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Wavefront Sensing

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Wavefront Sensing Applications

What is a wavefront ?

A wavefront is an essential parameter in the propagation of light and can be used to characterize optical surfaces, align optical assemblies or help to improve the performance of optical systems. In this application note we will cover most common applications of wavefront sensors and illustrate with a few examples.

In physics, the term light refers to electromagnetic radiation of any wavelength, whether visible or not and like every type of EM radiation it propagates as waves and the set of all points where the wave has the same phase of the sinusoid is called the wavefront.

The wavefront can be plane or spherical and carries the aberrations which are the differences to the perfect sphere or plane. Aberrations are generated when light goes through media or optical components.

What is a wavefront sensor ?

A wavefront sensor is a device for measuring the aberrations of the optical wavefront, and this term is normally applied to instruments that do not require an unaberrated reference beam to interfere with to deliver the wavefront or phase measurement.

It provides a direct measure of the phase and intensity of a wavefront. The most common type of wavefront sensor is the Shack–Hartmann wavefront sensor (SHWFS). This apparatus is associating a 2D detector with a lenslet array. Those devices were developed for adaptive optics and have been  widely used in optical metrology and laser diagnostics. Their level of performance has met with typical standards in optical metrology.

The best factory calibrated Shack–Hartmann wavefront sensors are able to provide nanometric accuracy. Thousands of waves of dynamic range with a linearity of 99.9%. This level of performance combined with the intrinsic properties of the instrument such as insensitivity to vibrations, speed and achromaticity. These features make the Shack-Hartmann wavefront sensor a key tool for a wide spectrum of applications in research and industry. Imagine Optic is the leading manufacturer of SHWFS.

Over the last decade, alternative wavefront sensing techniques to the Shack–Hartmann system have been emerging. Mathematical techniques such as phase imaging or curvature sensing are also capable of providing wavefront estimations. While Shack-Hartmann lenslet arrays are limited in lateral resolution to the size of the lenslet array, mathematical techniques such as those mentioned above are only limited by the resolution of digital images used to compute the wavefront measurements. That being said, those wavefront sensors are suffering from linearity issues and are much less robust than the original Shack–Hartmann wavefront sensor.

Measurement principle of the SHWFS

Coarse description of the SHWFS wavefront measurement method. From left to right: Wavefront sampling – Centroid determination – wavefront reconstruction

Shack–Hartmann wavefront sensor is measuring the phase and the intensity in the same plan. This allows to calculate many parameters describing the propagation of light such as the Point Spread Function  or the Modulation Transfer Function, with accuracy less than 1%.

A wavefront sensor is able to deliver the following parameters

– Tip and Tilt
– Curvature
– Refractive power
– Focal point positions
– Wavefront PV and rms
– Intensity
– Spot diagram
– Zernike coefficients
– Encircled energy
– MSquare

and many more…

Above MTF calculation based on a wavefront measurement. The advantage of the SHWFS on that specific measurement is to provide a 2D measurement of the MTF allowing to select planes of interest.

Applications of the Shack–Hartmann wavefront sensor in Optical metrology

Optical testing in reflection (double pass)

The characterization of optical surfaces is an essential step in the manufacturing of any type of optical components. Interferometers such as Fizeau were developed for that purpose but the Shack–Hartmann wavefront sensor is a competitive alternative because it offers an excellent trade-off between performance and versatility/ease-of-use.

For reflective optics and especially large mirrors, the Shack–Hartmann wavefront sensor can perform a rapid and accurate measurement of the radius of curvature. When measuring the radius of curvature using accessories such as the R-FLEX system developed by Imagine Optic, can increase the versatility of the Shack–Hartmann wavefront sensor and simplify the measurement setup without degrading the performance of the wavefront sensor.

The R-FLEX can adapt with the f/# of the component to be tested thanks to a large choice of optical focusing modules. The measurement is then performed after a reference measurement is recorded, in order to distinguish the aberrations coming from the component under test or coming from the measurement system itself.

Characterization of the primary mirror of Herschel space observatory

A- telescope characterization set up with waverfont sensor standing om top (yellow). B- wavefront measurement (2.1 um rms in ambient conditions). C- comparison of optical images of M51 galaxy taken by spitzer left in the MWIR and Herschel in the FIR at 100um. D- comparison of the PSF, predicted based on WFE measurement left and imaged at 70um wavelength

The Herschel Space Observatory was a space observatory built and operated by the European Space Agency. It was active from 2009 to 2013, and was the largest infrared telescope ever launched, carrying a 3.5-metre mirror and instruments sensitive to the far infrared and sub mm wavebands. The characterization of the primary mirror was challenging since the mirror (SIC) was polished to perform imaging in the far infrared and the wavefront measurement made in the visible . The required dynamic range was extremely high (1.2mm) and only a Shack–Hartmann wavefront sensor (Imagine Optic HASO) could make that measurement possible.

Thin Dielectric Mirror Characterization in Reflection

The application case above shows an example of a measurement of a large dielectric mirror in reflection with a R-FLEX Large Aperture, which is used to characterize the wavefront error of some region of interest  of the optical component.

Optical testing in transmission

For the test of optics in transmission, the measurement can be made in single pass or double-pass. For the test of filters and dichroics, the Shack–Hartmann wavefront sensor has the advantage to be achromatic and perform characterization at several wavelengths. The main challenge for this application is the adaptation in size of the area of interest on the component under test and for this some accessories such as the R-FLEX LA  were designed to allow seamless integration of a Shack–Hartmann wavefront sensor for the measurement of aperture up to 200 mm in double path.

Optical testing of eye wears

In the past few years smart glasses have been made accessible to mass market. Those devices offer several features including hands-free access to all sorts of information directly relayed into the pupil of the eye, potentially improving user’s safety for a number of applications, professional or not. While reducing the production costs, manufacturers of this type of optical systems have to follow some quality standards defined for safety eye wear by norms such as

– EN166: European Standards for Eye protection
– ANSI Z87.1: Eye protection from The American National Standards Institute
– SANS 1404: Eye-protectors for industrial and non-industrial use in South Africa

Accuracy of vision is one of the four optical clarity classes. It qualifies image distortion through eye wear. The highest level of optical clarity or correctness is defined as Class 1 (0.06 diopters),

Double pass Characterization of ski googles with HASO RFLEX Large Aperture Imagine Optic

In general the Shack–Hartmann wavefront sensor are used for the characterization of a wide variety of optical components such as:

– Concave and convex mirror
– Toroids mirrors
– Flat windows such as filters, dichroics, Vacuum viewport flanges
– Curved windows such as heads up displays, TV displays, heated windshield

Assistance for optical alignment

The alignment of optical assemblies for the minimization of aberrations became more and more critical in optical systems dedicated to produce images. Over the past decade the need for high performance optical alignment increased drastically with the constant evolution of imaging devices. Cameras for smartphones, VR devices, inspection lenses for semiconductor and optical systems for defense and security industry are some of the examples.

The first optical adjustment in which a Shack–Hartmann wavefront sensor can be used is the collimation, the Shack–Hartmann wavefront sensor measures the curvature information with a sensitivity that can reach 1/1000 m-1, in real time .

The Shack–Hartmann wavefront sensor is also able to provide a Zernicke polynomial decomposition  which can be compared for instance with a wavefront error (WFE) established by simulations. The alignment can be performed by minimizing the off-axis aberrations with a sensitivity on the wavefront as low as l/200 rms on zernikes coefficients of interest.

Those alignment processes can be automated thanks to communication between the simulation and the degrees of freedom made available on the system being aligned.

Over the past few years standard off-the-shelf Shack–Hartmann wavefront sensor have proven their ability to perform optical alignment on very demanding optical systems. The space telescope GAIA was able  reach diffraction limited performance thanks to R-FLEX.

GAIA space observatory optical payload. Courtesy of Airbus / CNES
doi: 10.1117/12.2309087

A standard HASO R-FLEX was used for the alignment and the optimization of the dual telescope system in two GAIA 3 mirrors anastigmatic telescopes. I was able to reach approximately 50nm wavefront error. The R-FLEX was located in the focal plane of the telescope system

In the industry the Shack–Hartmann wavefront sensor is used as the primary tool for the alignment of some complex optical system dedicated for the inspection of wafers or 8″ telescope which is used for earth observation. Thanks to its versatility the Shack–Hartmann wavefront sensor is also a prime tool in industrial R&D.

Top Alignment of a 8″ Shmidt Cassegrain telescope with R-FLEX in the focal plane, bottom left wavefront error before alignment 226 nm rms , bottom right wavefront error after alignment 19nm rms

Laser beam diagnostic

The Shack–Hartmann wavefront sensor measures the phase term but also the amplitude or intensity term. The characterization of those 2 terms in a single plan allows to propagate the electro-magnetic field everywhere in free space. Furthermore, the phase has more weight than the amplitude in the propagation of a laser beam. This makes the Shack–Hartmann wavefront sensor a remarkably interesting option for applications related to the development, integration, or maintenance of a laser system.

Just like for any optical system the Shack–Hartmann wavefront sensor can be used to minimize the wavefront aberrations of the output beam going out of the laser cavity. The measurement can be made in the near field and the reduction of the aberrations will allow to obtain an optimized far-field, by maximizing the encircled energy for instance.

Furthermore, some lasers are emitting on a broader spectral bandwidth and can produce aberrations that vary in function of the wavelength. The Shack–Hartmann wavefront sensor and its achromatic nature combined with filters can be used to characterize the spatio-temporal coupling in ultra-short pulses or continuum laser sources.

Characterization of the aberrations produced in A high-beam-quality NdYAG rod laser. https://doi.org/10.1016/j.ijleo.2018.12.095

Here a Shack–Hartmann wavefront sensor (HASO Imagine Optic) was used to characterize the wavefront error of the output beam of a NdYAG rod laser before and after static correction of spherical aberration by a variable radius mirror (VRM).

Some amplification methods being used in lasers can introduce a thermal lensing effect which will affect the beam propagation over time.  The Shack–Hartmann wavefront sensor can be used to simply characterize and monitor the beam curvature variations. Additionally it can measure pointing stability.

Characterization of thermally induced aberrations introduce by different gain media

Above Characterization of thermal properties of different gain media with a Shack–Hartmann wavefront sensor (HASO Imagine Optic) Measured aberrations are dominated by focus (thermal lensing) and shows detailed residual for the different media.

The full characterization of the electromagnetic field in one snapshot and the possibility to monitor / measure the curvature allows the Shack–Hartmann wavefront sensor to provide advanced beam diagnostics. Thanks to its very fine collimation of laser diodes can be performed along with MSquare (M2) measurement. Measuring the M2 with a SHWFS is surely possible, however, initial conditions are very important to obtain reliable measurements. The beam needs to be single mode transverse, the measurement has to be done within the Rayleigh length and the sampling of the beam needs to be sufficient to accurately measure aberrations and the feet of the gaussian beam.

Adaptive optics

The history of the Shack-Hartmann wavefront sensor is linked to Adaptive Optics (AO). It was developed to measure phase distortions so they could be corrected with a deformable mirror. Applications of AO have boomed over the past 2 decades and the Shack-Hartmann wavefront sensor is still the most common wavefront sensor being used in:

– Astronomy
– Biomedical imaging
– Ultra-High Intensity Lasers
– Free Space Optics

Beyond the native applications of monitoring the closed loop the it can also be used to optimize the AO system in some other ways and to characterize the wavefront threat of a system. The analysis of the wavefront threat can be used to determine the necessity of deploying an AO correction or not, choose the deformable mirror and also study the temporal properties of the wavefront distortions.

Study of the wavefront threat of HAPLS pump laser

Every adaptive optics system is associating a wavefront sensor, a control system (RTC or computer) and a deformable mirror. The adaptive optics can be functioning in close loop or open loop but the performance of these 2 control mode rely on the interaction matrix. On that matter, the linearity of the wavefront sensor is crucial in order to get the closed loop to converge and obtain a stable correction. The Shack–Hartmann wavefront sensor is a very robust candidate for that application as a result of its linearity.

Every adaptive optics system requires a wavefront sensor for the correction and some advanced systems rely on another wavefront sensor. These setups typically use a Shack–Hartmann wavefront sensor to monitor the corrected wavefront and adjust the closed loop correction by reinjecting non common path aberrations (NCPA). NCPA are the aberrations not seen by the wavefront sensor upstream in the closed loop. These are called truth wavefront sensors and the Shack–Hartmann wavefront sensor because of its linearity is a very interesting candidate for this application.

GPI’s view of the Beta Pictoris star/planet system as each component is turned on. Image credit: GPIES team; Beta Pictoris: C. Marois/NRC Canada, Gemini Observatory

Gemini Planet Imager (GPI) is an ExAO system dedicated to directly image planets located inside and outside of our solar system. This is the state of the art AO system coupling athnospheric correction to a coronograph allowing imaging and spectrometry of exosuns companions under extreme angular resolution.

The spectrum of applications where the Shack–Hartmann wavefront sensor is being used is very broad. Visit Imagine Optic website to explore the application notes available to download and have an overview of the publications.

Comparison of the Shack Hartmann Wavefront sensor with interferometers

Interferometers have for a long time been the reference tool in optical workshops and polishing labs. The characterization of surface roughness / finish, Mid Spatial Frequencies are inevitably reserved to interferometry based techniques such as optical profilers, interferometric microscopes and state of the art interferometers.

Fizeau interferometers have been also the tool of reference for the characterization of optics in reflection and transmission, optical systems and components. Over the past 2 decades, commercial Fizeau interferometers have evolved and overcome part of its inherent limitations related to environmental conditions such as temperature drift, air turbulences and vibrations thanks to innovative phase-shifting techniques. On the other hand their limited dynamic range requires the use of nulling optical components which can dramatically increase cost and complexity.

SHWFS exhibits lower spatial resolution but provide higher dynamic range and less sensitivity for environmental conditions thanks to their measurement principle and smaller footprint. High performance SHWFS such as the HASO from Imagine Optic have a factory calibration that allows direct wavefront measurement with a lambda/100rms accuracy and lambda/200rms sensitivity in referenced mode. On top of those technical advantages, the SHWFS is also quicker to set up and much more compact, a system such as the R-FLEX from Imagine optic can be set at the center of curvature of a large concave mirror and perform a precise characterization within minutes.

Eventually the overall budget for an high performance SHWFS is usually much lower compared to an interferometer set up. In conclusion, the SHWFS could be employed as a cross check system or even replace the interferometer in applications where the measurement of low frequencies aberration of a component (zernike’s coefficients) is the main objective or for the alignment of optical systems such a collimator.

The spectrum of applications where the Shack–Hartmann wavefront sensor is being used is very broad. Visit Imagine Optic website to explore the application notes available to download and have an overview of the publications.