Introduction to classical Cassegrain telescopes

Coma is the main aberration of the classical Cassegrain telescope.

The flat diffraction limited field is smaller than the Newtonian having the same resulting F/D ratio (a F4-F15 Cassegrain is equivalent to a F/8 Newtonian), but is still larger than the Newtonian having the same F/D ratio as the Cassegrain primary miroir.

The field curvature (given by 1/R = 2/ r1 - 2/r2) is stronger than the one of a Newtonian. It increases with the secondary magnification and is concave to the sky. Higher focal ratio on primary miroir decreases field curvature.

The main advantages of the classical Cassegrain in HR imaging are :

- a relatively large diffraction limited flat field,

- the possibility to reach a high F/D ratio in a short optical tube,

- no additional refractive element in the optical path (if long native F/D ratio), which means top resolution from UV to IR.

The main draw-backs are :

- the difficulty to make such a small diameter hyperbolic secondary with the required accurary,

- the required level of accuracy for centering and aligning the secondary mirror, which asks for an excellent mechanical design,

- hardly none are manufactured ...

Some lessons learned from the simulations :

- Attention should be given to keep close to the nominal back focus. A +/-80 mm tolerance is allowed for the Cassegrain 200 mm F/4 F/15 (Strehl > 0.95)

- Even is the radial centering of the hyperbolic secondary miroir can be tricky, a 1 mm radial offset can be easily corrected by a tilt of the secondary miroir without too much loss in the radius of diffraction limited flat field.

Cassegrain 200 mm F/4-F/15

Cassegrain 350 F4.9-F29.2

Cassegrain 200 mm F/4-F15 :

OSLO model :

From [1]

Diffraction limited flat field (550 nm) :

About +- 0.2° (according to [1]), ie. four times the diffraction limited flat field of the DK 200 mm F4-F15, and equivalent to the diffraction limited field of a Newton F/8.

NB : very often, it is said that the diffraction limited field of a Cassegrain is the same as a Newtonian of equivalent focal ratio. This is true only when a curved field is accepted. However, a Cassegrain telescope has a significant smaller flat field that a Newtonian of same F/D because of the increase field curvature.

Field curvature :

- 413 mm (theoritical), same as the DK 200 F4-15 by construction.

Sensitivity to backfocus :

The Cassegrain is clearly more sensitive to the backfocus than the equivalent DK. However, a +/- 80 mm is hardly detremental to optical performance (Strehl > 0.95)

Sensitivity to radial off-centering of the secondary mirror (550 nm):

An off-centering of the secondary miroir can be pretty well corrected by correction with a tilt of the secondary miroir. Once corrected by the secondary mirror tilt, a Cassegrain has a much larger flat field than the equivalent DK affected by the same secondary miroir off-centering. This is what is shown in these 3 successive figures.

 

(a) Centered optics and nominal back-focus : note the inward (to the sky) curvature of field visible at 0.2° angle from axis (limit of the diffraction limited flat field).

 

(b) With a 1 mm radial decentering of the secondary mirror (and refocussed on axis) :

 

(c) - With a 1 mm radial decentering of the secondary mirror, secondary mirror tilted by -0.27° to maximise Strelh on axis (and refocussed on axis) :

The radius of the diffraction limited field is now about 0.18°, still much larger that a DK with the same 1 mm radial shift of the secondary corrected by a tilted secondary mirror.

 

 

Cassegrain 346 mm F/4.9-F29.45 :

OSLO model :

Diffraction limited flat field (550 nm) :

About +- 0.13°, equivalent to the diffraction limited field of a F/8.5 Newtonian .

Field curvature :

Inward curvature, R = -426 mm.

Sensitivity to radial off-centering of the secondary mirror (550 nm):

(a) Centered optics and nominal back-focus : note the inward (to the sky) curvature of field visible at 0.13° angle from axis (limit of the diffraction limited flat field).

(b) With a 1 mm radial decentering of the secondary mirror (and refocussed on axis), the performances are still good on axis (Strelh = 0.88) and stay diffraction limited of over the 0.13° field (Optical Path Difference < 0.007 wave) on one side of the field, but is reduced de 0.075° on the other side of the field :

(c) With a 1 mm radial decentering of the secondary mirror and a 0.2° tilt of the secondary (and refocussed on axis), the performances come back close to the original ones. The focus plane is now slightly tilted. Still, the radius of the diffraction flat limited field is 0.12° on both side of the field ::

One side of the field	Other size of the field

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