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 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 go to the full explanatory article about the crop factor and “telephoto advantage” of an APS-C camera.

 

Note that Appendix 2 of the above article includes the following sections:

 

Calculation of pixel pitch

 

Calculation of the area of one pixel

 

Why is pixel size important - increasing pixel count increases noise?  (Click  here  to read the full article)

 

Pixel level vs image level in digital photography (also refers to the new  Studio Test Scene  published by Digital Photography Review)

 

Case study: High ISO low light images of the Sony A77 compared with those of the Sony A55

 

Downscaling and upscaling images for comparative purposes  (can apples be compared with oranges?)

 

Practical examples of the application of the "pixel density advantage" template

 

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:

 

A 36mp full frame camera (such as the Sony Alpha 7R or the Nikon D800) compared with a 24mp APS-C camera (such as the Sony A77 or the Nikon D3200)

 

A 36mp full frame camera (such as the Sony Alpha 7R or the Nikon D800) compared with a 16mp full frame camera (such as the Nikon D4)

 

A 36mp full frame camera (such as the Sony Alpha 7R or the Nikon D800) compared with a 22 mp full frame camera (such as the Canon 5D Mark III)

 

A 24mp FF camera (such as the Sony A99) compared with a 24mp APS-C camera (such as the Sony A77 or the Nikon D3200)

 

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 A6000 (ILCE-6000) compared with the 36mp Sony A7R (ILCE-7R)

Sony SLT-A77 / A65 compared with the 36mp Sony A7R

Sony SLT-A77 / A65 compared with the Sony A99 / Sony A7

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
Sony RX100 compared with the Sony A900 / Sony A850
Sony RX10 / RX100 compared with the Sony A99 and the compact 35mm fixed lens full frame 24.3mp Sony RX1



Click  here  to go to an article titled "Advantages and disadvantages of cropping images to gain extra reach".

 

Click  here  to see examples of the outstanding resolution of the full frame Sony A900.

 

Click  here  to go to the home page of Rob’s Photography New Zealand.

 

 

 

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