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Round Wedged Prisms
Introduction and Setup
An Applciation Note was prepared to descirbe this process in further detail, and will be referenced periodically here. For a full download of the Applicaiton Note, click the button at the upper right of this tab. To the upper right is also a a download for an Excel spreadsheet which can be used to model a Risley Prism Scanner.
Tracing a Circle with One Prism
This is equation 9 in the Applciation Note linked above. In this equation r' is this circle's radius, S is the distance from the last surface of the prism to the scanning surface, T is the center thickness of the prism, Φo is the beam angle relative to the original optical axis after exiting the second surface of the prism, Φi is the angle created from the beam's incidence on the first surface of the prism according to Snell's Law, and Φp is the resulting angle the beam takes inside the prism relative to the first surface's normal according to Snell's Law.
Tracing a Circle with Two Prisms
This is equation 18 in the Applciation Note linked above. In this parametric equation, rmax is the radius of this circle (any subsequent shape created by this setup is enclosed by this radius), T is the middle thickness of the fist prism, T' is the effective thickness of prism 2 after the deviated beam travels through it, Φi is the angle created from the beam's incidence on the first surface of the fist prism according to Snell's Law, Φp is the resulting angle the beam takes inside the prism relative to the first surface's normal according to Snell's Law, z is the distance from the second surface of the second prism to the scanning surface, S is the distance between the prisms, and Φo is the beam angle relative to the original optical axis after exiting the second surface of the first prism.
This is equation 21 in the Applciation Note linked above; please reference that Applciation Note or the accompanying spreadsheet for the definitions of these variables. As an example, the long-exposure photograph to the right shows two wedge prisms being used to trace out a spiral. This was realized by first setting the beam to be undeviated, and then having the prisms rotate in the same direction, with one prism set to rotate 0.5 deg/s faster than the other. This, and many other shapes, can be created on the "Third Approx." sheet of the downloadable Excel sheet above. To create this spiral, try inputting 25 deg/s to ω1 (rotation speed of prism 1), 24.5 deg/s to ω2 (rotation speed of prism 2), and 80 seconds to t (run time), with a Δθ (home position offest) of 180 degrees.