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Resolution and Total Dot Count      Back to Notes on Photography
by Makoto Honda                September 12, 2005

General

The resolution is a measure of detail. The higher the resolution, the more detail you can see. The resolution is defined by the number of lines you can distinguish in a given unit length (one millimeter, in metric). Each line is actually a line pair, to be precise, consisting of a black line followed by a white line of the same thickness. The resolution is thus expressed in terms of line pairs per millimeter, or lp/mm for short. For example, the resolution of 100 lp/mm means you can resolve 100 line pairs (black & white) in the space of 1 mm. This is equivalent of 200 dots/mm, since each line, black or white, must be represented by one dot

Once the resolution is known, you can multiply it by the width of the area in question to get the number of dots along the width. Do the same for the height to get the number of dots along the height. (Do not forget the multiplication factor of 2 to convert "line pairs" to "dots".) Then, multiply height-wise and width-wise dot counts to get the total number of dots in the area. This total dot count is really an ultimate measure of how sharp the picture can be. (We are only talking about resolution here, not other factors affecting picture quality, such as contrast, various aberrations, and so on.)

So, if we want to compare two cameras, say, an 8 mega pixel point-and-shoot and a 6 mega pixel digital SLR camera, what we have to do is to get the resolution of the captured image (system resolution based on lens and sensor resolution) and compute the total dot count from it.   

1.  Resolution - expressed in lp/mm (line pairs per millimeter)
2.  Area Size - expressed in width and height in mm
3.  
Dots (height & width) - dot counts along the height and width of the area
4. 
Total Dot Count (area) - height dots times width dots

This same relation holds for lens, film, digital camera (sensor) and scanner (sensor). This is how you convert the resolution to the corresponding total number of dots for a given area size. You can calculate backwards to obtain the resolution if the total dot count is known. (For instance, many digital cameras are advertised using their sensor pixel count. This is the total dot count based on their digital sensor resolution and its sensor size. See below.)

For the camera lens, if you know the aerial resolution of the lens, you can apply this relationship to obtain the total number of dots in the image formed by the lens. (The resolution of the lens is dependent on the aperture used, subject to the diffraction-bound theoretical maximum.) Note that this is not the dot counts you get on the film, though. How much you can capture on the film depends on how good the film is. You must first get the system resolution of lens and film, and then use that resolution to obtain the total dot count. For instance, Fujichrome Velvia (color slide film) has the resolution of 80 lp/mm. Take a picture using the lens having 300 lp/mm resolution on this film. The system resolution becomes around 63 lp/mm. Given the 35mm film area size of 24 x 36mm, the total number of resolvable dots in the final image captured on the film is 63 x 2 x 24 (height) times 63 x 2 x 36 (width), or about 13.7 million dots.

For a digital camera, we go backwards. Using the mega-pixel count of the camera (that is the total dot count of this "digital" film), we get the height and width dots, and then the resolution. As an example, let us use Nikon D70s, the 6 MP digital SLR camera. The 6 mega pixels translate to 2000 x 3000 dots, height and width. The sensor area size is APS-C format, or 16 x 24mm. This gives 2000 dots / 16 mm  = 125 dots/mm, or 62.5 lp/mm resolution. Taking a picture using the 300 lp/mm resolution lens, the system resolution of the final image captured on the digital sensor becomes 52 lp/mm. Converting this back to the total dot count (using 16 x 24mm areas size) gives around 4.2 million dots. You may wonder how this could be. The camera has 6 million pixels (microscopic sensors) which correspond to 6 million dots. This is an undeniable fact. You could count 6 million pixels on your computer monitor if displayed on a one-to-one pixel level. What happened to the remaining 1.8 dots? A simple explanation here is that some pixels may not be distinguishable from their neighbors, i.e., two pixels may be used to express one resolvable dot.

One must understand the formula we used to calculate the system resolution is an approximation, yielding a statistical result (as opposed to deterministic numbers). In the above example, we get only 4.2 million dots in the final image, using a 6 million pixel camera, on average. It is easy to see you will never get more than 6 million dots under the sun, but could you get 6 million? Yes, but in a very specific situation. Suppose you have a resolution test chart comprising a black and white dot checker board, 2000 dots vertically and 3000 dots horizontally. If you fill your image with this test chart, with the camera's 6 million pixels aligned precisely with the test chart dots, you could achieve 6 million resolvable dots in your final digital image! If you are going to try this, good luck. All the system resolution equation is saying is that "on average" you get around 4.2 resolvable dots in the final image...

How about the film scanner? The same thing. The scanner resolution is often expressed in dpi, or dots per inch. Nikon Coolscan 5000 ED has 4000 dpi. This translates to 157 dots/mm, or around 79 lp/mm resolution. The scanner scans the image already captured on the film. So, we use the above example of 35mm Velvia film. The resolution of the final image was 63 lp/mm. The system resolution of the image captured on the scanner is thus calculated by using 79 lp/mm and 63 lp/mm, yielding around 35 lp/mm. Multiplying by the area size (24 x 36mm), we get the total dot count of 4.2 million resolvable dots .......
 

 

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