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Thread: I'll Never Understand the Simple Math

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    Default I'll Never Understand the Simple Math

    Standing in the same spot with the same lens, which get more pixels on the subject: 7D or 5D III. An explanation of the math would be greatly appreciated .
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    The 7D will get more pixels on the subject. It has twice the pixel density compared to the 5D3 (5.42 megapixels/square cm of sensor vs. 2.63 for the 5D3), and it also has a 1.6 crop FOV. Let's say you take a photo of a scene using a 5D3 and a given focal length of lens. One of the objects in the frame fills up 1 square cm of the sensor. You will have 2.63 megapixels on that object in your photo using the 5D3 (2.63 megapixels/square cm x 1 square cm). Now you switch to the 7D and take the same photo with the same lens and distance to subject. Because of the focal length multiplier, that same object will occupy 1.6 square cm of the sensor on the 7D (1 square cm x 1.6). At 5.42 megapixels/square cm of sensor, the same object will occupy 8.67 megapixels on the 7D (5.42 x 1.6). The 7D will put 3.3x more pixels on the subject than the 5D3 will. I think this math is correct. Let's see what the scientists have to say.
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    Doug the subject will occupy the same area on the FF and crop sensors (i.e it is 1cm^2 for both). Note that focal length or optical magnification does not change with sensor size.


    The correct formula is :

    total number of 7D pixels on the subject / total number of 5D3 pixels on the subject =(5D3 pixel size / 7D pixel size )^2 = (6.25um/4.3um )^2=2.11 so it's like 1.4X convertor.

    This is only true for fixed sensor to subject distance.

    The crop sensor is just a smaller piece of silicon, its size has nothing to do with the image that is projected on its surface by the lens.

    I think this was previously discussed in several older threads.
    Last edited by arash_hazeghi; 04-25-2012 at 08:06 PM.
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    The megapixel rating of a sensor is a function of sensor size and pixel size. Some FF sensors such as the 5DIII and the D800 appear to be high-resolution, but they do so because of sensor size not necessarily pixel size. I find it useful to standardise sensor size to a crop sensor- 1.5/1.6- and look at megapixels then. Doing so is like taking an Exacto knife and cutting a FF sensor down to the size of a crop sensor and then counting pixels. Looking at it this way, a 5DIII cut down to a 1.6 crop sensor is roughly a 8.1 mp camera, the D800 is a 14mp camera, the D3S is a 4.6mp camera (!). If this is in the back of your mind, the answer to the question of whether a 5DIII (8.1) or a 7D (18mp) puts more pixels on the subject is a proverbial "no-brainer".

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    Here's another way to get the answer by looking at the relative area of the 2 sensors :

    5D = 24mm x 36mm = 864 sq. mm
    7D = 22.3mm x 14.9mm = 332 sq. mm

    Hence, the area of the 7D sensor is 38% of the 5D.
    So for the same lens at the same distance, you would take 38% of a 5D image to get the "7D equivalent" angle of view.
    The 5D is 22.3 MP, so 38% (22.3 MP) is 8.47 MP compared to the 7D's 18 MP.
    So you get about 2.1 times as many "pixels on the subject" with the 7D.

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    Quote Originally Posted by John Chardine View Post
    The megapixel rating of a sensor is a function of sensor size and pixel size. Some FF sensors such as the 5DIII and the D800 appear to be high-resolution, but they do so because of sensor size not necessarily pixel size. I find it useful to standardise sensor size to a crop sensor- 1.5/1.6- and look at megapixels then. Doing so is like taking an Exacto knife and cutting a FF sensor down to the size of a crop sensor and then counting pixels. Looking at it this way, a 5DIII cut down to a 1.6 crop sensor is roughly a 8.1 mp camera, the D800 is a 14mp camera, the D3S is a 4.6mp camera (!). If this is in the back of your mind, the answer to the question of whether a 5DIII (8.1) or a 7D (18mp) puts more pixels on the subject is a proverbial "no-brainer".

    the above is not the best method because the crop factors are approximate and sometimes there are some finite gap (FOX) between the pixels that is dead area, although in this case error is just 5%.
    Last edited by arash_hazeghi; 04-25-2012 at 09:46 PM.
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    Bottom line is the 7D has more pixels on the subject if the same lens and distance to the subject is used.

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    Quote Originally Posted by arash_hazeghi View Post
    Doug the subject will occupy the same area on the FF and crop sensors (i.e it is 1cm^2 for both). Note that focal length or optical magnification does not change with sensor size.
    Well at least it sounded plausible!

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    Quote Originally Posted by Doug Brown View Post
    Well at least it sounded plausible!


    I think the manufacturers are at fault calling this a "focal length multiplier" as opposed to a "field of view reduction factor" which is what it really is. But I can see why they chose this terms, it makes buyers think their cheap 400mm lens will become a 640mm lens...great lol
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    'Cheap 400 lenses': Freudian slip here Arash?...it applies to all lenses, expensive ones too

    The use of the term 'crop factor' in so far as it relates to a pretence that focal length increases is at best a demonstration of ignorance by those who swallow it and at worst a lie by manufactures who publish it. I am surprised it has not been legally challenged on the basis that it is a misrepresentation.

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    Thanks Arash,

    re:


    The correct formula is :

    total number of 7D pixels on the subject / total number of 5D3 pixels on the subject =(5D3 pixel size / 7D pixel size )^2 = (6.25um/4.3um )^2=2.11

    Does ^2 mean squared?

    What are the units (um)?

    Does the 2.11 mean that the 7D gets 2.11 more pixels on a subject with distance to the subject and lens being equal?

    Where do the 6.25 and 4.3 um come from?

    Are they related to the size of the respective images in megapixels?


    This is only true for fixed sensor to subject distance.

    I am confused as to what you mean by the above. Please explain.


    The crop sensor is just a smaller piece of silicon, its size has nothing to do with the image that is projected on its surface by the lens.

    I think this was previously discussed in several older threads.

    It has, but I did not fully understand it then so I asked again and look forward to understanding it better when the questions here are answered :). So thanks a stack.

    Being a bit dense can be a challenge when it comes to understand the technical issues dealing with digital photography.....
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    I find that the quickest and easiest way to compare cropped sensors vs full-frame sensors is to calculate what the cropped sensor's MP size would be if it were full-frame. To calculate this, multiply the MP times the crop factor squared. Using the 7D as an example:

    18 x 1.6 x 1.6 = 46mp.

    Compared to the 5D Mark III, the 7D's sensor has more than double the number of pixels (22mp vs 46mp) when photographing a subject from a fixed distance using the same lens.

    - Alan

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    And by the way Alan, the Canon S100 would be 250mp!!!

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    re:


    The correct formula is :

    total number of 7D pixels on the subject / total number of 5D3 pixels on the subject =(5D3 pixel size / 7D pixel size )^2 = (6.25um/4.3um )^2=2.11

    Does ^2 mean squared?


    yes

    What are the units (um)?

    micro-meter

    Does the 2.11 mean that the 7D gets 2.11 more pixels on a subject with distance to the subject and lens being equal?

    yes

    Where do the 6.25 and 4.3 um come from?

    given in camera's spec sheet

    Are they related to the size of the respective images in megapixels?


    of course total sensor area/ pixel area = total number of pixels.

    This is only true for fixed sensor to subject distance.

    I am confused as to what you mean by the above. Please explain.


    not sure what makes you confused?

    The crop sensor is just a smaller piece of silicon, its size has nothing to do with the image that is projected on its surface by the lens.

    I think this was previously discussed in several older threads.

    It has, but I did not fully understand it then so I asked again and look forward to understanding it better when the questions here are answered :). So thanks a stack.

    Being a bit dense can be a challenge when it comes to understand the technical issues dealing with digital photography.....
    Last edited by Arthur Morris; 04-26-2012 at 01:19 PM.
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    Lifetime Member Doug Brown's Avatar
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    Artie, if you drop the 1.6 multiple off of my formula, you'll get the correct answer. The 7D has a sensor size of 2.23 cm by 1.49 cm; multiply the two numbers to get sensor area. The result is 3.32 cm squared. At 3.6 cm by 2.4 cm, the 5D3 has a sensor area of 8.64 cm squared. Divide each camera's total number of megapixels by its sensor size and you come up with these numbers: 5.42 megapixels per cm squared of sensor area for the 7D, and 2.63 megapixels per cm squared for the 5D3. Divide 5.42 by 2.63 and you get about 2.1x difference. That number tells you that you'll get slightly more than 2x as many pixels on an object photographed at a fixed focal length and fixed distance to subject when you shoot with the 7D vs. the 5D3.

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    Thanks Arash for Pane #14 answers.

    re:

    This is only true for fixed sensor to subject distance.

    I am confused as to what you mean by the above. Please explain.


    not sure what makes you confused?

    Me neither. I reread it and it makes perfect sense. Guess that I got confused as it was part of my original question .
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    Quote Originally Posted by Doug Brown View Post
    Artie, if you drop the 1.6 multiple off of my formula, you'll get the correct answer. The 7D has a sensor size of 2.23 cm by 1.49 cm; multiply the two numbers to get sensor area. The result is 3.32 cm squared. At 3.6 cm by 2.4 cm, the 5D3 has a sensor area of 8.64 cm squared. Divide each camera's total number of megapixels by its sensor size and you come up with these numbers: 5.42 megapixels per cm squared of sensor area for the 7D, and 2.63 megapixels per cm squared for the 5D3. Divide 5.42 by 2.63 and you get about 2.1x difference. That number tells you that you'll get slightly more than 2x as many pixels on an object photographed at a fixed focal length and fixed distance to subject when you shoot with the 7D vs. the 5D3.

    This is my shot at redemption....I hope I didn't screw it up!!!
    It's beginning to make sense. Thanks. That leads to the same question over and over again: why do most experienced folks (except possibly for Dan Cadieux) far prefer Mark IV or 5D Mark II image quality to 7D image quality?

    Does the answer have to do with the size of the individual pixels (larger is better???) or with the quality of the sensor? Or both?
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    As a sort of novice, I used to think (because I was told) that DX was a focal length mutiplier.
    When you use the D800, it is much more apparent what a hoax that is. I can change the crop factor (FX, 1.2, DX, OR 5x4) Just turning the wheel.
    The crops are just black line boxes on the FX view. The photo is the box size but the bird is the same distance away, nothing changed except the
    camera cropped it for me.
    I can take FX photos and just crop them to DX on the computer, or have the camera do it. The subject got no closer and the pixels on the subject don't change either.
    The total number pixels of the photo changed because of the crop.
    I use the 1.2 crop mostly only because the file sizes are smaller and load faster to the computer. The photo itself doesn't get better/worse, no change except the ease
    of loading.
    Alas, my lens is still the same length!
    Pretty simple to understand when you see it like this.
    Dan Kearl

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    Quote Originally Posted by Arthur Morris View Post
    It's beginning to make sense. Thanks. That leads to the same question over and over again: why do most experienced folks (except possibly for Dan Cadieux) far prefer Mark IV or 5D Mark II image quality to 7D image quality?

    Does the answer have to do with the size of the individual pixels (larger is better???) or with the quality of the sensor? Or both?
    I chose a used 1D MKIII over a 7D for the quality of the files mainly the better dynamic range and tonal reproduction of colors that Canons pro series cameras produce as to why their is a difference i will let the better educated users explain but I do see a difference.
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    Quote Originally Posted by Arthur Morris View Post
    It's beginning to make sense. Thanks. That leads to the same question over and over again: why do most experienced folks (except possibly for Dan Cadieux) far prefer Mark IV or 5D Mark II image quality to 7D image quality?

    Does the answer have to do with the size of the individual pixels (larger is better???) or with the quality of the sensor? Or both?
    A similar discussion between the D800 & D4 is taking place. I think it is pretty difficult to compare IQ from cameras of significantly different sensor resolution in an apples to apples manner. People tend to go with the sensor that serves their preferred output better (when they actually spend the time to do comparisons). Printing large or small, viewing on a monitor or printing or pixel peeping, even matte vs glossy prints can push the comparison in different ways, not to mention amenability to an array of post-processing possibilities.

    Besides, IQ tends to be in the eye of the beholder. My 2 cents.

    Cheers,

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    Quote Originally Posted by Alan Stankevitz View Post
    I find that the quickest and easiest way to compare cropped sensors vs full-frame sensors is to calculate what the cropped sensor's MP size would be if it were full-frame. To calculate this, multiply the MP times the crop factor squared. Using the 7D as an example:

    18 x 1.6 x 1.6 = 46mp.

    Compared to the 5D Mark III, the 7D's sensor has more than double the number of pixels (22mp vs 46mp) when photographing a subject from a fixed distance using the same lens.

    - Alan
    Arash, Is Alan's formula in Pane #12 close enough to correct to use?

    Alan, Assuming that it is, would this be correct for comparing the 1D IV and the 5D III? 1.3 X 1.3 X 16.1 for the MIV = 27.21 mp and 1 X 1 X 22.3 = 22.3 for the 5D III shows that the 1D IV puts more pixels on the subject than the 5D III.
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    Lifetime Member Doug Brown's Avatar
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    Mark IV pixel density does in fact give you a 27 MP full frame body when scaled up. My dream camera would have Mark IV pixel density in a FF body with the 5D3/1Dx AF system. Perfection!
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    Thanks Doug. If the "crop factor is not real" as noted above by several folks, how can the crop factor turn a 16 mp camera into a 27mp body?????
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    Quote Originally Posted by Arthur Morris View Post
    It's beginning to make sense. Thanks. That leads to the same question over and over again: why do most experienced folks (except possibly for Dan Cadieux) far prefer Mark IV or 5D Mark II image quality to 7D image quality?

    Does the answer have to do with the size of the individual pixels (larger is better???) or with the quality of the sensor? Or both?
    Artie I can speak for myself, for me bird photography is not fixed distance photography. I have learned how to get within ideal range of my subject with any camera that I have at hand, so more often than not larger sensor produces a better IQ for me because it collects more light. If the birds are too far I go home rather than settling for a tight crop and low IQ image.

    Re pixel size: This is a rather complicated subject because of the non-idealities in CMOS sensors. It depends on particular image sensor technology, for e.g. Nikon CMOS technology scales very well almost along the ideal (theoretical) trend so they shrunk the pixels and improved high ISO at the same time (D800). Canon technology has not scaled in the past few years and pattern noise, CMOS noise, hot pixels, spectral response as well as the low-pass filter are really poor in the case of 7D thus most competent photographers with critical eyes do not like the field results from that camera. However this is mostly due to non-ideal image sensor performance, not necessarily the small pixel size alone.

    I think this topic has been discussed many times before and the technical details are somewhat beyond the scope of this forum but overall I much prefer the overall IQ of 5D2/3 or 1D4 over 7D for the reasons I mentioned above. But if I had Nikon I would pick a D800 over a D4 for IQ alone any day despite the fact that it has much smaller pixels.
    Last edited by arash_hazeghi; 04-26-2012 at 09:51 PM.
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    Quote Originally Posted by Arthur Morris View Post
    Thanks Doug. If the "crop factor is not real" as noted above by several folks, how can the crop factor turn a 16 mp camera into a 27mp body?????
    it does not turn a 16 mpixel camera into a 27 mpixel camera, the camera is 16 mpixels. what this means is that if you had a larger sensor packed with pixels identical to those of 1D4 you would get 27 million of them.

    As I mentioned the only independent variable here is pixel size, not crop factor or sensor size. However pixel size can be described as total number of pixels / sensor size (crop factor) so it is implicit in the alternative calculation methods above. For the reason I mentioned in pane #6 I like to work with pixel size and not the crop factor.

    hope this helps!
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    Quote Originally Posted by arash_hazeghi View Post
    it does not turn a 16 mpixel camera into a 27 mpixel camera, the camera is 16 mpixels. what this means is that if you had a larger sensor packed with pixels identical to those of 1D4 you would get 27 million of them.

    As I mentioned the only independent variable here is pixel size, not crop factor or sensor size. However pixel size can be described as total number of pixels / sensor size (crop factor) so it is implicit in the alternative calculation methods above. For the reason I mentioned in pane #6 I like to work with pixel size and not the crop factor.

    hope this helps!
    Arash, if we compare the 1D IV with the 1Dx/5DIII, donīt looking to other improvments just to pixel size, in that case, the 1D IV would be a better camera is that correct?

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    While the thread has discussed numerous ways to compute pixels on subject, in my opinion, many methods seem to add confusion, especially throwing in crop factor. I think it is simpler to look at the problem linearly, not area. So instead of how many total pixels on the subject, look at it as how tall is the subject? How tall is the bird in pixels? So to compare two cameras, the size of a bird in the frame with the same lens is simply related to the ratio of the pixel size. For example, if camera A has 4.3 micron pixels, and camera B has 6.25 micron pixels (7D and 5DIII) then the size ratio is 6.25/4.3 = 1.45. So if a bird is 1000 pixels tall with a 5DIII, then it will be 1450 pixels tall in the 7D. Keep crop factors out of the equation to avoid further confusion.

    Roger

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    Artie, you are getting confused because of the math. Your question is simple: Standing in the same spot with the same lens, which camera gets more pixels on the subject?

    for a moment, forget about crop factor, megapixels and sensor size.

    Smaller the pixels, more the pixels on the subject. If you go through current canon cameras( and drop in Nikon D800 and Nikon D4) then this would be the order...starting with most pixels per subject and ending with least pixels per subject.

    7D & 60D, Nikon D800, 1D mark IV, 5D mark III, 1DX, Nikon D4.

    Now, if you go into IQ, noise, dynamic range, Af at f/8 and other things, discussions will become complex..we've had those before. I just wanted to give a simple answer to your question.

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    Quote Originally Posted by Arthur Morris View Post
    Alan, Assuming that it is, would this be correct for comparing the 1D IV and the 5D III? 1.3 X 1.3 X 16.1 for the MIV = 27.21 mp and 1 X 1 X 22.3 = 22.3 for the 5D III shows that the 1D IV puts more pixels on the subject than the 5D III.
    Artie,

    That is correct. The Mark IV puts more pixels on the subject than the 5D III. But as others have alluded to, it's not just the number of pixels on a subject that determines image quality.

    Personally, I am pleased that Canon has upgraded the 5D Mark II to the Mark III. It now has an excellent autofocus system and there's enough resolution that feather detail is not a concern of mine. Also, with a full-frame sensor there's less of a chance of clipping a wing out-of-frame.

    Alan
    Last edited by Arthur Morris; 05-04-2012 at 01:49 PM. Reason: alluded is correct not eluded :)

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    Thanks Alan. Agree 100% on the killer AF system. The other factor that Arash mentions often and correctly is that in situations where you can get closer to the subject full frame cameras like the 5D III will put lots more pixels on the subject.
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    Quote Originally Posted by Arthur Morris View Post
    Thanks Alan. Agree 100% on the killer AF system. The other factor that Arash mentions often and correctly is that in situations where you can get closer to the subject full frame cameras like the 5D III will put lots more pixels on the subject.
    Absolutely. In situations in which you can move closer to your subject, the 5D Mark III will provide the highest resolution and lowest noise out of all of the Canon cameras. There is a lot of versatility with the 5D Mark III. I have been using it extensively over the past month (primarily bird images) and have no complaints.

    Alan

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    Quote Originally Posted by Alan Stankevitz View Post
    Absolutely. In situations in which you can move closer to your subject, the 5D Mark III will provide the highest resolution and lowest noise out of all of the Canon cameras. There is a lot of versatility with the 5D Mark III. I have been using it extensively over the past month (primarily bird images) and have no complaints.

    Alan
    Alan,
    I'll challenge this a bit. I agree that if one has plenty of light and can fill the frame, the 5DII and III give great images. However, if one needs to push dynamic range limits, e.g. lift shadows, the 5D series give lower image quality because of the fixed pattern noise (banding). I do a lot of night images and have been quite frustrated at the fixed pattern noise (FPN) of the 5DII in the sky unless I am at ISO 3200 or higher. My 7D has lower FPN than my 5DII (and 5DIII reportedly has similar FPN to the 5DII with only a slight improvement). The 1DIV has much lower FPN and I am now using it as my choice for night images and my second choice is the 7D. So the 5DII is getting left home more and more. Pixels on subject are not everything, and FPN really ruins some images. I wish Canon would solve this problem like Nikon seems to have done. If I had the money, I would switch to Nikon. I may still get a D800 and some wide angle lenses for night photography.

    Roger
    Last edited by Roger Clark; 04-28-2012 at 11:27 AM.

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    Quote Originally Posted by Roger Clark View Post
    Alan,
    I'll challenge this a bit. I agree that if one has plenty of light and can fill the frame, the 5DII and III give great images. However, if one needs to push dynamic range limits, e.g. lift shadows, the 5D series give lower image quality because of the fixed pattern noise (banding). I do a lot of night images and have been quite frustrated at the fixed pattern noise (FPN) of the 5DII in the sky unless I am at ISO 3200 or higher. My 7D has lower FPN than my 5DII (and 5DIII reportedly has similar FPN to the 5DII with only a slight improvement). The 1DIV has much lower FPN and I am now using it as my choice for night images and my second choice is the 7D. So the 5DII is getting left home more and more. Pixels on subject are not everything, and FPN really ruins some images. I wish Canon would solve this problem like Nikon seems to have done. If I had the money, I would switch to Nikon. I may still get a D800 and some wide angle lenses for night photography.

    Roger
    Point well taken. The D800 appears to be an excellent camera and if I didn't have a major investment in Canon glass, I'd be tempted to buy one as well.

    I will state that I just returned from SE AZ and did some night sky imaging with the 5D Mark III under dark sky conditions. I did not notice any banding at ISO 1600 and ISO 3200, although my exposure times were only 15 sec. (Stacked multiple images.)

    Alan

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    To help to compare crop - look the 5D mk3 as a camera without a 1,4tc and the 1dmk4 -7d as a camera with a 1.4 tc. thats how i see it for fov its close enough as a guide.
    Rob.

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    Quote Originally Posted by Kaustubh Deshpande View Post
    Artie, you are getting confused because of the math. Your question is simple: Standing in the same spot with the same lens, which camera gets more pixels on the subject?

    for a moment, forget about crop factor, megapixels and sensor size.

    Smaller the pixels, more the pixels on the subject. If you go through current canon cameras( and drop in Nikon D800 and Nikon D4) then this would be the order...starting with most pixels per subject and ending with least pixels per subject.

    7D & 60D, Nikon D800, 1D mark IV, 5D mark III, 1DX, Nikon D4.

    Now, if you go into IQ, noise, dynamic range, Af at f/8 and other things, discussions will become complex..we've had those before. I just wanted to give a simple answer to your question.
    Thanks for trying but now I am more confused than ever :). One thing. Why is the MIV (16mp) ahead of the 5DIII (22mp) if ... Ah, I see my answer now. The 1D IV has smaller pixels than the 5D III (even though the 1D III has more pixels...)

    I am on record as liking my 1D IV and my 5D III images a lot more than I liked my 7D images.....
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    Quote Originally Posted by arash_hazeghi View Post
    it does not turn a 16 mpixel camera into a 27 mpixel camera, the camera is 16 mpixels. what this means is that if you had a larger sensor packed with pixels identical to those of 1D4 you would get 27 million of them.
    Seems like a somewhat confusing semantic argument, but heck, I was confused to start with. I think that I will keep to making images with the cameras that I like and forget about the rest :).
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