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 Analysis  of  the  "Pixel  Density  Advantage” 

 

A  "theoretical"  36  megapixel  full  frame  camera  compared  with

a  "theoretical"  22  megapixel  full  frame  camera

 

 

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.  In particular, note the reservations expressed  here  about calculating the "exact" width and area of one pixel. This summary shows that, when compared with a "theoretical" 22 megapixel (mp) full frame (FF) camera, a "theoretical" 36 mp FF camera has a linear pixel density that is about 28% greater than that of a full frame 22 mp FF camera. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

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 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. These relationships are present in the theoretical example that follows.

 

Note: The Sony A7R and the Nikon D800 are examples of a 36mp full frame camera.  

 

The Canon 5D Mark III, announced in March 2012, is an example of a 22mp full frame camera, and  Digital Photography Review  reports that it has image dimensions of 5760 pixels x 3840 pixels and a sensor size of 36mm x 24mm.

 

However, the cameras referred to below are "theoretical" cameras only and although their specifications are similar to those of the Nikon D800 and Canon 5D III, they are  not  identical. Therefore, the results shown below should not be regarded as those that would be obtained when using the relevant specifications of the Nikon D800 and the Canon 5D III.

 

 

Relevant  specifications  of  "theoretical  cameras"

 

36 mp FF: Image dimensions: 7353 pixels x 4902 pixels; sensor size: 36mm x 24mm

 

22 mp FF: Image dimensions: 5754 pixels x 3836 pixels; sensor size: 36mm x 24mm

 

 

 Linear  relationships  of  "theoretical cameras"

 

 

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

 

36 mp FF =          2042.500    (7353 / 3.60)

22 mp FF =          1598.333    (5754 / 3.60)

 

Pixel Density Advantage:  36 mp FF is about 27.8 % greater than 22 mp FF

 

 

Difference in image width (in pixels) as a result of the above 27.8% pixel density advantage

 

Image width of 36 mp FF = 7353 pixels

 

Image width of 22 mp FF = 5754 pixels

 

Relationship: 36 mp FF is about 27.8% greater than 22 mp FF

 

 

Gain in comparable widths of print sizes as a result of the above 50% pixel density advantage

 

If a 36 mp FF image (of 7353 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is 36.765 inches (7353 / 200).

 

If a 22 mp FF image (of 5754 pixels width) is printed at 200 ppi, the width of the print is 28.77 inches (5754 / 200).

 

Relationship: The net effect of the 27.8 % pixel density advantage of 36 mp FF, is to produce a print at 200 ppi, that is about 8 inches wider (or about 27.8% wider) than that produced with the same field of view from 22 mp FF.

 

 

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

 

36 mp FF =         4.89596   (36.0 / 7353 x 1000)

22 mp FF =         6.25652   (36.0 / 5754 x 1000)

 

Relationship: 22 mp FF is about 27.8% greater than 36 mp FF

 

Note: Based on the specifications given above, the Nikon D800 also has a pixel pitch of approximately 4.9 microns (35.9 / 7360 x 1000) and the Canon 5D III also has a pixel pitch of approximately 6.25 microns (36.0 / 5760 x 1000).

 

 

Crop an image from 36 mp FF to the same  image width  as an image from 22 mp FF, and compare the changed field of view of 36 mp FF with that of 22 mp FF: Assume that a 300mm lens is on both cameras

 

Field of view of both 36 mp FF and 22 mp FF =  300mm

 

Changed field of view of a 36 mp FF image when it is cropped to the same  image width  as a 22 mp FF image

 

= uncropped image width of 36 mp FF  /  cropped image width of 36 mp FF  x  focal length of lens  =  383.4mm  (7353 / 5754 x 300mm)

 

Relationship: 36 mp FF is about 27.8% greater than 22 mp FF

 

Note:  Click  here  to go to an article titled "Advantages and disadvantages of cropping images instead of using lenses with longer focal lengths". 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.

 

  

Area  relationships  of  "theoretical  cameras"

 

 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

 

36 mp FF =         4.172    (36.0444 / 8.64)      or pixel density in pixels per linear centimetre squared / 1,000,000 = (2042.5 x 2042.5 / 1,000,000)

 

22 mp FF =         2.555    (22.0723 / 8.64)      or pixel density in pixels per linear centimetre squared / 1,000,000 = (1598.3 x 1598.3 / 1,000,000)

 

Relationship: 36 mp FF is 63.3% greater than 22 mp FF

 

 

Gain in image area  (in megapixels)

 

Image area of 36 mp FF = 36.044406 megapixels  (7353 pixels x 4902 pixels)

 

Image area of 22 mp FF = 22.072344 megapixels  (5754 pixels x 3836 pixels)

 

Relationship: 36 mp FF is 63.3% greater than 22 mp FF

 

 

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

 

36 mp FF =          23.9704     (864,000,000  / 36,044,406)   or pixel pitch squared   (4.895961 microns x 4.895961 microns)

 

22 mp FF =          39.1440     (864,000,000 / 22,072,344)    or pixel pitch squared   (6.25652 microns x 6.25652 microns)

 

Relationship: 22 mp FF is 63.3% greater than 36 mp FF

 

 

 

 

Click  here  to go to an index of further camera comparisons showing the mathematical relationships between image size, pixel size, pixel density, and reach etc.

 

Click  here  to go to the index of all the technical articles and blogs on this site.

 

 

 

 

 

 

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