2 A B C D E F G H I K L M N O P R S T U V W
Ra Re


for a circle of radius r is ‘1 rad’ the angle corresponding to length r on the circle,

1\,\mathrm{rad} = \frac {360^\circ} {2 pi} = \frac {180^\circ} {\pi} \approx 57{,}29577951^\circ

accordingly :
1\,\mathrm{mrad} = \frac {1 rad} {1000} :

1\,\mathrm{mrad} = \frac {360^\circ} {2000 \pi} = \frac {180^\circ} {1000 \pi} \approx 0{,}05729577951^\circ


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Rayleigh Criterion

The diameter of the smallest disk that a lens can produce as image of a point size object is called Airy-disk

According to the so called “Rayleigh Criterion” holds:

The smallest possible Airy-Disk that a (diffraction limited) lens can generate is

D = 2 * 1.22 * Wavelength * F\#

The best possible resolution on image side (at 20% contrast) is the radius of this smallest possible Airy-Disk

R = 1.22 * Wavelength * F\#

When you double the F#, you lose factor 2 of resolution in each x and y direction.
If the lens supported 5 Megapixel before, then it supports only 1.3 Megapixel after
When you double the wavelength (for example 850nm IR instead of 420nm blue), you lose factor 2 of resolution in each x and y direction. If the lens supported 5 Megapixel before, then it supports only 1.3 Megapixel after

See F-number


A normal lens has pincushion distortion or barrel distortion which can be corrected to give a perfect perspective projection, like the image of a pin-hole camera.
This process is called “rectification” and is often applied for stitchich images, for example, in panoramic photography.
The resulting images has no distortion.

refractive index

refractive index = \frac{speed\ of\ light\ in\ vacuum}{speed\ of\ light\ in\ the\ current\ medium\ (eg.\ glass)} =: \frac{c}{v}

With c = 2.99792458 \cdot 10^8  \frac{m}{s} , roughly 300000km per second

In other media than vacuum the light is slower. Therefore, the smallest refraction index is 1.
The speed of light in the medium is v = \frac{c}{v}.
Therefore the speed of light in a medium is factor “refractive Index” slower than the speed of light c in vacuum.
Glass slows down light of different wavelengths (“colors”) by different factors.
Results are different refractive indices, “depending on the color (wavelength) of light .”
The higher the refraction index, the stronger the change of direction at the boundary between different media
As media have different refraction index for blue, green red light, red/green/blue light takes a different path through a lens!
Medium typical refractive index
Vacuum 1
Air 1.000293
Helium 1.000036
Hydrogen 1.000132
Carbon dioxide 1.00045
Water at 20 °C 1.333
Ethanol at 20 °C 1.36
Olive oil at 20 °C 1.47
Ice 1.31
PMMA (= acrylic = plexiglas) 1.49
Window glass 1.52
Polycarbonate (Lexan™) 1.58
Flint glass (typical) 1.62
Sapphire 1.77
Cubic zirconia 2.15
Diamond 2.42
Moissanite 2.65
After a reflection light propagates from right to left, and it’s velocity can be regarded as negative. Using velocity instead of speed in the above equation, the index of refraction can also be regarded as negative.