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Analysis  of  the  “Pixel  Density  Advantage” 

 

Sony  A7S  (ILCE-7S)  compared  with  the  Sony  SLT-A77II   / A77  /  A65 

 

 

 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 A99 state that it has 24.3 million effective pixels, and that the image size is 6000 pixels x 4000 pixels. But, when you multiply 6000 pixels x 4000 pixels, you obtain 24.0 million pixels, not 24.3 million pixels.

 

The full frame  Sony A7S  was announced in April 2014 and is a 12.2 megapixel full frame mirrorless camera that has 4K video capability. The specifications for the Sony A7S are published  here.

 

The announcement of the Sony A7S was made on April 6, 2014 and can be seen  here. The announcement mentioned that:

"The innovative α7S camera features a newly developed, 12.2 effective megapixel 35mm Exmor® CMOS sensor paired with a powerful BIONZ X image processor, allowing it to shoot at a sensitivity range of ISO 50 – 409600 with unprecedented dynamic range and low noise.

The new model is also the world’s first camera to utilize the entire width of a full-frame image sensor in 4K video acquisition, and does this without cropping or line skipping as it can read and process data from every one of the sensor’s pixels.  This allows 4K video shooters to utilize all of the artistic and creative benefits provided by the unique sensor.

The  Sony A77II  was announced in May 2014 and is an upgrade of the Sony A77. The specifications for the Sony A77II are published  here.

 

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 A7S, the Sony A77II has an approximate linear pixel density that is about 116% greater than that of the A7S. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

If the (full frame) Sony A7S had the same pixel density as the (APS-C) Sony SLT-A65 / A77, it would have approximately 56 megapixels. In addition, if the Sony A65 / A77 had the same pixel density as the Sony A7S, it would have only about 5.2 megapixels.

 

 

Relevant  Specifications

 

Sony A7S: Image dimensions: 4240 pixels x 2832  pixels (approx. 12.2 million effective pixels); sensor size: approx. 35.8mm x 23.9mm

 

Sony SLT-A77 / A77II / A65: Image dimensions: 6000 pixels x 4000 pixels  (approx. 24.3 million effective pixels); sensor size: approx. 23.5mm x 15.6mm

 

 

Crop  Factor

 

Approximately 1.5x  (35.8mm / 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)

A7S =      1184   (4240 / 3.58)

 

Pixel Density Advantage:  A77  is approximately 116% greater than A7S

 

 

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)

A7S =     8.443    (35.8 / 4240 x 1000)

 

Relationship: A7S is approximately 116% greater than A77

 

 

Crop an image from A7S to the same  field of view  as an image from A77

Gain in image width (in pixels) as a result of the above 116% pixel density advantage

 

Uncropped image width of A77 = 6000 pixels

 

Cropped image width of A7S

to same field of view as A77      = approx. 2783 pixels  (4240 x 23.5 / 35.8)

 

Relationship: A77 is approximately 116% greater than A7S.

 

 

Crop an image from A7S to the same  field of view  as an image from A77

 

Gain in comparable widths of print sizes as a result of the above 116% 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 A7S (of 2783 pixels width) is printed at 200 ppi, the width of the print is about  13.9 inches  (2783 / 200).

 

Relationship: The net effect of the 116% “pixel density advantage” of A77, is to produce a print at 200 ppi, that is about 16.1 inches wider (or about 116% wider) than that produced with the same  field of view  from the cropped image of A7S.

 

 

Crop an image from A7S to the same   field of view  as an image from A77, and compare the changed field of view of A7S with that of A77:

 

Assume that a 300mm lens is on both cameras and that the field of view of an uncropped A7S image is 300mm

 

Field of view of A77 = focal length of lens  x  crop factor of A77 = approx. 457mm  (300mm x 35.8mm / 23.5mm)

 

Changed field of view of an A7S image when it is cropped to the same field of view as an A77 image

 

= uncropped image width of A7S  /  cropped image width of A7S  x  focal length of lens  =  approx. 457mm  (4240 / 2783  x  300mm)

 

Relationship: The fields of view of A77 and A7S are the same, that is, approx. 457mm.

 

Note: The image width of an A7S image, when it is cropped to the same field of view as an A77 image, is approx. 2783 pixels (4240 x 23.5 / 35.8). 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 A77 to the same  image width  as an image from A7S, and compare the changed field of view of A77 with that of A7S:

 

Assume that a 300mm lens is on both cameras

 

Field of view of an A7S image with a 300mm lens = 300mm

 

Field of view of an A77 image when it is cropped to the same image width as an A7S image

 

= uncropped image width of A77  /  cropped image width of A77  x  focal length of lens x crop factor  =  647mm  (6000 / 4240 x 300mm x 35.8mm / 23.5mm)

 

Relationship: A77 is approximately 116% greater than A99.

 

 

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

 

A77   =   6.628    (24.3 / 3.666)

A7S =     1.426    (12.2 / 8.5562)

 

Relationship: A77 is approximately 365% greater than A7S

 

 

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)

A7S =    70.133    (855,620,000 / 12,200,000)

 

Relationship: A7S is approximately 365% greater than A77

 

 

Crop an image from A7S 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 A7S

to same field of view as A77   = approx.  5.164 megapixels  (2783 pixels x 1855 pixels)

 

Relationship: A77 is approximately 370% greater than A7S

 

 

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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