Ray Transfer Matrices allow representing multiple optical elements with a single matrix. This technique uses the paraxial approximation, which means rays are assumed to be at a small angle and a small offset from the optical axis. See general introduction to Ray Transfer Matrices on Wikipedia.
RayLab offers three analysis modes for computing Ray Transfer Matrices. These can be selected from the main model options menu.
All three modes use a reference ray leaving the object in order to determine the order in which optical surfaces are encountered. RayLab then computes the Ray Transfer Matrix by combining the RTMs for the encountered surfaces, as well as the RTMs representing their distances.
The 3 different analysis modes are as follows:
- Basic Axial Analysis: This approach uses a 2×2 matrix. It assumes all elements are on the z axis. Any tilt or decenter is ignored. Only the z coordinate of the surface vertices are used. This is the technique in most introductory descriptions of Ray Transfer Matrix analysis.
- Axial Analysis with Tilt/Decenter: This approach uses a 3×3 matrix. In addition to the usual ABCD elements, two additional elements, E and F, are used to account for tilt and decenter of the optical surfaces. The technique is valid for nearly axial systems with small tilt or decenter relative to the z axis.
- Analysis Relative to Reference Ray: This approach uses a 2×2 matrix as well. However, unlike the basic approach, ray offsets and angles are measured relative to the reference ray. This requires more sophisticated calculations for each surface to account for change in coordinate system. The technique is valid for analyzing a narrow pencil of rays which are close to the reference ray, even for non axial systems.
When performing Ray Transfer Matrix analysis, RayLab generates a report of all relevant matrices. It also uses the information to compute the cardinal points and surfaces for the system, and displays them in the main window.