There are certainly limits as to how well a singlet can perform, but ZEMAX can still be used to find a better solution than the one which currently exists.  In doing so, it is important to first determine how many degrees of freedom the current design has.  That is, how many parameters are free to adjust?  For the singlet in this exercise, one of the parameters (the Radius on Surface 2), can no longer be considered a freely varying parameter since it is controlled by a solve to meet a specific design constraint.  However, the center thickness of the lens (the Thickness on Surface 1), the radius of curvature of the front surface (Radius on Surface 1), and the distance from the back of the lens to the image plane (the Thickness on Surface 2) can all be varied in attempt to minimize the RMS spot radius of the singlet.

To allow ZEMAX to consider a parameter as a degree of freedom during optimization, a Variable solve type must be placed on the cell in the LDE which represents that parameter.  You may set the solve type by right-mouse-clicking on the desired cell or by highlighting the appropriate cell and pressing Ctrl+Z on the keyboard.  In the solve dialog which appears, select Variable as the "Solve Type" and press "OK."  The letter “V” next to the parameter is indicative of a variable in place.  Place a variable solve on all three of the parameters which are free to vary during optimization:

Once the variables are set, we can now construct the Default Merit Function.  The merit function is constructed in a completely separate editor from the LDE, called the Merit Function Editor (MFE).  Open the MFE by selecting Editors > Merit Function from the main menu in ZEMAX.

The merit function is a numerical representation of how closely an optical system meets a specified set of goals.  From within the MFE,  ZEMAX uses a list of operands which individually represent different constraints or goals for the system. Once the Merit Function is complete, the optimization algorithm in ZEMAX will attempt to make the value of the merit function as small as possible.

Although it is possible to construct a merit function by hand, it is much easier to have ZEMAX construct one for you.  A default merit function can be constructed by selecting Tools > Default Merit Function from the menu bar in the MFE.



Upon selecting this option, the Default Merit Function dialog will appear, from which various options may be selected for defining the default merit function.  Each of the options available in this dialog is discussed in detail in Chapter 14 of the ZEMAX User’s Guide. 

For the current exercise, the singlet is to be optimized for RMS Spot Radius with respect to the centroid, all of which are options already built-in to ZEMAX’s default merit function capabilities.  Select RMS, Spot Radius, and Centroid under the Optimization Function and Reference portion of the Default Merit Function dialog.

To prevent the singlet from becoming too thick or to thin, it is important that we set boundary constraints on the thickness of this element.  The default merit function has options to set boundary constraints on both glass and air thicknesses.  By checking the “Glass” option, minimum, maximum, and edge thickness values can be manually typed into the appropriate entries. 

As was described in the system requirements, the singlet center thickness shall be no larger than 12mm, no smaller than 2mm, and shall have an edge thickness greater than 2mm.  Type the appropriate values into the Default Merit Function dialog for the "Min", "Max", and "Edge" glass thickness entries.

Other than the selection of the appropriate Optimization Function and Reference and the Thickness Boundary Values modification, all other parameters may be left as the default for the purposes of this exercise.

Click "OK" to close the dialog.