surfaces (in mid air) of constant OPL (optical path length)

In a perfect optical system or a first order optical system all wavefronts are either planar or spherical.

Wavefronts stay after reflection perpendicular to the propagation direction of the light.

number of wavelengths per cm

[table caption=”sample wavenumbers” width=”300″ colwidth=”100|100|100″ colalign=”left|left|left”]

wavenumber (cm^-1),wavelength (um),frequency (THz)

22727,0.440,682

18181,0.550,545

15152,0.660,455

11765,850,353

10000,1,300

1000,10,30

[/table]

Entocentric lens with a focal length smaller than the sensor diagonal, eg an f = 6mm lens on a 1/2″ sensor (the sensor size has 8mm).

When we use the word “wide angle lens”, it must be clear what sensor is used.

The same lens can, depending on the sensor, be wide-angle, telephoto lens and normal lens.

A

lens of f = 8mm on a 1/3 “sensor (6mm diagonal) a slight telephoto

lens.

On a 1/2 “Sensor (8mm diagonal) it is a

normal lens and on a 2/3” sensor (with 11mm diagonal) a wide-angle

lens.

see discussion under normal lens

Distance between mechanical front of lens and object.

When you insert distance rings between camera and

lens you might have noticed that the image gets darker and the

field of view gets smaller.

As the

lens was not changed, the

F-number of the

lens still must be the same. The darker image and the reduced

field of view are described by the working

F-number, also called effective

F-number.

The F-number is only defined for objects at infinite distance.

The sensor has according the definition of the focal length exactly the distance “focal loength” from the principal plane when the lens is focussed to infinity.

When an object comes closer, it’s image moves in the same direction. It moves further away from the principal plane.

To keep the object focussed, the distance of lens and sensor must be increased. This is equivalent with adding distance rings reagrding the infinity position of the lens. As result the images gets darker the field of view gets smaller , the therefore the magnification changes.

It holds:

where

working F-number or effective F-number.

image side numerical apertur,

the magnification for this focus distance and

is the pupil magnification.

Especially:

For an objective used for a 1:1 mapping holds:

The effective F-number can also be described by the height “delta” of the inserted distance rings:

because

and

From (1) we get

with this we get from (2) :

From this we can derive a third way to calculate the working F# :

From above we learnt

With the length of the needed distance rings delta

we get

or shorter

q.e.d.

see also:

F-Number

Pupil magnification

Numerical Aperture