Summary: These products are misleading in their marketing and do not return a result that is worth your money.
This is intended to be a warning message that I'd copy/paste to people considering buying one of these filters, but I figured I'd post it as well in case it helps anyone. This discussion has come up a few times in different places online and I don't want to keep typing it out, so here it is for me to link to. I don't mean to insult anyone for buying these or call any companies bad because they offer these filters. I'm of the opinion that the consumer gets the (very) short end of the stick here since a lot of the marketing around these filters is very misleading, and it doesn't help that a decent portion of it is true in specific cases. Namely the fact that these filters worked pretty well 20+ years ago, and have been rapidly falling off almost entirely due to the LED. This is all intended to be for astrophotography, do visual how you like you heretics. All this is intended to be in reference to DSLR/Mirrorless or OSC cams. If you're using one of these filters on mono I'm guessing you know more than me or are too far gone to save.
I believe the overall information of this post is accurate, and while my numbers are probably decently close, some generalizations I make may not be. Feel free to correct/add to in the comments.
CLS Filters
I'll be starting with CLS (city light suppresion)/light pollution filters. 20+ years ago these things were pretty nice. As I'm sure most people know we used to have a lot more sodium vapor lamps which produced light in that 589nm range. This was great for astronomy, 589nm is pretty easy to supress and pretty far away from anything we really care about, namely Ha, Sii, and Oiii (656nm, 671nm and 673nm, and 501nm). This puts this product in a great position - a widely had problem with a relatively simple fix. Everyone's happy. Unfortunately this was 20+ years ago. Everyone and anyone who's something these days uses LED's, and boy do we love our LED's! Here's the first of all my sciency stuff: Looking at the graph included in the introduction of this paper in Nature [1], you can get a rough visualization of what our light pollution looks like. This data is from NOAA, specifically the LED Lamp Spectra here [2]. I've copied a version of that chart with wavelength ranges 400-699nm, and relative light pollution values from 0 to 1. For my purposes here the actual values of light pollution don't really matter, rather their relative intensities.

That vertical dotted line isn't a mistake, that's the poorly added reference for where the sodium vapor emmision line at 589 is, for easier visualization. This is to show that there isn't a single emmision line to filter out. Meanwhile, if we look at CLS/Light pollution filter charts, they seem to imply that there's a big source of light pollution they're cutting out. Here is use Astronomik and Optolong, they were just the first two results, the rest look relatively similar.
[3]

[4]
If you compare the CLS charts vs the actually Light Pollution spectrum chart, the CLS filters do cut out some light pollution. The issue arises when you consider the purpose of these CLS filters. If you wanted to take a narrowband image - you wouldn't use this filters. If you wanted to take a "true color" image (which is a whole debate in itself), you couldn't use these filters. So these filters intended purpose is for broadband targets which the user accepts they won't have an accurate represenation of. This is fine, if you like the look these filters give you that's perfectably acceptable. I would heavily suggest that anyone looking to use these filters looks at the spectra of their intended target and considers what they're losing. For a specific example, here's the spectra of the Pleiades [5].

Approximating our bandpasses as 450-540nm and 640-700nm, these CLS filters would be cutting out a significant portion of the Pleiades! Ignoring the loss of color information, this just cuts out so much signal! As per the Lowell Observatory in 1912, the source of the spectra of the Pleiades is most likely the stars themselves [6]. In 1912 they weren't so sure, but it's pretty common knowledge in our hobby today that the class of nebula labeled as reflection nebula reflect light, most often of a star. Stars of course are well known broadband emitters. I think I've been beating a dead horse for a while now, but there are plenty more examples if needed.
If you wanted to us a CLS filter as a boost for an emission nebula, that would "work". Clearly these filters do further isolate the emission lines, but there are a number of issues here which will be expanded on in the next section on Tri/Quadband filters. The major two issues are the lack of an accurate representation of signal (as mentioned), and the inability to differentiate between emission lines, giving you what I lovingly refer to as a "sausage nebula".
Plus, its not like the light pollution disapears from the rest of the image, these CLS filters still pass light pollution.
To sum it up for CLS filters: This has all been a common sense-esq argument. I haven't delved into numbers really but I don't think it's difficult to see that while CLS filters kinda supress light pollution, they also negatively impact the acquisition of broadband targets.
Edit: What those finding sucess with these filters are likely seeing is an increase in contrast. This varies between filter to filter as different areas will have different spectra of light pollution sources, and so one filter may cut out a peak while another includes it. This also commonly results in a purple hue in images, most easily seen in galxies. This is of course due to the fact that green is largely filtered out, with red and blue being passed.
(Added after considering Rock Veregin's comment.)
Tri/Quadband Filters
Once again these filters don't neccessarily lie, they do have three of four narrowbandpasses. The issue arises in their use case and performance once more. Of the emission lines to choose from we have... [7, also myself since you can just do the math with the Balmer series and such]
- H-alpha 656.3nm
- Oiii 500.7nm (actually a doublet emission line with 495.9nm, though we ussually just refer to the 500.7nm figure because it is nearly 3x more intense)
- Sii 671.6 and 673.1 nms (another doublet but we don't care since they're close enough that we don't need to choose between the lines with a 3nm bandpass)
- Nii 654.8 and 658.4 nms
- Helium 468.6 nms
- H-beta 486.1 nms
In practice, we can find a number of filters passing the H-alpha, Oiii, and H-beta lines. This is the most common combination, with some filters having more emission lines included. For reference I looked at the Antlia Triband, Altair Triband, Optolong L-eNhance (which is actually marketed as a duoband filter), IDAS NB1, and finally the Radian Triad Ultra Quad-Band Filter. That last one was mostly included for the absurdity of the name, "Triad Ultra Quad-Band".
Of these lines H-alpha and Oiii are almost always the main lines considered for duoband filters. This is because they're bright and in different parts of the spectrum. Notice as well that Neon is at 654.8 and 658.4. Awfully close to H-alpha! Turns out this doesn't impact the majority of objects. Due to the abundance of objects with strong H-alpha, and the relative rarity Neon, for the most part if you're shooting Neon you've sought it out. This is all to say that any claim of "extended bandpasses to capture H-alpha and Nii" are providing a weak and misleading reason for wider (cheaper) bandpasses. This applies for advertising grouping H-alpha and Sii together, or Oiii and H-beta as well.
Quick side note, another reason for wide bandpasses that's often given is functionality for fast (f/2 for example) systems. While true that sufficiently wide bandpasses will ensure functionality at fast focal ratios, this is a convient excuse for more lax quality controll and cheaper production. Having worked in filter production, it is signficantly easier to hit wider specs.
In the case of which the filters actually do have isolated bandpasses for whatever combination of H-alpha, Nii, Sii, Oiii, or H-beta, you're still better off with a duoband filter. The first issue is seperation of emission lines. This can be passed off as artistic choice, but it is something that should be seriously considered when creating an image. If you're shooting with (for example) a triband filter passing H-alpha, Oiii, and H-beta (arguably the most common example), you're capturing H-alpha in red, and Oiii + H-beta in green/blue. There is no seperation of color between H-Beta and Oiii, and no way (without a neat fact mentioned later) to isolate Oiii. The same goes for H-alpha Oiii and Sii. No way to seperate H-alpha and Sii. The jist of this argument is that you will not end up with an image that is properly manipulateable it will effectively be a duoband image since you can't isolate emission lines. To be clear, this is perfectly fine if you intend to capture the image that way, however the true failure of this filters is when we consider the SNR of the image.
Without further adue, the true crime of these filters is the addition of the H-beta bandpass. H-alpha and H-beta have the extact same spatial structure. This means that where this is H-alpha, there is H-beta; and where this is H-beta, there is H-alpha. The important detail hinted at above is that in the vast majority of circumstances, H-beta is roughly 0.35x the intensity of H-alpha [8*]. This means you can litterally sperate out your H-alpha data, multiply it by 0.35, and with near accuracy simulate H-beta. The benifits of this is simply cutting out the H-beta emission line. To display the benifits, let us take two idealized filters, one duoband and one triband. The duoband will be an H-alpha and Oiii filter, and the Triband a H-alpha, H-beta, and Oiii filter. These filters have perfect 1nm bandpasses. Taking into account our light pollution data from before, the duoband filter will have 0.21L (Oiii) + 0.27L (H-alpha) = 0.48L. These are the normalized light pollution values from the chart. The triband filter has 0.21L (Oiii) + 0.27L (H-alpha) + 0.15L (H-beta) = 0.63L. As we can see, the triband filter recives more light pollution due to the increased bandpass. As mentioned above, we can achive the same effective H-beta signal by multiplying our H-alpha by 0.35, thus the triband is just letting in more light pollution. Furthermore, since we have seperated Oiii and H-alpha, we can achive an HaHbOiii image by assigning the artificial H-beta to one of the three color channels (this could be done by subtracting out 0.35*H-alpha from the mixed Oiii/H-beta in the triband, but at that's beyond the point).
An issue could be brought up that H-beta is just a weak link, if we use Sii or Helium for example we may gain signal. This may be true for a small number of objects, but you still (almost definetly) won't be able to seperate two of the emission lines from each other as they will be in the same color channel. I would also like to point out common cases such as the rosette nebula:
[9]
Clearly the H-alpha signal is much more intense than the Sii signal. This is a vast generalization, but there are much better ways to get Sii data than one of these filters. If only someone were to provide a solution...
Solution
So what should you do? Here are a few solutions:
1. Just get a duoband filter, probably H-alpha and Oiii. If you're after that H-beta, I really think that in 99% of cases it can be artifically inserted. If you really want that H-beta, find an isolated filter and move to mono.
2. If you really want that Sii and don't want to move to mono, get two duoband filters, an H-alpha Oiii and an Sii Oiii. Or get a single bandpass Sii filter and begin your transition to mono.
3. Save the money you'd spend on a crappy filter and take a trip to dark skies. That CLS filter isn't worth it, take a weekend, go see the stars for yourself and get a good pic while you're there.
4. You want that Helium or Nii? That tri/quadband won't isolate it anyway. Pony up some $$$ to go mono and get single bandpass filters for Helium or Nii or whatever other emission line you're after.
5. Shoot longer. More data is always better, though at some point you will need to accept that the only way to get some targets is to travel to darker skies.
6. Consider purchasing software such as pixinsight, the AI RC Astro tools, etc. Though you can't sell them to recoup cost, they are worthwhile (pix especially).
[1] The spectral and spatial distribution of light pollution in the waters of the northern Gulf of Aqaba (Eilat) (Nature)
[2] NOAA Labratory Spectra (NOAA)
[3] Astronomik CLS Filter (Astronomik)
[4] Optolong CLS (City Light Supression)... (Optlong)
[5] Spectra of the Pleiades (Cloudy Nights)
[6] On the spectrum of the nebula in the Pleiades (Lowell Observatory Bulletin)
[7] Basic Atomic Spectroscopic Data (NIST)
[8] Intensity Mapping of Ha, Hb, [OII] and [OIII] Lines at Z < 5 *This paper quotes Osterbrock & Ferland 2006 for this source, which I did locate and briefly skim through, but cannot determine exactly where this number is comming from. The number is similar to the ratio thrown around often on the internet, and in my own studies so I'm willing to call it good enough for astrobin.
[9] 5 minute subs of Ha/Sii. Asi2600mm, Antlia 3nm Ha/Sii, 70mm f/4.8.
Hope you enjoyed.
Editted to provide software solutions.
This is intended to be a warning message that I'd copy/paste to people considering buying one of these filters, but I figured I'd post it as well in case it helps anyone. This discussion has come up a few times in different places online and I don't want to keep typing it out, so here it is for me to link to. I don't mean to insult anyone for buying these or call any companies bad because they offer these filters. I'm of the opinion that the consumer gets the (very) short end of the stick here since a lot of the marketing around these filters is very misleading, and it doesn't help that a decent portion of it is true in specific cases. Namely the fact that these filters worked pretty well 20+ years ago, and have been rapidly falling off almost entirely due to the LED. This is all intended to be for astrophotography, do visual how you like you heretics. All this is intended to be in reference to DSLR/Mirrorless or OSC cams. If you're using one of these filters on mono I'm guessing you know more than me or are too far gone to save.
I believe the overall information of this post is accurate, and while my numbers are probably decently close, some generalizations I make may not be. Feel free to correct/add to in the comments.
CLS Filters
I'll be starting with CLS (city light suppresion)/light pollution filters. 20+ years ago these things were pretty nice. As I'm sure most people know we used to have a lot more sodium vapor lamps which produced light in that 589nm range. This was great for astronomy, 589nm is pretty easy to supress and pretty far away from anything we really care about, namely Ha, Sii, and Oiii (656nm, 671nm and 673nm, and 501nm). This puts this product in a great position - a widely had problem with a relatively simple fix. Everyone's happy. Unfortunately this was 20+ years ago. Everyone and anyone who's something these days uses LED's, and boy do we love our LED's! Here's the first of all my sciency stuff: Looking at the graph included in the introduction of this paper in Nature [1], you can get a rough visualization of what our light pollution looks like. This data is from NOAA, specifically the LED Lamp Spectra here [2]. I've copied a version of that chart with wavelength ranges 400-699nm, and relative light pollution values from 0 to 1. For my purposes here the actual values of light pollution don't really matter, rather their relative intensities.

That vertical dotted line isn't a mistake, that's the poorly added reference for where the sodium vapor emmision line at 589 is, for easier visualization. This is to show that there isn't a single emmision line to filter out. Meanwhile, if we look at CLS/Light pollution filter charts, they seem to imply that there's a big source of light pollution they're cutting out. Here is use Astronomik and Optolong, they were just the first two results, the rest look relatively similar.


[4]
If you compare the CLS charts vs the actually Light Pollution spectrum chart, the CLS filters do cut out some light pollution. The issue arises when you consider the purpose of these CLS filters. If you wanted to take a narrowband image - you wouldn't use this filters. If you wanted to take a "true color" image (which is a whole debate in itself), you couldn't use these filters. So these filters intended purpose is for broadband targets which the user accepts they won't have an accurate represenation of. This is fine, if you like the look these filters give you that's perfectably acceptable. I would heavily suggest that anyone looking to use these filters looks at the spectra of their intended target and considers what they're losing. For a specific example, here's the spectra of the Pleiades [5].

Approximating our bandpasses as 450-540nm and 640-700nm, these CLS filters would be cutting out a significant portion of the Pleiades! Ignoring the loss of color information, this just cuts out so much signal! As per the Lowell Observatory in 1912, the source of the spectra of the Pleiades is most likely the stars themselves [6]. In 1912 they weren't so sure, but it's pretty common knowledge in our hobby today that the class of nebula labeled as reflection nebula reflect light, most often of a star. Stars of course are well known broadband emitters. I think I've been beating a dead horse for a while now, but there are plenty more examples if needed.
If you wanted to us a CLS filter as a boost for an emission nebula, that would "work". Clearly these filters do further isolate the emission lines, but there are a number of issues here which will be expanded on in the next section on Tri/Quadband filters. The major two issues are the lack of an accurate representation of signal (as mentioned), and the inability to differentiate between emission lines, giving you what I lovingly refer to as a "sausage nebula".
Plus, its not like the light pollution disapears from the rest of the image, these CLS filters still pass light pollution.
To sum it up for CLS filters: This has all been a common sense-esq argument. I haven't delved into numbers really but I don't think it's difficult to see that while CLS filters kinda supress light pollution, they also negatively impact the acquisition of broadband targets.
Edit: What those finding sucess with these filters are likely seeing is an increase in contrast. This varies between filter to filter as different areas will have different spectra of light pollution sources, and so one filter may cut out a peak while another includes it. This also commonly results in a purple hue in images, most easily seen in galxies. This is of course due to the fact that green is largely filtered out, with red and blue being passed.
(Added after considering Rock Veregin's comment.)
Tri/Quadband Filters
Once again these filters don't neccessarily lie, they do have three of four narrowbandpasses. The issue arises in their use case and performance once more. Of the emission lines to choose from we have... [7, also myself since you can just do the math with the Balmer series and such]
- H-alpha 656.3nm
- Oiii 500.7nm (actually a doublet emission line with 495.9nm, though we ussually just refer to the 500.7nm figure because it is nearly 3x more intense)
- Sii 671.6 and 673.1 nms (another doublet but we don't care since they're close enough that we don't need to choose between the lines with a 3nm bandpass)
- Nii 654.8 and 658.4 nms
- Helium 468.6 nms
- H-beta 486.1 nms
In practice, we can find a number of filters passing the H-alpha, Oiii, and H-beta lines. This is the most common combination, with some filters having more emission lines included. For reference I looked at the Antlia Triband, Altair Triband, Optolong L-eNhance (which is actually marketed as a duoband filter), IDAS NB1, and finally the Radian Triad Ultra Quad-Band Filter. That last one was mostly included for the absurdity of the name, "Triad Ultra Quad-Band".
Of these lines H-alpha and Oiii are almost always the main lines considered for duoband filters. This is because they're bright and in different parts of the spectrum. Notice as well that Neon is at 654.8 and 658.4. Awfully close to H-alpha! Turns out this doesn't impact the majority of objects. Due to the abundance of objects with strong H-alpha, and the relative rarity Neon, for the most part if you're shooting Neon you've sought it out. This is all to say that any claim of "extended bandpasses to capture H-alpha and Nii" are providing a weak and misleading reason for wider (cheaper) bandpasses. This applies for advertising grouping H-alpha and Sii together, or Oiii and H-beta as well.
Quick side note, another reason for wide bandpasses that's often given is functionality for fast (f/2 for example) systems. While true that sufficiently wide bandpasses will ensure functionality at fast focal ratios, this is a convient excuse for more lax quality controll and cheaper production. Having worked in filter production, it is signficantly easier to hit wider specs.
In the case of which the filters actually do have isolated bandpasses for whatever combination of H-alpha, Nii, Sii, Oiii, or H-beta, you're still better off with a duoband filter. The first issue is seperation of emission lines. This can be passed off as artistic choice, but it is something that should be seriously considered when creating an image. If you're shooting with (for example) a triband filter passing H-alpha, Oiii, and H-beta (arguably the most common example), you're capturing H-alpha in red, and Oiii + H-beta in green/blue. There is no seperation of color between H-Beta and Oiii, and no way (without a neat fact mentioned later) to isolate Oiii. The same goes for H-alpha Oiii and Sii. No way to seperate H-alpha and Sii. The jist of this argument is that you will not end up with an image that is properly manipulateable it will effectively be a duoband image since you can't isolate emission lines. To be clear, this is perfectly fine if you intend to capture the image that way, however the true failure of this filters is when we consider the SNR of the image.
Without further adue, the true crime of these filters is the addition of the H-beta bandpass. H-alpha and H-beta have the extact same spatial structure. This means that where this is H-alpha, there is H-beta; and where this is H-beta, there is H-alpha. The important detail hinted at above is that in the vast majority of circumstances, H-beta is roughly 0.35x the intensity of H-alpha [8*]. This means you can litterally sperate out your H-alpha data, multiply it by 0.35, and with near accuracy simulate H-beta. The benifits of this is simply cutting out the H-beta emission line. To display the benifits, let us take two idealized filters, one duoband and one triband. The duoband will be an H-alpha and Oiii filter, and the Triband a H-alpha, H-beta, and Oiii filter. These filters have perfect 1nm bandpasses. Taking into account our light pollution data from before, the duoband filter will have 0.21L (Oiii) + 0.27L (H-alpha) = 0.48L. These are the normalized light pollution values from the chart. The triband filter has 0.21L (Oiii) + 0.27L (H-alpha) + 0.15L (H-beta) = 0.63L. As we can see, the triband filter recives more light pollution due to the increased bandpass. As mentioned above, we can achive the same effective H-beta signal by multiplying our H-alpha by 0.35, thus the triband is just letting in more light pollution. Furthermore, since we have seperated Oiii and H-alpha, we can achive an HaHbOiii image by assigning the artificial H-beta to one of the three color channels (this could be done by subtracting out 0.35*H-alpha from the mixed Oiii/H-beta in the triband, but at that's beyond the point).
An issue could be brought up that H-beta is just a weak link, if we use Sii or Helium for example we may gain signal. This may be true for a small number of objects, but you still (almost definetly) won't be able to seperate two of the emission lines from each other as they will be in the same color channel. I would also like to point out common cases such as the rosette nebula:

[9]
Clearly the H-alpha signal is much more intense than the Sii signal. This is a vast generalization, but there are much better ways to get Sii data than one of these filters. If only someone were to provide a solution...
Solution
So what should you do? Here are a few solutions:
1. Just get a duoband filter, probably H-alpha and Oiii. If you're after that H-beta, I really think that in 99% of cases it can be artifically inserted. If you really want that H-beta, find an isolated filter and move to mono.
2. If you really want that Sii and don't want to move to mono, get two duoband filters, an H-alpha Oiii and an Sii Oiii. Or get a single bandpass Sii filter and begin your transition to mono.
3. Save the money you'd spend on a crappy filter and take a trip to dark skies. That CLS filter isn't worth it, take a weekend, go see the stars for yourself and get a good pic while you're there.
4. You want that Helium or Nii? That tri/quadband won't isolate it anyway. Pony up some $$$ to go mono and get single bandpass filters for Helium or Nii or whatever other emission line you're after.
5. Shoot longer. More data is always better, though at some point you will need to accept that the only way to get some targets is to travel to darker skies.
6. Consider purchasing software such as pixinsight, the AI RC Astro tools, etc. Though you can't sell them to recoup cost, they are worthwhile (pix especially).
[1] The spectral and spatial distribution of light pollution in the waters of the northern Gulf of Aqaba (Eilat) (Nature)
[2] NOAA Labratory Spectra (NOAA)
[3] Astronomik CLS Filter (Astronomik)
[4] Optolong CLS (City Light Supression)... (Optlong)
[5] Spectra of the Pleiades (Cloudy Nights)
[6] On the spectrum of the nebula in the Pleiades (Lowell Observatory Bulletin)
[7] Basic Atomic Spectroscopic Data (NIST)
[8] Intensity Mapping of Ha, Hb, [OII] and [OIII] Lines at Z < 5 *This paper quotes Osterbrock & Ferland 2006 for this source, which I did locate and briefly skim through, but cannot determine exactly where this number is comming from. The number is similar to the ratio thrown around often on the internet, and in my own studies so I'm willing to call it good enough for astrobin.
[9] 5 minute subs of Ha/Sii. Asi2600mm, Antlia 3nm Ha/Sii, 70mm f/4.8.
Hope you enjoyed.
Editted to provide software solutions.