, fixed variables, etc, is the same reason to compare different formats regarding noise performance, resolution, or any other measurable variable. Just as a shallower DOF can be desired for portraits, etc, a shallow DOF can also be desirable in sports, birding, wildlife, stage performances, etc and by altering only the sensor size, you do in fact gain a shallower DOF which can be handy if you’re unable to get physically closer, or have to rely on cropping after the fact.

On point two though, you’re incorrect. Different formats will provide different depths of field when that is the only variable and all other variables are constant. While cropping into an image captured on a larger format after the fact will produce an image with the same spatial relationship (ie: field of view as per above), it will have an altered DOF by comparison where the smaller the format, the shallower the DOF (again, all other things being equal).

If you want to educate your audience (and it looks like you do), why not debunk the zooming-with-your-feet myth instead, and simply leave it out of discussions on DoF, focal length, aperture and sensor size? Because people DO zoom with their feet?

Much of the conversation, or debate, revolves around the perceived ability, or inability to achieve shallow depth of field enabling a separation of subject and background elements (see bokeh, etc), or conversely enabling a deeper depth of field at larger apertures to enable a greater ability to capture a full scene in focus with faster shutter speeds for say, handholding (see street shooting, landscape, etc).

This article was largely born so that I could reference how a smaller format allows for a shallower DOF in certain situations compared to a “Full Frame” camera, namely when shooting from a fixed location and all other variables (aside from the sensor size) are constant. So often I hear people making statements like “FF provides shallower DOF” or “That is like a 100mm f/2.8 lens on a FF camera” which are only situationally true, yet never eluded to, nor discussed to show that they can in fact be wrong if taken as statement of fact, and just as easily disproved, again based on situational fact.

2) “If you’re on a safari, or taking pictures at a sporting event for instance (shooting from a jeep/fixed location ie: you aren’t able to run toward a lion, or players to decrease the distance) and have the option to bring a full frame camera or a micro 4/3 camera let’s say, and you have a 300mm f/5.6 lens for each camera, the micro 4/3 camera would not only crop the image to the EFOV of a 600mm lens on that full framer from that same location, but you’d have a shallower depth of field at the same aperture setting allowing for the ability to more easily separate the subject from the background.”

Okay, much like the “effective focal length” discussions, there seem to be many “effective aperture” discussions going around as many of these mirrorless interchangeable lens compact system cameras begin to really round out their lens offerings.  Well, I guess the micro 4/3 system has while the Samsung NX is getting there and Sony NEX system users still have a small handful of options, but not really here nor there.  The fact that so many lenses can be adapted across various formats can complicate the discussion.  Along with those who shoot with APS-C DSLR cameras, all references for focal length and depth of field seem to fall back to a full frame/35mm sized sensor as the benchmark.  There are some misconceptions as to how the aperture, or focal length affects the exposure or depth of field in these varying formats.

I appreciate the comment, but feel you didn’t actually read through or view the diagrams because I pretty much map out exactly what your asking me to do, so please feel free to correct me if I’ve assumed incorrectly.

If you were to then plunk an 800mm f/2.8 (assuming one would exist) lens on the Full Frame camera to match the angle of view without needing to crop, then you would halve the DOF achieved with the micro 4/3 camera using the 400mm f/2.8 lens from that same location, but then, you could further halve that DOF if you were to fix that same lens on the micro 4/3 camera… For certain applications, this can be very handy (ie: when wanting to more easily separate your subject from the background when needing to shoot from a fixed location, etc).

Aperture focal lengthcalculator

*You can check to see what the DOF, CoC and acceptable focus would be using online DOF calculators, like THIS ONE.  Input your camera, focal length, distance to subject and it will let you know what you’re working with.

I’ll be in Amsterdam this November! I’m there for the Marine equipment trade show which has me pretty busy each year, but there is always time for a beer and conversation 🙂

1) “If you are able to physically decrease the distance between the camera and the subject being focused on to match the same field of view (or conversely increase the distance with a smaller sensor format to equal the field of view) […]”

“The idea of matching the DOF by altering the aperture when the distance is also adjusted to acquire the same angle of view […]”

I think you and I would have a great time shooting together and discussing over coffee, or perhaps liven it up with some beer :). I do really appreciate this.

When you fix the focal length, aperture, camera position, and camera direction, you fix the in-camera projection. Regardless of the sensor it falls on. When it’s a small one, you capture a smaller portion of what you would capture when it were a big one. The bigger capture can be reduced to the crop (!) sensor one, by cropping away what did not fall on the latter. This way you’d end up with two pictures that are a recording of the same portion of the same projection. There is simply no way for these two to show differences in depth of field. I sincerely hope this comes across. If not I suggest you ask any friend physician to explain it further, for instance with a proper drawing.

When you fix the focal length, aperture, camera position, and camera direction, you fix the in-camera projection. Regardless of the sensor it falls on. When it’s a small one, you capture a smaller portion of what you would capture when it were a big one. The bigger capture can be reduced to the crop (!) sensor one, by cropping away what did not fall on the latter. This way you’d end up with two pictures that are a recording of the same portion of the same projection. There is simply no way for these two to show differences in depth of field. I sincerely hope this comes across. If not I suggest you ask any friend physician to explain it further, for instance with a proper drawing.

In relative terms, to equal DOF and relative framing, you need to open up one stop for APS-C or two stops for Micro 4/3 comparatively speaking in relation to full frame, (you have the same DOF with a full frame @ f/4 as you would with an APS-C @ f/2.8 or a m4/3 @ f/2 when the focal length is fixed and the angle of view/framing is equaled by way of adjusting the distance between the subject and sensor plane).  Example: a 50mm lens at f/4 on a full frame shot at 5 feet will have the same DOF (and relative framing) as a 50mm lens at f/2.8, on an APS-C sensor shot at 7.5 feet, or a 50mm lens at f/2, on a micro 4/3 sensor shot at 10 feet.  If adjusted to these settings, you’d have three very similar looking shots regarding subject framing and DOF.  Keep in mind that the angle of view is still tighter when shooting on a smaller format which will affect the actual angle.  By “relative” framing, in this case, we’re discussing the desire to have your subject occupy the same amount of space in the frame.

I use the term “relative framing” in the sense that at that focal point, the subject will relate to the frame similarly to what it would on another format. The angle of view will always be different when using the same focal length on different sensor sizes, essentially eliminating the ability to gather the same amount of the scene in relation to the focal point as there is no way to physically change the actual angle being viewed through (assuming we’re talking about a fixed focal length). Herein, I assume, is where you refer to the “zoom with your feet myth” and I apologize for not catching this sooner 🙂

Apertureandfocal lengthin photography

You’re absolutely right in that the angle cannot be replicated to provide an identical image pertaining to the spacial relationship between the subject captured at the focal point of the image, and any potential subjects that would otherwise fall within the original angle. This article was never really meant to illustrate how to produce two identical images, but merely attempt to explain the DOF replication (as well as “relative framing” of the subject) and expel the misinformation that seems to be regurgitated regarding the relationship between DOF and exposure when relating to sensor size.

Alright! Alexander, having had the time to finally reread through all of this, I now see where I was misreading your understanding.

Doesfocal lengthaffectaperture

Let’s look at the light transmission, or rather dispel any misconception that a lens with a large maximum aperture works any differently on any given format regarding light.  The light let through a lens, any lens, at a stated aperture will allow for the same shutter speed if all other exposure elements are equal.  This is important for many shooters who don’t want to use flash, or bump their ISO too far when shooting in less than good light.  For instance, a 14mm lens at f/2.8 will allow for the same light and shutter speed as a 200mm lens at f/2.8 (of course the subject, and field of view may change how the light interacts with the scene (potentially affecting the metering), like getting the sun, or bright light included in frame for instance, but let’s not get hung up on that for now).  Also, a 14mm lens set to f/2.8 on an APS-C, or micro 4/3 camera will allow the same light, and relative exposure as that 14mm f/2.8 lens would on a full frame (or any other) camera.  Exposure differences on digital cameras can be equated with incorrect listings on exposure variables on different cameras or formats, wherein the amplification is incongruous with the listings via other formats (i.e.: one company’s ISO200 isn’t the same amplification as another’s, etc) or may be a variable in the processing.  For all intents and purposes, you should be able to essentially use one camera to meter for another camera (I use a 5D2 to meter for my meter less medium format Hasselblad 500cm film camera all the time) as exposure is exposure and if there are sample differences, it is down to the translation by a particular camera and its processor, of the physical makeup of a lens, not the numbers.

Because you allow yourself to compare two shots at different camera positions, you make the discussion much more confusing and lengthy than necessary. In a properly structured discussion on what the title suggests this article to be about, one should start out by stating that two pictures taken from different positions are principally incomparable. What you do here is the opposite. Basically you are saying well if you don’t do it too much and squint your eyes a bit, for all intents and purposes, they are comparable, at least framing-wise, if you move the camera over the correct distance after applying your new AoV.

Simply put, there are two major factors that the aperture affects, firstly, the light allowed through the lens enabling a faster shutter speed and secondly, the depth of field, or area parallel to the sensor that is in focus.  Very simply, the larger the aperture, the more light allowed through the lens, the faster the shutter speed and the shallower the depth of field. (click here for a more in depth article on lens aperture)  We hit on the DOF above, now here’s the exposure side of it.

Digital crop factor, in this way, is not going to exhibit the same image if you were to merely crop a full frame image in post as the physical measurements will actually alter the depth of field, altering the appearance of the image, depending on the DOF, all other elements being equal.  However, if you were shooting so that everything was in focus for instance (think a distant landscape shot), and cropped into a full frame image file to replicate the digital crop factor, the two images would appear the same (barring resolution disputes, etc) as if you would have shot it at the same focal length, but recorded on a smaller format.

Thanks for your reply. (Not sure why I can’t reply to it myself again, if it was you closing the discussion, my apologies for this one.)

While the physical, spacial relationship between elements in the frame will appear exactly the same on a smaller sensor as it would if you were to crop into an image captured on a larger sensor, the depth of field does in fact change, period.

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For example, if you were to shoot a uniformly lit scene with a micro 4/3 camera and a 50mm f/1.4 lens wide open, shutter speed manually set to 1/100 second at ISO 200, it will show the same exposure as that same lens, opened to f/1.4, shutter speed set to 1/100 at ISO 200 shot on a full frame camera.  On the micro 4/3 camera, the angle of view will be cropped to the same angle of view as a 100mm lens would appear on a full frame camera, but assuming that the light hasn’t changed, the two images will show the same basic tonal and luminosity values for any congruous subjects in the images.  There may be firmware or processing variables, jpeg compression, etc, that could affect the way the final image is rendered, but the exposure will be the same.  If you have your metering set up differently, and attempt to adjust the exposure manually based on what your light meter shows, you may come up with differing exposure settings based on how, and what your camera may be metering, but this is beside the point.  Exposure is exposure.  You may see slight variances from one format to the next, or even two cameras with the same sized sensor, but this is more down to differences in how sensors, or pixels are able to gather light, S/N ratio, or other factors in how any individual electronic device translates analog data, through a lens, onto a sensor, and into a digital file.  For all intents and purposes, they should register and expose light near identically (numerically speaking).

Correction, ‘equivalent field of view’ in the last line should read ‘equal FOV’ or ‘matched FOV’. Apologies for the confusion.

Apertureof lens

“[…] (ie: “a 75mm f/1.8 lens for micro 4/3 is just like a 150mm f/3.5 lens on Full Frame” – which is situationally incomplete and technically incorrect.)”

By “situationally incomplete” when referring to someone making the statement that a m4/3 75mm f/1.8 lens is the same as a FF 150mm f/3.5 lens, I mean to say that it is definitively incorrect just as it is situationally correct. A 75mm f/1.8 lens is a 75mm f/1.8 lens, regardless of the format. If you wanted to frame an image on a micro 4/3 camera (with this lens) as you would on a full frame camera, then yes, you would need to back up, subsequently altering the DOF to match that of a FF camera using a 150mm f/3.5 lens, wide open. But here’s the thing, f/1.8 from an exposure standpoint is f/1.8 period (again why I divided the article) enabling the same shutter speed as a 150mm f/1.8 lens would on a full frame camera. Also, no one says you need to frame images on a smaller format as you would with a larger format using a longer lens, maybe (depending on the min focus distance for instance) you can achieve a better magnification rate with this shorter focal length and smaller format enabling a shot that would be unachievable with the larger format, which may also decrease the DOF, etc. It’s not apples to apples and that is what I’m trying to get to with all of this. SITUATIONALLY, these formats can match certain measurements, DOF, aperture, exposure, focal length, etc. But it’s these types of statements that are only partially true. You’ve even outlined it with your ISO differences and essentially answered the question.

Sorry for perhaps having been unclear on this, but field of view and angle of view are synonyms that can be used interchangeably. Check for instance Wikipedia on this. They denote the same concept, which is the angle that determines what a sensor/lens combination is able to see. Moving back and forth doesn’t change this angle (field) itself. It only changes what falls inside or outside of the camera’s angle (field) of view. The brick wall test you use in your article is a very special case in which you can’t tell from the end result if the angle (field) of view was changed (e.g. by means of zooming/cropping), or the camera position. This makes these actions look like they are essentially equivalent but this is really not the case. Any other setup would show this difference immediately. It is a theoretical but also artistical fallacy to see the brick wall test as a useful simplification for argument’s sake. Instead it’s an inappropriate, 2D model for describing effects and behaviours which inherently take place in 3D space.

To be honest, I’m not sure what ‘situationally incomplete’ means, but the quote is technically 100% correct. It can be shown that under the same circumstances, both quoted setups use exactly the same set of light rays to record their picture. The two pictures will be equivalent in terms of both angle of view and depth of field. The only difference is that these two sets of rays will be bundled stronger in the MFT camera, in order to cover a smaller area, resulting in a brighter projection inside the MFT camera. This is the reason why the MFT camera requires a lower ISO to reach the same brightness in the final picture when the same shutter speeds are applied (to eliminate motion blur differences). To be precise, if in these two setups the MFT camera were set to ISO100, the FF camera had to be set to (MFT ISO * (MFT crop factor ˆ 2)) = ISO400. Note that these ISO differences are perfectly in line with the f-number differences between the two setups.

Indeed this second comparison assumes equal camera positions. Sorry for missing that one. Still I don’t see what the value is of comparing two different crops, or more generally, two pictures which are different content-wise, to reach conclusions on depth of field characteristics of camera formats. I also don’t think it’s the assumption behind the concept of ‘equivalent aperture’ the article starts out with mentioning. On the contrary I think equivalent apertures are there to compare the behaviour of two camera setups of different format but equivalent field of view, resulting in the same crop when taking a picture from the same spot in the same direction.

The idea of matching the DOF by altering the aperture when the distance is also adjusted to acquire the same angle of view is only to help fully explain how the basic math works by showing it in diagram form. So often we hear “smaller the format, deeper the DOF/larger the format, shallower the DOF” and I wanted to explain kind of how that was both correct, and also incomplete. If I wanted to get the same angle of view using full frame on a smaller format, using the same lens, and wanted to equal the shallow DOF/defocused background while doing so, I merely wanted to show that to equal that DOF, you’d need to open up the aperture on smaller formats while decreasing your distance to achieve that. The incorrect assumptions that some have about the aperture acting differently regarding exposure was something I wanted to correct as well and this article kind of evolved into a conversation on Depth of Field AND Exposure since it was based on these types of comments coming from forums where people were making generalizations regarding both in relation to different formats (ie: “a 75mm f/1.8 lens for micro 4/3 is just like a 150mm f/3.5 lens on Full Frame” – which is situationally incomplete and technically incorrect.)

A m4/3 75mm f/1.8 lens is equal to a FF 150mm f/3.5 lens, ONLY IF the angle of view is matched, AND you’re talking about matching the DOF. Exposure wise, it is an incorrect and false statement. See what I’m saying here? Situationally incomplete. If someone making these types of comments were to elaborate as to what they mean, then I think it may eliminate much of this stuff, but too often, incomplete statements are made and can be very misleading to those who don’t quite understand.

If you look at the diagrams, you’ll see that I’ve taken actual focal length and made that the constant (50mm) for illustrative (and easy mathematical and relative) purposes. I pretty plainly lay out that if shot from a fixed location, using the same exact 50mm lens on three different formats (the variable), with all other variables constant the depth of field is shallower, and angle of view narrower, the smaller the format. When wanting to frame a scene the same way (ie: zooming with your feet by way of varying the distance), still using this 50mm lens on the three formats, to achieve the same DOF measurements, the aperture will need to be adjusted depending on the format (again to EQUAL DOF) and if aperture is not varied, what happens to the respective DOF for each format.

“If I were shooting birds, and wanted a nicely defocused background, and knew I would be doing so from a set, fixed location and had a 400mm f/2.8 lens available to me let’s say, (let’s assume that the 2x or 1.5/1.6x crop factors and the subsequent AOV would be preferable from that fixed location, or I’d be cropping into the image to match that anyway) I would more easily achieve that shallow DOF/defocused background by using a smaller sensor vs. using a full frame sensor and cropping after the fact.”

Going by this math, and while the angle of view on the m4/3 camera will essentially “crop” the image to what an 800mm lens would “look like” on a full frame camera, even cropping into the full frame image, it will still exhibit the deeper DOF, hence, when the only variable is the sensor size, the smaller the sensor, the shallower the DOF. Using the same lens, same aperture setting and from the same fixed location, the smaller sensor produces a DOF that is half as deep (or twice as shallow) as that of the larger sensor.

Your mathematical breakdown assumes different circle of confusion criteria for the different sensor sizes. This is the reason you end up with different depth of field numbers. This is correct as long as you don’t crop. The point here is that we do crop in this specific comparison. Please make sure you see why this is important. Otherwise, please try and find a valid reason for my same-projection-same-portion argument to be incorrect. Or ask someone else to find it. You will see it doesn’t exist.

Now, to kind of contradict my original oversight regarding the semantics between “Angle” and “Field” of view, while they are very often used interchangeably, there is a technical difference in that it does not account for spatial differences when altering the camera location to match the angle of a lens on a different format. To me, the angle is more technically definitive as it is mathematically measurable. The Field of view, while often used synonymously, to me applies to the physical relationship of objects in frame within the field of view, and how that interacts within the frame (or within that angle of view), that the camera is able to capture. Whether this is technically incorrect or not, I should more readily default to the Angle of view, which is more accurate. Two pictures, captured to mirror the same angle of view on two different sensor sizes, will have different spatial relationships between subjects, and elements in frame, but can show the same exact angle of view. If you’re altering the focal length to achieve this (ie: a 25mm lens on a micro 4/3 camera and a 50mm lens on a full frame camera), keeping the different cameras in a fixed location, then yes, these images will retain the same spatial relationship between subjects within the frame, or using the same lens on two different formats, and then cropping into the larger format’s image, it will also retain the same physical relationship. This is an entirely separate point to depth of field though.

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This is the zoom-with-your-feet myth. Field of view is a property of a sensor/lens combination and can not be changed by choosing a different camera position. Also, because of this, there is no need for such a thing as ‘EFOV’. It’s a magnitude that is by definition comparable across camera formats. This is why I personally prefer to use the term angle of view.

Aperture focal lengthformula

I was unsure about this until I started trying this out for myself by using the same exact lens on three different cameras from a fixed location a while back and kind of revisited it for this article. Just something I’ve found to be interesting and something I’d not really thought about before actually seeing it for myself.

That said, I do go into detail when outlining all variables for both situations when wanting to equal depth of field from a fixed location, and what happens when you vary that location (ie: zoom with your feet let’s say). I’m not sure how much more I should have said about it, as you’ve pointed out (and I’m very well aware of) I’m nothing if not long winded.

Regarding point one, I see now what you are saying and agree that I should have clarified the difference between “angle” and “field” of view.