Reverse Engineering Lens Elements

Introduction

• Need for reverse engineering
• Properties necessary for reverse engineering
• How to make necessary measurements
• How to calculate the paraxial properties
• Use of a spreadsheet for the solution
• Use of a lens design program to find a solution

Need for reverse engineering

• Actually want to copy someone’s design
• Concern that lens may be wrong glass
• Lenses got mixed up, need to sort out
• Lens system does not work – right elements?

Properties needed to reverse engineer

• Just looking for paraxial properties
  • These are the properties on an optical drawing
• Two radii
• Glass type or index at the measurement wavelength
• Center thickness
  • Could measure physically, but may not want to, or can’t

Measurements needed

• Radius of curvature but may not have working distance – reverse lens so backside concave
• Optical center thickness to rear vertex
• Back focal length from one or both sides
• Need at least 4 measurements to solve for 4
  unknowns
• Extra measurements increase confidence

Measurements that can be made

Center thickness

Rear Radius

Back focal length

No closed form solution for unknowns

• Use spreadsheet
  • Find difference between measured & guessed values
  • Square differences and sum
  • Make sum zero by varying unknowns
• Use a lens design program
  • Model the various measurement configurations
  • Use multi-configuration option
  • Use plane surfaces, guess thickness and a model for index
  • Use optimizer to find solution

Spreadsheet example

N, t and r₂ were estimated and a, b and c calculated

Solver used to minimize lower right hand cell to give calculated n, t and r₂ shown above.

Lens design example

Configuration 1 shown for calculation of bfl

Grayed out lines are ignored

Lens design example con’t 1

Configurations 1, 2 and 3 are looking thru short radius first
Configurations 4,5 and 6 are looking thru long radius first
Line 2 shows what the measurements should be knowing the index, thickness and two radii

Lens design example con’t 2

Lens design example con’t 3

Radii, thickness and index are set as variables

Optimized with small entrance pupil for paraxial solution

Conclusions

• Use all practical conjugate measurements in model
• Works with interferometer or autostigmatic microscope
• Works for doublets as well as singlets
  • Can usually see cement interface
  • Often better reflection than AR coated surfaces
  • Just a more complicated lens design model
• Need to know surfaces from centers of curvature
• Remember to stop down model before optimization
  • Model must find first order solution
• All in all, pretty easy to do