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Analysis  of  the  “Pixel  Density  Advantage” 

 

APS-C  Sony  A77II  (ILCA-77M2)  compared  with 

the  full  frame  Sony  A7R  (ILCE-7R)

 

 

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 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 A7R state that it has approximately 36.4 million effective pixels, and that the image size is 7360 pixels x 4912 pixels. But, when you multiply 7360 pixels x 4912 pixels, you obtain 36.15 million pixels, not 36.4 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 A7R, the Sony A77II has an approximate linear pixel density that is about 24.5% greater than that of the A7R. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

Note: If the (full frame) Sony A7R had the same pixel density as the (APS-C) Sony A77II, it would have approximately 56 megapixels. In addition, if the Sony A77II had the same pixel density as the Sony A7R, it would have about 15.5 megapixels.

 

 

Relevant  Specifications

 

Sony A77II (ILCA-77M2): Image dimensions: 6000 pixels x 4000 pixels  (approx. 24.3 million effective pixels); sensor size: approx. 23.5mm x 15.6mm

 

Sony A7R (ILCE-7R): Image dimensions: 7360 pixels x 4912  pixels (approx. 36.4 million effective pixels); sensor size: approx. 35.9mm x 24.0mm

 

The specifications for the  Sony A7R  were obtained from  here  and the specifications for the Sony A77II were obtained  here

 

 

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

 

A77II   =    2553   (6000 / 2.35)

A7R =        2050   (7360 / 3.59)

 

Pixel Density Advantage:  A77II  is approximately 24.5% greater than A7R

 

 

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

 

A77II   =   3.917    (23.5 / 6000  x 1000)

A7R =       4.878    (35.9 / 7360 x 1000)

 

Relationship: A7R is approximately 24.5% greater than A77II

 

 

Crop an image from A7R to the same  field of view  as an image from A77II

 

Gain in image width (in pixels) as a result of the above 24.5% pixel density advantage

 

Uncropped image width of A77II = 6000 pixels

 

Cropped image width of A7R

to same field of view as A77II      = approx. 4818 pixels  (7360 x 23.5 / 35.9)

 

Relationship: A77II is approximately 24.5% greater than A7R.

 

 

Crop an image from A7R to the same  field of view  as an image from A77II

 

Gain in comparable widths of print sizes as a result of the above 24.5% pixel density advantage

 

If the uncropped image of A77II (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 A7R (of 4818 pixels width) is printed at 200 ppi, the width of the print is about  24.1 inches  (4818 / 200).

 

Relationship: The net effect of the 24.5% “pixel density advantage” of A77II, is to produce a print at 200 ppi, that is about 5.9 inches wider (or about 24.5% wider) than that produced with the same  field of view  from the cropped image of A7R.

 

 

Crop an image from A7R to the same   field of view  as an image from A77II, and compare the changed field of view of A7R with that of A77II:

 

Assume that a 300mm lens is on both cameras and that the field of view of an uncropped A7R image is 300mm

 

Field of view of A77II = focal length of lens  x  crop factor of A77II = approx. 458mm  (300mm x 35.9mm / 23.5mm)

 

Changed field of view of an A7R image when it is cropped to the same field of view as an A77II image

 

= uncropped image width of A7R  /  cropped image width of A7R  x  focal length of lens  =  approx. 458mm  (7360 / 4818  x  300mm)

 

Relationship: The fields of view of A77II and A7R are the same, that is, approx. 458mm.

 

Note: The approximate image width of an A7R image, when it is cropped to the same field of view as an A77II image, is approx. 4818 pixels (7360 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 A7R to the same  image width  as an image from A77II, and compare the changed field of view of A7R with that of A77II:

 

Assume that a 300mm lens is on both cameras

 

Field of view of A77II is 300mm x crop factor = approx. 458mm  (300mm x 35.9mm / 23.5mm)

 

Field of view of an A7R image when it is cropped to the same image width as an A77II image

 

= uncropped image width of A7R  /  cropped image width of A7R  x  focal length of lens  =  368mm  (7360 / 6000 x 300mm)

 

Relationship: A77II is approximately 24.5% greater than A7R.

 

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

 

 

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

 

A77II   =   6.628    (24.3 / 3.666)

A7R =       4.225    (36.4 / 8.616)

 

Relationship: A77II is approximately 56.9% greater than A7R

 

 

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

 

A77II   =   15.086    (366,600,000 / 24,300,000)

A7R =       23.670    (861,600,000 / 36,400,000)

 

Relationship: A7R is approximately 56.9% greater than A77II

 

 

Crop an image from A7R to the same field of view as an image from A77II

Gain in image area  (in megapixels)

 

Uncropped image area of A77II = approx.  24.3 megapixels  (6000 pixels x 4000 pixels)

 

Cropped image area of A7R

to same field of view as A77II   = approx.  15.475 megapixels  (4818 pixels x 3212 pixels)

 

Relationship: A77II is approximately 57% greater than A7R

 

 

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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