optimal f# with diffraction

Wed can now make an estimate of the optimal f# to use in order to have the minimum blur between our near/far limits.

The optimal f# will be reached when the focus blur wil be equal to the diffraction blur at these limits.

We can model the diffraction blur with the formula: c* n,

we will note:

• c a constant = 0.0147mm (corresponding to the middle of the visible spectrum (~550 nm)
• a the aperture
• n the numerical aperture
• L the height of the image sensor
• r the ratio, of the image that we want in acceptable focus.

So at the limits of the area we want to optimise

$\Large \frac{a}{h} \times r \times L = c \times n$

with a = f/n this means:

$\Large \frac{f}{nh} \times r \times L = c \times n$

$\Large n = \sqrt{\frac{L}{c} \frac{rf}{h}}$

$\Large \frac{L}{c}$ is a constant. We can take c = 0.0147mm (corresponding to the middle of the visible spectrum (~550 nm), L=24mm (in landscape mode)

This gives: $\Large n = 134 \sqrt{\frac{rf}{h}}$

In case h = 1600 we have this simple equation: $\Large n = 3.35 \sqrt{rf}$

Comparison with the usual method