ZEMAX Development Corporation thanks Mr. Robert E. Fischer of Optics 1 for the permission to use the graphics from his book Optical System Design, and also for providing us the original graphic files.

Many surfaces in ZEMAX can have diffractive power in addition to refractive power. Diffractive power is independent of the index and the surface sag and changes the phase of the rays.  For more information on how diffractive surfaces are modeled in ZEMAX, please refer to the article "How Diffractive Surfaces are Modeled in ZEMAX."

The diffractive power in a Binary 2 surface introduces continuous phase change across the surface according to the following formula:


 where the coefficients A_i are in units of radians.

Since the phase change is continuous across the surface, a Binary 2 surface represents an ideal binary diffractive optical element, in which the size of the binary (discrete) steps are infinitesimally small or at least very small compared to the wavelength.

Generally, the physical DOE modeled by the Binary 2 surface will have diffractive zones with varying period as a function of radial distance from the vertex, as shown in the following diagram. ZEMAX can calculate the radial coordinates of each diffraction zone, where the phase differs exactly by 2p from adjacent zones.

Figure 13.5 from Optical System Design


The amount of phase in waves added by a Binary 2 surface at a particular radial coordinate is independent of wavelength. The wavelength-dependent optical path length (OPL) is given by

OPL = (Phase*wavelength)/ (2p)

The following layout shows the chromatic effect due to a Binary 2 surface.



 

The Binary 2 surface is often used for achromatization. Consider a simple singlet lens in which the longer wavelength focuses at a larger Z distance from the lens than the short wavelength. A rotationally symmetric DOE such as Binary 2 surface can be used to minimize the longitudinal color.

Figure 13.13 of Optical System Design

Let's go through the process of designing the Binary 2 optics in the above figure. If you are not familiar with any of the steps in the exercise, please refer to the article Designing a Singlet in ZEMAX.

We will design a DOE using the Binary 2 surface with diffraction order m=1 to correct longitudinal color. The completed design can be downloaded from the last page of this article.

Set the system length units to mm (System > General > Units)
Set the system aperture as Entrance Pupil Diameter of 30 mm (System > General > Aperture)
Set the wavelength to F, d and C. (System > Wavelengths); select "F,d,C" from the drop-down menu in the Wavelength Data window.
Set one field with values X=0 and Y=0 (System > Fields)

Set surfaces in the LDE with following parameters.




The 3D layout shows the singlet.

Optimize the system for best focus using the RMS Spot Radius default merit function.

After optimization the variable in the editor, the thickness of surface #2, will be close to 51.608 mm.

The longitudinal aberration plot under Unalysis>Miscellaneous>Longitudinal Color shows significant amount of longitudinal color abberation.

We will now add some diffractive power to the Binary 2 surface.

Open the Extra Data Editor and set the following parameter values and set the coefficients of r^2 and r^4 as variables..



Re-optimize the system.

Notice that the longitudinal color is now much smaller than before.

 

Now that we have the coefficients for the Binary 2 surface and know the phase profile, we need to calculate the radial coordinates of each 2*m*p diffraction zones to be used for the fabrication. The phase at each diffraction zones will differ exactly by +2*p or -2*p radian from the adjacent zones as shown in figure 13.3 (a).

Run the macro “Phases.zpl” and specify surface #2 when prompted.

The result shows that there are 246 zones with the last zone being at 14.94 mm from the vertex of the surface.



The diagram below illustrates several different possibilities for the DOE surface profile.


Figure 13.9 from Optical System Design

This article has demonstrated the basic use of Binary 2 surface. In summary:

• ZEMAX can calculate the 2mp diffractive zone coordinates for the Binary 2 surface 
• Achromatization using the binary 2 surface has been demonstrated using an example.
  

References

1. Optical System Design by Robert E Fischer / Biljana Tadic-Galeb

2. ZEMAX user manual