Basic Lens Design of a Cooke Triplet

In OPT242: Aberration Theory, our final project was designing a Cooke Triplet for imaging infinite conjugate objects. The project began with a thin lens design, followed by a thick lens design using the thin lens design as a starting point. Finally, we wrote up a metrology plan for testing some key characteristics of the lens system.

The Thin Lens Design

The design process began by devising formulas, based on the power and shape factors of the lenses relative to one another, that would set certain aberration values to predetermined goal values(Petzval Curvature, Lateral Color, Astigmatism, Coma). This information was then put into a thin lens design, taking care to keep the marginal and chief rays and the EFL consistent to their goal values. Other aberrations were solved for along by the way by altering various system features that were either not being used to set other aberrations or that were themselves the principle variable in setting other aberrations (Spherical, Transverse Color).

The final step was to check for % Distortion, as that was not an aberration we set a specific goal for. If it was not within specification, I had to go back and alter the relationship between the powers of the first and third lens and reoptimize the system for the other aberrations that I had already corrected.

This entire process was completed using a Microsoft Excel Brick diagram and the Microsoft Excel Goal Seek and Solver features.

The Thick Lens Design

The thick lens design began with determining the relationship between the powers of the surfaces of a lens, the shape factor of the lens and the total power of the lens. This was used to set up a traditional brick diagram (with discrete surfaces). For the initial state of the brick diagram, the powers and shape factors of the lenses were left as variables and the initial lens center thicknesses were set to 0.001 of their goals.

To calculate these goal center thicknesses, we used the information about the radii of the lens and the radii of curvature of the lenses to calculate the sag of the surfaces of the lens. By setting a goal edge thickness for the lenses, I was able to use the formula

where t is the center thickness and the z's are the sags of the surfaces of the lens to graphically solve for the center thickness.

Next in the process was to use the Excel Solver tool to vary the lens powers, shape factors, and air gap thicknesses in order to minimize the aberration errors. I then gradually increased the thickness of the lenses, using the Solver in the same fashion, until the lenses were at their ideals thicknesses and the system was aberration-free.

The last part of the thick lens design was to ensure that the distortion was within specification again.

Metrology Plan

We were then asked to put together a testing plan for measuring several key characteristics of the lens system including:

• EFL and BFL

• On-Axis Aberrations

• Aberrations at the edge of the FOV

• Field Curvature

• Distortion

Given these instruments:

• A travelling microscope- rail assembly with an illuminator

• A nodal slide with collimator, Tee-bar and viewing microscope

• A 4” phase-shifting Fizeau interferometer with the following accessories:

  • Transmission Flat

  • Transmission Spheres

  • Convergers and Divergers

  • Reference Flat

  • Reference Sphere (25-mm concave ROC)

• A 1-meter square grid target with high-quality digital camera and image processing software.

If you are interested in seeing a copy of the full report document, feel free to contact me.