Wavefront Sensor Applications

What is a Wavefront Sensor ?

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.

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 Shack-Hartmann Wavefront sensor (SHWFS)

Shack-Hartmann Wavefront Sensor wavefront measurement method.

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 a LIFT Wavefront Sensor ?

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

Click HERE to view the HASO LIFT Wavefront Sensor from Imagine Optic. 

 

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 Wavefront Sensors 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.

measuring lenses on-axis and characterizing lenses in the field

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).

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 on waveview software

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.

measuring flat or concave mirror with rflex la Wavefront shown on waveview software

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 Waveview4 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

Wavefront on Waveview4 Software pupil automatic detection and tracking on waveview software

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

telescope characterization set up with wavefront sensor with wavefront measurement