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Wavefront Sensing Applications

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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 the most common applications of wavefront sensors and illustrate them with a few examples.

In physics, the term light refers to electromagnetic radiation of any wavelength, whether visible or not. 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.

Huygens' principle - Wavefront Sensing
Types of Wavefronts
The wavefront can be planar 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. This term is typically referring to an instrument capable of direct wavefront measurement which does not use interferences between beams to reconstruct a wavefront.

Wavefront sensors provide 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 combines a 2D detector with a lenslet array. These 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 is 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.

(L-R): Wavefront sampling – Centroid determination – wavefront reconstruction

A Shack–Hartmann wavefront sensor is measuring the phase and the intensity in the same plane. This allows you 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
– MTF
– PSF
– MSquare

and many more…

What is the LIFT Revolution?

The LIFT (Linearized Focal Plane Technique) technology corresponds to the combination of the standard Shack-Hartmann technology with one image only phase retrieval algorithms running at a microlens scale.

One advantage of the LIFT technology is that the “hartmanngram” (the raw signal of a Shack-Hartmann sensor) contains much more information than what is commonly exploited by standard Shack-Hartmann software: in addition to the spot displacements due to local tilts of the incident wavefront, the deformation itself can be analyzed and provides the map of the wavefront intercepted by this microlens.

LIFT Wavefront Sensing Principle

LIFT principle. Reconstructed wavefront exhibits high orders aberrations in front of each microlens. This property drastically enhances spatial resolution.

Based on algorithms developed by researchers at ONERA in 2010 [S Meimon, “LIFT: a focal-plane wavefront sensor for real-time low-order sensing on faint sources”, Opt. Lett., Vol. 35, No 18 (2010)], Imagine Optic has developed very fast phase retrieval algorithms which results in an improvement of a factor of 16 (4×4) of the spatial resolution. These new wavefront sensors combine all the advantages of the Shack-Hartmann technology, in particular its huge dynamic range and excellent accuracy with the high resolution provided by the LIFT technique.

Transfer Function Graph

Transfer functions for standard SH sensors and LIFT wavefront sensors using a SLM to generate Sinusoidal phase patterns with increasing spatial frequencies.

Shack Hartmann Lift Comparison

Comparison of standard Shack-Hartmann and LIFT reconstructions with a high spatial frequency phase hologram

Comparison of the LIFT 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 also been 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 their inherent limitations related to environmental conditions such as temperature drift, air turbulence 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 exhibit 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 a 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 frequency aberrations of a component (zernike’s coefficients) is the main objective or for the alignment of optical systems such a collimator.

The phase LIFT technology is a recent innovation that Imagine Optic implements in its HASO Shack-Hartmann Wavefront Sensors. It is a revolution that radically improves standard Shack-Hartmann WFS resolution. In this configuration, each subaperture is not only used to measure a local tilt (slope) but a complete local phase by performing phase retrieval. This way, the resolution is multiplied by 16 and leveled up close to interferometers standard.

 

Accuracy             

Dynamic Range

Sampling             

Spectral Bandwidth

Insensitivity to Mechanical Noises

Footprint              

Acquisition / Infrastructure Costs

Interferometers

HASO LIFT Shack Hartmann WFS

Commercial Lateral Shearing

★★★★ very high/good

★★★ high/good

★★ medium

★ poor/limited

Comparison between different technologies

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

Applications of the HASO Wavefront Sensor in Optical Metrology

On-axis & Off-axis Metrology

The characterization of the optical quality of a lens is a recurrent subject in the field of optics. The measurement of the wavefront is certainly the most complete way to assess the quality of an optical system. Imagine Optic has developed a whole range of instruments, based on wavefront measurement, perfectly adapted to the characterization of optical systems in single or double pass configuration.

In single pass configuration, the objective to be characterized is placed behind a collimator, and the wavefront measurement is performed with a wavefront analyzer from the HASO range placed behind the focal point of the objective.

In double pass configuration, the use of the R-FLEX2 (self-illuminated wavefront sensor) allows easy measurement of the optical quality of the lens of interest. The R-FLEX2 illuminates this lens, via the focal plane, with a beam whose numerical aperture is adapted to that of the lens, and a plane mirror can be placed in auto-collimation at the lens’s exit to measure its aberrations (see example of assembly below). Whether in single or double pass configuration, these  measurement solutions allow on-axis and off-axis measurements.

Once the setup is done, a single wavefront measurement allows a complete characterization of the lens: both the measurement of aberrations decomposed on the basis of Zernike polynomials and the measurement of the MTF (Modulation Transfer Function) on all azimuths (what we call the 3D MTF). Knowing the aberrations is key for pinpointing the origin of possible problems in case the MTF of the lens is not as good as expected.

Modulation Transfer Function – MTF

The MTF (Modulation Transfer Function) measurement of a lens is the most common way to characterize the optical quality. There are many ways to perform this measurement. Most of them are based on measuring the contrast of a specific test pattern imaged by the lens of interest. This type of measurement is a direct way to qualify the MTF of a lens, but it does not allow tracing the origin of the problem if the lens does not have the expected optical quality.

Wavefront measurement is an alternative way to measure MTF, and it is certainly the most complete way to characterize the quality of an optical system. Indeed, one single wavefront measurement gives direct access to the aberrations of the lens of interest and also to the MTF measurement in all directions. Knowing the aberrations is key for pinpointing the origin of possible problems in case the MTF of the lens is not as good as expected.

Modulation Transfer Function

Mirrors Metrology

The metrology of mirrors during or after polishing is an element key to obtaining the desired optical quality.

Imagine Optic has developed a range of metrology solutions that allow precise and reliable measurement of mirror shape. Whether it is concave, parabolic or flat, Imagine Optic offers an adapted solution for each configuration.

The R-FLEX2 (self-illuminated wavefront sensor) is particularly well suited for measuring concave or parabolic mirrors. The R-FLEX LA, which is used as a Fizeau interferometer, is the ideal system for the qualification of plane mirrors. These systems are insensitive to vibrations, and they have high measurement accuracy as well as a huge measurement dynamic. These characteristics make these mirror metrology systems both convenient to use and entirely reliable. In combination with the HASO LIFT wavefront sensors, these systems offer up to 340,000 measuring points on the surface of interest.

Telescope & Optical Systems Alignment

Lens alignment is an extremely common problem. This task can be complicated and very time consuming. The HASO wavefront sensors developed by Imagine Optic provide a valuable aid, allowing you to perform this task quickly and precisely.

Whether in a single or double pass configuration, the Shack-Hartmann HASO wavefront analyzers and R-FLEX2 modules with Waveview4 software provide the reliability and ease of use needed to successfully align your lens or collimate your collimator. The Waveview 4 software’s automatic detection and tracking of the measurement pupil and the SpotTracker software module’s absolute measurement of the beam tilts are two essential features for a successful alignment operation.

The HASO4 and R-FLEX2 have been successfully used for the alignment of prestigious instruments, including the Herschel, GAIA, and Euclid spatial telescopes.

Publication: The optical alignment of the two GAIA three mirror anastigmatic telescopes

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, 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

Herschel

Herschel Herschel

A- telescope characterization set up with wavefront sensor standing on 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 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-meter 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 below 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.

Thin Dielectric Mirror

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. 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 in Transmission

Interferometer vs. HASO RFLEX LA

(L) Interferometer (ZYGO GPI)      vs.        (R) HASO4 R-FLEX LA

Optical Testing of Eye Wears

In the past few years, smart glasses have been made accessible to the mass market. These devices offer several features including hands-free access to all sorts of information directly relayed into the pupil of the eye, potentially improving user safety for a number of applications, professional or otherwise. 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).

Eyewear Optical Testing

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

In general the Shack–Hartmann wavefront sensor is 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

Collimator Characterization

It is possible to use the R-FLEX LA platform to characterize components as systems with an external source, such as collimators. Below is a direct characterization of the illumination beam of a Fizeau Interferometer.

Collimator Characterizatiom

Fizeau Beam

Real Time Alignment of Optical Systems

The alignment of optical assemblies for the minimization of aberrations became more and more critical in optical systems dedicated to producing images. Over the past decade the need for high performance optical alignment has increased drastically with the constant evolution of imaging devices. Cameras for smartphones, VR devices, and inspection lenses for semiconductor and optical systems used in the defense and security industry are some 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 sensors have proven their ability to perform optical alignment on very demanding optical systems. The space telescope GAIA was able to 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. It 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 systems dedicated to the inspection of wafers or 8″ telescopes which are 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, (middle) wavefront error before alignment 226 nm rms, (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 two terms in a single plane allows propagation of 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 introduced by different gain media 10.1109/JQE.2004.833198

Characterization of thermal properties of different gain media with a Shack–Hartmann wavefront sensor (HASO, Imagine Optic) is shown above. Measured aberrations are dominated by focus (thermal lensing) and show 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. 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 two 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, it can also be used to optimize the AO system in 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

(L) Simulation with Zemax of the wavefront on the 47×47 square of the beam size. FWHM.

(R) Simulation with HASO software of the wavefront to correct.

(L) Less than 50% of the total dynamic of the deformable mirror is used to correct the beam.

(R) The wavefront correction residual is around 150nm RMS wavefront error. 

(L) The focused spot has a Strehl ratio of 58%. (R) 85% of the total energy is contained in five times the diffraction limit. 

Every adaptive optics system associates a wavefront sensor, a control system (RTC or computer) and a deformable mirror. The adaptive optics can be functioning in closed loop or open loop but the performance of these two control modes 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 re-injecting 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 imaging planets located inside and outside of our solar system. This is the state-of-the-art AO system coupling atmospheric correction to a coronagraph allowing imaging and spectrometry of exosun companions under extreme angular resolution.

The spectrum of applications where the Shack–Hartmann wavefront sensor is being used is very broad. 

Improvement of the Trap Arrays

Over the past years, an interest in advanced optical trapping of atoms has arisen. From simple initial configurations such as crossed optical dipole traps, researcher’s needs have evolved towards more complex light fields such as two-dimensional arrays of microtraps. These configurations open appealing applications in quantum-information processing and quantum simulation, for example.

HASO4 First is an off-the-shelf wavefront sensor able to provide a simple, direct measurement of the wavefront quality, enabling researchers to greatly improve the quality of the intensity distribution of the light used for atom trapping experiments.

Vacuum Chamber Wavefront

(a) The wavefront is distorted after the vacuum chamber. (b) The wavefront obtained after the vacuum chamber with a correction applied to the SLM.

PSF of Optical Setup

(a) The PSF of the optical setup before the correction. (b) The PSF of the optical setup with a correction applied to the SLM.

The correction leads to an improvement that can be observed for arrays of several traps: