Measurement of Aberrations

As discussed in the previous section, aberrations are important characteristics of lenses and affect the overall performance of the optical system integrating the lenses. There are a few ways to measure the aberrations. First, if the geometric profiles of the lens and the materials of which the lens is made (refractive indices) are known, ray tracing can predict how the rays would be bent as they pass through the lens and thus calculate the aberrations. This essentially utilizes the definitions of the aberrations described above. To obtain a lens profile, mechanical profilometers [5,6] or white light interferometry [5,7] can be used. 

Chromatic aberration and plot of focal length versus wavelength. 

The second approach to measuring aberrations is by interferometry. The aberrations are, after all, essentially imperfections that appear when the lens focuses the incoming light and causes distortion in the output wavefront. Such deformation would be reflected from the interference patterns between the output wave and a reference wave (usually a plane wave). The measured interference patterns can be used in turn to determine the aberrations, usually using Zemike pol5momials [8-10]. 

Many types of interferometry can be used for this purpose. For instance, the Twyman-Green interferometer [11] is suitable for surface testing in reflection. The Mach-Zehnder interferometer permits lens testing in transmission [12]. The third interferometric technique utilizes a Shack-Hartmann wave-front sensor [10,13,14]. This method can be applied to both reflection and transmission. Interestingly, the Shack-Hartmaim sensor utilizes a microlens array in front of a CCD imager array to create a series of focal spots that are recorded by the CCD imager to obtain the wavefront. 

---