Image Display

This is related to an upcoming blog post. I wanted to make a single technical statement that I "knew" was true but didn't have the proof. Here is the proof which I think turned out to be an interesting exercise in itself. Let me apologize now for the formatting of the tables. I have tried to format them, but blogger decides that it wants to trash them.

The question is something along the lines of "How much of my image is displayed on X" where X is a monitor or physical print. Let us also introduce the variable Y, different camera models.

Why this situation is the least bit interesting is that one measure of a camera is how many mega-pixels it has. That isn't what one really cares about anyway you slices it. Quality of the image is mostly subjective, granted dynamic range can be measured to some extent. What one wants to do at the end of the day is display the beautiful image that you took somehow. This is measured in area (length x width) with some number of dots per inch (DPI) on a print or some resoultion on a monitor. The numbers on your camera are not directly related to the numbers on the print. Very quickly a modern camera sensor will have some pixel height and width as will a monitor. A print will have a height and width measure in inches and DPI. A very simple way to compare the two is to look at the number of total pixels each contains. This may be a problem in some cases where one dimension of the image is larger then the corresponding dimension on the print. This case is left as an exercise to the reader. To find the total number of pixels of the camera sensor or monitor simply multiply the resolution out (height x width). For the print one does the same thing but needs to multiply the both the height and he width by the dpi (typically 300 but also possible 200). That is length x dpi x width x dpi. This gives the physical print a large scaling factor, which shortly we will see is important.

First let us look at a couple of camera sensors.

Camera px px Total Pixels
------------ ----- ------ -----------------------
Nikon D70 3008 2000 6016000 (6MP)
Nikon D80 3872 2592 10036224 (10MP)
Nikon D90 4288 2848 12212224 (12.2MP)
Nikon S550 3648 2736 9980928 (9.98MP)

I own a D70 and S550. It just so happens that the S550 sensor produces just about the same number of pixels as the D80, not making any statements about image quality. We will take the D70, D90 and S550 as test cases as they offer different numbers of total pixels.

Let us first look at how many pixels can be displayed on a monitor. I have one that is 1900x1200. Something that always happens is that you can't display the full resolution because the image has too many pixels and the monitor doesn't have enough. Photoshop often reports that it is only able to display 33% or 25% of the total image. In this data I will use the percentage of display as it is close to the real answer, still makes the point and camera independent.

Height Width Total Pixels
------ ------ -----------
1900 1200 2280000 (2.3MP)
33% 752400 (0.75MP)
25% 570000 (0.57MP)

That total number of pixels sure does shrink fast! What does that mean in terms of how much of the image can be displayed at any given time on a monitor? Below we take the three above discussed resolutions and the previous mentioned cameras and show what % of the total number of pixels can be displayed.

Resolution %of D70 % of S550 % of D90
------------ --------- --------- --------
1900 37.89 22.84 18.67
33% 12.50 7.53 6.16
25% 9.47 5.71 4.67

In the realistic cases only a very small part of the image can be displayed, typically between 5-10%. This doesn't give a one a very good idea of what is happening with the details of the image. If we look at what happens when we print the images we might find a solution.

Height (in) Width (in) pixels @ 300 dpi
4 6 2160000 (2.1MP)
8 10 7200000 (7.2MP)
16 20 28800000 (28.8MP)

These images get big very quickly. How does the print size relate to how much of the image can be fit on it?

Height (in) Width (in) %of D70 % of S550 % of D90
4 6 35.90 21.64 17.69
8 10 119.68 72.13 58.96
16 20 478.72 288.55 235.83

The 4x6 can fit about 36% of the D70 image on it, which is very close to what the monitor can do in the unrealistic situation where we assume that all of the pixels can be used. What this shows us is that even a lowly 4x6 print can display 3-4x more information then can a monitor. There is interest in the print size range between the 8x10 and 16x20 print if you have a D90 and want to print entire images. Not presented here, but an entire D90 image fits very nicely on a 16x20" print at 200dpi.

Printing technology has come a long ways. It has a very good dynamic range and from this analysis we can see has great density of information.

Nothing new here, but as it is very cheap to change the image on a monitor it makes for a good way to scan through images to find which to print. For detail work it is less expensive to change the size of your print then to change the number of pixels your monitor can display. In the next part of this series I will take a look at the cost trade off of proofs and full prints.

In a related note, all of those years writing physics lab reports, posters and papers helped in writing this greatly. The major limiting factor was how fast I could type.