Sensitivity of telecentric assembly to tilt

(Copyright  Christian Viladrich)

Telecentricity in the image space (Edmund Optics schematic):

Definition: A system is telecentric in the image space if all the chief rays are parallel to the optical axis in image space (i.e. after the last lens).
The chief rays are oblique rays passing through the center of the aperture stop. Chief rays can also be understood as the axis of symetry of the light bundle falling onto the focal plane.

Use: Telecentric systems are used in narrow band observation (Ha) in order to achieve a constant CWL (Center Wave Length) and FWHM over the field of view (no sweet spot effect).

Note: defocus in the image plane does not change image height or magnification, which means image-space telecentric system has changeless magnification. In other words, the magnification factor does not change with the back focus.

Telecentric system for solar observation:

A typical telecentric design for solar observation consists in a divergent group (B) followed by a convergent group (C).

The focus of the divergent group (B) is placed at the focus of the main objective (O), so that the light beam between O and B is collimated .

The distance between B and C is set to that the chief rays (= axis of symetry of the light cones) are parallel to the telescope optical axis between (C) and the focal plane.

The magnification factor M of the telecentric system  is equal to fc/ fb 

Because the angle of the chief rays is constant over the the surface of the filter (i.e. the chief rays are normal to the filter), there is no change in CWL of FWHM over the field of view (i.e. no sweet spot).

Focuser "droop" case: What happens when the telecentric system is tilted ?

Suppose the telecentric assembly and the etalon are aligned along the same optical axis, but with a tilt i relative to the telescope optical axis.

In the following OSLO simulation (Newton 300 mm f/5.5 with 5x telecentric)  the telecentric system is tilted by 2° relative to the telescope optical axis (solid line pink color).
Light comes from the left side.

The chief rays angle is no more normal to the etalon, but tilted by an angle on the order of  i / M. This angle is relatively constant over the field covered by the camera.

Here are the results of the simulations of two configuration using ray-tracing software.

The tilt of the chief ray results in a blueshift of the CWL and a broadening of the FWHM of the etalon which can be calculated with the formulae given on this paget :

Noteworthy, in both simulation the degradation of image quality due to the telecentric tilt is very limited.

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