How to optimize at intermediate surfaces

This article demonstrates how to optimize at any intermediate surface or surfaces, using the default merit function tool and the IMSF operand.

Authored By Nam-Hyong Kim


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It may be the case that the optical system you want to model needs to be optimized at some intermediate surface, rather than at the image plane. A classic example is a scope system that takes an object at infinite distance, focuses the image, and then collimates that image for coupling with the eye. OpticStudio provides an optimization operand for this purpose: the IMSF operand. 

IMSF redefines the image surface within the Merit Function Editor so that image quality can be optimized at the preferred intermediate surface instead of at the true image plane. This article will discuss the use of and important considerations regarding the IMSF operand. 

The IMSF Operand

The Optimization Wizard, located in the in the Merit Function Editor, builds merit functions that are evaluated at the current image surface (i.e. the last surface in the Lens Data Editor). For example, the RMS spot size optimization function evaluates the spot size at the last surface and the RMS wavefront optimization function at the exit pupil of the current system with the last surface being the image.

The IMSF optimization operand allows the default merit function to be calculated at any surface in your system. In the included sample file, let's suppose that we want to optimize for minimum RMS spot at surface #3 while at the same time achieve best collimation at the image surface (#6). This can be done using the default merit function tool and the IMSF optimization operand. The variables in this system are the radii of curvature of surfaces #2 and #5 and the conic of surface #2.


If you are not familiar with optimizing with the default merit function, please refer to this Knowledgebase article.

To learn about the IMSF operand, open the attached sample file and follow the steps below.

Open the Optimization Wizard and build the default RMS spot radius merit function.

Default merit function

Insert an IMSF operand before the DMFS and specify surface #3 as the surface on which the default RMS spot radius merit function is calculated.

Merit function editor

Insert a blank line after the last operand (BLNK as operand #12). Insert a new RMS angular radius default merit function starting from line 12.


Insert another IMSF operand before the second DMFS and set the surface parameter to 6 the image surface.


This merit function will optimize for minimum RMS spot size at surface #3 and best collimation, i.e. minimum angular spot radius, at surface #6 (image).

Click Optimize...Optimize! and press Start. You should get the following result.


OpticStudio has optimized at two surfaces, with two different criteria, simultaneously. With multiple IMSF operands in the merit function, you can optimize at several intermediate surfaces at the same time with the same merit function, which can contain different criteria for each surface.

Considerations When Using the IMSF Operand

There are a few things of which to be careful when changing the image surface value. First, if the field type is either real or paraxial image height, the field type is changed to angle or object height for infinite or finite conjugate systems, respectively. The angles and heights used correspond to the primary wavelength chief ray angles and heights as computed for the unaltered system.

Secondly, imagine a system where you set the image surface to be prior to the currently defined stop surface. OpticStudio moves the stop surface to a (possibly virtual) dummy space prior to the existing surface 1. Unless the system aperture is set to Object Space NA or Cone Angle, the system aperture is changed to Entrance Pupil Diameter, and the aperture value is set equal to the original paraxial entrance pupil diameter computed for the original stop position. Note this assumption might not be valid for systems that require ray aiming.

An alternative method for computing system performance on multiple surfaces is to use multiple configurations. In the tool bar of the MC editor, click on Make Conjugate icon. This tool lets you re-define the object, stop and image surfaces, plus make any desired changes to system aperture, field definitions, use of ray-aiming etc that you need.


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