Maybe I can throw in my 2ct here. While I'm new to LPF, I'm not new in the physics involved.
Take a quick look at *
this explanation of the diffraction grating formula*. It breaks down the complicated looking math into some easy triangulation. The essence is: The lower the spacing (higher number of lines/mm) the wider the angle of the diffraction orders.
The diffraction angle certainly cannot exceed 90°, even with a theoretically perfect grating with a totally flat surface profile. If you use the *
calculator on this page*, you can see that a 1000 lines/mm grating "should" produce a second order spot as long as the wavelength is below 500nm - where this spot would be exactly 90° to the incomming beam. With 488nm this second order beam should be 77° off axis.
It now depends on the physical parameters of the actual grating, whether a beam at this angle may be blocked geometrically. A square shaped photographic grating surface hardly gets a fan angle wider than 90° in total, so every higher order with deflections greater than 45° get lost. The same is true for a symmetric triangular surface.
A high quality etched sawtooth (Echelle) grating will give you more usable angle as the harmonics are favored asymmetrically in one direction.
With above linked calculator you can find that a 250 lines/mm grating gives you one beam roughly every 7° off axis with a 488nm Laser, which fits 5 harmonics into ~45 degrees to each side totalling 11 rays.
