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Analysis  of  the  “Pixel  Density  Advantage” 

 

Sony  SLT-A57  /  Sony  SLT-A37  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 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 SLT-A57 / Sony SLT-A37 has a linear pixel density that is approximately 24% greater than that of the A900. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below. Note that, both the Sony A57 and the Sony A37 have 16.1 megapixels and a maximum image size of 4912 pixels x 3264 pixels.

 

Note: If the (full frame) Sony A900 / A850 had the same pixel density as the (APS-C) Sony SLT-A57 / A37, it would have approximately 37.5 megapixels, and image dimensions of approximately 7500 pixels x 5000 pixels.

 

 

Relevant  Specifications

 

Sony SLT-A57 and Sony SLT-A37: Image dimensions: 4912 pixels x 3264 pixels  (approx. 16.1 million effective pixels); sensor size: approx. 23.5mm x 15.6mm

 

Sony A900 and Sony 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 site of "Digital Photography Review".

 

 

Crop  Factor

 

Approximately 1.5x  (35.9mm / 23.5mm).

 

 

 

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

 

A57   =    2090   (4912 / 2.35)

A900 =    1685   (6048 / 3.59)

 

Pixel Density Advantage:  A57 is approximately 24% 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

 

A57   =   4.784    (23.5 / 4912  x 1000)

A900 =   5.936    (35.9 / 6048 x 1000)

 

Relationship: A900 is approximately 24% greater than A57

 

 

Crop an image from A900 to the same  field of view  as an image from A57

 

Gain in image width (in pixels) as a result of the above 24% pixel density advantage

 

Uncropped image width of A57 = 4912 pixels

 

Cropped image width of A900

to same field of view as A57      = approx. 3960 pixels  (6048 x 23.5 / 35.9)

 

Relationship: A57 is approximately 24% greater than A900.

 

 

Crop an image from A900 to the same  field of view  as an image from A57

 

Gain in comparable widths of print sizes as a result of the above 24% pixel density advantage

 

If the uncropped image of A57 (of 4912 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is 24.56 inches (4912 / 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 24% “pixel density advantage” of A57, is to produce a print at 200 ppi, that is about 4.8 inches wider (or about 24% 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 A57, and compare the changed field of view of A900 with that of A57:

 

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 A57 = focal length of lens  x  crop factor of A57 = 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 A57 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 A57 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 A57 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 instead of using lenses with longer focal lengths". 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 A57, and compare the changed field of view of A900 with that of A57:

 

Assume that a 300mm lens is on both cameras

 

Field of view of A57 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 A57 image

 

= uncropped image width of A900  /  cropped image width of A900  x  focal length of lens  =  approx.  369mm  (6048 / 4912 x 300mm)

 

Relationship: A57 is approximately 24% greater than A900.

 

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.

 

 

 

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

 

A57   =   4.392    (16.1 / 3.666)

A900 =   2.855    (24.6 / 8.616)

 

Relationship: A57 is approximately 54% 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 in square microns = area of sensor in square microns  divided by  the number of pixels on the sensor

 

A57   =   22.77    (366,600,000 / 16,100,000)

A900 =   35.02    (861,600,000 / 24,600,000)

 

Relationship: A900 is approximately 54% greater than A57

 

 

Crop an image from A900 to the same field of view as an image from A57

Gain in image area  (in megapixels)

 

Uncropped image area of A57 = approx. 16.1  megapixels  (4912 pixels x 3264 pixels)

 

Cropped image area of A900

to same field of view as A57   = approx. 10.45 megapixels  (3960 pixels x 2640 pixels)

 

Relationship: A57 is approximately 54% greater than A900

 

 

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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