Measuring Wavefront errors in real systems By tracing a number of rays through the pupil,and measuring the TRA of each, we can get the slope of σ then by numerical integration, we can find the wavefront aberrations, σ. Since rays are always perpendicular to wavefronts, a wavefront tilt error (at some location in the pupil) corresponds directly to a Transverse Ray error (TRA) at the image plane. Zemax does not normally propagate waves through an optical system but rather uses a geometric relationship between Ray errors and wavefront errors to calculate the wavefront error map. This is known as “Transverse Ray Aberration”, or ‘TRA’. In a system with aberrations, rays from different positions in the exit pupil may miss the ideal image position by various amounts when they reach the image plane. The errors are the difference between the actual wavefront and the ideal spherical wavefront converging on the image point. Ray trace programs will report “Wavefront Errors” at the Exit Pupil of a system. If the center of the better reference sphere is at a different lateral location than the expected image location, there is a “tilt error” in the wavefront If the center of the better reference sphere is at a different axial location than the expected image location, there is a “focus error” in the wavefront. It may be that a different reference sphere will fit the actual wavefront better. When calculating the wavefront error, the reference sphere is centered on the “expected” image location (usually the image surface location of the chief ray). The RMS value expresses statistical deviation from the perfect reference sphere, averaged over the entire wavefront. Here we will just say that the RMS wavefront error is given by a square root of the difference between the average of squared wavefront deviations minus the square of average wavefront deviation. We are not going to derive the equation to physically calculate the RMS wavefront error. Basically, we compare the real wavefront with a perfect spherical wavefront. RMS wavefront error is a way to measure wavefront aberration. 2 Measuring Wavefront errors in real systems
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