The “Reverse Elements” tool is intended to be used to reverse a single element or series of elements in an optical system. While it was not created for the purpose of reversing an entire optical system, by taking a few simple extra steps, it certainly can be adapted for this purpose.

To demonstrate how to reverse an entire optical system in ZEMAX, please download the attached sequential ZEMAX file on the last page of this article:

FILE:  “Reverse_Start.ZMX”

This is a typical Cooke triplet photographic objective system at infinite conjugates.

The first step you should take in reversing a system is to consider what system aperture definition to use in the reversed system. If possible, change the system aperture definition to “Float By Stop Size”. This definition is preferred as the same system aperture definition can then be used for the original and reversed systems. If this is not possible, you will need to consider how to translate your system aperture definition from image space to object space (i.e. swapping the entrance pupil diameter with the exit pupil diameter). In the case of this example, “Float By Stop Size” will work fine. This can be changed via the menu option, “System > General > Aperture”:

Next, it is a good idea to turn on Paraxial Ray Aiming. Even if the original system does not have pupil aberration, this may not be the case for the reversed system. Ray aiming can be turned on via the menu option, “System > General > Ray Aiming”. Go ahead and do this for this example:

More information about using Ray Aiming in ZEMAX can be found in the Knowledge Base article, How to use Ray Aiming.

So that the sizes of our optics do not change when we reverse the system, we will fix the Semi-Diameters of each surface. This is easily done by using the menu option, “Tools > Apertures > Convert Semi-Diameters to Circular Apertures”.

Before continuing, we also need to give consideration to how we will define the field points in the reversed system. In order to do this, you will need either the position or angle of incidence for the chief ray from each field point on the image surface in the original system. If the reversed system will be focal in object space, either the position or angle of incidence data could then be used to specify field points using either Angle or Object Height definitions. On the other hand, if the reversed system will be afocal in object space, the fields will need to be specified in terms of Angle using the chief ray angle of incidence data. The position and angle of incidence data can be determined from the Ray Trace calculation (menu option, “Analysis > Calculations > Ray Trace”). The position data can also be determined using the Spot Diagram analysis (using a chief ray reference).

In this example, the reversed system will be focal in object space so we can utilize the position of the chief ray for each field point on the image surface. Click on the “Spt” button in the button bar to open a Spot Diagram window. Then, make a note of the IMAge coordinates for each field point:

In this case, the image coordinates are 0, 12.419 and 18.137 mm. These will be used in the Object Height field point definition in the reversed system.

Next, reverse all of the optical surfaces in the system. This is easily done using the Reverse Elements tool (menu option, “Tools > Miscellaneous > Reverse Elements). When specifying the range of surfaces to reverse, include all surfaces except the Object surface and Image surface:

What needs to be done in the next step depends upon the nature of the original system:

Object Space	Image Space	How to convert thicknesses
Focal	Focal	Swap the Thickness of the Object surface with the Thickness of the surface prior to the Image surface
Afocal	Focal	Copy the Thickness of the surface prior to the Image surface to the Object surface
Focal	Afocal	Copy the Thickness of the Object surface to the surface prior to the Image surface; Set the Object Thickness to “Infinity”
Afocal	Afocal	No changes are necessary

In this example, the original system was afocal in object space and focal in image space, so, copy the Thickness from the surface before the Image surface to the Object surface:

We now have:

Next, we may need to change the “Afocal Image Space” check box in the Aperture tab of the General dialog. If the original system was afocal in image space, you should uncheck this box. On the other hand, if the original system was focal in image space (as is the case in this example), you should check the “Afocal Image Space” check box.

Likewise, we may need to change the “Telecentric Object Space” check box in the Aperture tab of the General dialog. If the original system was telecentric in image space, you should check this box. On the other hand, if the original system was not telecentric in image space (as is the case in this example), you should make sure this box is unchecked:

Lastly, we will need to convert our field definition as mentioned earlier. Since our original system was afocal in object space and focal in image space, we will use the original chief ray image coordinates to set the field points in the reversed system as Object Height:

If you now open a new layout window, you can see that the optical system has been successfully reversed:

While not its intended purpose, the “Reverse Elements” tool in ZEMAX is very useful for reversing an entire optical system. By utilizing this tool, along with a few other simple steps, an optical system can easily be reversed in ZEMAX.