37

So, I mount a 200mm lens on my Canon 450D. It effectively becomes a 320mm lens. Is this the equivalent of 320mm on a full frame camera? That is, from what I've figured out I get an equivalent field of view but nothing I've read is indicating that I get the magnification to go along with it.

So as my question says in the title, does my crop sensor camera really turn my lens into a longer one (in terms of magnification), or does it just look like it based on the reduced field of view I get?

38

The lens does not actually turn into a different focal length, since that's a real, physical property of the optics that can't be changed without more optics. So from that point of view, the answer is a definitive no.

However, when you get to the question of is it effectively the same in terms of magnification, the answer is "pretty much, given some assumptions."

A key assumption is that you're printing at the same size. That means: you're increasing the magnification of the image from the smaller sensor. If you print at sizes different by the same ratio of the crop factor, you get exactly the same result as if you just took a full-frame photo, printed large, and then cropped out the middle.

So, if you print your full-frame picture at 12×9", and print your crop-factor picture at 7.5×5.6" (for Canon; 8×6" for others, or 6×4.5", or whatever), and then chop down the full-frame print to match, they'll be roughly the same.

"Roughly" comes in because, of course, the actual sensors won't be equivalent in image quality. (The crop-factor print may have larger resolution, but from denser photosites, depending on the technology generation used in each camera.)

Blowing up that cropped image — either from the full-frame cropped print, or from the cropped sensor — has two effects which are very like changing the focal length. And these two things are the most visible effects of changing focal length — field of view, as you've noted; and depth of field, which changes (almost) exactly as if you'd adjusted the f-stop by the amount of the crop.

If you've ever used a point and shoot camera with "digital zoom", that's what's actually going on. It's cropping the photo and then expanding it. From a practical point of view, zoom is indistinguishable from cropping. But of course, that raises the spectre of decreased image quality — we all know that digital zoom can be awful. The answer is simply that sensor technology is really very good, and amazing, excellent results can be produced at even large print sizes even with a 1.5 or 1.6× crop — but if you do want to go larger with your prints, eventually you need a larger sensor. And, equivalently, if you want to zoom in more, you can do that with more cropping, but eventually, you need actual higher-focal-length glass.

Note that this doesn't address macro shooting. I don't really do any of that, so I'll let someone else handle that aspect of the question — which I think is well-addressed here: Does a camera's crop factor apply to the magnification of macro shots?

  • Thanks for the description. I'd never considered the crop factor in these terms. I'd also never considered what "digital zoom" is actually doing. This is probably the best justification for getting a full frame I've read. +1 – Mike May 4 '11 at 10:40
  • @Mike: yeah, there's pretty much no real downside to a full frame camera except for size, weight, and cost. (See photo.stackexchange.com/questions/3986/… for more....) – mattdm May 4 '11 at 12:06
  • I did find another justification for getting an EOS1D - if you forget your hammer, you can use one of these to bang in your tent pegs. It's just that it makes for a really expensive hammer that's all... – Mike May 5 '11 at 4:56
21

The crop sensor does not change any property of the lens – but by seeing just the center of the image it makes it look like everything is multiplied by the crop factor.

The focal length does not change – but by looking only at the center of the image makes it look similar to what you get by using a longer lens.

The magnification also does not change, a macro lens with 1:1 magnification will still have 1:1 magnification (object size in reality = object size on sensor) but now that the sensor is smaller the object on the image will be 1.6 bigger, for example:

Full frame:                              Crop Sensor:
+-sensor----------------+
|                       |
|   +-subject--------+  |                +-subject--------+
|   |                |  |                |   +--sensor--+ |
|   |                |  |                |   |          | |
|   |                |  |                |   +----------+ |
|   +----------------+  |                +----------------+
+-----------------------+        
subject is entirely inside image         subject is exactly the same size and 
                                         position but is now larger than image

The subject projection on the sensor is exactly the same size (lens magnification didn't change) but it takes a larger area of the image because the sensor is smaller.

  • @Sean: When I saw the ASCII art, I immediately felt a strong urge to post that very comment – Anto Apr 27 '11 at 17:11
  • Thanks for the added bit of info regarding macro photography. It added to what mattdm has said. +1 – Mike May 4 '11 at 10:45
6

The depth of field, as defined by the aperture, also does not change. The only reason it is larger (more in focus) than on a full frame sensor, is because of the cropping factor, the person must move backward (or zoom out) to achieve frame something the same within the image.

In other words, if you had a full frame body setup with a 50mm lens at F/1.8 aimed at a subject 2m away then replace the camera with a crop sensor body but use the same lens and position (2m), the depth of field will still be exactly the same, but you will see less of the image seen in the full frame body (crop).

As the depth of field increases with focus distance, and due to the fact that you must move back to frame the same composition, your focus distance on the crop body is increasing, effectively increasing the depth of field to something larger than the full frame image's depth of field.

enter image description here

  • 1
    Or stand in the same place, and crop off the edges of the full-frame image, and then display both at the same size. :) – mattdm Nov 8 '11 at 4:32
  • 1
    Yep. Exactly the same composition (disregarding difference in sensor quality). Snip snip! – Nick Bedford Nov 8 '11 at 4:49
3

I once asked this and got many confusing answers, but in the end I understood it, and I will try to explain it as simply as I can:

  1. Nothing about the lens is ever changed. It is not a Transformer after all, so every property of it remains the same.

  2. A photo taken with an APS-C camera is like taking photo on a Full-Frame camera and then printing it out, and then you crop it to make it smaller by chopping off a portion from all four sides.

If you understand (1) and (2), you will immediately understand that nothing has changed, not even Depth Of Field, not focal length, etc.

  • However, when you take that smaller chopped up print and enlarge it to make it as big as the original you do reduce the DoF because you've changed the acceptable circle of confusion. – Michael C Jul 8 '16 at 2:09
1

So as my question says in the title, does my crop sensor camera really turn my lens into a longer one (in terms of magnification), or does it just look like it based on the reduced field of view I get?

The size of the image projected on the sensor is the same in both cases.

But a smaller sensor with the same aspect ratio and same total number of pixels will have smaller pixels. So if you take a lens off say a 10 megapixel full-frame camera and put it on a 10 megapixel crop sensor camera (with the same settings, same distance to subject etc) the size in pixels of objects in the image will increase.

0

It was mentioned that two sensors of different dimensions but containing an equal number of pixels (for instance, a 1" x 1" sensor with a million pixels and a 2" x 2" sensor with a million pixels) would give different results if the 1" sensor was expanded (enlarged) to 2".

It should be noted that, if, for the sake of argument, both sensors in their original configuration had pixels butted against each other with no space between them, then when you enlarged the 1" sensor, the pixels would now have space between them in whatever amount was necessary to reach the 2" size.

This would make for a very pixelated, low quality image, much like people would due with dot matrix printers in days of old.

Another way to think of it is, we have all seen the pictures of the head of a pin with the preamble to our Constitution written on it, or a grain of rice with the Lord's prayers written on it.

So, imagine if you took that pin head and stretched the metal until it was the same size as the actual page of the preamble. While technically all the words would still be there, they would be illegible and would take quite a bit of visualization to even "see" the words. That same thing happens, to a much smaller extent, when you expand a cropped sensor version to the size of a full sensor capture. Thus, we now turn the conversation to apples and oranges because we aren't talking about the same thing.

Expand the full frame sensor by the same amount and it also takes a much more magnified look.

The important thing to remember is, the lens captures and transmits the same information irrespective of what is capturing its contents. However, the size of the image (magnification) depends on where you place the focal plane and the quality of the sensor at the focal plane distance.

So, if you took the same setup, removed the back of you camera and let the lens project to a white wall 10' behind the camera, your subject may be 20' tall. Now all you need to do is invent a sensor that can capture a 20' tall image.

So, as the previous person said, an APS-C sensor with 21MP and a full frame sensor with 21MP, you will have larger pixels on the FF and smaller on the cropped, or there will be more space between pixels (less dense) but the captured images will be identical and will only reflect their traits (quality) when changing sizes.

0

Effectively, a crop sensor camera does the following transformations:

fcrop,eff = fcrop,real * C
Ncrop,eff = Ncrop,real * C
ISOcrop,eff = ISOcrop,real * C2

where f is the focal length and N is the aperture number. These transformations, when applied, give the (1) same field of view, (2) same depth of field, (3) same background blur, (4) same noise given equivalent sensor technology, (5) same exposure.

An example: you have a Canon crop sensor (1.6x crop) camera with 50mm f/1.2 lens are are shooting at ISO 100. Effectively, the lens is a 80mm f/1.92 lens and you are effectively shooting at ISO 256. So, to take an equivalent picture using a full frame camera, you need to find a 80mm f/1.92 lens (closest you will find is 85mm f/1.8 lens), and shoot at ISO 256 (closes you will find is probably ISO 250).

What some people forget is the transformation to aperture. For example, if you have a 17-55mm f/2.8 crop zoom, you cannot claim it's equivalent to 24-70mm f/2.8 full frame zoom. The focal lengths are close enough: 17-55mm is equivalent to 27.2-88mm, but the aperture is equivalent to f/4.48! So the f/2.8 crop zoom is more like a f/4 full frame zoom.

If you forget to transform the aperture, you are forgetting two things:

  • Equivalent depth of field and background blur: a full frame camera will have shallower depth of field and more background blur at the same aperture number. But, if you transform the aperture as well, you are getting equivalent DoF and background blur.
  • A full frame sensor can be used with 1.62 = 2.56 times the ISO sensitivity at the same noise level, because the sensor area is 2.56 times bigger.

To remind you of the importance of the aperture, think in the following way: if you have a 50mm f/1.2 lens, and make the sensor very tiny (8x crop), do you have 400mm-equivalent f/1.2-equivalent lens? Of course not, as even 400mm f/2.8 is huge, costing over $10000! You have 400mm-equivalent f/9.6-equivalent lens then.

So, to answer your question: yes, a crop sensor camera effectively multiplies the focal length with the crop factor. But, at the same time, it multiplies the aperture too with the crop factor.

  • I had to downvote for the following specific reasons: 1. You didn't make it clear that the effective focal length is fundamentally about field of view. The actual focal length of the lens (which is determined solely by the shapes, positions, and refractive properties of the lens elements) is not affected by crop factor. 2. Crop factor applied to aperture is with respect to depth of field only, not with respect to exposure. 3. Crop factor when applied to ISO (ISO-squares, as you noted) is with respect to image noise only; again, crop factor has no bearing when it comes to exposure. – scottbb Jun 19 at 18:53
  • To be clear, except for the mention in your bullet points, there's no indication that crop factor applied only to DoF and noise with respect to aperture and ISO, respectively. I don't think anything you said is actually incorrect, just that I don't think you emphasized where crop only applies. – scottbb Jun 19 at 18:55
  • I don't entirely understand the criticism. If you apply all of the transformations, you get (1) the same angle of view, (2) the same depth of field, (3) the same background blur, (4) the same noise (assuming equivalent sensor technology -- you can't compare a 20-year old sensor to a new sensor), (5) the same exposure. – juhist Jun 20 at 16:47
  • Your edit helped put the DoF & noise "equivalence" more up front. I just meant to emphasize that crop, when applied to f-number, doesn't change the exposure of a particular scene just because a crop sensor is being used. An EV 15 scene is still EV 15 — say, Tv = 1/1000 s, Av = f/5.6, doesn't need to be adjusted because of crop factor. However, in order to maintain equivalent DoF and apparent noise (as you well note) and maintain the same exposure with C = 1.6, then aperture needs to be adjusted by 2*log2(C) = 1.35 stops and ISO needs to be similarly adjust by 1.35 stops. – scottbb Jun 21 at 3:27

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