# Which lens parameters determines it's format?

I'm working with a megapixel sensor with a 1/2" format. I would like to know which parameters have to be taken into account in order to design a lens that can be fit with 1/2" format.

The light source wavelenght is 850 nm produced by high power leds. The working distance is about 15 meters.

Thanks,

Raphael

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When a lens designer is asked to make a lens for a specific sensor size, there are a couple of important factors that come in to play. The most obvious of course, is that the image must fill the sensor. This can be verified by a simple equation which calculates the height of an optical ray as it strikes the image plane:

$$h=f \tan{\theta}$$

where $f$ is the effective focal length of the lens, and $\theta$ is the field of view. It is important to note that the sensor may be 1/2", so you might expect that the maximum ray height above the optical axis would be 1/4", but because the array is usually not circular, the corner of the array will have a height above the optical axis of more the 1/4". For a square array it would be $\frac{\sqrt{2}}{4}$ inches.

Of course, the focal length and field of view are themselves important lens parameters, so appropriate choices must be made for those values. IF the requirements of the lens being designed specify a particular sensor size and field of view though, this equation exactly selects the focal length.

In a case like yours, where the object distance is known and fixed, designers also often talk about the "Reduction Ratio" or magnification of the lens, which is the ratio of the size of the image of an object, to the size of the object itself. If you were trying to have your object fill the image plane, this would set your reduction ratio. The reduction ratio is not independent of the equation I stated above, it is just another way to express a design specification for a given field of view at a given object distance. It is obviously undefined for a lens which images objects at infinity, such as a telescope.

This is a pretty good picture of how first order lens parameters are chosen to give you a specific image size, but in designing a good lens, there is a lot more to consider. Most of the work in lens design happens after these first order parameters are chosen. Then the designer must make countless choices in order to produce a lens which has good optical performance over the full field of view. This is a process that takes a number of graduate level courses and years of experience to master, and is in some ways still as much an art as a science.

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Colin K, Thanks a lot for the answer. The image is more "clear" right now. –  Raphael Mar 31 '11 at 15:18
Good answer - one detail: Sensor sizes are confusing, the quoted value doesn't relate directly to the physical size (for historical reasons), a 1/2" sensor is 6.4x4.8mm with a diagonal of 8mm –  Martin Beckett Mar 31 '11 at 15:19