By the way,what is "solar continuum" ?
Solar continuum is generally considered to be light coming from the photosphere. In the context of what we are discussing, it is where your Ha narrow-band filter goes off-band, and you begin to lose disc detail and prominences begin to fade or disappear.
All H alpha narrow-band filters have an "acceptance angle," which defines how much of an angle can pass through an etalon before the design wavelength (or center wave length - CWL) shifts un-acceptably "off-band." This is naturally one-half the diameter of the Jacquinot Spot diameter, other wise known as the "sweet spot." The Jacquinot spot is defined as the field about the optical axis within which the the peak wavelength variation [ Δλ ] with field angle does not exceed √2 of the etalon bandpass. This angular field can be used to perform close to monochromatic imaging.
So you can see that tilt-tuning the etalon can only be accomplished to the degree in which the tilt doesn't exceed the acceptance angle.
Equation 1: Δλ = √2 x FWHM
The tilt (field) angle verses wavelength change can be found with formula for the CWL shift:
Equation 2: Δλ = ½ (CWL / n^2) θ^2
We can now solve for θ:
√2 x FWHM = ½ (CWL / n^2) θ^2
θ^2 = √2 x FWHM ÷ ½ (CWL / n^2)
For an air spaced etalon (n = 1.00) with a FWHM of 0.7 Å at the H alpha line (6563 Å), with θ in radians (1 radian = 57.2957795 degrees):
θ^2 = 1.4142 x 0.7 ÷ ½ (6563 / 1.00)
θ^2 = 0.98994 ÷ 3281.5
θ^2 = 0.000301673
θ = √0.000301673
θ = 0.017368736 (radians) x 57.2957795 degrees
θ = 0.9951553 degree
Therefore the Jacquinot spot is ~ 1.0 degree, and the “acceptance angle” (field angle) for this size a spot would be ~ 0.5 degree, as is the frequently cited acceptance value for a 0.7 Å FWHM etalon. Outside this "sweet spot" radius H alpha detail will begin to fade.
Next, for a double stacked etalon system with a 0.5 Å FWHM, and assuming a DS system follows the same rules, we get the following;
θ^2 = 1.4142 x 0.5 ÷ ½ (6563 / 1.00)
θ^2 = 0.7071 ÷ 3281.5
θ^2 = 0.00021548
θ = √0.00021548
θ = 0.0146792 (radians) x 57.2957795 degrees
θ = 0.841058 degree
Therefore the Jacquinot spot is ~ 0.84 degree, and the “acceptance angle” (field angle) for this size a spot would be ~ 0.42 degree. Christian Valadrich produced a great graph of these relationships for various band-passes and refractive index materials which is quite useful:
Used with permission.
You can see that for higher index of refraction materials (mica focuser-based filters) the acceptance angle (Jacquinot spot diameter) is larger than for air-spaced stalon filters, and they are more tolerant of tilting and field angle magnification and instrument angles. This also explains why pressure tuning an air-spaced etalon is vastly superior to tilt tuning for internally etalons located within the collimator optics.
Using my double stacked SM90/90 filter system, and using the first ghost image placed directly in contact with the primary image, you can see how the detail begins to go off-band at the ~ 0.4 degree radius, and the filter further shifts outside of this radius to the blue wing and loses prominence and surface detail, and by the radius of the outside limb of the ghost image the filter is essentially completely off-band: