In Zemax OpticStudio, a toroidal lens can be simulated to model an optical surface that has different curvatures in two orthogonal directions. This type of lens is useful for applications like astigmatism correction and beam shaping, where separate focal lengths along the X and Y axes are required.
Creating a toroidal lens in Zemax can be in the steps. First start with a standard lens surface in Lens Data Editor with suitable lens material. Then apply a toroidal surface, which allows us to specify different curvatures along the x and y directions. Next input different values for the curvatures X and Y parameters in the Surface Properties window. These curvatures correspond to the radii of curvature in the X and Y directions. By adjusting these values independently, the toroidal effect is created.
A toroidal lens consists of lens with possibly aspheric toroidal surfaces on the front and back faces. A toroidal surface is defined by a curve in the YZ plane which is then rotated about an axis parallel to the Y axis but displaced by a distance R. The radius of rotation. Where c is the reciprocal of the radius of curvature in YZ plane, the curve in the YZ plane is defined by the equation below.
In an imaging system, a toroidal lens can be defined as a nonsequential component with mixed mode of OpticStudio, which is a sequential system that contains non-sequential objects. To perform a ray trace through such a system, entry and exit ports must be used to define the beginning and the end of the NSC group. Details can be found in this knowledgebase article.
The toroidal lens is defined by the parameters below. Data from “Rotation” to “Conic1” are the radius of rotation, front surface radius of curvature, and conic for the front surface. Data from “Coeff1 y^2” to “Coeff1 y^12” are coefficients on the powers of y for the front surface.
Data from “Rotation R2” to “Conic2” are the radius of rotation, back surface radius of curvature, and conic for the back surface. Data from “Coeff2 y^2” to “Coeff2 y^12” are coefficients on the powers of y for the back surface.
With lens defined in the Lens Data Editor below,
as well as the appropriate exit location of the toroidal surface,
The location of the toroidal lens is fully defined in a sequential model. With the field definition of incident angel at Y = 0 and Y = 5, the two fields are colored in blue and green individually.
At the image plane, the spot diagram of both fields at focus points presented below, with the image surface 50 mm away from the cylindrical lens. The geometrical length horizontal direction is ~260 um and ~250 um at both fields. At vertical direction, the RMS size is about 0.36 um in radius at 0 field, 5.6 um at 5-degree field.
The spot information reveals size distribution in both directions and both fields. The maximum spot radius reveals the longest dimension in radius (half of the length of the image bar) of the spot.
From MTF below, it is seen that in the one direction (sagittal) drops much faster than the other (tangential). When the focal spot presents sharper resolution in one direction compared to the other, MTF can present a much different trend. This presents the image resolution deviations in the two directions.