Area measurements for "gain in image size" and pixel density
This appendix is part of this article about the “telephoto advantage” and "pixel density advantage" of an APS-C camera.
We have dealt with the “pixel density advantage” of APS in terms of the width of the full sized image of APS, compared with the width of the cropped image of FF. However, it is also possible to look at this advantage in terms of the percentage difference between the pixel count (expressed in megapixels) of the comparable images of APS and FF. Calculating megapixels, is just like calculating the area of a photograph. For example, a photograph that measures, say, 6 inches x 4 inches, has an area of 24 square inches.
Gain in image size based on the pixel counts of the images (expressed in megapixels)
The uncropped image of APS has 15.36 megapixels (4800 pixels x 3200 pixels). In contrast, the cropped image of FF has 10.67 megapixels (4000 pixels x 2667 pixels).
Therefore, the “total area” gain in image size of APS is 44%, because the pixel count of APS is 44% greater than the pixel count of the cropped image of FF (15.36 megapixels / 10.67 megapixels).
We shall now use the megapixels per square centimetre method to show that this 44% gain can be reconciled with the percentage difference between the pixel densities of APS and FF.
Megapixels per square centimetre method
Under the megapixels per square centimetre method, pixel density is calculated by dividing the number of megapixels on the sensor, by the sensor area in square centimetres. Therefore, in this example, the pixel density for APS is 4 (15.36 / 3.84), and for FF it is 2.778 (24 / 8.64). So, in this example, the pixel density of APS is 44% larger than that of FF (4 / 2.778).
This reconciles with the pixel count (expressed in megapixels) of the full sized image of APS, which is also 44% greater than the pixel count of the cropped image of FF (15.36 megapixels / 10.67 megapixels).
Note: The above arithmetical reconciliation works exactly, only when 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, must give exactly the same answer as the sensor width divided by the sensor height. In this example, exact reconciliations can be made because the above conditions have been met.
Appendix 2 of the above article provides calculations of the estimated width and area of one pixel, and shows the relationship of these calculations to image size and pixel density.
Appendix 3 provides a very valuable summary of the mathematical relationships between image size, pixel density, and pixel size. The information in Appendix 3 can be used as a template for calculating the pixel density and pixel size of any camera with a 3:2 aspect ratio.
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