## Effective F-Number and relative Signal amplitude

### Effecive F-Number

For small magnifications β< 0.1 when calculating signal amplitude or the limit of lens resolution caused by diffraction, the F-number K (=focal length/aperture diameter) is replaced by an effective F-number K’(=image distance/aperture diameter).

With a nominal F-number K and small magnification β the effective F-number K’ is calculated from

### Example

Nominal F-number K = 4

Magnification β = 1

Effective F-number K ’ = 2 · K = 8

### Relative signal amplitude

F-number K | Relative signal amplitude R |
---|---|

1.4 | 1 |

2 | 0.5 |

2.8 | 0.25 |

4 | 0.125 |

5.6 | 0.06 |

8 | 0.016 |

### Imaging Parameters

Schematic depiction of the imaging system and definition of variables used.

f = Lens focal length (mm)

S = Sensor length (mm)

L = Length of Region of Interest (ROI) of object (mm)

a = Object range (mm)

a’ = Image distance: Distance from sensor to HH’ (mm)

β = Magnification

w = Field angle

OO’ = Distance from sensor to measured zone (mm)

s’A = Flange focal length (mm)

∆s’ = Lens extension (mm)

LT = Tube length

A = Working distance (mm)

HH’ = Principal point distance (mm) (can lengthen or shorten OO’)

s’K = Camera flange length consisting of focus adapter series FA22 and extension rings series ZR (mm)

LO = Lens length (mm)