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

say

accordingly :

:

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

say

accordingly :

:

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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

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

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

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.

** **

In other media than vacuum the light is slower. Therefore, the smallest refraction index is 1.

Glass slows down light of different wavelengths (“colors”) by different factors.

Result is different refractive indices, “depending on the light color.”

Result is different refractive indices, “depending on the light color.”

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 | – |