## jueves, 28 de agosto de 2014

### Testing camera lens. Where is infinity?

Abstract
The best way for Testing cameras focused at infinite requires complex instrumentation for simulating "the infinite" by means of an optical collimator. If we have enough space, the cheaper and cost effective way for simulating the "infinite" is to place a target far away from the camera but... where we can considerer is "infinite"?

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According to MIL-STD-150A paragraph 5.1.1.3, when testing a lens at "infinite" focus by means of a target at infinite distance, the distance shall be considered approximately infinite when it is greater than D measured in feet.

$$D[ft]\geq 400\cdot EFL_{i}\cdot ED_{i}\ \ (1)$$
Where
$$D[ft]: Minimum\ \ distance\ \ in\ \ feets\\ EFL_{i}[inch]: Lens\ \ Effective\ \ Focal\ \ Length\\ ED_{i}[inch]: Lens\ \ Effective\ \ aperture$$

The f-number f# is given by the following dimensionless equation:
$$f\#=\frac{EFL_{i}}{ED_{i}}\ \ (2)$$
Putting the equation (1) in an user-friendly format, we will substitute the equation (2) into the equation (1) and converting to the SI, we can write the minimum distance "D" to considerer infinite as:

$$D[m]\geq 0.216\frac{EFL^{2}}{f\#}\ \ (3)$$
Where
$$EFL[mm]:Lens\ \ Effective\ \ Focal\ \ Length\ \ in\ \ mm$$

EXAMPLE

Problem: We have a lens NIKON 16-85mm working at 50 mm and f#5.6. Calculate the minimum distance to place one target for considering it focused at infinite.

Solution:
Applying the equation (3)
$$D[m]\geq 0.216\frac{50^{2}}{5.6}\simeq 96\ \ m$$

REFERENCES
[1] - Military Standard Photographic Lenses MIL-STD-150A