You can buy circuit board presensitized with a coating similar to silk screen photo emulsion. IIRC you wash the sheet after exposure to remove unexposed resist and then use Ferric Chloride to remove the copper where not required. Coating would work with sunlight exposures.
Why are there no speaker jacks on a stereo camera?
A half tone, or screen ruling picture, is one that simulates a continuous tone picture (a photograph)
If you look with a loupe at a printed with ink, good quality magazine colour or B&W picture, you will see various coloured and various shaped dots.
Most magazine printing would be around 150# (# denotes the word screen) and a higher quality (mostly) version may go as high as 300#.
I would suggest a screen ruling around 40# to about 60# could be suitable and achievable in a home environment using very basic equipment.
This is usually done with a four colour process CMYK (Cyan, Magenta, Yellow and Black).
The link Whitey gave brought back memories of proofing with originally zinc acid etched plates, then magnesium water etched plates sitting on the form platten, just like that orange polymer plate.
That printer looks to be motor driven, you may find quite a few that are hand driven, these are excellent and quite cheap, or at least they were once.
Regarding rubber, well I'm a rubber stamp manufacturer and generally the stamp (or marking in the USA) industry uses rubber with a shore hardness around 35-40. Polymer plates would be a better bet as their printing plate shore hardness, is normally much higher.
You can purchase liquid polymer from USA firms and their range of product is very good and may be useful in your search:- 
I have used these products, mainly the i40 (shore hardness 40) and seen the i95 which is incredibly hard.
With these processes you can manufacture very hard plates with total control over almost anything, including overall plate thickness.
Essentially you will need a vacuum of some sort to enable enough suck to hold your negative and/or positive down. Then you need some UV source.
If you scroll down you will also see a daylight negative system. This is brilliant, you need a sheet of glass to sit the exposed negative on, spray the activator on, wait about 45 seconds, then wipe off and or quickly rinse under cold water.
I could go on, but a ring around smaller rubber stamp shops in your locale, may unearth a myriad of possibilities for you.
I had used a photographic process for many years to produce printed circuit boards. The process may possibly be adapted to your purposes.
One produces either a positive or negative high-contrast transparency of the pattern you wish to produce.
One lays this hard up against a plolymer board which has been plated with a few thousands of an inch of copper and then 'Kodak photoresist' (KPR) or a similar product whch may be either positive or negative working.
One then exposes this to UV light until those portions of the resist below the transparent part of the transparency undergoes a chemical change - softening if positive working or hardening if negative-working (like KPR). The board is then washed with a solvent which preferentially removes the softer resist followed by a chemical etch (ferric chloride in the case of copper circuit boards) which dissolves away the copper not protected by hard photoresist. Drill appropriately and you have a circuit board.
Printing plates for half-tones are made by a very similar process excepting that the areas not solid black or white in the original image are represented on the high-contrast transparency by a 'grid' of dots of different densities as has been discussed above. If your original image is digital then many programs are capable of transforming a greyscale image to a gridded litho-film image. How one does this without computer help, I don't know.
My brother-in-law is a printer who makes his own plates, so I wiill ask.
So if these polymer plates usually have a much higher shore hardness, does this make them less suitable for "hand" pressing? There's no way I can afford a printing press or anything like that, so I was hoping to do this all by hand, maybe a clamp or something at the most. Then again.... how cheap is "quite cheap"?
Having just learned about liquid photo-polymer and PP in general, I can't yet fathom the possibilities, but they seem endless!
I am curious to know more about halftone screens. Don't they have to go between the image and the plate? How would this work w/ contact printing? This is totally new to me, so forgive my ignorance.
Thanks for the input on PCB's as well guys!
Just lay the paper on the plate and use a hard rubber roller to transfer the ink. To my knowing, you won't be able to get continuous tone with relief printing BTW...
Well not continuous tone, but how about acceptable half-tone?
To my knowing relief printing (see woodcut also) is a monotone printing method, you can only print solid areas of color (ridges), OR no color (grooves). Halftones are possible only with intaglio aquatint printing (w/ trad. acid etched - through gelatin carbon tissue - copper/zinc/steel plates, or photopolymer plates) which absolutely necessitates an expensive etching press.
I think you should read some books about printmaking and photogravures beforehand, in order to learn about the principles...
Loris Medici, it seems like what you're saying and what others have said in this thread are at odds. How do you respond to what Whiteymorange said about using a halftone screen?
In my mind, it seems reasonable to assume that if you use a half-tone screen to create the relief, then you will get very tiny areas of monotone, that is, half-tones.
That being said, I do agree with you, I need to learn more about printmaking.
Your statements match my experience of print making. I have read a bit on photogravure and tried (failing miserable with both a presensitized polymer and traditional carbon tissue) You must use a mezzotint screen between your continuous tone negative and sensitized plate.
Also the expensive printing press isn't exactly right (just mostly ). I've seen videos of artists using steam rollers to make massive prints. Making your own photogravure IS possible in a home set up with very basic supplies... But for your own sanity- take a class.
If you expose a plate through the positive alone, and here I speak of gravure printing, you will get uneven ink distribution on the plate. This is equivalent to "open bite" in etching. What you need to get an even tone is a scattering of small, ridged dots across the area which each catch and retain some of the ink. I use an aquatint screen from Dan Welden at solarplate.com. Halftone screens serve the same purpose. The screen I have is digitally printed with a stochastic pattern, not a rigid series of dots-per-inch, and leaves a far less visible trail in the final print.
Originally Posted by holmburgers
Fine halftone screen can be used with a good press and careful inking methods, but the previous posters are correct in that they are too fussy for homemade work. A rougher screen will leave a visible pattern, but may be better to work with in making the photo positive through which you expose your plate. Think Litho film - this is what it was invented for. Without any translation of gray areas into a dot pattern, you have only the edges of broad areas to differentiate between your colors. Simple silkscreen prints are the best example i can think of to describe this. The polymer plates are perfectly capable of resolving dot patterns that will allow you to print color separation plates into a pleasing full-color image, but yes, you will really should have access to a press. They are often available through extension programs at universities that have art classes or in group studios where they may be rentable by the hour. Or find a friend with a press. I'm spoiled in that I live in, or near, a city with all of these things, but many of my prints have been made on a press that a friend has lent me- a cheap Dick Blick etching press sold to allow portable printmaking for art fairs, etc.