Wavefront sensors: the ultimate optical diagnostic tool?

Characterizing a laser beam is a growing concern in the industry. A great number of instruments are available on the market, each with their specialities. When it comes to analysing the spatial behaviour of a laser beam, the most common solution is the beam profiler. However another solution starts to be affordable and user-friendly enough to be seriously considered by anyone who wishes to take laser beam characterisation to a whole new dimension. It extends its capabilities far beyond the laser applications, and is of very high interest for astronomy, microscopy, optics caracterisation and more.

Wavefront deformation and poor focus or poor image.

Since light can be modelled as an electromagnetic wave, one can define a surface of constant phase, called wavefront. This is much like the crest of a wave in the water. The little animation below can help understand this concept quite easily.

Optical wavefront curved by a lens

Because of imperfections of the media in which the light is going through, the wavefronts are normally deformed and are not a perfectly curved (or “flat”) surface anymore. This in turn affects the propagation of the light rays and makes it impossible for them to focus in a single point (one can demonstrate that in any point the ray of light is perpendicular to the wavefront). The result is lower intensity at focus, blur and in general, aberrations.The picture below can give an example, it compares a perfect situation with a case where the wavefront is heavily deformed.

Deformation of the optical wavefront through the eye.

There is a number of very common reasons for this to happen. Heating up of the optical system, atmospheric turbulences, inhomogeneities of the media in which the light propagates, gradient of density in the air (mirage effect), etc…

Wavefront deformation and destructive interferences.

In addition of what we just mentioned above, aberrations in a beam of light will greatly reduce the intensity at focus due to destructive interferences. Once again, the images below will help understand why. First, keep in mind light is an electromagnetic wave. As it goes along, the electrical field E⃗  varies from +E to -E

Light as an electromagnetic wave

In the ideal case, when there is no wavefront deformation, the light going through a media or an optical system will arrive at focus at the same time whatever the path it goes through. In this situation (picture below), the electrical fields add up at focus, and the intensity of the light is thus greatly increased.

Ideal lens

In reality, because of the wavefront is deformed, some of those electrical fields will arrive at the focus point at different “times” (phase). The electrical fields do not have the same values and their addition will be counter-productive, leading to reduced intensity in places.

Lens with aberrations

This leads to the intensity patterns at focus you can see below, and to a reduced Strehl ratio. It creates obvious problem when the aim is to get the highest possible intensity at focus or the best quality image.

Point Spread Functions

Practical consequences of poor wavefront quality.

As a direct result of what has been said above, a poor wavefront will:

  • Reduce intensity at focus. In case of a welding/cutting laser this mean decreased efficiency. Any laser application that focuses the light down would be impacted by poor wavefront, such as welding, cutting, plasma generation, surgery, fluorescence or Raman excitation, etc… It is to be noted that a laser beam can potentially heat up the optics inside itself and create thermal lensing, which in turn will deform the wavefront.
  • Create hotspots. This is particularly crucial in Chirp Pulse Amplification lasers. All the optical components of an amplification chain can induce phase aberrations responsible for spatial intensity modulations. These distortions can generate energy hot-spots and irreversible optical damages of the components, some of which are prohibitively expensive.
  • Lower resolution. Aberrations are the plague of imaging systems, because they create blurry images and effectively reduce the imaging system resolution. This can be caused by the imaging system itself (poor quality lenses, for instance, or mis-alignment), of by the environment (the turbulence in the atmosphere create dynamic aberrations which lower the capabilities of non-adaptive optic telescopes)

What technology is currently available to measure wavefront aberrations?

SHACK-HARTMAN

This is the most wide-spread type of wavefront sensor. A micro-lens array focuses the incident wavefront into a number of small spots on a CCD. Aberrations in the beam will make the spots move away from the place they would occupy in front of the centre of each micro-lens if the wavefront was perfectly flat. The deviation of each spot is directly proportional to the gradient of the wavefront, which can then be reconstructed.

The Shack-Hartman is the most versatile wavefront sensor available at the moment. It can measure wavefront aberrations 1,500 bigger than the wavelength at a precision of one-hundredth of a wavelength. It is the easier to align, the most documented and is already designed-in a number of turnkey solutions for industrial need.

Its main weakness is its poor spatial resolution. With a number of measurement points equal to the number of micro-lenses, it is typically of the order of 1000 to 5000 data points per wavefront.

This instrument is best suited for general measurements, when you need both a good dynamic range and good precision (resolution of the phase), but do not need a high spatial resolution (or transverse precision, helping with high spatial frequency aberrations).

Realistically, this includes most of the cases, since a wavefront reconstructed from 1000 points is able to include aberrations of well past beyond the 10th order.

HARTMAN

Same as above with a holed mask in place of the micro-lenses array. This could be considered as obsolete technology only interesting when you cannot use lenses (for X-ray wavefront sensing for instance).

CURVATURE SENSORS

They measure the intensity profile of the beam in two different planes along the optical axis. By comparing the intensities, the software will compute the axial derivative of the intensity, and then calculate the second derivative of the wavefront using Poisson’s equation. This technique gives a very good spatial resolution because one pixel gives one phase data point. One of the main drawbacks of this technique is its limitation in terms of dynamic range, typically limited to a few microns (typically 3 µm). Just as critically, since it is working on the second derivative of the wavefront, it is by nature unable to measure tip-tilt aberrations. Finally, the light beam must be collimated and of reasonable intensity.

This has some uses to measure wavefront with high spatial frequencies of aberration, of low amplitude.

MULTI-LATERAL SHEARING INTERFEROMETER

A 2D diffraction grating replicates the incident beam into four beams which are propagated along slightly different directions. The interaction between the beams produces an interference pattern which is imaged on a CCD.

When aberrations are present on the beam, the interference pattern is distorted. The pattern deformations are directly connected to the phase gradients. A spectral analysis using Fourier transforms allows the phase gradient extraction in 2 orthogonal directions. The phase map is finally obtained by integration of these gradients.

Typically you can tune the position of the diffraction grating to change the behaviour of the sensor: either you get high precision measurement of the phase or you get high spatial resolution (to see high spatial frequencies). Also the overall dynamic range of the instrument is limited, so you can tune it either for high precision measurement of the phase or for measurement of a highly aberrated wavefront, but you cannot measure high level of aberration with a good precision. This would probably mean that you need to pay extra care to the alignment when making a precision measurement, otherwise the tip-tilt will bring the wavefront out of the dynamic range.

The wavelength range is the one of the CCD used (generally 350-1100nm), it is insensitive to vibrations. Finally, because the beam is split into 4, you need a reasonable intensity.

This type of instrument is suitable when the measurement you want to make do nottick all the boxes of high aberration amplitude, high precision and high spatial resolution at the same time.

In practice, what help can you expect from a wavefront sensor?

    • Characterise optical aberrations and obtain their projection on Zernike polynomials. This is precious information to understand easily the imperfections of an optical system. Since wavefront sensors are relatively fast (tens of Hertz), they can as well characterise dynamic aberrations such as those induced by thermal effects. High end systems running at a kHz can even measure aberrations due to atmospheric turbulence.
    • Characterise completely the light propagation. The characterisation of a beam of light in terms of intensity and wavefront allows a certain number of its fundamental parameters to be calculated by simply processing the initial measurement data. Using the Fresnel propagation equations, one can reconstruct the phase and intensity profile in any plane along the optical axis.

Laser true 3D profile

  • Measure the intensity profile at focus of a laser (also known as Point Spread Function or PSF). Or, rather, reconstruct it. This is just a consequence of the point above. A number of people are experiencing issues while trying to measure the intensity of their laser at focus. A Wavefront sensor capable of measuring the intensity as well can reconstructs the PSF while being meters away from the focus, and can then become part of the solution.
  • Characterise an optical system by measuring the Mode Transfer Function MTF. This is only the Fourier transform of the PSF.
  • Measure a number of laser parameters such as M2, beam waist, optical intensity propagation along the optical axis.

Watch out for an exact software description before buying anything! Some of the above features involve advanced data processing and are not proposed by every wavefront sensor manufacturers.

A wavefront sensor will also:

  • Help align the optics of your system. Some of those sensors make it very easy: the idea is to position the first optic of the system, and align it while using the wavefront sensor to find the position that minimizes the aberrations. After having found the right position you would then take a measurement as a reference, introduce a second optic, and subtract the reference to the new wavefront. What you then measure are the aberrations introduced by the latest optic alone, the positioning of which you can now optimise. And so on…
  • Help improve the optical resolution of your system.
  • Help increase the power at focus.
  • Help produce tighter focal spots.

Those last three points all come from the same property. As shown in the point spread functions pictures above, aberrations reduce the quality of the response of an optical system, spreading its PSF (focal spot size) and reducing the intensity at its centre. This results in blurry images and effectively reduce the resolution. By characterising the aberrations introduced by an optical system, a wavefront sensor helps in taking the relevant actions to minimise them (through better alignment or adaptive optic for instance).
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