A tilt-tuned etalon that is mounted before the objective theoretically should have better performance in terms of a sweet spot since the sweet spot is a function of incidence angle. With the etalon being the first optical element, and with the sun's distance, the incidence angle will likely be 0 degrees, +/- the tilt of the etalon itself.
The downside of the tilt-tuned etalon is that the sweet spot is a linear gradient across the image, aligned with the tilt axis of the etalon. A pressure-tuned etalon mounted before the objective would be superior in this regard, however most PT etalons are smaller than the objective and mounted somewhere behind the objective where angle of incidence becomes a function of focal ratio. The sweet-spot in this case is circular, and can be large enough to adequately cover the entire disc of the sun, making it a non-issue.
A bit of clarification. An talon is only exactly "on-band" when light rays pass through normal to the etalon plates. But the Sun - being an extended object 0.5 degree in diameter - can never have all its rays pass through an etalon normal to it. When centered on-axis, the central ray will, but the rays from the edge will subtend a 0.25 degree angle, and an etalon placed before the objective will have zero instrument angles and no increase of the field angles. Unfortunately there is no optical system that can change this.
Every etalon has an "acceptance angle" which is by definition one-half the diameter of the "sweet spot," more technically referred to as the "Jacquinot spot." The Jacquinot spot is defined as the field in which essentially monochromatic viewing/imaging occurs, and outside of which the image begins to shift "off band." For an air-spaced etalon of about 0.7 FWHM, the Jacquinot spot is about 1 degree in diameter. Since the limb of the Sun subtends 0.25 degrees off-axis, its "field angle" is 0.25 degrees compared to the center of the on-axis center of the Sun. When such an etalon is placed ahead of the objective, there are no instrument angles or field angle magnification, and the entire disc of the Sun fits well within the Jacquinot spot, and the large size of the spot allows for tilt tuning to be accomplished, and if the etalon is suitably close to being on-band without much tilting, no banding or other untoward effects will be noted.
With the smaller pressure tuned etalons mounted behind the objective in a collimator and refocusing lens system, the collimator lens renders on axis rays parallel (i.e. as if at infinity and no instrument angle) and therefore the focal ratio of the instrument is irrelevant. What becomes relevant is the field angle magnification, which just like for an eyepiece, increases the angle of the off-axis rays. It can be seen that if the focal length of the collimator lens is one-half the objective focal length, the field angle magnification becomes 2x, and the field angle for the Sun will subtend 0.25 x 2 = 0.5 degree. Therefore when centered on axis, the Sun's limb will lie 0.5 degrees off axis, and the limb of the Sun will lie essentially on the circumference of the "sweet spot." If you shift the image of the Sun off-axis, part of it will fall outside the Jacquinot spot, and appear as Warren has depicted in his post above. If the etalon is tilt-tuned, tilting may introduce some degree of banding due to the increased tilt of the field angles perpendicular to the tilt axis. Theoretically, pressure tuning would not introduce any banding.
It is when the etalon is placed near the focus (usually using a Barlow or a telecentric based lens system), such as with the DayStar and Solar Spectrum filters, the focal ratio is increased, reducing the convergence angles. If the on-axis light cone of the converging rays exceed the acceptance angle, the filters bandpass will widen beyond the on-band acceptance angle. If the on-axis convergence angles are too large, the filter will not be anywhere near its theoretical FWHM - tyically you need to be at a focal ratio of 45 or greater to be close to the specified FWHM. Additionally, if the lens system is not truly telecentric, the off-axis rays may also be shifted in incident angle beyond the acceptance angle, and the field angle angle of the Sun's limb will lie 0.25 degrees beyond the already tilted central rays. Thus the importance of utilizing a true telecentric lens system of long enough focal ratio so as not to exceed the acceptance angle of the etalon for good full disc contrast, uniformity, and specified bandpass.
Edited by BYoesle, 01 February 2020 - 10:26 AM.
