Wavefront Detection

For assessment of the light field's phase distribution apart from mere beam profiling, camera based wavefront sensors according to the Hartmann-Shack principle are being utilized. The determination of (interpolated) beam profile, wavefront and beam parameters such as diameter, divergence and M² value for coherent radiation enables a complete description of the propagation behavior (cf. Figure 1) via solution of the Fresnel diffraction integral. Thus, the intensity distribution e.g. in far field or at the beam waist may be calculated.
The derivation of these values from a single measurement with an accuracy of a few percent makes the device especially suitable for pulsed or strongly fluctuating laser sources.

The wavefront sensor is available as a commercial product, distributed by LOT-Oriel for the European market (USA: Lightspeed Technologies), that is already applied by several companies and institutes.

: Figure 1: Propagation behavior of an aberrated HeNe-laser. The picture shows the comparison between measured sites (above) and calculated intensity distributions (below) in the range of the beam waist.

A sketch of the principle setup of a Hartmann-Shack sensor is depicted in Figure 2. The incoming light field is divided into a number of sub-apertures by a microlens array. From the deviation of the spot pattern from a reference measurement the local direction angles can be derived which allows the reconstruction of the wavefront. In addition the intensity distribution of the light field within the detector plane can be obtained by integration and interpolation between the microfoci.

For near circular beam profiles a modal expansion into a series of Zernike polynomials is favorable since the corresponding coefficient are directly related to Seidel's aberration theory. Consequently Hartmann-Shack sensors may be utilized for evaluation of beam aberrations in strict analogy to quality assessment of optical components.

: Figure 2: Left - Principle of Hartmann-Shack wavefront sensors (red: wavefront, blue: microlens array, black: CCD-Chip, profile: integrated intensity distribution); Right - relevant data within each subaperture: focal length f, local deviation in x- and y-coordinates of center of gravity with respect to reference measurement [(xc-xr),(yc-yr)] and resulting local direction angle β.

Further reading:

Flyer: Wavefront sensor