There are a few different definitions for a direction in OpticStudio. It might be good to discuss them in one place.
Note we won’t repeat the information that is already mentioned in Rotation Matrix and Tilt About X/Y/Z in OpticStudio – Knowledgebase. It’s suggested to also reference to this place.
Unit vector
We use (L,M,N) to represent the unit vector of a ray, which is, in other words, the direction cosines of the ray.
Direction cosine space (L,M)
This is simply the first two elements of the unit vector. It’s sufficient for describing a ray because N can always be restored by the rule L^2+M^2+N^2 = 1. Note in this space we don’t distinguish rays between -z and +z directions because the N is always positive.
Spherical coordinate (θ, ϕ)
This is the standard spherical coordinate, where we ignore the radial dimension as we only need to describe the angle. It’s not exactly used in any analysis in OpticStudio, but we can still find it somewhere. For example, the RAID is basically the absolute value of θ. The Maximum Field shown in Field Data Editor, when the Field Type is Angle, is also the θ.
Field Angle in sequential mode (αx, αy)
This is mainly used in Field Data Editor for defining the angle of a field.
At first, it might look weird , but there are some benefits. For example, imagine we have an object plane at finite space with half width X and Y, and its distance from entrance pupil is Z. If we send a ray from object point (0, Y) to the center of entrance pupil, the ray angle on YZ plane is atan(Y/Z). Similarly, the angle in XZ plane is atan(X/Z) for object point (X,0). Now if we want to define the angle for corner object point (X,Y), the corresponding angle settings is straight forward: (atan(X/Z), atan(Y/Z)). In other words, this angle definition has a good similarity when you want to match your angle definition to an object point, even if the object is virtual and at infinity. It’s often the case, we need to define the field for finite or infinite rectangular object plane and this is where this definition can be useful. Note this coordinate is similar to Cosine Space, that we cannot distinguish directions at -z and +z sides. When the absolute value of αx or αy is larger than 90 degrees, we need to handle it differently. See Help File for more information.
Detector intensity (luminous intensity) view (θx, θy)
The good point of this definition is the distance of any point to the origin on this coordinate is exactly the angle θ. And the rotation angle from +x axis is exactly same as the definition of spherical coordinate ϕ. From this coordinate, it’s easier to imagine the direction at any given point. Note this coordinate is similar to Field Angle or Cosine Space, that we cannot distinguish directions at -z and +z sides.
Theodolite angle (Azimuthal, Elevation)
Note this is different to spherical coordinate. If we only use its “Azimuthal” angle, it’s equivalent to the θ in Spherical coordinate. However, if you further add “Elevation” angle, it’s not equivalent to the ϕ in Spherical coordinate.
The mathematical way to understand how this works in Zemax OpticStudio is described as below.
1. When both are zero, the direction points to exactly +z.
2. When one or both are non-zero, we first handle Azimuthal angle and then handle Elevation angle.
* First rotate around Y axis by Azimuthal angle. We get new z axis and new x axis.
* Second rotate around new X axis by negative Elevation angle.
3. The above method is called intrinsic rotation because we use the new axis. It’s equivalent to extrinsic rotation with inversed order, as below.
* First rotate around X axis by Azimuthal angle. We get new z axis and new x axis but don’t use them.
* Second rotate around old Y axis by Elevation angle.
In contrast, in the same, the spherical coordinate can be considered as one of the following rotation
1. Extrinsic rotation: X (theta), Z (phi)
2. Intrinsic rotation: Z (phi), X (theta)
FAQ about Max Field and Normalized by in Field Data Editor
In Field Data Editor, when the Field Type is Angle, we show Max Field and Normalized by in the dialog as below.
The Normalized by represents the distance of the point to the origin in Field Angle space, which means it’s calculated as sqrt(αx^2 + αy^2), while the Max field is the θ, which is the Spherical coordinate.
