Analysis of the "Pixel Density Advantage”
Full frame Sony A900 / 850 compared with the full frame Nikon D3S
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 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). For example, the specifications for the Sony A900 state that it has 24.6 million effective pixels, and that the image size is 6048 pixels x 4032 pixels. But, when you multiply 6048 pixels x 4032 pixels, you obtain 24.386 million pixels, not 24.6 million pixels.
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 full frame Nikon D3S, the full frame Sony A900 has a linear pixel density that is approximately 42% greater than that of the full frame D3S. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.
Relevant Specifications
Sony A900: Image dimensions: 6048 pixels x 4032 pixels (24.6 million effective pixels); sensor size: 35.9mm x 24.0mm
Nikon D3S: Image dimensions: 4256 pixels x 2832 pixels (12.1 million effective pixels); sensor size: 36.0mm x 23.9mm
Click here to see the “Digital Photography Review” buying guide from which these specifications were obtained.
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
A900 = 1685 (6048 / 3.59)
D3S = 1182 (4256 / 3.60)
Pixel Density Advantage: A900 is approximately 42% greater than D3S
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
A900 = 5.936 (35.9 / 6048 x 1000)
D3S = 8.459 (36.0 / 4256 x 1000)
Relationship: D3S is approximately 42% greater than A900
Crop an image from the A900 to the same field of view as an image from the D3S
Gain in image width (in pixels) as a result of the above 42% pixel density advantage
Uncropped image width of A900 = 6048 pixels
Cropped image width of D3S
to same field of view as A900 = 4244 pixels (4256 x 35.9 / 36.0)
Relationship: A900 is approximately 42% greater than D3S
Crop an image from the A900 to the same field of view as an image from the D3S
Gain in comparable widths of print sizes as a result of the above 42% pixel density advantage
If the uncropped image of A900 (of 6048 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is about 30 inches (6048 / 200).
If the cropped image of D3S (of 4244 pixels width) is printed at 200 ppi, the width of the print is about 21 inches (4244 / 200).
Relationship: The net effect of the 42% pixel density advantage of A900, is to produce a print at 200 ppi, that is about 9 inches wider (or about 42% wider) than that produced with the same field of view from the D3S.
Crop an image from the A900 to the same image width as an image from the D3S, and compare the changed field of view of A900 with that of D3S: Assume that a 300mm lens is on both cameras
Field of view of full frame D3S = 300mm
Changed field of view of an A900 image when it is cropped to the same image width as a D3S image = approx. 426mm (6048 / 4256 x 300mm)
Relationship: A900 is approximately 42% greater than D3S
Note: Click here to see a web page which has pictures that illustrate the above principle. 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. 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.
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
A900 = 2.8552 (24.6 / 8.616)
D3S = 1.4063 (12.1 / 8.604)
Relationship: A900 is approximately 103% greater than D3S
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
A900 = 35.0244 (861,600,000 / 24,600,000)
D3S = 71.1074 (860,400,000 / 12,100,000)
Relationship: D3S is approximately 103% greater than A900
Crop an image from the A900 to the same field of view as an image from the D3S
Gain in image area (in megapixels)
Uncropped image area of A900 = 24.6 megapixels (6048 pixels x 4032 pixels)
Cropped image area of D3S
to same field of view as A900 = 12.01 megapixels (4244 pixels x 2829 pixels)
Relationship: A900 is approximately 105% greater than D3S
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:
Sony SLT-A77 / A65 compared with the Sony A900 / A850
Sony SLT-A55 / A580 compared with the Sony A900 / A850
Sony A700 compared with the Sony A900 / Sony A850
Sony NEX-3 / NEX-5 compared with the Sony A900 / A850
Nikon D300S compared with the Nikon D3S
Canon EOS 7D compared with the Canon EOS 5D Mark II
Sony A900 compared with the Nikon D3S
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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