Understanding Projection Lens Parameters

The Projection lens should be seen as a two-sided lens.

The Back face and Front face of the lens can have different shapes or types.

Construction settings

• Focal point: the focal point allows you to position the lens along the optical axis.
• Optical axis: line that corresponds to the light direction after passing through the lens.
• Back Focal Length: the back focal length corresponds to the distance between the focal point and the lens' back face.
• Refractive index: pure number that describes how light propagates through that medium. Most transparent materials have refractive indices between 1 and 2. Here the refractive index refers to the index of the lenses' material.
• Orientation axis (beta): The Orientation axis is used when a Face is defined as Zernike, to consider the polar coordinates for the Zernike coefficients.

• Thickness

  • Lens Thickness: size of the central part of the lens.
  • Edge Thickness: size of the lens from the back to the front face of the lens.

Face Types

Compatibility Table

The following table provides you with the compatibility between the Front and Back Face types.

	Plan	Aspherical	Automatic	Zernike
Plan
Aspherical
Automatic
Zernike

Plan

Defining a plan face allows you to create a plano-concave/convex lens.

• Aperture Diameter: diameter of the Front Face or Back Face of the lens.

• Aspherics: corresponds to the 29 aspherical coefficients that you can set to adjust the lens or remove the aberrations.

  Note: The index 1 is no longer present in the interface as it is always 0. Only edible coefficient are present.

The formula of the aspherical coefficients is with α_i the i^th aspherical value.

Aspheric

• Aperture Diameter: diameter of the Front Face or Back Face of the lens.
• Curvature: radius of curvature for the spherical part of the Front Face or Back Face of the lens.
• Conic Constant: conic constant of the lens.

• Aspherics: corresponds to the 29 aspherical coefficients that you can set to adjust the lens or remove the aberrations.

  Note: The index 1 is no longer present in the interface as it is always 0. Only edible coefficient are present.

	r: variable corresponding to the position on the lens k: conic constant R: radius of curvature αi: ith aspherical value

Automatic

• Aperture Diameter: diameter of the Front Face or Back Face of the lens.

• Refractive Index: refractive index of the lenses' material. This is a pure number that describes how light propagates through that medium. Most transparent materials have refractive indices between 1 and 2. The refractive index impacts how the face of the lens is constructed. Combined with the specified Focal point, and the specified Back Focal Length, it automatically adjusts the shape and curvature of the lens face.

  Note: This face type results in a lens without spherical aberration that focuses all rays of a collimated beam on the specified point regardless of whether they are paraxial or marginal. Accordingly, it perfectly collimates all the diverging rays originating from a point source.
• Fresnel mode

  • Constant step: creates grooves of the same length.

    Note: Only full grooves are built. If the last groove cannot be built, a flat face appears instead.
    
    
    

  • Constant height: creates grooves of the same height.

    Note: Only full grooves are built. If the last groove cannot be built, a flat face appears instead.
    
    
    
• Draft Angle: angle to respect to be able to remove the lens from the mold when the face is in Fresnel mode. The draft angle should be between 0° and 15°.

Zernike

• Aperture Diameter: diameter of the Front Face or Back Face of the lens.
• Curvature: radius of curvature for the spherical part of the Front Face or Back Face of the lens.
• Conic Constant: conic constant of the lens.
• Aspherics: corresponds to the 8 aspherical coefficients that you can set to adjust the lens or remove the aberrations.

• Zernike coefficients: correspond to the 28 first Zernike coefficients that you can set to adjust the lens or remove the aberrations.

  The Zernike coefficients are ordered according to the Noll convention.

  The angle φ is measured counter clockwise from the local +x axis.

  The radial coordinate is the normalized dimensionless parameter ρ.

  
  
  
  The formula of the zernike coefficients is with

  • r: variable corresponding to the position on the lens
  • k: conic constant
  • R: radius of curvature
  • α_i: i^th aspherical value
  • β_i: i^th zernike coefficient

Construction Type

Revolution

With the Revolution type, the Back Face and Front Face profiles are revolved around the optical axis to create a spherical lens by default or a Custom Revolution axis to create a toroidal lens.

Figure 1. Spherical lens (Optical axis as revolution axis)

Figure 2. Toroidal lens (Custom revolution axis)

Extrusion

With the Extrusion type, the Back Face and Front Face profiles are extruded along the extrusion axis to create a cylindrical lens.

Figure 3. Cylindrical lens