Growing up, my parents had a half-frame camera. Which meant 72 photos on a reel of film. Since they weren’t shutterbugs we’d get two Christmas’s on a reel of film if they forgot to pack the camera on vacation.
When I first worked in a photo lab, years ago, I’d regularly come across a 12-exposure 126 film with Christmas for the first three or so frames, then Summer in the middle, then Christmas. Those films were always “left in the car’s glove compartment so the heat can fry them” fogged.
I’ve never heard of the term ‘focal node’. Probably meant ‘focal point’, no?
These things all have mathematical formulas… (Note, I’m doing all this from memory, so feel free to catch me out of mistakes.)
Focal length: Distance from focal point to plane of sharp focus when focused at infinity.
How can I determine where the heck the focal point is? Easy: When the focal point of the lens is double the focal length’s distance from the image, the subject and the image are the same size. (Also, the distance from focal point to image is the same as focal point to subject.)
So, take a target (with a scale on it), and ‘focus’ the lens (that is, adjust the lens so that the image is close to the same size as the target) then move the groundglass/CCD/whatever closer or farther from the lens until it’s in focus.
Nope, not the other way around: When you’ve got the lens very close to the subject, focusing the lens, which changes the distance from the lens to the subject, has a greater effect of the size of the image than does moving the film or CCD (given a constant distance between subject and image). Up to the point where the image and subject are the same size. Trust me on this. I can provide mathematical proof.
When you’ve got the image in focus and the same size as the subject/target, mark a spot on the lens. Now move the lens back until objects at infinity are in focus. Except for very long lenses, almost anything over 10km is far enough - stars are pretty useful here, their pinpoint-edness is handy.
Now, measure how much that spot has moved. This is the focal length of the lens. Next, measure out that focal length from the image to the lens, while focused at infinity, to find that lens’s focal spot. For some lenses (shorter lenses used on SLRs with mirrors and on ‘folded’ lenses (with mirrors), you’ll find that the focal spot is actually physically outside the lens.
OK, you’ve got the focal length now. Great.
Next: the f-stop or f/-number. That’s a pretty simple formula: it’s focal length divided by diameter of the opening at the focal point (or at the aperture - as close as possible near the focal point).
The number should have been, as was pointed out, the area of the opening, but in the old days, lenses used to have things called ‘Waterhouse’ stops. Lenses had slots, at/near the focal point, where you could drop in a small metal plate with a round hole in it. These Waterhouse stops would have the diameter of the stop’s hole written on them. The stops could be used on a number of different lenses, each of which might have difference focal length.
The photographer, deciding that a certain f-stop was needed for a photograph, would choose the ‘stop’ which would give him this. So, given a 90mm lens, if a f/11 stop was required, an 8mm stop was used - 90mm / 8mm = f/11. Yes, that’s why f-numbers are expressed as fractions.
Why use the diameter rather than the area? Simpler (though not really representative) math, that’s all.
(Side note: the fact that for almost all lenses, the aperture is not at the focal point, is one of the things that introduces diffraction when the lens is ‘stopped down’ quite a bit.)
Now, since the amount of light passing through a lens is a function of the area of the aperture, doubling the diameter of the Waterhouse stop gives you four times (that is two squared) the amount of light. So photographers memorize the doubling/halving sequence of f-stops: f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, etc. Sharp eyes will notice that every other number is doubled. Sharper eyes will notice that the 1.4 in f/1.4 is the square root of two, or nearly so, and guess that the f-stop ‘before’ f/1.4 is f/1…
And why doubling/halving the shutter speed doesn’t double/halve the f-stop number.
Next, left as an exercise for the student, with hints:
- The relationships between focal length and size of image (why is 100mm ‘telephoto’ on 35mm cameras but ‘wide-angle’ on 4x5 cameras?) (why do old-timers like me really want to know the size of CCD on their cameras, anyways?);
- depth of field - what are the factors? (look up ‘circle of confusion’);
3a) What’s this ‘depth of focus’ I keep hearing about? Or;
3b) What’s this ‘depth of focus’ that I’ve never heard about until now? (very useful for macro photography and when using large-format and graphic arts cameras); - “Really? There’s a formula for print viewing distance?” (Next time you’re staring at the ‘distortion’ of a fish-eye photo, maybe you’re the wrong distance from the print, eh.)
You might be technically correct, but you’ve gone about determining the focal length in the most obtuse way possible, and I’ve also never heard of your “focal point” term before.
By definition, a lens’ focal length is the distance the lens (if it were a simple lens comprised of only one element) would be from the film/sensor plane when focused at infinity. In order to focus on closer objects, you move the lens further away from the film/sensor plane. When you focus down to 1:1 (i.e., a 1" object takes up 1" of the sensor/film), the simple lens is twice as far from the sensor plane as it is when you are focused at infinity. So while its true that the difference between 1:1 and infinity is the same as the focal length, this is not how focal length is defined.
I’ll repeat your point that these definitions have little correspondence to the real world, as complex lens designs with multiple elements and both telephoto and retrofocal formulas mean that the lens is often nowhere near where you would expect a simple lens to be (in particular, for many wide-angle lenses you would expect a simple lens to be within the mirror box… and this explains why wide angle lenses are larger and more complex on SLRs than they are on rangefinders and point and shoot cameras that don’t require a mirror box).
Oops, I forgot to clearly include that definition of focal length, and I shouldn’t have relied of my memory for ‘focal point’. Thanks for the correction.
The focal point is actually the point where the rays converge, that is the plane of sharp focus. My method (and it is just a method) can be used to determine where that theoretical “middle of the that thin lens” in a complex (or ‘thick’) lens is.
Over the years I’ve spent in the photo industry, I’ve seen lots of lenses with precise focal lengths hand-engraved on them, by the manufacturer (say, a 127mm lens would have 128.1mm hand-written on it). I’m quite confident that methods similar to my round-about method were used to actually measure their focal length (using a specialized machine or setup).
Focal node is an idea that is not usually very relevant unless you design cameras or other things with optical systems or optical like systems.
thaumatechnicia is mostly right, only there are actually two focal nodes, the actual and the virtual one in a compound lens design. A 200mm telephoto is usually much shorter than 200mm, the virtual focal node is actually outside the lens in front of the filter mount. In a telephoto the virtual focal node is in front of the actual one and in a retrofocus it is behind it. In a normal lens the two are in the same position. Which is why my 85mm f/1.4 is listed as a ‘normal’ lens by Nikon rather than a telephoto. It is actually the lens design that determines if a lens is normal, not the focal length. Though Nikon marketing do list the f/1.8 as normal as well even though the formula looks like a tele to me.
The focal point is the point at which the light rays converge. If that part of the image is in focus, the focal point and the focus plane (i.e. sensor) are at the same point (coincident).
The focal node is one of the names for the place inside the lens where the light rays cross over and the image inverts. It is usually only of interest if you are shooting a panoramic picture.
If you are designing a camera, you can choose the distance between the focal node and the sensor. Move the sensor back and the image will be bigger. Move it forward and it will get smaller. Moving the sensor will change which parts of the image are in focus and require something of an adjustment but lets ignore that.
The magnification factor of the image is determined by the distance to the focal node, the point where the light rays cross over. If you have a 12MP sensor the amount of light falling on a sensor cell will be the same whether you have a tiny sensor close to the lens or a huge sensor far away.
There is an advantage to a larger sensor but it isn’t the one that folks on the boards bring up. Light is a quantum phenomena and has a finite wavelength. The sensor can’t resolve finer than the wavelength of light. So the 40MP phone cameras can’t possibly resolve that fine. But a CX sensor like this is good for 50MP, DX for about 100MP and FX for at least 200MP. But because of diffraction you need an f/4 lens or faster to get there.
Answering bwv812, you need to change your attitude, if you don’t understand a term that someone uses then use the Google before assuming that they must have got it wrong. I do know the physics of lens design. I also have a D300 and a D800 and I have a lot of experience of the difference between how they respond.
I do know the difference between focal length and the focal node. I also know the difference between the aperture and the focal ratio which is often called the relative aperture. It is clear that you don’t. So next time you post check your facts and imagine that you are trying to argue about physics with someone with a doctorate from the department of nuclear physics at Oxford University because thats what you are doing.
Of course changing the sensor size in an existing camera design is going to reduce quality. The Nikon F-Mount was designed for a particular size of sensor, 35 mm film. To allow use of existing lenses, the sensor has to be mounted the same distance from the lens flange and thus the same distance from the focal node in the lenses. Otherwise it would be necessary to recalibrate the lenses to use them on DX format or in some cases redesign them completely.
Even so, if you go to this site and use the ‘depth of field equivalents’ you will find that a 50mm f/2 on FX is equivalent to 35 f/1.4 on DX if you use the focal ratio to calculate the aperture you will find that they are both 25mm. It is the diameter of the lens and the number of elements that has the biggest impact on cost. The cost of grinding aspherical lenses goes up with the cube of the diameter, for spherical it is just the square.
http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm
If you want good shots then you need a big lens. In a new camera design sensor size doesn’t matter but lens size does. In a legacy camera design, reducing the size of the sensor causes problems for designers at the wide end.
[Stupid site won’t allow me more replies]
The definition of a ‘normal’ lens was only necessary when telephoto and retrofocus designs first appeared. This was in the early movie industry, a wide cine lens has to be retrofocus because of the need for a cine shutter and film advance.
If you look at the early camera magazines you will see discussion of long lenses as being ‘normal’ versus ‘telephoto’ designs. Telephoto quickly dominated in the early rangefinder era. That is why Nikon don’t call their 85mm lenses telephoto even though the field of view is a lot narrower than that of the eye (which is the usual popular definition).
Telephoto, normal and retrofocus have very particular meaning in lens design. They are descriptions of the type of lens, not the focal length. The reason these get confused is that a long lens is almost always a telephoto these days.
The Nikon marketing people are very precise (no doubt their engineers will carp otherwise). They describe the 85 f/1.8 as a ‘telephoto lens’ which it is. But the 85 f/1.4 which I use and is the one I cited is described as having a ‘telephoto field of view’. This is the same in the specs ‘Fast 85mm lens with a maximum aperture of f/1.4’ vs ‘A fast, fixed-focal-length, medium telephoto lens with 85 mm focal length’
The nikon guys are engineers who care a LOT about lens design. The reason the f/1.4 costs more than three times as much for 2/3rds of a stop is that it is a normal lens rather than tele and this allows better handling of the bokeh.
Um, unless the nomenclature has changed since, oh, when photography started, a normal lens is one whose focal length is roughly the same as the length of the diagonal of the film or sensor. Because the size of the film or sensor also dictates the angle of the field of view, the terminology (wide-angle, normal, telephoto) is useful and changes based on situation. The focal length of a lens (more properly ‘an objective’), does not, by itself, determine whether a lens is called this or that.
For 35mm full-frame (or in Nikon parlance, FX-format), that diagonal is about 43mm, so 50mm is close enough, and, in this case, they are called ‘normal’. Lenses shorter than roughly 36mm are considered wide-angle, longer than 55mm are considered telephoto. Again, this applies to a 24x36 film/sensor.
For Nikon’s DX-format cameras (24x16, almost half-frame), normal is about 29mm. So, for a DX camera, a 35mm lens is wide-angle, where it’s ‘normal’ for FX. But 85mm is telephoto for both of them.
According to the Nikon USA website, the 85mm is called a “medium telephoto portrait lens”. Me, I would have called it a “short telephoto formal portrait lens”. I guess the “medium telephoto” is when it’s used on a DX. Likewise, I consider the 105mm is a “short telephoto candid portrait lens”. In my day, the 105mm f3.5 Micro Nikkor was THE lens to get. Superb optics…beautiful plumage.
One of the disadvantages, if you ask me, of using zoom lenses all the time is that one loses (or never acquires) a feel for the subtle effects that focal length (per film/sensor size) has on perspective and depth of field.
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This definition makes no sense in the context in which you used it:
You make it sound like there is only one focal point for any given lens, and that this singular focal point is used to determine the focal length. If the focal point is in front of the lens, and is simply wherever you are focused, then the focal point when focused at infinity will be infinity, and the first sentence quoted above makes no sense (not does the second, for that mater). Or if you mean that the focal point is behind the lens (which is what we typically think of when we talk about the plane of sharp focus), then you entire procedure makes no sense given the terms you are employing.
I highly doubt it. Very few lenses can focus down to 1:1, and those that do employ things like floating elements that effectively change the focal length in order to optimize optical quality at close focus. The much simpler method would be to use the field of view at infinity focus, which (for any given format) has an established relationship with focal length.
Why don’t you actually try explaining these things you understand, then? It’s true that a 25mm f/2.0 will give the same intensity of light to a small 1"x1" sensor that a 50mm/2.8 will give to a large 2"x2" sensor. This means that both cameras can use the same shutter speed and ISO at f/2.0. But in absolute terms, the 2"x2" has four times the area and is exposed to 4 times the number of photons. So if both sensors have the same number of megapixels, the smaller photosites/pixels of the small sensor receive only 1/4 the number of photons as the larger photosites/pixels of the larger sensor. The fewer number of photons per photosite/pixel is going to mean reduced performance at high ISO and low light, due to reduced signal:noise ratios. The small 1"x1" sensor will have the same per-pixel noise/quality at 10megapixels that the larger sensor will have at 40 megapixels, because this is when their pixel-density is the same — and this is true regardless of whether the camera is a SLR or a compact point and shoot. It’s simply physics, albeit not nuclear physics.
Also, the only term I questioned was “focal point,” and Googling that would be no use because of the way the term was (mis)used would have eliminated they typical interpretation of the term.
Cool. Did they teach a lot of lens design and digital sensor courses when you did your studies? Are we discussing nuclear physics? Is this relevant? Shall I trot out my computer science degrees? Or my ones that are even less relevant?
And I’ve pointed out mistakes you’ve made, and shown how you are wrong. You’ve waved your hands and made noises without showing how my understanding is wrong (but I guess it is hand waving from someone with a doctorate in the relevant field of nuclear physics, so there’s that). In fact, I specifically made reference to simple lenses (and the optical size of apertures as opposed to their true physical sizes) because with compound lenses it isn’t easy to determine the optical center of a lens (and this goes for your 85/1.4, as well).
Again, you just don’t seem to be able to talk to people without respect. What prey is your experience in the field?
The term Nuclear Physics is obsolete as we worked on particle physics by the time I was there. But the experiments make use of optical sensors and magnetic fields and the like. And even though those are not precisely the same as the optical systems in cameras, many of the principals are the same. And more importantly, all the teaching materials begin on optical systems for cameras and microscopes as a way to demonstrate the principles.
You are right about ‘focal length’ being a proxy for the field of view when focused at infinity. If you think about it, the focal length of every camera lens has to be adjustable because that is exactly what has to be done to focus the lens.
You are not right about the other claims you make and having already misunderstood ‘focal point’ for ‘focal node’ then tried to correct me rather rudely, I think it rather behooves you to admit you were wrong and apologize. Instead you launch into another rather confused attack and accuse me of not understanding the subject.
You are now confusing a 25 mm aperture with a 25mm focal length and so your latest ‘explanation’ makes no sense at all. These terms do actually have meanings. I suggest you try to find out what they are before any further ‘corrections’.
Hint, most of the people whose ignorant opinions you are repeating have no more understanding of optics than you do.
Hey, before I made my first comment you were telling people that they didn’t understand things (e.g., “You don’t seem to understand the difference between depth of field and exposure”—a common mistake, I’m sure—and “You also seem to be confusing…”); I was simply replying in a similar vein.
No. The focal length, by definition, is the distance the simple/thin lens would be from the camera in order to focus at infinity. Focusing closer does not change the focal length of the lens. The field of view is only a proxy for focal length if the sensor size is the same. But an 80mm Medium Format lens is going to have a different field of view than either an 80mm Large Format or 80mm 35mm-format lens. That being said, if you are using a baseline format such as 35mm, then knowing the field of view at infinity (field of view also narrows as you focus closer) means you can easily determine the focal length.
I haven’t said a darn thing about “focal node.” If I have, quote me on it. If you can’t, maybe it’s you who should apologise.
I’m not confusing focal length with aperture at all. There a reason nobody actually uses a lens’s physical aperture size, and instead uses its F-stop: for all practical purposes the actual physical size of opening is unimportant. I haven’t spoken of the physical aperture size except for a very limited purpose, and haven’t mentioned it at all in the comment you’re replying to.
Again, all you are doing is waving your hands and saying I’m wrong without even attempting to show how. And you’ve totally ignored the fundamental issue of the size of photosites/pixels, and the implications this has for the light-gathering ability of different sensor sizes. Smaller photosites = less photons = more noise = worse low-light performance.
And if we want to talk about how technical words have meaning, then why don’t you actually use those technical words instead of saying very vague things like “[i]t is the size of the lens that determines low light performance and depth of field,” as though “size” has some clear and unambiguous technical meaning.
1 inch eh? well, it’s not the size of the sensor that matters, it’s what you shoot with it! 
In a word, wrong.
You need to take camera brands, models, etc, with all the different-sized buttons and knobs and rings and floating elements and sensor sizes out of this particular discussion, as this only introduces confusion - without illuminating anything.
Take any converging lens, simple or compound, so that it focuses light coming from an object on one side of the lens into an image on the other side of the lens.
If that object is an infinite distance away (so that its light rays are parallel), the distance between the (converged-to/sharp/in focus) image on the other side of the lens and the (apparently nameless) something somewhere in the universe is called the focal length of the lens.
For simple double-convex lenses, this ‘something’ is usually in the middle of the lens. For many compound lenses, it can be on ‘in front of’ or ‘behind’ that lens. This ‘something’, is what I incorrectly called the ‘focal point’, and doesn’t appear to have an official scientific name. Photographers, when considering the Scheimpflug principle, call it the ‘lens plane’.
You can disassemble that very expensive, complex, difficult-to-take-apart, and probably glued-together compound lens, measure all the curvatures, air gaps, and then sample all the different elements (glass or plastic) used and find their refractive indices, and then try to calculate approximate the focal length of that, will-never-work-again lens. Or,…
…you could look up star charts, find the distance/angles between two objects in the sky, and wait for a clear, cold, clear night (away from civilization’s light pollution), and measure their size on the film or sensor. Not really practical. Especially for when trying to find the focal length of very short lenses - those two objects in the sky might end up being resolved into one pixel.
Or, you can simply find the point where an object is focused by the lens into an image that is the same size as the object. The ‘lens plane’ will be exactly halfway between the object’s plane and the image plane. See ‘Case 2’ in the link. There’s no need to disturb/move/rearrange anything inside the lens. Don’t believe me? Try it!
The image plane (or, as I like to call it, “the plane of sharp focus”) will then be exactly the focal length’s distance farther from the lens as it was when the object was at infinity. Further, the distance between the object and the image will be EXACTLY four times the lens’ focal length - giving you even greater precision for measuring that lens’ exact focal length. Clear enough?
Before anyone raise this point: Of course, it’s possible, even likely, that a particular compound lens doesn’t provide its best sharpness when the distance between the lens and the image is greater than the distance between the lens and the object. In this case, what you do, is turn the lens around. In case you wondered why a ‘reversing ring’ was sometimes needed, this is why. I’ve shot many a macro shot, in the field, removing the wide-angle lens from the camera’s body and hand holding it reversed against/near the camera body and using the lens’ sun shade (and my hand) as a shield against extraneous light. This is very handy when you need to shoot closer than your lens’ minimum focusing distance. But then again, back in the day, you had to grok his stuff, 'cuz the hardware was expensive, or didn’t exist.
Now, if anyone is still reading: I keep googling this term ‘focal node’, and get no results related to optics or cameras. Can anyone tell me what the heck is being referred to?
OK, I suppose you could do that, but in real life it wouldn’t get you very far. It will work only on non-retrofocus, non-telephoto lenses, which eliminates many —if not most—lenses. With telephoto and retrofocus designs your methodology would only double the telephoto or retrofocus offset inherent in the design.
It’s also far, far easier to actually employ the technical definition of focal length, which—once again—is the distance from the sensor the thin-lens equivalent of the lens would be when focused at infinity. And the much more practical approach would be to simply take the field of view at infinity focus, and then figure out the the focal length from that. I don’t think anybody is taking their lenses and putting them on bellows or extension tubes and focusing rails when they measure focal length.
I believe our esteemed doctor of nuclear physics is calling this the focal node. The Sheimplfug principle applies to the tilt aspect of tilt-shift photography, and has nothing to do with where the thin lens equivalent would be located. Instead, it is the degree to which the lens has been tilted. The illustration on the wiki page uses a thin lens for illustration, but the principle would be the same with a complex lens.
This is news to me. Bokeh character depends on how spherical aberration is handled. Over-correction of spherical aberration leads to bad background bokeh, while under-correction leads to bad foreground bokeh. Japanese manufacturers other than perhaps Minolta/Sony and Olympus have tended to prefer to over-correct, as this leads to higher contrast and more apparent sharpness at the expense of busy background bokeh. German manufacturers, and Leica in particular, have typically under-corrected, leading to creamy backgrounds in combination with lower contrast and lower apparent sharpness. I don’t believe that a lens being telephoto or normal has much of anything to do with this, and I imagine that Nikon’s DC lenses (105mm and 135mm), which allow bokeh to be adjusted, are evidence of this.
There’s a semi technical article on Bokeh written by a lens designer at Zeiss
Thanks for the link. The section on bokeh is pretty much the same as what I posted earlier, emphasizing that spherical aberration and how highly it is corrected as the primary determinant of bokeh character. Obviously things like aperture size determine how out of focus something is (though the ppr digs into this a lot more than I’ve seen before), and aperture shape clearly affect OOF highlights (though neither of these are really bokeh in the truest sense).
The rest of the paper looks interesting and I’ll read it later; thanks.
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