Analysis of the “Pixel Density Advantage”
Sony SLT-A77 / A65 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 image size and 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 SLT-A77 has an approximate linear pixel density that is about 52% 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 SLT-A77, it would have approximately 56 megapixels, and image dimensions of about 9166 pixels x 6111 pixels.
Relevant Specifications
Sony SLT-A77 / A65: Image dimensions: 6000 pixels x 4000 pixels (approx. 24.3 million effective pixels); sensor size: approx. 23.5mm 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
The specifications for the Sony SLT-A77 / A65 were obtained from the site of "Digital Photography Review", in a "Hands-on" Preview published on 24 August 2011.
Crop Factor
Approximately 1.5x (35.9mm / 23.5mm).
Approximate Linear Relationships
Approximate 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
A77 = 2553 (6000 / 2.35)
A900 = 1685 (6048 / 3.59)
Pixel Density Advantage: A77 is approximately 52% greater than A900
Approximate 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
A77 = 3.917 (23.5 / 6000 x 1000)
A900 = 5.936 (35.9 / 6048 x 1000)
Relationship: A900 is approximately 52% greater than A77
Crop an image from A900 to the same field of view as an image from A77
Gain in image width (in pixels) as a result of the above 52% pixel density advantage
Uncropped image width of A77 = 6000 pixels
Cropped image width of A900
to same field of view as A77 = approx. 3960 pixels (6048 x 23.5 / 35.9)
Relationship: A77 is approximately 52% greater than A900.
Crop an image from A900 to the same field of view as an image from A77
Gain in comparable widths of print sizes as a result of the above 52% pixel density advantage
If the uncropped image of A77 (of 6000 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is 30 inches (6000 / 200).
If the cropped image of A900 (of 3960 pixels width) is printed at 200 ppi, the width of the print is 19.8 inches (3960 / 200).
Relationship: The net effect of the 52% “pixel density advantage” of A77, is to produce a print at 200 ppi, that is about 10.2 inches wider (or about 52% 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 A77, and compare the changed field of view of A900 with that of A77: Assume that a 300mm lens is on both cameras and that the field of view of an uncropped A900 image is 300mm
Field of view of A77 = focal length of lens x crop factor of A77 = approx. 458mm (300mm x 35.9mm / 23.5mm)
Changed field of view of an A900 image when it is cropped to the same field of view as an A77 image
= uncropped image width of A900 / cropped image width of A900 x focal length of lens = approx. 458mm (6048 / 3960 x 300mm)
Relationship: The fields of view of A77 and A900 are the same, that is, approx. 458mm.
Note: The image width of an A900 image, when it is cropped to the same field of view as an A77 image, is approx. 3960 pixels (6048 x 23.5 / 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 A77, and compare the changed field of view of A900 with that of A77: Assume that a 300mm lens is on both cameras
Field of view of A77 is 300mm x crop factor = approx. 458mm (300mm x 35.9 / 23.5)
Changed field of view of an A900 image when it is cropped to the same image width as an A77 image
= uncropped image width of A900 / cropped image width of A900 x focal length of lens = approx. 302mm (6048 / 6000 x 300mm)
Relationship: A77 is approximately 52% 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
Approximate 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
A77 = 6.628 (24.3 / 3.666)
A900 = 2.855 (24.6 / 8.616)
Relationship: A77 is approximately 132% greater than A900
Approximate 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 in square microns = area of sensor in square microns divided by the number of pixels on the sensor
A77 = 15.086 (366,600,000 / 24,300,000)
A900 = 35.024 (861,600,000 / 24,600,000)
Relationship: A900 is approximately 132% greater than A77
Crop an image from A900 to the same field of view as an image from A77
Gain in image area (in megapixels)
Uncropped image area of A77 = approx. 24.3 megapixels (6000 pixels x 4000 pixels)
Cropped image area of A900
to same field of view as A77 = approx. 10.45 megapixels (3960 pixels x 2640 pixels)
Relationship: A77 is approximately 132% greater than A900
Excellent reach of telephoto lenses on Sony A77: Compare with A900, A700, A55
The following example shows the fields of view for both a 300mm and 400mm telephoto lens on the following Sony cameras:
24.6mp full frame A900;
12.2mp APS-C A700;
16.2mp APS-C A55; and the 24.3mp APS-C A77.
The sensor size of the Sony A900 is
35.9mm x 24.0mm and for all the APS-C cameras it is 23.5mm x 15.6mm.
A crop factor of 1.528x is used for
the APS-C cameras (35.9mm / 23.5mm).
The image dimensions (in pixels) of
these cameras are: A900: 6048 x 4032;
A700: 4272 x 2848;
A55: 4912 x 3264; A77:
6000 x 4000.
Approximate
field of view for images that have not been cropped
300mm lens: A900
= 300mm; A700 = 458mm;
A55 = 458mm;
A77 = 458mm
400mm lens: A900
= 400mm; A700 = 611mm;
A55 = 611mm;
A77 = 611mm
Approximate
field of view for images that have been cropped to an image width of 3960
pixels
300mm lens: A900
= 458mm; A700 = 494mm;
A55 = 568mm;
A77 = 694mm
400mm lens:
A900 = 611mm; A700 =
659mm; A55 = 758mm;
A77 = 926mm
Consider this, if you put a 300mm lens on the A77 and crop a full sized image to a width of 3960 pixels, you get a field of view of about 694mm (6000 / 3960 x 458mm).
But, even if you put a 400mm lens on the A700 and crop a full sized image to a width of 3960 pixels, you only get a field of view of about 659mm (4272 / 3960 x 611mm).
Click here to go to an article titled "Advantages and disadvantages of cropping images to gain extra reach".
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 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
Click here to see examples of the outstanding resolution of the full frame Sony A900.
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