Crop sensors

[michael_ryan6]

<p>Hi guys,</p>

<p>I've searched through the forums, and I've found a lot of answers that are *close* to what I'm looking for, but not quite...</p>

<p>I'm wondering about the effects of using a crop sensor on the aperture of a lens. I understand how apparent focal length changes, I understand how effective apertures change with the use of *teleconverters*, and I understand how DOF changes (or, rather, doesn't change) when a *crop sensor* is used, but I'm not sure I follow how the amount of light hitting the sensor is reflected by the aperture of the lens when we're discussing crop sensors.</p>

<p>If I use a 300 mm f/4 on a crop sensor (for ease, lets say a hypothetical 2x crop), I'd end up with the same field of view of a 600 mm and the depth of field of the 300 mm f/4 (ie, the same DOF as a 600 mm f/8), but what shutter speed would I need to end up with the same exposure as I did with that unmodified 300 mm f/4? Would it be the same? Or would it be 4x (or 2 stops) *slower* since only a quarter of the light is actually hitting the sensor? Ignore speed needed to hand hold, lets say this was on a tripod.</p>

<p>My question stems from some of the discussion about using the new Nikon mirrorless systems with existing lenses. Some sites have talked about the extra light gathering abilities of old lenses (ie keeping their large apertures with now longer effective focal lengths). For example, they're saying that using the above setup would give you the light gathering capability of a 600 mm f/4 (but without the narrow depth of field). On the one hand, it makes sense, since you don't lose light when you crop a picture, but, on the other, it seems like you're only getting a quarter of the photons actually hitting the sensor as you would with an actual 600 mm f/4. Which is correct?</p>

<p>Hopefully, this isn't *too* long winded, but I've just found so much info that's *almost* what I'm looking for! I'm sure the answer will be obvious when someone posts it, and this is just a case of a Sunday afternoon brain freeze...</p>

<p>Thanks!</p>

<p>Mike</p>

[Michael R Freeman]

<p>You're making it way more complicated than it needs to be. :)</p>

<p>Instead of thinking of it as the *total* light (number of photons) that hits the image plane, think of it as the *intensity* of light that hits the image plane (photons/mm²). That remains unchanged regardless of the crop factor (assuming an evenly lit subject) and that is what the exposure metering system uses to determine the appropriate shutter speed.</p>

[Peter_in_PA]

<p>The difference in depth of field between a 300mm f4 lens on full-frame vs. 200mm f4 (equivalent field of view is 300mm) on a Nikon DX sensor is minimal. The difference in light gathering doesn't seem to matter at all.</p>

<p>I think it's much better to think in terms of "crop". The 200mm f4 lens is always 200mm, and it's also always f4. You are merely cropping in to the image on the crop frame camera.</p>

[stephen_doldric]

<p>I think of crop as having an FX sensor, but when you crop you simply use a smaller portion of the sensor area (draw DX size over top of a FX sensor size). Its literally like cropping an FX photo down to size. F4 remains F4 on DX or FX, but you are only using the center portion of the sensor on DX. Of course when they make a DX sensor they save money by not making the FX portion.</p>

<p>If you shoot FX and DX both at F4 @ 50mm from 20 feet away you end up with everything identical - EXCEPT that on FX you have extra area in the frame around the edges. If you crop your FX photo to match the DX the photos will look the same (well very close pixel count, etc). On FX if you want to fill the frame to match your DX photo you need to move closer and thus decreasing your DOF.</p>

 

[hans_janssen]

<p>Put one piece of paper on your table, see how bright it is, fold it to half and put it back. What is the difference? The only difference is that it is smaller, but as bright as before. There is nothing changed to the light only to the surface that it is hitting.</p>

[joe_c5]

<p>To get the same exposure on the crop sensor in your example, you would use the same shutter speed on both the full frame and the crop cameras. Exposure is a measure of light per unit of area. Since the 2x crop sensor has only one quarter as much surface area, it does only collect one quarter as many photons compared to an actual 600mm f ⁄ 4 lens on a full frame 35mm camera. In this example, the crop camera will therefore have twice as much photon shot noise.</p>

<p>To get an image that is photon-for-photon identical (including depth of field) to 600mm f ⁄ 4 at 1 ⁄ 600s and 400 iso on a full frame camera, the 2x crop camera would need 300mm f ⁄ 2 at 1 ⁄ 600s and 100 iso. <br /><br /></p>

[CvhKaar]

/' I'm wondering about the effects of using a crop sensor on the aperture of a lens. '/

 

Well , the answer is in your question : None. the sensor does not change the physical properties of the lense in front of it in any way......

 

teh effective aperture is a function of the focal length and the entrance pupil ( being the the image just in front of the aperture,

 

But this is explained much better in wikipedia, then i can ever explain it in my crooked english :-) so here you go... : http://en.wikipedia.org/wiki/F-number

[michael_ryan6]

<p>Ah! So the 1/4 light hitting the sensor doesn't change the exposure (same light density), but it changes the noise (1/4 of the original signal/noise ratio, since the noise stays the same, but the signal is 1/4 of the original, hence the 4x iso)!</p>

<p>Makes sense. Thanks guys!</p>

[ilkka_nissila]

<p>The noise <em>doesn't </em>stay the same. A good part of the noise in the recorded image is due to the scarcity and random arrival of the photons and it's the square root of the number of photons recorded. Thus if you have a 2x crop sensor the total number of photons recorded is 1/4, but noise is 1/2 of what it would be with the full frame camera. So in the end, SNR(2x crop camera) = 1/2*SNR(full frame camera). That's a two stop difference in ISO to get comparable SNR in the final image. This consideration excludes other sources of noise in the sensors themselves (dark current) but you can get a ball park idea of the relative performance by looking at just the photon noise.</p>

[Peter_in_PA]

<blockquote>

<p>To get an image that is photon-for-photon identical (including depth of field) to 600mm f ⁄ 4 at 1 ⁄ 600s and 400 iso on a full frame camera, the 2x crop camera would need 300mm f ⁄ 2 at 1 ⁄ 600s and 100 iso. </p>

</blockquote>

<p>How do you figure? (I'm genuinely curious how you arrive at this...</p>

[ilkka_nissila]

<p>A 300/2 at f/2 on a 2x camera gives the same DOF as a 600mm at f/4 on a full frame camera. The amount of light both sensors receive is also the same, and hence SNR is also approximately the same (implementation details can change the numbers slightly).</p>

[joseph_smith3]

<p>These subjects are very technical, especially Depth of Field, which is correctly stated below. Look at these links here for excellent explanations and calculators. For sensors and apertures, look under Advanced topics.<br>

<a href="http://www.cambridgeincolour.com/tutorials.htm">http://www.cambridgeincolour.com/tutorials.htm</a></p>

<p>Joe Smith</p>

[scott_ferris]

Peter and Michael, and anybody else interested in understanding, read this article on equivalence, it explains it all in detail.

 

http://www.josephjamesphotography.com/equivalence/

[Andrew Garrard]

<p>Here's my paraphrasing of it, in part for Peter: A 2x crop camera (e.g. micro 4/3, if you ignore the different aspect ratio) has a sensor 1/2 the width and height of a full frame sensor. You get the same field of view if you use a lens half as long as a full-frame sensor, so you get the same framing if you put the cameras at the same place (strictly speaking, lens nodal points at the same place, but let's not worry about macro for now).<br />

<br />

A 600mm f/4 lens has a (600/4=) 150mm entrance aperture. Depth of field depends on the entrance aperture of the lens and its distance from the focal plane - for the same size final image, you can imagine the "cone of confusion" that comes from the front of the lens and passes through every point in the focal plane; anything intersecting that cone (and not blocked by something else) contributes to where that point in the focal plane would appear in the image plane. From the subject's perspective, the size of the sensor is irrelevant, so to get the same depth of field as a 600mm f/4 lens on a full frame sensor, you need a 300mm lens (for the same field of view) used at f/2 (to get the 150mm aperture and same depth of field).<br />

<br />

A 300mm f/2 lens lets in four times as much light (two stops, or twice the aperture = 4x the area) to any given point on the focal plane as a 600mm f/4 lens. ISO measures response to light per unit area, so a full frame sensor needs to run at 4x the ISO to get the same exposure as the 2x crop sensor (just as you'd need to increase the ISO 4x to get the same exposure if you stopped down any lens from f/2 to f/4). Note: if you're just using the camera's meter, you don't have to worry about this - we're only talking about the situation if you want to match depth of field.<br />

<br />

However, the full frame sensor is 4x larger in area than the 2x crop sensor, so it gets the same total amount of light (not surprising - the same amount of light going through the lens entrance aperture is contributing to the image - there's no magic). Therefore, considered over the total image, the full-frame sensor is going to appear about as noisy at ISO 400 as the 2x crop sensor does at ISO 100.<br />

<br />

A crop sensor is very much like using a 2x (in this case) teleconverter, except that the aperture and ISO are all read as if the teleconverter had no effect.<br />

<br />

The same is true of bigger formats - large format film is less grainy because, for a given f-stop, more light contributes to the image as a whole. Correspondingly, depth of field is smaller with large format film because, in 35mm terms, it's as if you were using a shorter but faster lens. A compact camera typically has a tiny entrance aperture for a given field of view compared with 35mm, so it has a huge depth of field and poor noise performance.<br />

<br />

If you want the same depth of field and same field of view, no format has a significant noise advantage. In practice, it appears that full-frame cameras do slightly better, I suspect because less pixel area is spent on peripheral circuitry (for the same reason that high pixel count sensors seem to do worse in noise handling even when binned than sensors with larger pixels), but the technology level of the sensor seems to be dominant.<br />

<br />

I hope that helps. I must finish putting some diagrams together for this.<br />

<br />

Note: There are totally different arguments about what happens if you use the same lens on a different-sized sensor (the field of view is different, so moving the camera to provide the same subject size still doesn't produce the same image), or what happens if you keep the same sensor and change the lens. But you can see that describing a focal length in terms of "35mm equivalent" only works if you define your terms. I'd argue that depth of field should also be discussed, or that ISO isn't such a useful measure when multiple formats are being discussed, but maybe anyone who's advanced enough to be concerned with depth of field is expected to be able to do the calculations themselves.</p>

 

[Dave Luttmann]

<p>Peter, f/4 is f/4. When I meter a scene on my Nikon D700, if I obtain a reading of 1/125 at f8 with iso 400....when using my 7D, and a lens that gives me the same FOV, they meter the same. The 7D will read 1/125 at f8 and iso 400. My Fuji X10 will also read exactly the same. </p>

[Andrew Garrard]

<p>What Dave said; f/4 is f/4, since the camera's ISO is set in terms of light <i>per unit area</i>, not <i>total light hitting the sensor</i>. It's this distinction that makes larger sensors better performers at higher ISOs (if you use the DX crop from a D800, the ISO performance will be similar to using a D7000). For so long as you're worried about getting the right exposure, the f-stop/shutter speed/ISO relationship doesn't depend on sensor size. Worry about matching depth of field with different sensors and different lenses and you have to start messing with ISO, but that's to compensate for f-stop changing as well.</p>

[mfophotos]

<p>This question never came up when people used medium format and 35mm film cameras, because we "knew" that f/4 is f/4, no matter what format. Just because things are mostly digital now, doesn't mean that we also have to make things more complex. </p>

[scott_ferris]

<p>Mark,</p>

<p>f4 is f4, when you refer to light gathering, it is when people try to think of f4 as an amount of depth of field that they start to run into issues. For instance, use a crop camera and full frame one from same place with same lens and the crop camera gives you less dof for the same aperture, but change the lenses to get the same framing again from the same place and the crop camera gives you more dof than the larger format for the same aperture.</p>

[Andrew Garrard]

<p>Mark - it was, of course, a tad more difficult to "change ISO" on older cameras (although not, I admit, impossible with removable film backs). Still, Ansel Adams wrote about the relationship between depth of field, film size, focal length, aperture and camera position - it's not a new thing.<br />

<br />

What <i>is</i> new is: 1) relative amateurs (no offence intended Michael) are trying to make sense of this, partly because some muppet decided that it was worth advertising DX lenses by their "35mm equivalent" even though I doubt the majority of DSLR owners ever owned a 35mm camera and knew what field of view a given focal length provided (seriously, sticking to degrees would have killed us?)* and, with compact cameras, the actual sensor format is far more hidden than in film days. 2) pixel peeping and the ability to take an arbitrary number of experimental shots means that people are actually in a position to care about exactly what effect various settings might have, and what they're paying for when choosing between (mid-priced) digital bodies; when (almost) everything was either 35mm or priced for experts, the people who needed to know didn't have a problem knowing.<br />

<br />

I've seen a number of threads where people have said that it's impossible to take the same image with cameras of different formats, or that there's no simple relationship. If you've got independently used to shooting with more than one format, you can go a lifetime without caring about the mathematical relationship between the different settings - that doesn't mean it isn't there, but it also means that you should only bother about it if you really want to. Whether that's because you're used to one format and are switching, or because (like me) you're just geometrically-predisposed, there are formulae, and they're pretty basic maths. If you just learnt what f/2.8 looks like when you shoot a portrait on your camera, there's no need to waste brain cells on this - just as there's no reason to know about integer powers of root two if it's easier for you to learn the f-stops.<br />

<br />

[* This is slightly unfair. But still, when the majority of the market is using DX sensors, describing everything in 35mm terms is more confusing than helpful.]</p>

[michael_ryan6]

<p>Thanks for all the additional info guys! And no offence taken Andrew; I'm definitely an amateur! Photography is not my full time job, and I use math equations far more than focal lengths when I am at work!</p>

<p>The main reason I'm trying to get a handle on the finer points of these equivalencies is because there *are* so many choices to mix and match now. It's fairly easy to find sites that compare two recent lenses for the same mount, but try finding objective comparisons of, say, a 70-200 VR I with a 2x teleconverter on a 1.5x crop body vs that lens with the adapter on a Nikon 1 body without the teleconverter (or cropping an image taken with that lens on an FX body, or using an adapter on m4/3 etc, etc...). Before I even start to decide on options, I'd like to know that I'm comparing apples to apples (or at least one type of fruit to another :).</p>

<p>Well, there's that, and then there's the fact that I just like math...</p>

[steve m smith]

<p>I don't use digital but I do use various film formats from 35mm up to 5x4. I have found that rather than trying to think of them all in terms of just one format, it is easier to just know what the standard lens is and work it out from there.</p>

 

[Andrew Garrard]

<p>Michael - a man after my own heart; I, likewise, get more chance to sit and think about equations than shoot, sadly.<br />

<br />

Steve - that doesn't surprise me. If you have the opportunity to learn the different formats through using them, I'm sure the intuitive approach (tuned by maths) is easier. Which, I'm sure, is why the manufacturers started describing field of view in 35mm terms - it's what they (and their initial customers) were used to. I'm just not sure it's the obvious approach for a novice who hasn't held a camera yet. Still, it's the terminology we've got, so I guess we have to live with it.</p>