So you want see all known halos? Then here is a list of the work ahead. As of now, there are 75 halos to catch and if we count also the components as separate halos then we have 94 halos. From the point of view of halo spotting, components are of course counted as separate entities. For example, 23° plate arc divides in upper and lower components, of which the lower component - although not necessarily rare as such - is nevertheless thus far exceedingly rarely observed.
We can add also to the numbers above the halos that appear solely on the snow surface. By doing that we have 77 / 96 halos. Notice that in the table there are also components (and one halo) that have not yet been observed in nature. These theoretical halos have not been included in the numbers above. More on these below.
For each halo in the table there is a frequency estimate. The table is for Finland and it is certainly not applicable to tropics, High Arctic or Antarctic. Even in the Middle Europe the frequencies seem to be different for some halos. Sure, the maximum sun and moon elevation encountered at different locations on Earth is of course a factor that affects the frequencies of some halos (for example, circumhorizon arc can not be seen in Finland because sun or moon never rises high enough) but mainly I am talking here of the differences that are caused by the properties or visibility of ice clouds.
The frequencies in the table are mostly given as a plain number (140, 7, 0.1, etc) indicating on how many days (sun) and nights (moon) a year the can halo be seen (surface or lamp light occurrences are not counted in these numbers). Or it is given as description (common, rare, etc) or a number of known observations (1 obs., ~10 obs. etc).
The plain number assumes a stationary observer who observers visually with a convex mirror never stacking any photos and never hunting the diamond dust halos from the snow guns. This observer won't see the additional rare halos in his photos that the stacking brings or experience the great diamond dust displays with some truly rare halos.
The descriptive estimate is for halos that have been only seen from an airplane or in diamond dust. It tells how common a certain halo is under these observing circumstances. Seeing them depends almost solely on how much one flies and hunts halos in the snow gun generated diamond dusts. If you do neither, you probably never see these halos. The subhorizon halos are easy to catch in diamond dust with a bright spotlight placed below horizon. This turns the halo sky upside down with subhorizon halos now visible above horizon.
For halos for which only very few observations are known, no estimate of the occurrence is made - instead given is the number of observations. I have used this when the number of observations does not exceed 10. Of course I may not know all the observations and there can be also differing opinions about some observations.
For some halos in the table - mostly components - there is no frequency estimate or number of observations. These are as of yet unobserved. Many of them probably stay that way, but nevertheless from these it is possible to find some prospects for discoveries. Often though, it seems, a new halo something totally unexpected - something for which the halo theory has been totally blind.
Naming of halos is an issue itself. For the well known halos I have followed a common practice. For the odd radius halos I have chosen the nomenclature used by Tape and Moilanen in their book. Then there are halos which have not been baptized in English yet. These are halos that have been discovered recently. In such cases I have given the Finnish name if such exists - the very latest finds are still unnamed. I will complement the table on these later on.
Some notes are given in the last column of the table. Halos that have been observed only in diamond dust and / or from airplane have been indicated, the "dd" meaning diamond dust. If there is a blank in the notes column for certain halo, it means it has been observed from the ground in ice clouds higher than diamond dust. For some halos, in addition to "dd" there is also "hc". This means that the halo is most likely in diamond dust, but has been documented also in high clouds. ""Lamp" tells that the halo has been observed with a bright spotlight - if no other light source is indicated, then this is the only method of observation. "Stacked" in the notes is to tell that the halo has been detected only from stacked images in certain situations, like in case of high clouds.
I emphasize again that the plain frequency numbers don't count the great diamond dusts from the snow guns. An observer who never hunts in these diamond dusts may never see some rare halos, such as the subanthelic arc or 44° parhelion. Also the numbers don't count what additional halos would appear in photos if stacking is employed. Many halos become much more common when photos are stacked. For example one can expect to see 35° halo visually in high clouds perhaps once or twice in 10 years, but with stacking it can be detected in odd radius displays at least once a year. Likewise, pyramid helic arc in high clouds is almost impossible to see visually, but stacking can bring it into light in displays with strong 23° plate arc.
Next I should write presentations of all these halos, because for many of them there is not really information in the internet. But that would be a huge job.