Why does a smaller sensor equal greater magnification?

[jason_b10]

<p>I understand why anything less than full-frame sensor will "crop" the image, but why do lenses have a longer reach/focal-length on a cropped sensor?</p>

<p>Sorry if this is a dumb question, but I just can't figure out the math on this. </p>

<p>Thanks in advance.</p>

[john_a5]

<p>Actually, they are not different on a crop or ff sensor, it just "looks" different because you don't see the peripheral data that the ff sensor also captures. There is no true magnification, unless the MP of the crop sensor is larger than that of the FF--but that is another issue.</p>

<p>The crop sensor is just that, it crops the coverage of the lens and so it appears that it is different--just like if you did it on a print from a FF camera. So, a 200mm might "look" more like a 300 on a FF sensor but is still only 200mm on the crop sensor.</p>

[lex_jenkins]

<p>While pondering this, consider it another way:</p>

<ul>

<li> It's a "crop" only if you accept the assertion that the 24x36mm horizontally oriented format is the paradigm by which all of photography is measured.</li>

<li>If an 80mm focal length is a short telephoto on the "full frame" or 35mm film paradigm, and a slightly longer telephoto on a "crop sensor"... what is it on medium format film? On 4x5 film? Does the magnification change? Does the actual focal length of the lens change?</li>

</ul>

[mendel_leisk]

<p><strong><em>If</em></strong> a cropped sensor camera had the same density as a full frame sensor camera, and you took a shot of say a bird in a distant tree, with a 200mm lens on the crop sensor camera, and then repeated the exercise with the full frame camera, and then cropped away the edges of the full frame image by an amount equivalent to the crop factor:</p>

<p>You would end up with 2 more-or-less identical images, same field of view, same horizontal and vertical quantities of pixels, same amount of details resolved, and so on.</p>

<p><em><strong>But</strong></em>, if the cropped sensor camera had higher pixel density, ie: more pixels per inch, and I believe without exception this is the case, and you repeated the previous exercise, then:</p>

<p>You would end up with 2 more-or-less identical images, same field of view, but with <em>increased</em> horizontal and vertical quantities of pixels in the image coming from the cropped sensor camera, and accordingly <em>more detail resolved</em>.</p>

<p>So, due to increased density sensors prevalant on most any cropped sensor camera, you do get increased reach, and that's real, increased detail reach, with any telephoto.</p>

[jason_b10]

<p>Easy to comprehend. Thanks for your speedy responses folks -- it makes complete sense now. I don't know why I couldn't see this before.</p>

[cabbiinc]

<p>Consider it this way. The sensor is physically smaller, yet the image projected by the lens is the same size. So you are capturing less of the image that the lens is being projected. The reason why it's considered a magnification is because you'll still print it at a 4x6.</p>

[scott_murphy_photography]

<p>All sensors crop the image Jason. The diagonal dimension of the image (in mm) is generally used to determine what a "normal" lens is for that format. A 50mm lens on FX or 35mm format produces a circular image of a certain diameter. A DX sensor has a smaller diagonal dimension, so it covers a smaller amount of that circle than does an FX sensor. Therefore it appears to have magnified it, whereas in reality all it has done is isolated a smaller area so it appears magnified.</p>

<p>Some cameras, like my D700, have the ability to do a DX crop on the FX sensor. This leads some people to mistakenly think that doing so will give them more magnification. In reality, all it has done is increase the crop. The actual image will be the same size.</p>

[steve_levine]

<p>Even though there isn't any magnifying or magic occurring. There is an approximate 30% (or greater) loss of depth of field with the smaller sensor. Go to any of the online DoF calculators and check it out. Same lens, same F stop, same distance,+ smaller sensor=smaller DoF.</p>

<p>The first time you try using fast glass ,wide open with a DSLR, this becomes apparent.</p>

[dan_south]

<p>DoF doesn't change unless the focal length changes.</p>

<p>50 mm @ f/4 on a crop sensor has EXACTLY the same depth of field as 50 mm @ f/4 on a full frame sensor or even a medium format sensor.</p>

<p>But if you change the focal length in order to try to yield and equal field of view, then depth of field will change accordingly. Example: I you set your crop camera to a 33 mm focal length in order to approximate the field of view of 50 mm on a full frame sensor, then the DoF will change. But as long as both cameras are shooting at 50 mm and the same aperture, the DoF will be exactly the same in both images.</p>

[dan_south]

<p>The magnification is the same on a crop frame sensor as on a full frame sensor for a given focal length. The difference is that you crop off the edges of the frame with the crop sensor.</p>

<p>Full-frame image:</p>

<p>XXXXXXXXXXXX<br>

XXAAAAAAAAXX<br>

XXAAAAAAAAXX<br>

XXXXXXXXXXXX</p>

<p>Crop-sensor image of the same scene (Note that all edges have been trimmed away.):</p>

<p>AAAAAAAA<br>

AAAAAAAA</p>

 

[blumesan]

<p>Mendel wrote:</p>

<blockquote>

<p><em><strong>But</strong></em>, if the cropped sensor camera had higher pixel density, ie: more pixels per inch, and I believe without exception this is the case, and you repeated the previous exercise, then:<br>

You would end up with 2 more-or-less identical images, same field of view, but with <em>increased</em> horizontal and vertical quantities of pixels in the image coming from the cropped sensor camera, and accordingly <em>more detail resolved</em>.<br>

So, due to increased density sensors prevalant on most any cropped sensor camera, you do get increased reach, and that's real, increased detail reach, with any telephoto.</p>

</blockquote>

<p>Increased pixel density often, but not always, yields an improvement in resolution. Increased pixel density always results in smaller pixels which in turn result in increased noise; particularly so at higher iso levels. </p>

[steve_levine]

<p><strong><em>""DoF doesn't change unless the focal length changes.</em></strong><br>

<strong><em>50 mm @ f/4 on a crop sensor has EXACTLY the same depth of field as 50 mm @ f/4 on a full frame sensor or even a medium format sensor.""</em></strong></p>

<p> Have you looked at a DoF chart to determine this? F4 at ten feet with a 50mm lens equals 1.84' total DoF on a crop sensor,2.94' with 35mm, and 4.53' with a 6x6cm camera.<em> </em>Depth of field diminishes as sensor size decreases, this is simple physics. Google "circle of confusion" to learn why.<strong><em><br /></em></strong></p>

<p><strong><em><br /></em></strong></p>

[blumesan]

<blockquote>

<p>Have you looked at a DoF chart to determine this? F4 at ten feet with a 50mm lens equals 1.84' total DoF on a crop sensor,2.94' with 35mm, and 4.53' with a 6x6cm camera.<em> </em>Depth of field diminishes as sensor size decreases, this is simple physics. Google "circle of confusion" to learn why</p>

</blockquote>

<p>Dear me, it's a good deal more than simple physics and even your statement is internally inconsistent. Your example shows the cropped sensor (with a 35mm lens) having a dof larger than an F4 (with a 50mm) but less than a 6x6cm (where you fail to specify the focal length).</p>

<p>The fact is that, to compare apples to apples, a good deal more than sensor size needs to be considered. By that I mean one should compare identical images, where the field of vew and the perspective (object distance) are the same and the final images should be of the same dimensions. This requires that a shorter focal length lens be used with the cropped sensor. Additionally the image from a smaller sensor size requires greater elargement which in turn means that one must employ a smaller value for the COC when computing the dof.</p>

<p>If, and only if all of these factors have been considered, can one state that a smalller sensor will exhibit a <strong>larger dof</strong>. But to state that "Depth of field <strong>diminishes </strong>as sensor size decreases" is neither simple physics nor correct under any circumstances.</p>

[steve_levine]

<p>My examples were all with 50mm lenses, at F4, focused to 10 feet. They are the total DoF for each format,1.5X crop has a total DoF of 1.84 feet, 35mm film has a total DoF of 2.94 feet, and 6x6cm film has a total DoF of 4.53 feet. I'm sorry you were confused by the above post.</p>

<p>If you check a DoF field chart or calculator you would see that the numbers are correct. With all else being equal, DoF diminishes as the sensor gets smaller. I first noticed this when I shot my fast glass on a DSLR. Wide open the DoF which is inches deep with 35mm film, is often less than an inch with a 1.5X crop camera.</p>

[blumesan]

<p>Steve,<br>

Sorry to have misinterpreted your post. You are quite correct, if you plug the numbers, exactly as you provided, into a dof calculator, you indeed get the results you stated.</p>

<p>However the problem is that, by using the same focal length lens on each format, you end up with 3 totally different images. You are comparing apples to pumpkins. If, on the other hand, you adjust the lens focal length used in such a way that the field of view is the same for all formats (keeping the aperture and focal distance the same), your dof calculator will give you entirely different results. You will find that the smaller the sensor, the greater the dof.</p>

<p>Cheers/M</p>

[dan_south]

<p>Okay, I took your advice and plugged some numbers into an online DoF calculator.</p>

<p>Focal length: 50 mm<br>

Aperture: f/4<br>

Subject distance: 10 feet</p>

<p>APS-C ("DX") sensor (16x24 mm) - D300, etc.</p>

<p>DoF = 1.94 feet (from 9.12 to 11.1 feet)</p>

<p>FX sensor (24x36 mm) - D3, etc.</p>

<p>DoF = 2.94 feet (from 8.74 to 11.7 feet)</p>

<p>Okay, this result is ludicrous. There's no way that a full frame camera gives GREATER DoF than a crop frame camera with all other factors being held constant. The "calculator" must be adding some sort of fudge factor for pixel size/density. Or maybe they're suggesting that a 12 MP APS-C image needs to be "blown up" by a larger factor than a 12 MP full-frame image to reach the same print size (which makes no sense at all).</p>

<p>My suggestion would be to refrain from using such toys unless the author discloses the underlying algorithm, because this one is inaccurate.</p>

<p>Try it for yourself:</p>

<p>http://www.dofmaster.com/dofjs.html</p>

<p>50 mm at f/4 should the same DoF at the same subject distance regardless of image circle size. As I mentioned before, if you replace the 50 mm focal length with 33 mm to give the same angle of view on APS-C, then you'll see a difference in DOF that favors the APS-C camera. This makes sense given that a shorter focal length yields deeper DoF when all other variable are held constant.</p>

 

[steve_levine]

<p>The answer my friend, is blowing in the circle of confusion. The crop sensor's CoC is .02mm, the 35mm's CoC is .03mm, and the 6x6's CoC is .045mm. This is the "simple physics".</p>

<p>It is common DSLR wisdom to use the next smaller DoF scale on a full frame lens. So a full frame lens set to F11, should use the F8 DoF scale to approximate the DoF loss with the smaller sensor.</p>

<p>If you have access to any fast glass, see how thin the DoF is wide open on a crop camera.</p>

[blumesan]

<p>Steve,<br>

As I mentioned before, your numbers are correct when you input the data into a dof calculator using the same focal length lens for each format. And your explanation is also correct. Any decent dof calculator makes an adjustment to the CoC based on the format size. This is also why Dan South got the same results and doubted them. And your observation when using fast glass on a cropped sensor is also correct. BUT:</p>

<p>But the bottom line is that any proper comparison (imho) must compare apples to apples. That means producing the same image with the same perspective and same field of view on each of the formats. That can only be done by using different lenses of appropriate focal length on each of the formats. For example, if you choose 50mm for the 24x36 format, then you must use a 33.3mm lens on the (1.5) cropped sensor and an 83.3mm lens on a (hypothetical; to keep aspect ratio the same) 4x6cm format. Try punching in these numbers into your dof calculator and see what you get.</p>

[kelly_flanigan1]

<p>One circle of confusion folks have on this thread is having actual goals for ones images.</p>

<p>****One CAN use the same circle of confusion too; for different formats.</p>

<p>(1) One can plan that 35mm Full frame and 6x6cm are BOTH going to be enlarged 10x; and thus apply the same 0.03mm COC criteria.</p>

<p>Thus with a 50mm lens at F8 on 35mm FF; one does get the same DOF as a 50mm at F8 on 6x6cm; BECAUSE one used the same COC criteria</p>

<p>All the MF 6x6cm shot then does is make a print that covers more angle. With a 10x enlargement; One gets about a 10x15" print with 35mm; and 21x21" print with 6x6cm; with both using a 50mm lens at F8; the 10x15 print just looks like one cut it out of the 21x21 inch one.</p>

<p>NONE of this is really anything new; 75 years ago Kodak published starting point COC numbers; and smaller formats often had tighter COC criteria. cine 8mm had 1/2000 inch in the 1930's; 16mm cine had 1/1000 inch in the 1930's; 35mm FF was often 1/500" in the 1930's; dumb NF folders were often just 1/200 inch in the 1930's.</p>

<p>The same 50mm F1.4 Nikkor here has been used on 35mm FF; 16mm cine; 8mm cine and modern digital cameras too; depending on the application; I use a different COC number.</p>

<p>the COC number is like how sharp a knife blade is. One that is sharp for wood might be too dull for surgery; and too sharp for butter.</p>

<p>(2) One to can say one is just making 8x10 prints from 35mm and MF and then assign a bigger COC to MF; since one is enlarging less.</p>

<p>In actual images for clients; one might be doing case (1) or case (2); thus the argument has no end; since folks have zero goals. </p>

 

[StuartMoxham]

<p>A 12mp APS-C image has to be blown up more than a 12mp full frame. Same as half frame film 35mm film has to be blown up more than full frame 35mm.</p>

[blumesan]

<p>How this thread took a sharp left turn from a question about the magnification produced by cropped sensors to a comparison of the dof achieved by sensors of various size, is a mystery.</p>

<p>Everything Kelly Flanigan wrote is 100% correct but has no real bearing on either subject. :>)</p>

[kelly_flanigan1]

<p>Ok original question:</p>

<p>"I understand why anything less than full-frame sensor will "crop" the image, but why do lenses have a longer reach/focal-length on a cropped sensor?"</p>

<p>This is like when a 8 oz steak is still an 8 oz steak ; but is small to a 300 Lb linebacker; ok for a 150 Lb person; and absolutely huge to a 1 year old; and about nothing for T-Rex.</p>

<p>In all three cases the steak still is 8 oz; but is viewed differently by the size of person.</p>

<p> The same "sized" object is viewed differently; it varies by the format. An ant might use the 8 oz steak to feed the entire colony for weeks; T-Rex views it as just a few minutes of go power.</p>

<p>A same 50mm lens covers less angle with a smaller format; ie inverse tangent of film height divided by focal length</p>

[blumesan]

<blockquote>

<p>"I understand why anything less than full-frame sensor will "crop" the image, but why do lenses have a longer reach/focal-length on a cropped sensor?"</p>

</blockquote>

<p>The answer really depends on how you define "longer reach". If you define it in terms of the size of any object in the frame <em><strong>as it is projected on the film/sensor </strong></em>(so called magnification factor); the the answer is there is no increased reach with a cropped sensor.</p>

<p>If you define it in terms of the pixel density of the sensor (assuming that higher density yeilds better resolution and thus better results when enlarging the image); then cropping a sensor while retaining the same number of pixels (=higher pixel density) does result in more "reach".</p>

[blumesan]

<p>Kelly,<br>

If I may rephrase your analogy: Eight oz. of filet mignon and 8 oz. of rump steak will appear identical if you only consider how they tip the scales as the basis of comparison. However there is a big difference when you sit down to eat them.</p>

[kelly_flanigan1]

<p>Mike my analogys was all steaks were 8oz and of the same quality/type; they just appear as a different portion; depending on the animals mass. Ants weight 3 milligrams; T-Rex more.</p>