Calculation of length measurement error for tilted objects

With the use of the telecentric lenses some unexpected measurement errors may occur. In principal different working distances between components and the camera cause no length measurement errors (within the telecentric range of the lens). But tilting the object can lead to changes in measured values.
When inspecting high or flat parts the length measurement error is calculated in different ways:

Calculating the visible pseudo length of high objects

Visible length L _new = L - L* (1-cos α) + H * sin α

Hinweis: Even when using the drop-down lists own values can be entered. Please use the first entry "user def."!

Object tilt/ rotation in degrees:	User def. (deg) 0 deg. 0.1 deg. 0.25 deg. 0.5 deg. 1 deg. 2 deg. 3 deg. 4 deg. 5 deg. 10 deg. 15 deg. 20 deg. 25 deg. 30 deg. 35 deg. 40 deg. 45 deg.
Real object length in mm:
Object heigth in mm:
Calculated visible "length":
Length deviation:

Calculating the visible pseudo length of flat objects

Visible length L _new = L - L*(1-cos α)

Note: Even when using the drop-down lists own values can be entered. Please use the first entry "user def."!

Object tilt/ rotation in degrees:	User def. (deg.) 0 deg. 0.1 deg. 0.25 deg. 0.5 deg. 1 deg. 2 deg. 3 deg. 4 deg. 5 deg. 10 deg. 15 deg. 20 deg. 25 deg. 30 deg. 35 deg. 40 deg. 45 deg.
Real object length in mm:
Calculated visible "length":
Length deviation: