
Analysis of the “Pixel Density Advantage”
Sony NEX-3 / NEX-5 compared with the Sony A900 / A850
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 Sony A900 (or the Sony A850), the Sony NEX-3 and Sony NEX-5 have a linear pixel density that is approximately 16.5% greater than that of the A900. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.
Note: If the (full frame) Sony A900 / A850 had the same pixel density as the (APS-C) Sony NEX-3 / NEX-5, it would have approximately 33 megapixels, and image dimensions of approximately 7045 pixels x 4697 pixels.
Relevant Specifications
Sony NEX-3 and NEX-5: Image dimensions: 4592 pixels x 3056 pixels (approx. 14.2 million effective pixels); sensor size: approx. 23.4mm x 15.6mm
Sony A900 and A850: Image dimensions: 6048 pixels x 4032 pixels (approx. 24.6 million effective pixels); sensor size: approx. 35.9mm x 24.0mm
These specifications were obtained from the "buying guide" on the site of "Digital Photography Review".
Crop Factor
Approximately 1.5x (35.9mm / 23.4mm).
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
NEX-3 = 1962 (4592 / 2.34)
A900 = 1685 (6048 / 3.59)
Pixel Density Advantage: NEX-3 is approximately 16.5% greater than A900
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
NEX-3 = 5.096 (23.4 / 4592 x 1000)
A900 = 5.936 (35.9 / 6048 x 1000)
Relationship: A900 is approximately 16.5% greater than NEX-3
Crop an image from A900 to the same field of view as an image from NEX-3
Gain in image width (in pixels) as a result of the above 16.5% pixel density advantage
Uncropped image width of NEX-3 = 4592 pixels
Cropped image width of A900
to same field of view as NEX-3 = approx. 3942 pixels (6048 x 23.4 / 35.9)
Relationship: NEX-3 is approximately 16.5% greater than A900.
Crop an image from A900 to the same field of view as an image from NEX-3
Gain in comparable widths of print sizes as a result of the above 16.5% pixel density advantage
If the uncropped image of NEX-3 (of 4592 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is 22.96 inches (4592 / 200).
If the cropped image of A900 (of 3942 pixels width) is printed at 200 ppi, the width of the print is 19.71 inches (3942 / 200).
Relationship: The net effect of the 16.5% “pixel density advantage” of NEX-3, is to produce a print at 200 ppi, that is about 3.25 inches wider (or about 16.5% wider) than that produced with the same field of view from the cropped image of A900.
Crop an image from A900 to the same field of view as an image from NEX-3, and compare the changed field of view of A900 with that of NEX-3: Assume that a 70mm lens is on both cameras and that the field of view of an uncropped A900 image is 70mm
Field of view of NEX-3 = focal length of lens x crop factor of NEX-3 = approx. 107mm (70mm x 35.9mm / 23.4mm)
Changed field of view of an A900 image when it is cropped to the same field of view as a NEX-3 image
= uncropped image width of A900 / cropped image width of A900 x focal length of lens = approx. 107mm (6048 / 3942 x 70mm)
Relationship: The fields of view of NEX-3 and A900 are the same, that is, approx. 107mm.
Note: The image width of an A900 image, when it is cropped to the same field of view as a NEX-3 image, is approx. 3942 pixels (6048 x 23.4 / 35.9). 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 A900 to the same image width as an image from NEX-3, and compare the changed field of view of A900 with that of NEX-3: Assume that a 70mm lens is on both cameras
Field of view of NEX-3 is 70mm x crop factor = approx. 107mm (70mm x 35.9 / 23.4)
Changed field of view of an A900 image when it is cropped to the same image width as a NEX-3 image
= uncropped image width of A900 / cropped image width of A900 x focal length of lens = approx. 92mm (6048 / 4592 x 70mm)
Relationship: NEX-3 is approximately 16.5% greater than A900.
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
NEX-3 = 3.890 (14.2 / 3.6504)
A900 = 2.855 (24.6 / 8.616)
Relationship: NEX-3 is approximately 36% greater than A900
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
NEX-3 = 25.7 (365,040,000 / 14,200,000)
A900 = 35.0 (861,600,000 / 24,600,000)
Relationship: A900 is approximately 36% greater than NEX-3
Crop an image from A900 to the same field of view as an image from NEX-3
Gain in image area (in megapixels)
Uncropped image area of NEX-3 = approx. 14.2 megapixels (4592 pixels x 3056 pixels)
Cropped image area of A900
to same field of view as NEX-3 = approx. 10.4 megapixels (3942 pixels x 2628 pixels)
Relationship: NEX-3 is approximately 36% greater than A900
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 / 580 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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