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How to Work in Global Coordinates in a Sequential Optical System
- By Mark Nicholson
- Published 22 June 2007
- 3D Geometries
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The Starting Design
Let's start by designing an optical system complex enough to be worthwhile for this kind of work, but simple enough to clearly demonstrate the principles. The last page of this article has a link to a zip file that contains the starting point of the design we will work on: single_prism.zmx:
Before proceeding, it is worth spending some time looking at how this file is set up.
Collimated light enters the system at surface 1. Surface 2 is a flat surface, with a rectangular aperture on it:
This surface is also tilted by 15 degrees with respect to the coordinate system established by surface 1. After the surface, we 'untilt' by -15 degrees so that subsequent surfaces lie in the original coordinate system:
In the jargon of 3-dimensional geometry, we have 'restored the original coordinate system'. Surface 3 is also tilted, this time by -15 degrees:
Another very useful control in setting up 3-D geometries is the ability to draw the local axis of each surface in the system. This is turned on surface-by-surface using the control in the Draw tab:
With this turned on for every surface, the 3-D layout shows:
Surface 1 (drawn in red) is the Global Coordinate Reference Surface and defines the starting coordinate system of the system. The arrow protruding from the surface is its local z, the red line moving straight up the page is its local y, and the local x is pointing into the screen and cannot be seen.
Surface 2 shows its +15 degree x-tilt, and surface 3 shows its -15 degree tilt.
Next, notice that surface 4 is a coordinate break surface, and scrolling the editor to look at the decenter x, y and tilt x, y parameters. Note that these are all controlled by chief-ray-follow solves:
Chief-ray-follow solves decenter of tilt the coordinate system such that the coordinate system is normal to and centered on the chief ray. Basically, it ensures that the following surface is centered on the optical beam:
This shows one of the key advantages of the local coordinate system. Because the local coordinate system 'follows the surfaces' it is easy to change on a surface-by-surface basis as the light propagates through the system. ZEMAX contains many ray-based solves to enforce common requirements, and ZPL-macro based solves can also be defined for more specific requirements.
However, we will now go on to extend this sample file in a way in which the local coordinate system is not so helpful, and see how to switch easily between local and global coordinate systems.
Before proceeding, it is worth spending some time looking at how this file is set up.
Collimated light enters the system at surface 1. Surface 2 is a flat surface, with a rectangular aperture on it:
This surface is also tilted by 15 degrees with respect to the coordinate system established by surface 1. After the surface, we 'untilt' by -15 degrees so that subsequent surfaces lie in the original coordinate system:
In the jargon of 3-dimensional geometry, we have 'restored the original coordinate system'. Surface 3 is also tilted, this time by -15 degrees:
Another very useful control in setting up 3-D geometries is the ability to draw the local axis of each surface in the system. This is turned on surface-by-surface using the control in the Draw tab:
With this turned on for every surface, the 3-D layout shows:
Surface 1 (drawn in red) is the Global Coordinate Reference Surface and defines the starting coordinate system of the system. The arrow protruding from the surface is its local z, the red line moving straight up the page is its local y, and the local x is pointing into the screen and cannot be seen.
Surface 2 shows its +15 degree x-tilt, and surface 3 shows its -15 degree tilt.
Next, notice that surface 4 is a coordinate break surface, and scrolling the editor to look at the decenter x, y and tilt x, y parameters. Note that these are all controlled by chief-ray-follow solves:
Chief-ray-follow solves decenter of tilt the coordinate system such that the coordinate system is normal to and centered on the chief ray. Basically, it ensures that the following surface is centered on the optical beam:
This shows one of the key advantages of the local coordinate system. Because the local coordinate system 'follows the surfaces' it is easy to change on a surface-by-surface basis as the light propagates through the system. ZEMAX contains many ray-based solves to enforce common requirements, and ZPL-macro based solves can also be defined for more specific requirements.
However, we will now go on to extend this sample file in a way in which the local coordinate system is not so helpful, and see how to switch easily between local and global coordinate systems.