How to limit the relation between thickness and radius to make sure the lens is realistic


I want to check how should we limit the diameter-to-radius ratio in Zemax? I’m using MNCG and MXCG to limit the thickness of the lens. However, during the optimization process, the lens radius can be negative and the absolute value is larger than the lens thickness which make these lens not real. Could we use some operand to avoid the situation? I’m trying to find the operand to get the radius and limit the thickness according to the radius but failed to find the operand. Do we have other operand to do that?


3 replies

Userlevel 6
Badge +2

Hi nicolexi,


There’s a series of operands for the Radius cells, and those are:

  • CVVA: Curvature value (radius of curvature)
  • CVLT: Curvature less than
  • CVGT: Curvature greater than

Then, there are the Maths operands that you can use to make computation between operands. You find those in the Help File (F1) under: The Optimize Tab (sequential ui mode) > Automatic Optimization Group > Merit Function Editor (automatic optimization group) > Optimization Operands by Category > General Math Operands. For example, DIVI gives the ratio of two operands, and PROD gives the product of two operands. In the problem you describe, I’m guessing you don’t find the lens realistic because its radius comes close to the thickness and therefore the lens almost takes the shape of a half ball, is that right? In this case, you want to the radius to be large in comparison to the thickness. The radius is the inverse of the curvature so you’d want to decrease the value of the product of CVVA and CTVA (center thickness value). I made a very dummy example for you (also attached to my reply):

I’ve made two configurations with the curvature of the lens as the only parameter. In addition to a default merit function, I’ve added the product of CCVA and CTVA and I’ve constrained the product (PROD) with OPLT (operand lesser than). In configuration one, the weight of OPLT is zero, or in other words it isn’t taken into account. In configuration two, I’ve made the weight of OPLT 100.0. After optimization, the curvature of the second configuration gets flatter but the performance is also degraded in this over simplistic scenario.

I just thought about PROD as a quick demo but you can compute any metric you like really.

Let me know if this helps and take care,



Userlevel 7
Badge +3

If your surfaces are spherical, controlling edge and center thicknesses should be all you need: there are no other extrema.

If you have aspheric surfaces, use FTGT/LT. This is full thickness greater/less than, and controls the thickness at (I think) 200 points across the aperture

  • Mark
Userlevel 6
Badge +2

Also, if you have a professional or premium licence, there’s the Optimization Goal: Improve Manufacturing Yield option in the Merit Function Wizard that you could try. Although, I’ve never actually used it myself.

Take care,