Aperture Area Calculator

Formula

The formula to calculate the aperture area (A) is:

$A = \pi \left(\frac{D}{2}\right)^2 = \pi \left(\frac{n}{2f}\right)^2$

Where:

$D$ is the aperture diameter (mm)
$n$ is the focal length (mm)
$f$ is the f-number
$A$ is the aperture area (mm²)

Definitions

Aperture Area: The surface area of an opening that allows light to pass through. It directly affects the amount of light entering a system, influencing the performance and quality of the image or measurement.

Example

Let's say the aperture diameter (D) is 50 mm, the focal length (n) is 100 mm, and the f-number (f) is 2. Using the formula:

$A = \pi \left(\frac{50}{2}\right)^2 = \pi \left(\frac{100}{2 \times 2}\right)^2$

We get:

$A = \pi \times 625 = 1963.50 \, \text{mm}^2$

So, the aperture area is approximately 1963.50 mm².

Extended information about "Aperture-Area-Calculator"

Calculating the Numerical Aperture

Definition: The numerical aperture (NA) of a lens or optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

Formula: $\text{NA} = n \sin(\theta)$

$\text{NA}$ : Numerical aperture
$n$ : Refractive index of the medium
$\theta$ : Half-angle of the maximum cone of light that can enter or exit the lens

Example: $\text{NA} = 1.5 \sin(30^\circ)$

Calculating Aperture of a Lens

Definition: The aperture of a lens is the opening through which light enters the camera.

Formula: $A = \frac{f}{N}$

$A$ : Aperture diameter
$f$ : Focal length of the lens
$N$ : F-number (f-stop) of the lens

Example: $A = \frac{50}{2.8}$

Measurement of Numerical Aperture

Definition: Numerical aperture is measured to determine the light-gathering ability of an optical system.

Formula: $\text{NA} = n \sin(\theta)$

$\text{NA}$ : Numerical aperture
$n$ : Refractive index of the medium
$\theta$ : Half-angle of the maximum cone of light that can enter or exit the lens

Example: $\text{NA} = 1.33 \sin(45^\circ)$