# lens question for the math geniouses



## axtstern (Feb 19, 2013)

Over the last month I'm trying to get rid of the "Edelschrott" aka "Noble Glas Garbage" in my lens stable and turn more and towards the L lenses. With no L crops and me usualy using a 60D I gain a lot of reach from those glases with the 1.6 crop factor. But... I'm usualy not going for reach but for shallow DOF.

It seems that my initial idea about optics from the analog age is not covering the whole reality. I always thought if I bring the subject close to the lens, have the background far away from the subject, the lens as wide open as possible and the lens as long as convinient for the job I end up with a very shallow DOF. That means with nothing else changing, the longer the lens the more shallow the DOF

Now I use for example the EF 135L at F:2.0 I can mount it to my 5D and or 60D and I get the same AE of 200/1 Second at 2.0. So the crop does not cost me any light while extending my lens to 216mm. 

If I mount the 70 200 L on my 5D I of course do not loose any light as well if I change the zoom from 130mm to 200mm at 2.8, however the DOF changes quiet a lot (gets more shallow)

The change from 135mm on the 5D to 216mm on the 60D however does not generate this effect (shallow DOF)
It actually looks more like I have now a wider DOF. To get a simmilar wide DOF with the 135mm still connected to the 5D I would have to change to F:3.5 or 4.5

All my friends say that is because FF gives a more shallow DOF than Crop anyway however I believe that this is not a fact of the sensor's build itself but of the distance of the lens towards the sensor.

If I'm not mistaken than 1:2.0 on the 135mm describes the relation between the diameter of the first optical element of the lens and the effective length of the lens 65.25/135 in this example. Putting the lens on a crop camera extends its effective length to 216 but does not change it's front element so we have now a 1:3.456 lens (which fits to my observation with the DOF on the 5D either by rule or incident) 

Now to my question: How can the crop change the F number in regards to DOF but not in regards to the speed of the lens? And applied to the rest of the universe does this mean I need not only to convert the mm up but also the DOF capabilities down by 1.6 on all EF-S lenses?


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## johann3s (Feb 19, 2013)

To get an equivalent shot on a FF and a crop body, you need to multiply both the focal length and the aperture by the crop factor. You can play around here to get a better feeling of the subject.

So a 100mm f2 on crop will give exactly the same photograph as a 160mm f3.2 on full frame. 

I am not sure if i understand your question. But does this help you?


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## awair (Feb 19, 2013)

This ties in with the 'depth of field calculators' found on the web, and the 'circle of confusion' factor quoted for FF & APS-C.

See here:

http://www.panohelp.com/hyperfocaldistance.html

and here:

http://www.dofmaster.com/digital_coc.html

Canon has a similar calculator on its site, but don't have the reference handy.


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## TrumpetPower! (Feb 19, 2013)

All else held constant, the larger the format the shallower the depth of field.

All else held constant, the larger the physical aperture the shallower the depth of field. (A 100mm f/2 lens has the same 50mm physical aperture as a 50mm f/1.0 or a 200mm f/4.)

All else held constant, the greater the distance between subject and background the more the background will be blurred resulting in a perceived (but not actual) increase in the depth of field.

All else held constant, the closer the subject the more out-of-focus distant objects become.

So, to create an image with the shallowest (perceived) depth of field, you'd use the largest possible format with the largest possible physical aperture at minimum focus distance with the background as far away as possible.

In practice, even an 85 f/1.2 on 135 format ("full frame") is overkill. Your subject's pupil will be in focus but the iris won't -- and, even then, of course, only in the one eye; the other will be a blur.

...and then, of course, you can use the Scheimpflug principle to angle the focal plane....

Cheers,

b&


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## rs (Feb 19, 2013)

As previously stated, the DoF of using a 135/2.0 on crop makes the DoF and framing identical to a 216/3.2 lens on FF. However, not only is this the effective focal length and effective aperture as far as DoF and framing are concerned, it is also the effective aperture as far as light gathering goes.

The sensor doesn't do anything magic, other than a FF sensor capturing more of the image circle than a crop camera. Using a FF camera cropped to that central 1.6x area that a crop body sees does the same thing.

By using only a fraction of the available imaging circle, you are using only a fraction of the light coming in through the lens. While a 135L wide open is f2.0, when cropped you've cut out a lot of the imaging circle and therefore a lot of the light coming in through that lens. So, to print this smaller part of the image circle at the same size as an entire FF image circle, you're enlarging the individual pixels more, which means the image and noise are magnified to a greater degree. This effect means that as far as the light gathering goes, a 135L at f2.0 on crop acts just like a 216/3.2 lens would on FF.

To put it in sensor/pixel/amplification terms (and sorry in advance about any long and heated debates this kicks off), if you compare an 18MP 7D and an 18MP 1D X (as they both conveniently have the same number of pixels), the area of each individual photosite/pixel on the 1D X is 2.56 (1.6x horizontal and 1.6x vertical) times bigger than each individual photosite/pixel on the 7D. All things being equal, that equates to each photosite being able to gather 2.56 times as much light on the FF sensor. ISO ratings should be calibrated to be identical - stick an f2.0 lens in front of both sensors with the same shutter speed and the same amount of light, and each camera should produce images of equal brightness. So the amplifiers on the crop sensor are turned up by a factor of 2.56 over and above the FF sensor at any given ISO. Which means ISO 10,000 on the 7D is equal to ISO 25,600 on the 1D X when it comes to amplification, and therefore noise. That difference is about a stop and a third, which the crop of 1.6x is equal to.

And yes, to compare like for like, multiply both focal length and aperture by 1.6x to work out what a FF equivalent would be. These compact cameras like the FZ200 with its 4.5-108/2.8 lens winds me up by proudly having 'f2.8 25-600mm' written in big letters on the side of the lens. If they quote the focal length in FF equivalent, the aperture should be written like that too. Its the equivalent of 'f15.7 25-600mm', and no more...


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## alek35 (Feb 19, 2013)

TrumpetPower! said:


> All else held constant, the larger the format the shallower the depth of field.


That depends on what "all else" is. Assuming you mean the same optics, then
if AOV is constant then yes - if it is distance to subject then no (cropping i.e. "changing the format" ) does not
affect DOF.

Br,
Thomas


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## caruser (Feb 19, 2013)

(Deleted -- neuroanatomist has a better and more elaborate response, read that instead.)


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## TrumpetPower! (Feb 19, 2013)

alek35 said:


> TrumpetPower! said:
> 
> 
> > All else held constant, the larger the format the shallower the depth of field.
> ...



Yes, of course. Focal length must be matched to the angle of view for the format. A 50mm lens is a normal lens on 135, but it's a full-circle fisheye on 8"x10" and a supertelephoto on a P&S.

The only reason there's ever any confusion on this subject is because we happen to be at an unusual point in history when it's common to mount the same physical lens to two different formats. But that same 50mm normal lens on 135 is really a short telephoto on APS-C. "All else held constant" between 135 and APS-C would mean swapping the 50 for a 35.

Cheers,

b&


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## viggen61 (Feb 19, 2013)

> If I'm not mistaken than 1:2.0 on the 135mm describes the relation between the diameter of the first optical element of the lens and the effective length of the lens 65.25/135 in this example. Putting the lens on a crop camera extends its effective length to 216 but does not change it's front element so we have now a 1:3.456 lens (which fits to my observation with the DOF on the 5D either by rule or incident)



Not exactly. The f/number is the relation of the "Entrance pupil" of the lens to the focal length. "Entrance Pupil" is the apparent size of the lens aparture, not the physical size of anything.

No, the lens does not change, Focal length is focal length, aperture is aperture, etc. regardless of sensor size or format.

DOF is a function of focal length, aperture and distance to subject. If you stand in the same place relative to a subject, and mount a given lens on both a crop sensor and full frame, the DOF will be exactly the same at any given f/number. If you change the camera to subject distance (move the crop further away, or the FF closer), THEN the DOF changes. It changes because of camera to subject distance, NOT because of the sensor size.

All a crop sensor does is take a smaller picture of what the lens sees than a full frame does. If you had a 46MP sensor, then you could take a 39% crop of the center of the image, and get the exact same thing as the 18MP sensor on a 7D.


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## Knut Skywalker (Feb 19, 2013)

Remember, the actual focal length of the lens won't change if you smack it on a crop body. 135mm on crop are still 135mm, but because of the smaller sensor, you see less of the frame. You have a 216mm field of view, but not the same level of compression like with a 216mm lens.


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## neuroanatomist (Feb 19, 2013)

axtstern said:


> Now I use for example the EF 135L at F:2.0 I can mount it to my 5D and or 60D and I get the same AE of 200/1 Second at 2.0. So the crop does not cost me any light while extending my lens to 216mm. ...Putting the lens on a crop camera extends its effective length to 216 but does not change it's front element so we have now a 1:3.456 lens (which fits to my observation with the DOF on the 5D either by rule or incident)



Putting a lens on a corp body does *nothing* to the lens. A smaller sensor doesn't cahnge the focal length, that's an intrinsic property of the lens. A smaller sensor merely samples a smaller area of the image circle of the lens, meaning you get a narrower AoV from the same focal length lens.



axtstern said:


> Now to my question: How can the crop change the F number in regards to DOF but not in regards to the speed of the lens? And applied to the rest of the universe does this mean I need not only to convert the mm up but also the DOF capabilities down by 1.6 on all EF-S lenses?



Exposure (shutter speed for a given aperture) is determined by light per unit area of sensor, so a smaller sensor does not change exposure. Under the same lighting conditions, a f/2 lens on FF will give the same exposure as an f/2 lens on a PowerShot with a 4.6x crop sensor. 

Practically, you multiply the aperture by 1.6x to get the equivalent DoF of a lens on a FF sensor. The underlying principle as that to get the same framing with FF, you are closer to the subject than with APS-C, and clsoer means shallower DoF. If you take a shot with the same focal length lens at the same aperture and distance on APS-C vs. FF, the DoF will actually be shallower with APS-C (because of the different circle of confusion), but of course the framing will be radically different.

The example I often use relates to people who shoot an EF-S 17-55mm f/2.8 IS on APS-C and claim they won't go FF because there's no FF equivalent to that lens. In fact, the FF equivalent to the 17-55mm is a hypothetical 27-88mm f/4.5 lens (in terms of DoF for the same framing), so the 24-105mm f/4L IS is wider, longer, gives shallower DoF, and has IS. The larger area of the FF sensor translates to 1.3-stops lower noise, which more than makes up for the stop of aperture lost in terms of shutter speed.


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## aj1575 (Feb 19, 2013)

This is a good question, and it took some time until I really understood what is going on.

The problem is, that if you mount the 135mm on the 60D its focal length does not change. The focal length is a physical attribute of the lens, like its diameter or length; it is given by the design of the lens.
But what happens if you mount the 135mm on an APS-C is, that the image gets croped. The picture then looks like it was taken with a 216mm lens on a fullframe camera; the APS-C picture has a field of view that is equivalent to the one taken with a 216mm on a full frame.
In that croped area everthing looks exactly the same as in the FF picture (DOF).

When you zoom with the 70-200 on the 5D on the other hand, the focal length of the camera does really change physically. And when the focal lenght changes, the DOF also changes.




The problem is, that the focal length is a rather theoretical number, that is not very helpfull when you are not really into photography. The field of view in degrees would be much more helpfull in many cases. The problem is, that the field of view in degrees also depends on the sensor size, and therefore is no physical attribute of the lens itself.


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## TrumpetPower! (Feb 19, 2013)

There's an easy way for a photographer to get a mental grasp on the meaning of focal length.

Take a sheet of cardboard and cut a hole in it the same size as your camera's sensor (or film or whatever). Hold it 50mm away from your eye, and you'll see exactly the same field of view as your camera captures with a 50mm lens. Hold it 24mm away and you see what you would with a 24mm lens. Hold it 50mm away but with a hole cut for a different format and you now see what that other format sees with a 50mm lens.

50mm is about two inches. Space your fingers about an inch and a half apart and hold them about two inches away, and you see what a 135 format ("full frame") camera sees with a 50mm lens. Hold your hand in the same spot but bring your fingers closer, to about an inch apart, and you now see what an APS-C camera does with a 50mm lens. Hold a sheet of paper two inches from your eye and what it covers is what a large format camera sees with a 50mm lens. Hold your little finger two inches from your eye and what the tip covers is what a P&S camera sees with a 50mm lens.

...and now you should understand all you as a photographer need to know about focal length and image format.

For bonus points, imagine a spot midway between your fingers and your eye where the light gets focussed through. That spot is the size of the focal length divided by the aperture. For f/2, it's half the size; for f/4, it's a quarter the size, and so on. Hold your fingers two inches away an inch and a half apart and imagine a 3/4" hole between; that's 50mm f/2. Keep your fingers an inch and a half apart but move them four inches away, but the spot stays at 3/4"; that's 100mm f/4.

Cheers,

b&


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## axtstern (Feb 19, 2013)

Many thanks to all the feedback.

Through your answers I actually now understand the flaw in my question.
I did understand that changing through the crop factor not only the effective length of the lens but also the effective minimum aperture increases. However I did not apply the logic to it's full end and believed that the amount of light passing through would not change. Reading about it in the answers I understand now that the amount of light has decraesed but however so did the surface of the senor need to flood with light. 

Furthermore thanks for enlighten me with the concept of physical DOF and percieved DOF by blur of distant backgrounds... todays posts spared me a long and boring study through theory books.


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## RS2021 (Feb 19, 2013)

The Field of View (FOV) and the Depth of field (DOF) are two independent parameters. 

For any given distance from the subject, the lens projects the SAME image on the focal plane, it doesn't care if you have placed a full frame senor, or a APS-C sensor, or a smaller MFT at this focal plane.

The Out of Focus blur (Bokeh) remains the same on all sensors placed at the same plane, because the lens is projecting the same image...it doesn't care or know what is at the capturing end. 

But as you go from full frame to APS-C to MFT camera placed at the same distance, you will capture a smaller and smaller sliver of the image the lens projects back. This is the "field" you are capturing or a "crop" of the full image the lens is producing. 

So DOF is a function of the 1) aperture of the lens 2) the distance from the subject to the lens 3) and the distance between the background and the subject. 

DOF is NOT a function of the size of the senor.

Where people get into all sorts of pretzel contortions comparing DOF on full frames and crops is when they start to move the full frame camera closer to the subject to get the same FOV as the crop camera or vice versa. Now you have changed the DOF, true, because you changed the distance between the subject and camera. 

But, you still have the same DOF on both FF and Crop cameras placed at that distance!

But the full frame will capture more of the field from that distance and crop will capture less of the field from that same distance.


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## bseitz234 (Feb 19, 2013)

TrumpetPower! said:


> There's an easy way for a photographer to get a mental grasp on the meaning of focal length.
> 
> Take a sheet of cardboard and cut a hole in it the same size as your camera's sensor (or film or whatever). Hold it 50mm away from your eye, and you'll see exactly the same field of view as your camera captures with a 50mm lens. Hold it 24mm away and you see what you would with a 24mm lens. Hold it 50mm away but with a hole cut for a different format and you now see what that other format sees with a 50mm lens.
> 
> ...



Perhaps the most intuitive, understandable explanation I've ever heard... This is tremendously helpful. Thanks!


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## TrumpetPower! (Feb 19, 2013)

bseitz234 said:


> Perhaps the most intuitive, understandable explanation I've ever heard... This is tremendously helpful. Thanks!



You're welcome. Glad to help. I don't remember where I first encountered it, but the idea if not the source obviously made an impression....

b&


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