Since I have been testing S-Mesh I have found that the 3.5 or 4.5 rule can be broken. On our 150/S we can hold 45 (20 degrees) and 55 line (29 degrees). The math doesn't support these line counts but in our tests we have found that open area of mesh can overcome the math rules. The thing about halftone angles is we all assume our mesh is captured perfectly square to the frame. In most cases this is plus or minus 2-3 degrees on most stretchers. On bar stretchers it is almost impossible to get the threads square to the frame as the bars tilt and angle the threads during stretching. Corners turn into parallelogram openings. The same can happen as you approach the corners of a softened Newman stretch. Statics offer a little more control to get square to the frame, and the mesh needs to have balanced warp and weft thread properties to maintain square openings and not rectangles.
It is possible to create a bitmap file in Photoshop with 90 different angles from 1-90. This yields a halftone area of about 1.5x3 inches. We put in a 0-100% gradient as well for each individual angle. We mark each individual file then place them into a master file to output. While it doesn't match a RIP output dot, the angles and dot fields are similar enough to view moire in the mesh. I highly recommend printing this screen as well to see if the best looking angle prints with no moire.
We then output a full 13x15" 0-100% gradient at this best angle via the RIP to see if it shows any moire. The shirt quality has a lot to do with moire. The cheaper the shirt the more mesh/weave interference you will see and this is not from the halftone and mesh but due to the shirt weave being very coarse with lots of air in the wales or valleys of the weave.
Our go to mesh counts for sim process are Smartmesh 225/S for the base and 350/S or T for the overprints with both at 22.5 degrees. This allows for a 65 line base and both 65 and stochaistic overprint colors. The base is key. 150/S works well for vibrancy and opacity, but needs a good shirt face to avoid mesh/fabric interference. Angles for Murakami Mesh, providing you have a good square capture to the frame.
45 Line
150S - 20 degrees
180S - 22.5
225S - 19
300T - 11
350S - 22.5
350T - 22.5
55 line
150S - 22.5 degrees
180S - 9
225S - 22.5
300T - 7
350S - 25
350T - 22.5
Again these angles are ballpark angles due to mesh capture, dot shape, imaging device, shirt type. I highly suggest making your own 1 thru 90 angle positive to test, and follow that up with a large halftone gradient at the chosen angle that almost fills the screen to see if the entire screen is moire free.
Al
