Developed by Optocraft, a member of the Micro-Epsilon group of companies, SHSLab Shack-Hartmann wavefront sensors (WFSs) are used for applications such as optics alignment, optics testing and laser beam characterisation. Wavefront sensors are used in optics, laser, astronomy and space R&D and production applications, as well as in the manufacture of various lenses, including contact and intraocular, camera and microscope lenses.
A typical application is for the alignment of optical systems, where wavefront guiding facilitates and speeds up the alignment process significantly. The following application describes the alignment of a collimation lens in front of a light source and the setup of a Kepler telescope. The discussed principle can be applied to many alignment applications.
In the test setup, a fibre-coupled LED emitting at 625 nm is used. In the first step, the fibre end and an SHSLab WFS are mounted on a rail on an optical table, as shown in figure 1. The WFS detects the spherical wave emitted by the fibre. In this situation, the wavefront curvature radius measured by the WFS is equal to the distance between the fibre end and the microlens plane of the WFS. This means it can be used to align the correct axial position of the fibre end.
Figure 1
A collimating lens is then placed (focal length ƒ=60 mm) in front of the fibre, as shown in figure 2.
Figure 2
First, the lens is aligned in the lateral direction by minimising the wavefront tilt α, which is directly related to the lateral misalignment Δx between the lens and the fibre end: Δx = ƒ . tan α. Next, the lens is aligned in the axial direction by minimising the spherical power of the wavefront (resp. wavefront defocus). The spherical power Dsp is directly related to the axial misalignment:
Next, using a relatively simple centering stage for X, Y alignment of the collimating lens, the tilt can be reduced to 0.007 mrad, as shown in figure 3. By displacing the lens along the rail in the Z-direction, the beam can be collimated and a wavefront curvature radius of Rwf ≥ 110m can be achieved (the achievable collimation is limited by the mechanical components of the setup, not by WFS measurement precision).
Figure 3
Now, a Kepler telescope can be set up, which consists of two lenses with 40 mm focal length. The first lens is mounted 40 mm in front of the WFS, and the second lens is initially mounted 80 mm in front of the first lens. In this roughly pre-aligned state, the wavefront shows a tilt of 0.5 mrad and a curvature radius of 0.85 m. Aligning the second lens of the Kepler telescope in the lateral and axial directions, again tilt is minimised and spherical power of the wavefront is transmitted through the telescope. In this way, the Kepler telescope can be quickly set up and precisely aligned to an afocal configuration. If tilt and defocus resulting from residual misalignments are subtracted, it is found that the setup consisting of collimating lens and Kepler telescope has a corrected wavefront rms of 0.027 µm (on 5 mm pupil diameter). This corresponds to a Strehl ratio of 0.92, i.e., the setup is well diffraction limited.
Sensitivity of alignment signal
In the aforementioned scenario, where the light emitted by the fibre is collimated by the collimating lens, the sensitivity of the wavefront tilt and refractive power need to be considered. To assess stability, the wavefront data is continuously recorded for five minutes, and the standard deviation of the temporal signals are calculated:σTilt=0.2 µrad; σD=0.06 mdpt, as shown in figure 4. Using the above noted relations between lateral displacement and tilt, and between axial displacement and curvature radius, these numbers translate into a theoretical sensitivity of the focus position measurement of ca. 12 nm in the lateral direction and ca. 220 nm in the axial direction (for a focal length of ƒ=60 mm of the collimation lens).
Figure 4
Phase plate and spatial filtering
In the second stage of the experiment, a phase plate (optical window with certain surface aberrations) is placed as a test object in the object plane of the telescope, as shown in figure 5. The WFS now detects the aberrations of the collimating lens, the Kepler telescope and the phase plate.
Figure 5
By recording a reference measurement of the system without the phase plate first, the aberrations of the system (spot reference) can be subtracted to obtain the wavefront that carries only the aberrations of the phase plate.
Many applications make use of spatial filtering methods to reduce wave aberrations. To demonstrate the effect of spatial filtering on the transmitted wavefront, a pinhole with 100 µm diameter can be inserted at the Fourier plane of the Kepler telescope, thereby low-pass filtering the wave generated by the phase plate (the pinhole must be aligned in the X-, Y- and Z-axis by minimising wavefront rms). The effect of this pinhole is small; the corrected wavefront rms decreases from 0.1 µm to 0.09 µm. So, the 100 µm pinhole is replaced by a 50 µm pinhole. The corrected wavefront rms distinctly decreases to 0.06 µm. When replacing the 50 µm pinhole with a 30 µm pinhole, the corrected wavefront rms decreases further to 0.02 µm. The point spread functions (PSFs) shown in figure 6 are calculated from the corrected wavefront with an added refractive power representing the effect of the telescope lens with 40 mm focal length.
Figure 6
Optocraft’s WFSs are distinguished by their high-speed, single-shot measurements, excellent unreferenced accuracy, extreme dynamics and broad spectral ranges. They are capable of measuring wavefronts with very strong, higher order aberrations. Moreover, they can measure large tilt angles and strongly defocused beams.
Micro-Epsilon
Optocraft