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 r_{2} were estimated and a, b and c calculated

Solver used to minimize lower right hand cell to give calculated n, t and r_{2} 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