Optical systems often have strict requirements on wavefront errors (WFE). An example of wavefront correction is shown here.

Curved mirrors are used in a variety of different types of optical systems, from pupil relays in Adaptive Optical (AO) systems to complex telescopes to laser resonators to pointing-and-tracking systems. A very simple embodiment of a multiple-image pupil relay mirror system is shown in the figure below.

This type of optical layout, in which a collimated beam is incident at an angle on a spherical mirror, has inherent astigmatism. The plot below shows the Wavefront Error (WFE) of this system.

A quick check of the wavefront’s Zernike decomposition shows that astigmatism (represented by the coefficients z5 and z6 in the figure below) is indeed the worst offender.

For many optical systems, this level of wavefront error is simply unacceptable. To correct this inherent astigmatism, we adjust the up-down angle of incidence of each mirror. The animated figures below show the imaging relay system before and after making such an “up-down angle” correction.

The wavefront map for the imaging relay system after “up-down angle” correction is shown below.

The Zernike decomposition of this new, improved wavefront shows that astigmatism (represented by the coefficients z5 and z6 in the figure below) is, for all practical intents and purposes, completely eliminated.

In practice, the spherical mirrors are never perfect. In order to take into account all the sources of wavefront error in a system, interferometric measurements of the mirrors must be made. We put phase maps, obtained from interferometric measurements of the individual mirror surfaces, into the ZEMAX model.

The wavefront map and Zernike decomposition of the wavefront for this “as-measured” imaging relay system are shown below.

The wavefront map shows over one-half wave of RMS WFE. The Zernike decomposition clearly shows that the wavefront error is dominated by spherical aberration (represented by the coefficient z9). To correct this spherical aberration, we designed an aspheric corrector plate (much like a Schmidt corrector plate in a Schmidt-Cassegrain telescope) to be inserted into the optical system at the exit pupil. With this aspheric corrector plate in place, the system’s wavefront is now fully corrected. The wavefront map and Zernike decomposition of the wavefront for this fully-corrected pupil relay system are shown below.

The wavefront map shows that the RMS WFE has been reduced to less than one-twentieth wave. The Zernike decomposition clearly shows that spherical aberration (represented by the coefficient z9) is now practically eliminated.

Wavefront error in this multiple-image pupil relay optical system has been drastically reduced by using a combination of “up-down angle” correction and introduction of an aspheric corrector plate.

 

SUMMARY

We solved a wavefront error problem for our client using a very simple wavefront correction method, saving them tens of thousands of dollars compared to alternative wavefront correction methods. Contact us to learn more about how Contrast Optical can solve your optical design problems.