To obtain pure water, you can either buy it in, or make it your selves by filtering it then boiling and condensing it. It is the soluble and insoluble substances that make ice cloudy. Air trapped in the ice can also make it look full of holes.
Freeze the water quickly in a single piece so as to avoid any fissures.
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There's them that knows and them that just thinks they know, whitch are you? Stir the pot and see what rises up. I have catalytic properties I get a reaction going.
The methods above are pretty good, but there is a limit to the quality they can produce. If you want the ultimate optical quality, you might consider some of the following
Distilling as suggested is good for removing solid inclusions, but you would need to be careful about the conditions for condensing the water if you want the ice to be free of bubbles. I would boil any purified water immediately before freezing it, as this will remove almost all dissolved gas. For this purpose, boiling does not necessarily mean warming it - if you have a vacuum pump that isn't bothered by moderate levels of water vapour, you could create a vacuum so that the water boils at (or even below) 25-degrees Celsius (N.B. if you are using any oil-based vacuum pump, a combination of heat and evacuation is not advisable).
What you do next depends on what properties you are after. Above -43degC, ice is always hexagonal and slightly birefringent (~0.01), and most "clear" ice is polycrystalline; this is what you will get with very rapid cooling - there will still be a small amount of scatter, but it is optically good for most purposes. Note that, if the water is truly pure (hard to achieve), it can stay liquid down to very low temperatures (below -45degC). However, if you drop a small particle into the water, it will start the freezing process.
If you need mono-crystalline ice, you will probably get the best results by freezing it slowly, and using a very small ice crystal to start the process. This can be rather tricky, as any remelting usually causes visible striations (albeit at a very low level). I've not done this with ice, but one method is to place a sealed-and-insulated crystal-growing bath inside another bath of liquid with a very slightly lower freezing point, and ensure the outer bath is maintained at its solid-liquid point. You could use water with a very small amount of dissolved salt for this outer bath.
Your knowledge is better than mine and I bow to your superior education. I just knew that boiling condensing the vapour would get rid of the solids and these mostly cause cloudiness in ice.
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There's them that knows and them that just thinks they know, whitch are you? Stir the pot and see what rises up. I have catalytic properties I get a reaction going.
What I'm describing is probably huge overkill for most practical purposes - in practice I'd follow your suggestion first and see if it is good enough for the application. The general method is based on experience growing various crystals, both "from the melt" and from solution. I looked the other stuff up - knowing that our form of life was only possible because of various anomalous properties of water, it was no surprise to find a few more...