﻿ Crop factor: An analysis of the "pixel density advantage" for the Sony A900 digital camera compared with the Nikon D3S. Sony A900 / 850 vs Nikon D3S Rob's  Photography  New  Zealand

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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 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

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 instead of using lenses with longer focal lengths". 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 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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