
Analysis of the "Pixel Density Advantage”
Canon EOS 7D compared with the Canon EOS 5D Mark II
Summary of approximate mathematical relationships between image size, pixel density, and pixel size
This summary should be read in conjunction with the full explanatory article that you can see here. Note that the analysis on this page does not include a discussion of the various complex issues that can arise in practice when estimating pixel density and the pixel pitch or area of individual pixels. It is recommended that you study a detailed technical article if you would like to become familiar with these issues. For example, you may find this DPR forum discussion about pixel density and pixel size to be helpful. Therefore, the calculations set out below are presented for the purpose of calculating only a very approximate measurement of pixel density, pixel pitch, and the area of one pixel, which can be used for comparing the approximate mathematical relationships between the pixel density and pixel size of different cameras.
This summary provides an example of how to apply the template that is published here. In this theoretical template, the reconciliations between the percentages shown for pixel density and pixel size, work out exactly, only because the number of megapixels on the sensor is exactly the same as the image width in pixels, multiplied by the image height in pixels. In addition, the image width divided by the image height, gives the same answer as the sensor width divided by the sensor height. In the theoretical template, the approximate area calculation for the size of one pixel is exactly equal to the pixel pitch squared. In addition, the approximate area calculation for the pixel density is exactly equal to the linear pixel density squared.
However, in the practical example that follows, the arithmetical reconciliations demonstrated in the template do not work out exactly because of roundings in the specifications used, and also because of the way the effective number of pixels of the cameras is calculated (that is, the image width multiplied by the image height, does not exactly equal the effective number of pixels published for the cameras).
Note: The information below is not designed to provide information about the quality of images or the quality of the cameras, because these are separate issues.
This summary shows that, when compared with the Canon 5D Mark II, the Canon 7D has a linear pixel density that is approximately 49% greater than that of the 5DII. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.
Note: If the (full frame) Canon 5D Mark II had the same pixel density as the (APS-C) Canon 7D, it would have approximately 47 megapixels, and image dimensions of approximately 8370 pixels x 5580 pixels.
Relevant Specifications
Canon 7D: Image dimensions: 5184 pixels x 3456 pixels (approx. 18.0 million effective pixels); sensor size: 22.3mm x 14.9mm
Canon 5DII: Image dimensions: 5616 pixels x 3744 pixels (approx. 21.0 million effective pixels); sensor size: 36.0mm x 24.0mm
Note: The Canon 5D Mark III was announced in March 2012. Click here to see a summary of the approximate mathematical relationships between image size, pixel density, and pixel size for the Canon 5D Mark III compared with the Canon 7D.
Crop Factor
Approximately 1.6x (36.0mm / 22.3mm)
Approximate Linear Relationships
Pixel density (in pixels per linear centimetre)
Pixel density in pixels per linear centimetre = image width in pixels divided by width of sensor in centimetres
7D = 2325 (5184 / 2.23)
5DII = 1560 (5616 / 3.60)
Pixel Density Advantage: 7D is approximately 49% greater than 5DII
Pixel pitch (in microns)
Refer to the
reservations
here about calculating the "true" width and area of an
individual pixel.
Pixel pitch in microns = width of sensor in millimetres divided by image width in pixels multiplied by 1000
7D = 4.3 (22.3 / 5184 x 1000)
5DII = 6.4 (36.0 / 5616 x 1000)
Relationship: 5DII is approximately 49% greater than 7D
Crop an image from 5DII to the same field of view as an image from 7D
Gain in image width (in pixels) as a result of the above 49% pixel density advantage
Uncropped image width of 7D = 5184 pixels
Cropped image width of 5DII
to same field of view as 7D = approx. 3479 pixels (5616 x 22.3 / 36.0)
Relationship: 7D is approximately 49% greater than 5DII.
Crop an image from 5DII to the same field of view as an image from 7D
Gain in comparable widths of print sizes as a result of the above 49% pixel density advantage
If the uncropped image of 7D (of 5184 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is about 25.9 inches (5184 / 200).
If the cropped image of 5DII (of 3479 pixels width) is printed at 200 ppi, the width of the print is about 17.4 inches (3479 / 200).
Relationship: The net effect of the 49% pixel density advantage of 7D, is to produce a print at 200 ppi, that is about 8.5 inches wider (or 49% wider) than that produced with the same field of view from the cropped image of 5DII.
Crop an image from 5DII to the same field of view as an image from 7D, and compare the changed field of view of 5DII with that of 7D: Assume that a 300mm lens is on both cameras and that the field of view of an uncropped 5DII image is 300mm
Field of view of 7D = focal length of lens x crop factor of 7D = approx. 484mm (300mm x 36.0mm / 22.3mm)
Changed field of view of a 5DII image when it is cropped to the same field of view as a 7D image
= uncropped image width of 5DII / cropped image width of 5DII x focal length of lens = approx. 484mm (5616 / 3479 x 300mm)
Relationship: The fields of view of 7D and 5DII are the same, that is, approx. 484mm.
Note: The image width of a 5DII image, when it is cropped to the same field of view as 7D, is approx. 3479 pixels (5616 x 22.3 / 36.0). Click here to go to an article titled "Advantages and disadvantages of cropping images to gain extra reach". This article gives further details in support of the formulas used above.
Crop an image from 5DII to the same image width as an image from 7D, and compare the changed field of view of 5DII with that of 7D: Assume that a 300mm lens is on both cameras
Field of view of 7D = focal length of lens x crop factor of 7D = approx. 484mm (300mm x 36.0 / 22.3)
Changed field of view of a 5DII image when it is is cropped to the same image width as a 7D image
= uncropped image width of 5DII / cropped image width of 5DII x focal length of lens = 325mm (5616 / 5184 x 300mm)
Relationship: 7D is approximately 49% greater than 5DII.
Note: Click here to go to an article titled "Advantages and disadvantages of cropping images to gain extra reach". This article gives further details in support of the formulas used above. Click here to see a forum discussion titled: "How do you calculate the reach advantage? Sony A900 vs Nikon D3S" Digital Photography Review, Sony SLR Talk Forum, April 2010.
Approximate Area Relationships
Pixel density (in megapixels per square centimetre)
Pixel density in megapixels per square centimetre = number of megapixels on the sensor divided by sensor area in square centimetres
7D = 5.4173 (18 / 3.3227)
5DII = 2.4306 (21 / 8.64)
Relationship: 7D is approximately 123% greater than 5DII
Pixel area (approximate area of one pixel in square microns)
Refer to the
reservations
here about calculating the "true" width and area of an
individual pixel.
Area of one pixel = area of sensor in square microns divided by the number of pixels on the sensor
7D = 18.4594 (332,270,000 / 18,000,000)
5DII = 41.1429 (864,000,000 / 21,000,000)
Relationship: 5DII is approximately 123% greater than 7D
Crop an image from 5DII to the same field of view as an image from 7D: Gain in image area (based on image sizes in megapixels)
Uncropped image area of 7D = 18 megapixels (5184 pixels x 3456 pixels)
Cropped image area of 5DII
to same field of view as 7D = 8.068 megapixels (3479 pixels x 2319 pixels)
Relationship: 7D is approximately 123% greater than 5DII
Click here to go to the full explanatory article about the crop factor and “telephoto advantage” of an APS-C camera.
Click here to see a comparison of two “theoretical” cameras, which permits the reconciliations between the percentages shown for image size, pixel density, and pixel area, to be exactly equal.
Examples of the practical application of the "pixel density advantage" template:
New: Sony SLT-A58 compared with the Sony A99
A 36mp full
frame camera (such as the Nikon D800) compared with a 22 mp full frame
camera (such as the Canon 5D Mark III)
A 36mp FF camera
(such as the Nikon D800) compared with a 24mp APS-C camera (such as the
Nikon D3200 or the Sony A77)
Canon EOS 7D compared with the Canon EOS 5D Mark II
Canon EOS 7D compared with the Canon EOS 5D Mark III
Nikon D300S compared with the Nikon D3S
Nikon D800 compared with the Nikon D3200
Sony SLT-A77 / A65 compared with the Sony A900 / A850
Sony SLT-A77 / A65 compared with the Sony A99
Sony SLT-A57 / A37 compared with the Sony A900 / A850
Sony SLT-A58 compared with the Sony A99
Sony SLT-A55 / A580 compared with the Sony A99
Sony A700 compared with the Sony A900 / Sony A850
Sony A900 compared with the Nikon D3S
Sony NEX-3 / NEX-5 compared with the Sony A900 / A850
Sony R1 compared with the Sony A900 / Sony A850
Click here to see examples of the outstanding resolution of the full frame Sony A900.
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