Lens mount developed by Nikon, typical used for line scan cameras

# Archives

# F-Number

= F-Stop = Aperture Value

# F-Stop

# F-Theta

F-Theta lenses are a class of Fisheye lenses

**Non distortion 180° F-Theta lenses**have an image circle or mm

Therefor a f=3.17mm F-Theata lens with an image diameter for 180° of 4.15mm has a distortion of (4.15/4.3)-1 = 0.965-1 = -3.5%

maintains angular distances

weak | medium | strong | max |
---|---|---|---|

115 | 159 | 217 | 360 and more |

# far point

Most distant point on the optical axis with an image of “acceptable sharpness”

Where CoC is the Circle of Confusion (the largest accepted Airy-disk) in **Millimeter**.

Alternatively, we can express the FarPoint using the magnification M :

**greyscale**Sensor mit 2.2 pixel pitch, we can use the pixel diagonal as CoC for crisp images, say

A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focused to an object distance of 100mm then has a far point of

und einen Nahpunkt von

and thus

**greyscale**Sony Sensor with 3.45 pixel pitch, we can choose as CoC the diagonal of the pixel for crisp images, say

A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focussed to 100mm then results in

mm

und einen Nahpunkt von

thus we get

**color**sensor instead we can use for crisp images. For the two sensors above we then get:

**same**DOF !!!

see also https://www.optowiki.info/blog/can-i-increase-the-dof-by-changing-the-focal-length/

The DOF is then, thus focussing to the hyperfocal distance results in the largest possible DOF.

# Fermat’s Principle

If light travels from one point to another, it takes paths of a length that in first approximation is equal to the length of optical paths length closely adjascent to the actual path.

The actual path taken has either a maximum or a minimum OPL compared to adjascent optical paths or is equal to the OPL of adjascent paths.

# Field of View

(usually horizontal) extend of an object that’s visible on a sensor.

Sometimes the HFOV (horizontal field of view), sometimes the VFOV (Vertical Field of View) and sometimes the DFOV (Diagonal Field of View) matters. It’s of utmost importance to state clearly which matters.

# first order optics

is the study of perfect optical systems.

Any imperfections and aberrations, also wavelengths, diffraction, interference etc. are ignored.

Parts of first order optics are Gaussian optics ( = paraxial optics).

Results of this analysis are image location and magnification.

Compare third order optics

# Fisheye Types

Various types of fisheye lenses are available.

Here a short overview:

Type | gnomonic | stereographic | F-Theta | equal area | orthographic |
---|---|---|---|---|---|

lens class | wide angle | Fisheye | Fisheye | Fisheye | Fisheye |

mapping function | |||||

normalized mapping function | |||||

meridional scaling | |||||

sagittal scaling | |||||

effective scaling | |||||

N from | 2 | 1 | 0 | -1 | |

Balance Deform. vs. Scaling | 0 | -2 | 2 | ||

Curvature | 0 | -1 | |||

Deformation | |||||

maintains | - | angles | angular distances | areas | planar illuminance |

AOV | <180° | <360° | >= 360° | 360° | 180° |

54° | 94° | 115° | 94° | 66° | |

75° | 131° | 159° | 131° | 90° | |

102° | 180° | 217° | 180° | 120° |

Source of the various angles and formulae: wikipedia

Here the angle is measured in Radians !

**
**

**equal area**lenses are also called “

**equisolid angle”**or

**“flächentreu”**

**F-Theta**lenses are also called “

**equidistant**“, “

**linear scaled**“, “

**äquidistant**” or “

**angular**”

**sterographic**lenses are also called “

**conform**“or “

**winkeltreu**”

**orthographic**lenses are also called”

**hemispherical**“or “

**orthographisch**“

For details see:

equal area

F-Theta

gnomonic

orthographic

stereographic

# focal length

The focal length is the distance from the Image side principal plane to the image of objects at infinity.

For single lenses in air that is equal to the distance from the first focal point to the first principal point.

(in each case measured from the left to the right)

Note that this is a positive value for converging lenses and a negative value for the divergent lenses.

The larger the focal length, the smaller the aperture angle of the lens and the smaller the object section that is displayed full-frame on the sensor.

The lens captures less of the object. Extremea are telephoto lenses and finally telescopes.

The smaller the focal length, the larger the aperture angle of the lens and the larger the object section which is displayed full-frame on the sensor.

The lens captures more of the object. Extreme forms are fisheye lenses.

Lenses are typically listed, sorted by focal length. As an approximation, lenses with larger focal length see a smaller portion of the object (in more detail).

There are exceptions! (See: pseudo-knowledge: viewing angle and focal length are equivalent)

However, Viewing angles change with the working distance! Also, a Pinhole lens model is assumed. Thus for wide angles a too small focal length is returned .. (as all focal length calculators on the internet do 😉 )

For the next calculator it is **very important** to correct the distortions before doing the calculation: