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Analysis  of  the  “Pixel  Density  Advantage” 

 

Nikon  D800  compared  with  the  Nikon  D3200

 

 

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. These relationships have not been met in the example that follows, so some of the arithmetical reconciliations demonstrated in the template do not work out exactly.

 

The Nikon D800, introduced early in 2012, is a 36.3mp full frame camera, and  Digital Photography Review  reports that it has image dimensions of 7360 pixels x 4912 pixels and a sensor size of 35.9mm x 24mm.

 

The Nikon D3200, introduced in April 2012, is a 24.2mp APS-C camera. The  Nikon D3200  has image dimensions of 6016 x 4000 pixels and a sensor size of 23.2mm x 15.4mm.

 

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 Nikon D800, the Nikon D3200 has a linear pixel density that is about 26.5% greater than that of the Nikon D800. The approximate “area” relationships for image size, pixel density, and pixel size, are also presented below.

 

Note: If the D800 had the same pixel density as the D3200, it would have approximately 58 megapixels. In addition, if the D3200 had the same pixel density as the D800, it would have about 15 megapixels.

 

 

Relevant  Specifications

 

D3200: Image dimensions: 6016 pixels x 4000 pixels; sensor size: 23.2mm x 15.4mm

 

D800:   Image dimensions: 7360 pixels x 4912 pixels; sensor size: 35.9mm x 24.0mm

 

 

Crop  Factor

 

Approximately 1.547x  (35.9mm / 23.2mm)

 

 

 

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

 

D3200   =    2593   (6016 / 2.32)

D800     =    2050   (7360 / 3.59)

 

Pixel Density Advantage:  D3200  is approximately 26.5% greater than D800

 

 

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

 

D3200   =   3.856    (23.2 / 6016  x 1000)

D800     =   4.878    (35.9 / 7360 x 1000)

 

Relationship: D800 is approximately 26.5% greater than D3200

 

 

Crop an image from D800 to the same  field of view  as an image from D3200

Gain in image width (in pixels) as a result of the above 25.5% pixel density advantage

 

Uncropped image width of D3200 = 6016 pixels

 

Cropped image width of D800

to same field of view as D3200      = 4756 pixels  (7360 x 23.2 / 35.9)

 

Relationship: D3200 is approximately 26.5% greater than D800.

 

 

Crop an image from D800 to the same  field of view  as an image from D3200

Gain in comparable widths of  print sizes  as a result of the above 25.5% pixel density advantage

 

If the uncropped image of D3200 (of 6016 pixels width) is printed at 200 pixels per inch (ppi), the width of the print is about  30.1 inches (6016 / 200).

 

If the cropped image of D800 (of 4756 pixels width) is printed at 200 ppi, the width of the print is 23.8 inches (4756 / 200).

 

Relationship: The net effect of the 26.5% “pixel density advantage” of D3200, is to produce a print at 200 ppi, that is about 6.3 inches wider (or about 26.5% wider) than that produced with the same  field of view  from the cropped image of D800.

 

 

Crop an image from D800 to the same   field of view  as an image from D3200, and compare the changed field of view of D800 with that of D3200: Assume that a 300mm lens is on both cameras and that the field of view of an uncropped D800 image is 300mm

 

Field of view of D3200 = focal length of lens  x  crop factor of D3200 = approx. 464mm  (300mm x 35.9mm / 23.2mm)

 

Changed field of view of a D800 image when it is cropped to the same field of view as a D3200 image

= uncropped image width of D800  /  cropped image width of D800  x  focal length of lens  =  approx. 464mm  (7360 / 4756  x  300mm)

 

Relationship: The fields of view of D3200 and D800 are the same, that is, approx. 464mm.

 

Note: The image width of a D800 image, when it is cropped to the same field of view as a D3200 image, is approx. 4756 pixels (7360 x 23.2 / 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 D800 to the same  image width  as an image from D3200, and compare the changed field of view of D800 with that of D3200: Assume that a 300mm lens is on both cameras

 

Field of view of D3200 is 300mm x crop factor = approx. 464mm  (300mm x 35.9 / 23.2)

 

Changed field of view of a D800 image when it is cropped to the same image width as a D3200 image

= uncropped image width of D800  /  cropped image width of D800  x  focal length of lens  =  approx.  367mm  (7360 / 6016 x 300mm)

 

Relationship: D3200 is approximately 26.5% greater than D800.

 

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

 

D3200   =   6.7734   (24.2 / 3.5728)             

D800     =   4.2131   (36.3 / 8.616) 

 

Relationship: D3200 is approximately 61% greater than D800

 

 

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

 

D3200   =   14.7636    (357,280,000 / 24,200,000) 

D800     =   23.7355    (861,600,000 / 36,300,000) 

 

Relationship: D800 is approximately 61% greater than D3200

 

 

Crop an image from D800 to the same field of view as an image from D3200

Gain in image area  (in megapixels)

 

Uncropped image area of D3200 = 24.20 megapixels  (6016 pixels x 4000 pixels)

 

Cropped image area of D800

to same field of view as D3200   = approx. 15.08 megapixels  (4756 pixels x 3171 pixels)

 

Relationship: D3200 is approximately 61% greater than D800

 

 

 

Click  here  to see 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 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.

 

Note that Appendix 2 of the above article includes the following sections:

 

Calculation of pixel pitch

 

Calculation of the area of one pixel

 

Why is pixel size important - increasing pixel count increases noise?  (Click  here  to read the full article)

 

Pixel level vs image level in digital photography (also refers to the new  Studio Test Scene  published by Digital Photography Review)

 

Case study: High ISO low light images of the Sony A77 compared with those of the Sony A55

 

Downscaling and upscaling images for comparative purposes  (can apples be compared with oranges?)

 

Index of practical examples of the application of the "pixel density advantage" template

 

The following supplementary notes are designed to give you further information about how to compare the cameras listed in the above index:

 

Relationships between crop factor, field of view, photographic reach, image size, pixel density, and pixel size

 

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.

 

Click  here  to see examples of the outstanding resolution of the full frame Sony A900

 

Click  here  to go to the home page of Rob’s Photography New Zealand.

 

 

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