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)
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.
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
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.
working F-number or effective F-number.
image side numerical apertur,
the magnification for this focus distance and
is the pupil magnification.
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:
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