Comparing Image Quality: DSLR vs. Point & Shoot vs. Smartphone

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A user borrowed a friend's DSLR to compare its image quality against a point-and-shoot and a smartphone camera. The comparison involved taking pictures of a newspaper under controlled lighting conditions. Despite expectations, the differences in image quality were minimal, raising concerns about the value of investing in a DSLR. Participants in the discussion noted that while the DSLR should theoretically outperform the others due to its larger sensor and interchangeable lenses, the test conditions may have favored the lower-end cameras. Suggestions were made for more challenging tests, such as varying lighting conditions and subjects, to better assess the DSLR's capabilities. Many agreed that the advantages of DSLRs lie beyond mere resolution, emphasizing features like low-light performance and depth of field control. Overall, the discussion highlighted the complexities of camera performance and the importance of context in evaluating image quality.
DaveC426913
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I've borrowed a friends' DSLR on pretense of buying it.

To test its quality, I took some pics and compared them to my point & shoot and to my camera phone. I find the results surprising.

Attached is a newspaper, shot from ~2ft away with a 500watt halogen light.
That capital Y is about 1.5mm high.
The pics are white balanced and enlarged by 200% (so each 1x1 camera pixel is 2x2 in the attached images)

The 3 pics are (randomly):
  • LG Smartphone 8MP (new)
  • Canon 630 6MP (5 years old)
  • Canon Rebel 10MP (5 years old)

1] Which pic do you think is best?
2] Can you match the pic to the camera?
 

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The mid one.

LG?
 
The third pic (rightmost).
 
Curious3141 said:
The third pic (rightmost).

My choice, too.
 
Is anyone concerned about the relative lack of difference between them, seeing as one is a camera phone, one is a point & shoot and one is a DSLR?
 
I enlarged the image you posted to 400% in photshop so the individual pixels are easy to see. To my eyes the left one looks over-compressed by JPEG. The middle one looks like it has gone through an over-enthusiastic image-sharpening filter.

The right hand one looks the "best" to me, except it's a bit out of focus, and the "unprinted" paper seems rather uneven in color (unless it's supposed to be like that, of course).
 
DaveC426913 said:
Is anyone concerned about the relative lack of difference between them, seeing as one is a camera phone, one is a point & shoot and one is a DSLR?

Not really. All three use the same principles and most likely the same technology with the major difference being the size/shape of the lens and size of the pixels. The DSLR should be the best for photography as a hobby, as it should have way more options available for it, while the other two are more for people who just want to point and shoot and not worry about all the details. That is my guess at least. I barely shoot any pictures other than astrophotography, so I'm basing this on my knowledge of optics and cameras I've gleaned from the hobby, so I could be wrong.
 
I'd pick the one that messes with the color of the paper the least, since I don't know what the color of the paper "actually" looks like, I can't say which one I'd prefer.

probably the one on the right though, based just on what I've got
 
DaveC426913 said:
Is anyone concerned about the relative lack of difference between them, seeing as one is a camera phone, one is a point & shoot and one is a DSLR?
No. You purposely set up the test to be easy. You'll see more differences if you make the test more difficult.
 
  • #10
I'd have preferred seeing them before they were white-balanced, since the balancing didn't come out uniform anyway. Better to figure out which captures the best color/light in the raw image than the corrected one.

Otherwise, I like the one on the right the best. The one on the left seems most pixelated and the one in the middle looks a little out of focus.

I was pretty impressed with the photo quality on my new smartphone too. It has an 8 MP camera, which is a much better detector than my old point and shoot, but I was skeptical about not having any optical zoom and limited ability to adjust anything (the point and shoot does have manual options). I got some great photos in a range of lighting conditions and distances. Of course, I'm not going to be attaching macro lenses to either of those, and the phone doesn't have a tripod app. :wink:
 
  • #11
russ_watters said:
No. You purposely set up the test to be easy. You'll see more differences if you make the test more difficult.
I wanted it to be easy. Easy means the camera is worth it. But the expensive camera doesn't stand out nearly as much as I hoped it would.

Why would I bother spending several hundred dollars for this small difference?
 
  • #12
AlephZero said:
I enlarged the image you posted to 400% in photshop so the individual pixels are easy to see. To my eyes the left one looks over-compressed by JPEG. The middle one looks like it has gone through an over-enthusiastic image-sharpening filter.

The right hand one looks the "best" to me, except it's a bit out of focus, and the "unprinted" paper seems rather uneven in color (unless it's supposed to be like that, of course).
Yea. I just checked it out in Paint. No question about it. The Right One.
 
  • #13
DaveC426913 said:
I wanted it to be easy. Easy means the camera is worth it. But the expensive camera doesn't stand out nearly as much as I hoped it would.

Why would I bother spending several hundred dollars for this small difference?

I think he means that shooting a piece of paper from 2 ft away isn't much of a comparison. Try a couple different objects in different light levels and different distances and at different zooms.
 
  • #14
I'd be interested in suggestions about some tests I could run to compare.
Low light, movement, colour, etc.

Not easy to do. This test was in highly controlled conditions, and it was quite a pain to get all three cameras to produce comparable images (partly due to focal length and partly due to auto-colour correction).
 
  • #15
Drakkith said:
I think he means that shooting a piece of paper from 2 ft away isn't much of a comparison. Try a couple different objects in different light levels and different distances and at different zooms.

Yes. I intend to. But the first comparison I wanted was one of raw crispness "horsepower". Would the expensive camera resolve better without all the sharpness compression and blurry edges??
 
  • #16
DaveC426913 said:
I'd be interested in suggestions about some tests I could run to compare.
Low light, movement, colour, etc.

Not easy to do. This test was in highly controlled conditions, and it was quite a pain to get all three cameras to produce comparable images (partly due to focal length and partly due to auto-colour correction).

Try more 3D objects where depth of field matters more, dim light, or overlaid objects without much contrast. And you partly answered your own question with regard to focal length. I'm guessing you'd get more range from the DSLR.
 
  • #17
DaveC426913 said:
I wanted it to be easy. Easy means the camera is worth it. But the expensive camera doesn't stand out nearly as much as I hoped it would.

Why would I bother spending several hundred dollars for this small difference?
Huh? You spend the extra money because you won't always have the option of carrying a 500W halogen light around with you and shooting from 2' away!

In the real world - in the vast majority of real pictures you will take - the difference will be huge.
This test was in highly controlled conditions, and it was quite a pain to get all three cameras to produce comparable images (partly due to focal length and partly due to auto-colour correction).
I wondered about that - were they really all 2' away and at no zoom or did you have to have some closer and some further due to resolution and focal length differences?
But the first comparison I wanted was one of raw crispness "horsepower". Would the expensive camera resolve better without all the sharpness compression and blurry edges??
No, of course not. In optimal conditions, any camera will be able to produce a sharp image at it's full resolution. All you did was prove there isn't much difference between 8MP and 10MP.
 
  • #18
I think the differences are surprisingly small. The rightmost looks best to me, i.e. good quality right out of the camera instead of an overload of post-processing.

The color balance of the naked sensor is irrelevant. You allways need some kind of white balance and color profile anyways. Color balance is easy to tweak in post-processing - if it is important, shoot a gray card or a white sheet of paper just before or after the "money shot". Blurry images and noise are more difficult to correct, and - for me - therefore sharpness and low-light performance are more important.

What lens did you have on the DSLR?

I would expect huge differences
  • in depth of field, if you can shoot the DSLR with aperture wide open. Shoot along the length of a tape measure, for example, with plenty of light. This is a property of the lens
  • in low light performance: Take a pic on a tripod or bean bag in very low light. Look at the noise in the near-black parts of the image. This is a property of the sensor.
  • in distortion: Shoot graph paper at the wide end of the zoom. Note that the phone probably has built-in post-processing to correct distortion. For the other two you would have to do that semi-manually in DxO or Photoshop or the like. This is a property of the lens.

For me personnaly, the DSLR has three main advantages, and one major disadvantage:
+ you can change lenses to match your needs. I can use a 20mm for landscape and a 300mm+TC for birding, and a 24-105 for travel.
+ viewfinder. Works under all light conditions, what you get is what you see.
+ depth of field and the ability to play with that - shoot af f/2.8 when I want, and at f/16 when I want.
- Size and weight. A lot of pictures were not taken because I could not be bothered to lug the thing+lenses around. I have just bought a P&S, which will only make me even more lazy...
 
  • #19
DaveC426913 said:
Is anyone concerned about the relative lack of difference between them, seeing as one is a camera phone, one is a point & shoot and one is a DSLR?
I'm curious why the picture on the right is not properly focused - assuming it is set up the same way and at the same location as the camera taking the center picture.

I would not be inclined to spend several hundred $ more for a system that yield no better picture quality.

As Moonbear and Russ indicated, test other capabilities, particularly ranges of illumination, depth of field and distance.

One problem I've had in nature shots is trying to focus (with a cheap through the lens 5 MP camera) on a small target in large complex field. The focus tended to shift to a different object nearby. That's one reason I've preferred fully manual cameras.

My favorite lens has been a 35-200 mm on a Canon F1.
 
  • #20
There is another difference that may not be obvious, a consequence of the unlikely coincidence of them all having exactly the same pixel scale: the fields of view are different and the higher resolution one is cropped more.
 
  • #21
russ_watters said:
In optimal conditions, any camera will be able to produce a sharp image at it's full resolution. All you did was prove there isn't much difference between 8MP and 10MP.
I was hoping to see that the more expensive camera had better optics and produced a clearer, sharper image, all other things being optimal.
 
  • #22
DaveC426913 said:
I was hoping to see that the more expensive camera had better optics and produced a clearer, sharper image, all other things being optimal.

Optimal for one camera is not optimal for another camera. Your DSLR most likely has many more features, better zoom, more light gather power, and numerous other benefits over the other two cameras. In a setup like the one you did you stripped all the benefits away from the good camera, so of course it's not going to out perform!
 
  • #23
Not only are all three roughly the same, they're all poor. The lettering in the bottom right is illegible in all three. The image on the right (is that a maple leaf?) is blurry. The image on the left is blurry and I can't guess what it is.
 
  • #24
I have also read that when you shoot with P&S or camera phones they have built in post-processing algorithms like sharpening filters because most people who take pictures with those will not be sitting down to post process in Photoshop.

DSLR's on the other hand are made for hobbyists or professionals. The unprocessed pictures from DSLR's will have none of those things done to them because its expected that people using these types of camera's will sit and do some processing themselves.

I have to agree with what has been said already. The differences between 8MP and 10MP are not THAT extreme (unless you want to make posters and such from your pictures). The advertisements just make it seem like you need the highest resolution because they want to sell stuff.

The advantages of DSLR's pretty much lie in all things OTHER than the resolution of the pictures.
 
  • #25
Drakkith said:
Optimal for one camera is not optimal for another camera. Your DSLR most likely has many more features, better zoom, more light gather power, and numerous other benefits over the other two cameras. In a setup like the one you did you stripped all the benefits away from the good camera, so of course it's not going to out perform!
Everybody keeps insisting on this. I keep saying I was really expecting that, all flexibility advantages aside, in a straight up comparison, the DSLR would produce a higher quality image - less noise, less fuzziness, more crisp.
 
  • #26
DaveC426913 said:
I've borrowed a friends' DSLR on pretense of buying it.

To test its quality, I took some pics and compared them to my point & shoot and to my camera phone. I find the results surprising.
<snip>

1] Which pic do you think is best?
2] Can you match the pic to the camera?

I haven't read the thread yet I don't know if you revealed which is which:

Personally, I like the middle image best. The image on the left seems to have more noise than the others, and the image on the right was slightly out of focus. The difference in quality between all three images is small, and the difference between center and right is very small (IMO). Were all three cameras set to 'auto' everything?

As pointed out, your object and lighting are optimal for typical inexpensive lenses. If you want to push the cameras a bit, try this:

Shoot something outdoors (or in a large room) with something very close, something at mid distance, and lots of texture in the far distance. Also, if you have a wide variation in light intensity (bright highlights and deep shadows), that will help emphasize any internal processing. Fine texture will help show chromatic aberrations, and having objects span a wide range of distance will help emphasize depth of focus and focus error.

That said, the best ‘test object’ for you are things you enjoy photographing- you are already familiar with the object, you know what image you want to get, and you have a good feel for what your current camera does.

Ok, now I'll read through...
 
  • #27
DaveC426913 said:
I wanted it to be easy. Easy means the camera is worth it. But the expensive camera doesn't stand out nearly as much as I hoped it would.

Why would I bother spending several hundred dollars for this small difference?

The reason for bothering to go for the more expensive camera, or not, is completely dependent on how you want to use your new device. You can buy nice(r) lenses for DLSRs, but not for a phone's camera.

My choice: rightmost pic.

Edit:
Everybody keeps insisting on this. I keep saying I was really expecting that, all flexibility advantages aside, in a straight up comparison, the DSLR would produce a higher quality image - less noise, less fuzziness, more crisp.
Are the results of this comparison weighed heavily in your decision? To me, it only makes sense to consider how you plan on using the camera as a basis for your decision.
 
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  • #28
The biggest advantages of a DSLR are the sensor size (which approaches that of a piece of film) and interchangeable lenses. The bigger sensor means bigger pixels which means better low-light sensitivity and lower noise at higher sensitivities. Paired with a nice lens (which range very widely, for example a 50mm f/1.8 which costs about $100 to a 50mm f/1.2 which costs about $1000) you can take pictures at much lower light levels than a point & shoot or cell phone. SLR's also typically have faster, more accurate autofocus and more "power user" settings (but you have to be a power user).

When you look at a phone with an 8mp camera, it's pixels are on the order of maybe 2 microns across. The SLR camera will have pixels which are 15 microns across, which means the pixels have effectively 50 times the area! This means the bigger sensor can collect 50 times the light in a given scene. Some good comparisons of noice levels at higher sensitivities for many cameras can be found here: http://www.dpreview.com (note the Canon XTi is highly rated there).

What camera are you using? I have a Canon DIgital Rebel XTi (10Mp) which it sounds like what you're using. I can give you some tips for settings to maximize your image quality, but in the end the camera is only a tool and a professional photographer can probably take nicer pictures with a point & shoot than Joe Blow off the street that doesn't know how to use his $700 SLR. Skill level matters!
 
  • #29
It's worth noting on a sunny day in direct light, all the cameras will probably take very similar pictures because light is not an issue. But take a picture inside in the evening, and the "small sensors" will start to really show their limitations.
 
  • #30
DaveC426913 said:
Everybody keeps insisting on this. I keep saying I was really expecting that, all flexibility advantages aside, in a straight up comparison, the DSLR would produce a higher quality image - less noise, less fuzziness, more crisp.

it's how they getcha!

"we have big numbers in this!"

"well we have big numbers in this, and this thing sounds more important!"

"well our numbers are big in THIS REALLY COOL THING!"


all in all it's just a big hooplah and I guess we just got to accept that right now fancy phones do not have the best cameras in them
 
  • #31
SHISHKABOB said:
it's how they getcha!

"we have big numbers in this!"

"well we have big numbers in this, and this thing sounds more important!"

"well our numbers are big in THIS REALLY COOL THING!"all in all it's just a big hooplah ...

Not amused. You are suggesting that I have been duped into thinking that gadgets on a camera make for camera that takes a "better quality" picture.

SHISHKABOB;3792987 we just got to accept that right now fancy phones do not have the best cameras in them[/QUOTE said:
Don't you mean we got to accept that DSLR cameras don't have the best optics?

My concern is that the DSLR is only incrementally better than as a cheap phone camera.
 
  • #32
Mech_Engineer said:
The biggest advantages of a DSLR are the sensor size (which approaches that of a piece of film) and interchangeable lenses. The bigger sensor means bigger pixels which means better low-light sensitivity and lower noise at higher sensitivities. Paired with a nice lens (which range very widely, for example a 50mm f/1.8 which costs about $100 to a 50mm f/1.2 which costs about $1000) you can take pictures at much lower light levels than a point & shoot or cell phone. SLR's also typically have faster, more accurate autofocus and more "power user" settings (but you have to be a power user).

When you look at a phone with an 8mp camera, it's pixels are on the order of maybe 2 microns across. The SLR camera will have pixels which are 15 microns across, which means the pixels have effectively 50 times the area! This means the bigger sensor can collect 50 times the light in a given scene. Some good comparisons of noice levels at higher sensitivities for many cameras can be found here: http://www.dpreview.com (note the Canon XTi is highly rated there).
The older DSLR and the newer camera phone might not be that different in detectors. A newer DSLR, on the other hand, will dance circles around the old DSLR. Our department has two DSLR cameras, and older one and newer one. Not much difference in MPs, but huge difference in the detectors. I can get crisp photos of things with the newer one that couldn't even be seen as more than a pixelated blur with the older one. The colors appear more "true" to what I see by eye with the newer one, and the ability to enlarge a photo for detail is where I REALLY see the difference. In a small jpeg clip, I won't see as much difference, but when cropping and enlarging to show an area of detail, the sorts of things we use macro lenses to photograph, the difference is astounding.
 
  • #33
DaveC426913 said:
Not amused. You are suggesting that I have been duped into thinking that gadgets on a camera make for camera that takes a "better quality" picture.

My concern is that the DSLR is only incrementally better than as a cheap phone camera.

didn't mean to insult, just meant that the high cost is due to the people adding fancy components to it, to make it appear to be worth the high cost

I don't think this has to assume that you've been duped
 
  • #34
The industry (or their marketing divisions at least) certainly believe they can dupe most of the market. It is easy to advertize a huge number of megapixels, or gizmos like eye and face detection, scene modes and what not. The latest craze is full HD video which just flaps the mirror up and out of the way, loosing the dedicated AF unit and viewfinder along the way, so that you end up with a glorified point-and-shoot camera (with a huge sensor, admiltedly).

AF quality is nearly impossible to quantify. How to you print that on an ad? Pixel size? 20 years ago pixels where huge, now they are getting smaller and smaller. You need to explain why bigger pixels are better - easily done in a physics forum, but in a 10sec TV ad?
 
  • #35
These are tested under fairly static and "easy" conditions. With today's technology, a digital camera (whether it's on a phone or a unit unto itself) should be able to capture a image of some text in a relatively well lit location. Test these same cameras with any sort of motion or lighting issues and you will see some very significant differences. You have very limited functionality with a camera phone whereas the DLSRs will allow you to play with shutter speeds, f-stop, etc...

So, yes, if you are taking pictures of well-lit, motionless objects then any camera will do the trick in this day and age. What you are paying for with the more expensive DLSRs is the ability to go beyond that and still take very good photos.
 
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  • #36
DaveC426913 said:
Everybody keeps insisting on this. I keep saying I was really expecting that, all flexibility advantages aside, in a straight up comparison, the DSLR would produce a higher quality image - less noise, less fuzziness, more crisp.
Ok, well now you know that in optimal conditions, cameras are chip resolution limited, not optics limited.

And now you should also understand that your test setup contradicts your stated goal: you said you wanted to test what you pay the extra $ for, then set up a test that eliminated the effect of the things that cost more $... like optics and a big chip.
 
  • #37
Mech_Engineer said:
The biggest advantages of a DSLR are the sensor size (which approaches that of a piece of film) and interchangeable lenses. The bigger sensor means bigger pixels which means better low-light sensitivity and lower noise at higher sensitivities. <snip>

That's partially correct: a larger sensor also increases the field of view.
 
  • #38
Bigger field of view is nice if you shoot wide angle.
 
  • #39
M Quack said:
Bigger field of view is nice if you shoot wide angle.

... so long as the optics can handle the bigger FOV without too much distortion, of course.

But if you just want bragging rights on pixels, Nokia just has announced a 41 Mp smartphone camera. http://www.bbc.co.uk/news/technology-17178014
 
  • #40
DaveC426913 said:
Everybody keeps insisting on this. I keep saying I was really expecting that, all flexibility advantages aside, in a straight up comparison, the DSLR would produce a higher quality image - less noise, less fuzziness, more crisp.

Yes, it is unfortunate that so many people expect a camera to simply be "better" just because it is more expensive. The truth is that there is so much more to a camera than simply resolution or image sharpness at a single distance.
 
  • #41
M Quack said:
Bigger field of view is nice if you shoot wide angle.

AlephZero said:
... so long as the optics can handle the bigger FOV without too much distortion, of course.

I do, and it does. (Nikkor 15mm f/3.5). Zero distortion.
 
  • #42
Andy Resnick said:
That's partially correct: a larger sensor also increases the field of view.

That assumes either sensor uses the same optics (for example in an SLR that has a full-frame chip vs. an SLR with a crop-format). For the purposes of comparing a cell phone camera to an SLR (which use completely different sets of optics) the FOV can be designed to be basically the same.
 
  • #43
Moonbear said:
The older DSLR and the newer camera phone might not be that different in detectors. A newer DSLR, on the other hand, will dance circles around the old DSLR.

It all depends on the SLR. I suspect he's got a Canon Digital Rebel XTi, in which case there really isn't a cell phone camera out there that can compete in anything other than sunny conditions. Paired with interchangeable lenses and superior autofocus, there really isn't a contest (but that of course assumes they're both being utilized to their potential).

Moonbear said:
Our department has two DSLR cameras, and older one and newer one. Not much difference in MPs, but huge difference in the detectors. I can get crisp photos of things with the newer one that couldn't even be seen as more than a pixelated blur with the older one.

Do you mind telling us which model cameras you're comparing? I've had problems with SLR's in the past, but it had more to do with my lack of understanding/locating the proper camera settings. It all goes back to seeing the camera as a tool, not a magical perfect picture taker.

Moonbear said:
The colors appear more "true" to what I see by eye with the newer one, and the ability to enlarge a photo for detail is where I REALLY see the difference. In a small jpeg clip, I won't see as much difference, but when cropping and enlarging to show an area of detail, the sorts of things we use macro lenses to photograph, the difference is astounding.

Sounds like color balance or white balance issues, but some cameras do a better job than others when it comes to their "AUTO" mode.

We got a Nikon D3X at work with a Nikkor 200mm f/4 Macro lens, that takes some of the most amazing macro pictures I've ever seen! 1:1 scale on a 24.5Mp sensor is just breathtaking!
 
  • #44
Mech_Engineer said:
For the purposes of comparing a cell phone camera to an SLR (which use completely different sets of optics) the FOV can be designed to be basically the same.

Really? good luck trying to design a distortion-free lens that provides a 118 degree FOV (the Nikkor 13mm on 35mm format) in even a 1.6x crop factor. A 60 mm Hypergon gives a 135 degree field of view on a large format image- translating that to a 1.6x crop sensor would require a rear focal length of 2mm... sure, "basically the same".
 
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  • #45
Mech_Engineer said:
Do you mind telling us which model cameras you're comparing? I've had problems with SLR's in the past, but it had more to do with my lack of understanding/locating the proper camera settings. It all goes back to seeing the camera as a tool, not a magical perfect picture taker.
I would if I could remember. They all sound like alphabet soup and random numbers to me. With the newer one, there are definitely a lot more settings to mess up. I get a lot of help from one of our technical staff who is geeky enough and has the patience to read the manual plus other books on how to use it when I tell him what I want to do. The downside is I usually have to listen to the SAME explanation of the gizmo he wants for the tripod to play with some technique he read about and wants to try, even though nobody can think of a good reason to need that.

Sounds like color balance or white balance issues, but some cameras do a better job than others when it comes to their "AUTO" mode.
I think it's more than color or white balance. I can't really correct for it to make up the difference, and when everything in the photo is shades of beige, picking up subtle color differences is a big deal. But, that's straying too much from what Dave wants to do to be relevant to this discussion. On the other hand, that might be the point too, knowing what you want to do and getting what you need for that. I'm perfectly happy with a camera phone picture for most things. The specific needs I have at work require something quite different. Different tools for different tasks.
 
  • #46
3 more tests. These ones at dusk. Medium to long range. No touchups at all.

These are a tiny 1/10x1/10 snippet from the whole pic - but at 100%.

I had no choice for the middle one but to boost the ASA to 400. I simply could not hold the camera steady. But the left & right two I took on auto.

You can definitely see how the DSLR pulls ahead of the other two.
 

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  • #47
DaveC426913 said:
<snip>

You can definitely see how the DSLR pulls ahead of the other two.

Indeed!
 
  • #48
Dave, I guess your potential 400D has the 18-55mm USM version. Ask Borek about the quality of that one and you know why the result is so blurry, also due to lacking image stabilisation. It's successor the 18-55mm IS is a huge improvement, which has a new successor too recently.
 
  • #49
It's true, the stock lens isn't the nicest one ever to exist. The great thing about SLR's is you can buy a lens to match your shooting style and needs.
 
  • #50
Andy Resnick said:
Really? good luck trying to design a distortion-free lens that provides a 118 degree FOV (the Nikkor 13mm on 35mm format) in even a 1.6x crop factor. A 60 mm Hypergon gives a 135 degree field of view on a large format image- translating that to a 1.6x crop sensor would require a rear focal length of 2mm... sure, "basically the same".

You have some special requirements, but the point is the field of view is dependent on more than just the size of the sensor. FOV is calculated using the sensor size, lens focal length, sensor distance, etc.

At very wide angles you may be right that a smaller crop-format sensor cannot compete, but it's because the focal length of the lens would have to get prohibitively small (e.g. less than 10mm) and you get into fisheye territory at that point.
 
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