Gus K on another topic asked:
... so what determines if an etalon is 1, 0.8 or 0.65 A.
Since this requires a rather in-depth response, I thought I'd address this question as a separate topic:
Everything you always wanted to know about Fabry Perot etalons but were afraid to ask.
A FP etalon is a type of “interference” filter which uses two highly polished, exceedingly flat, and precisely spaced partially reflective mirrors facing each other to achieve an ultra-narrow bandpass of usually less than ~ 0.1 nm (1 Ångstrom). The gap between the mirrors can be either solid or open (air-spaced). Light entering the etalon is reflected in the gap and resonates back and forth, and depending on the wavelengths being in or out of phase, can either be reinforced or destroyed – e.g. constructive or destructive interference.
Several interacting factors can affect how such an etalon filter performs:
Peak Transmission – Depending on the spacing of the etalon plates (gap thickness), various wavelengths can be selected, with their associated harmonics falling on either side of the desired wavelength of light. This spacing of solar filter etalon plates generally needs to be changed in order to “tune” the etalon, which shifts the etalon peak to account for environmental conditions, or allows better viewing of off-band phenomena. Solid etalons usually do this by changing the etalon temperature, and thermal expansion and contraction changes the spacing of the mirrors; or tilting the etalon, which results in a greater path-distance for light to travel between the etalon plates. Air-spaced etalons can change the spacing by several methods: tilting as just described; pressure tuning, which changes the air density – and hence gap refractive index -- and slows down the light making it “feel” as if it is going a longer distance resulting from increased air pressure/density; or mechanical pressure on the etalon spacers which changes the etalon plate separation.
Bandpass -- technically referred to as the FWHM - full-width half-maximum - is the width of the transmission profile at one-half of the filters maximum transmission at the design frequency/wavelength, usually denoted in Ångstrom units for solar filters. For solar applications, narrower is generally considered to be better. Bandpass is a function of the size of the gap between the reflective surfaces, and the reflectivity of the mirror coatings: The larger the gap, or the higher the reflectivity, the narrower the bandpass.
However, as one might infer, the higher the reflectivity, the less the transmission: at 100% reflectivity no light would pass through, and at zero reflectivity there would be 100% transmission, but no interference, and hence no narrow-band filtering. The reflectivity at the desired wavelength is therefore chosen somewhere in between, and usually results in a peak transmission of around 60% for a single etalon.
Etalons can generally be made down to a FWHM of 0.03 nm (0.3 Ångstrom) but will be rather dim in overall view when this "narrow." Narrower bandpasses can also be achieved by “stacking” multiple etalons, but the overall transmission will also be lowered. For example: the practice of double stacking two etalons with 60% transmission will have a combined transmission of 36% (0.6 x 0.6 = 0.36).
Free Spectral Range -- the distance between the harmonic resonant peaks passed by the etalon. The smaller the etalon gap, the wider the FSR becomes. If the resonant peaks are too close together, they become harder to block using standard dielectric interference filters, and therefore the blocking filters become more expensive to make. Therefore the FSR is usually chosen to be around 1.0 nm (10 Ångstroms), and this value aids in keeping the out-of-band continuum light from getting through via the blocking filter.
Finesse -- defined as the ratio between the the FSR and bandpass, and the higher the better. An etalon with a finesse of 2 has a very broad and flat transmission curve, with a lot of out-of-band leakage and poor performance. An etalon with a finesse of 30 will have a very tall and narrow transmission curve with very good perfromance and virtually no out of band leakage. The typical solar etalon with a bandpass of 0.7 Ångstrom and FSR of 10 Ångstroms would therefore have a theoretical finesse of ~ 14 if perfectly made. This is where the optical flatness and parallelism of the etalon plates is of critical importance in the filter performance. When these are less than ideal, the noise floor of the etalon transmission curve rises significantly above zero, and background glow begins to be visible and interferes with faint prominences and low contrast disk detail.
So once we have established the basics of reflectivity and gap spacing, we can determine the filters bandpass. But this is a theoretical value only. Several issues can render the bandpass specification almost meaningless, such a the previously discussed etalon flatness, parallelism, and resulting finesse.
Another major factor to consider is the nature of how light passes through the etalon. An etalon only performs ideally with perfectly parallel light passing through it normal - or perpendicular - to the etalon plates.
Most eltalons have another specification known as the “acceptance angle.” The acceptance angle is the angle away from normal (perpendicular) to the etalon that a ray of light can deviate and still be within the specified bandpass. As described above for tuning, as a light ray begins to deviate away from normal through the etalon, the path length through the gap increases, and the transmission peak is shifted toward the blue end of the spectrum, and the bandpass begins to widen as well. If the ray exceeds the acceptance angle, the filter falls “off band.” This has very important consequences for etalon design and placement.
If the sun were a point source of light, all would be easy. Unfortunately, the sun is a rather large object subtending a half a degree. When placed on the optical axis of a telescope, light from the sun’s disk center will be exactly normal to the etalon, but light rays from the sun’s limb will subtend about 1/4 a degree before it even enters the telescope. With a front mounted etalon, this usually is no problem, as the acceptance angle for a 0.7 Å filter is usually about half a degree, and the entire disk remains on band. A front mounted etalon using tilt tuning therefore has about another 1/4 of degree or so of tilt available for tuning before the filter will begin to shift off-band, and therefore contrast uniformity is minimally affected.
And we can now see why an etalon placed on the front of an objective has the best possible performance – there are no instrument angles to contend with, and the etalon deals only the field angle of the sun’s limb - which is low as can be obtained. However, as filter size increases, it becomes increasingly difficult to make with good flatness and parallelism, and the practical limit is based on funds available to achieve an acceptable finesse. For this reason, etalons are rarely made larger than about 15 cm (six inches) in diameter.
As smaller etalons are more easily (economically) made to an appropriate finesse, an alternative placement is within the optical system behind the objective. This is usually done in one of two ways: via a collimator lens system or a telecentric lens system. However, one or both of these systems can introduce additional ray angles to contend with in the form of instrument angles and magnified field angles, which can degrade etalon performance, especially when these angles exceed the etalon acceptance angle. Using tilting for tuning the etalon only exacerbates the situation, and that is why pressure tuning or mechanical pressure tuning are much preferred. These issues can result in poor contrast uniformity, “sweet posts,” and “banding.” Properly configuring and optimizing the placement of an internal or rear mounted etalon is therefore supremely important if one is to realize the maximum filter performance possible.
Lastly, another word about double stacking: As previously described, double stacking is used to decrease filter system bandpass, and this also results in a reduction in overall transmission. However, the filter becomes a “double cavity” filter verses a single “cavity,” and the transmission curve will be narrower and have greatly suppressed "tails" compared to an equivalent single filter with the same bandpass specification and finesse. A double stacked pair of 0.7Å filters will have a bandpass of ~ 0.5Å, but a transmission profile of a much narrower (higher finesse) filter. This keeps out-of-band energy from degrading contrast, and therefore the transmission profile of a solar H alpha filter system seems equally if not more significant than a bandpass specification alone.
A comparison from George 9 of transmission curves, showing the improvement stacking of multiple filters provides. The transmission peaks have been normalized to better the comparison. While bandpass is reduced significantly, note the vast reduction in the filter "tails" from single to double stacking 0.7 Å filters. While triple or quad stacking offers a marginal improvement in both bandpass and tail suppression, in reality they would also have drastically reduced peak transmissions.
This representation, also from George 9, shows the difference between filters with an identical FWHM bandpass, but using a different number of "cavities." The blue curve is a single stacked filter, the red curve is a double stacked filter, the green curve is a quad stack filter, and the purple curve is and ideal Gaussian curve. Again the transmission peak is normalized.
Edited by BYoesle, 02 November 2014 - 07:54 PM.
Means a lot coming from someone with your credentials and expertise...
