Reverse Engineering Lens Elements


  • 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
  • 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


  • 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
Worldwide Representatives


Armstrong Optical
+44(0) 1604 654220

All Asian Countries

清 原 耕 輔   Kosuke Kiyohara
清原光学 営業部   Kiyohara Optics / Sales

Kiyohara Optics Inc.
3-28-10 Funado Itabashi-Ku Tokyo, Japan 174-0041

Australia & New Zealand

Mersenne Optical Consulting

Optical Perspectives Group, LLC

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