Adaptive optics provide real-time compensation for atmospheric turbulence. The correction quality relies on a key element: the wavefront sensor. We have designed an adaptive optics system in the mid-infrared range providing high spatial resolution for ground-to-air applications, integrating a Shack-Hartmann infrared wavefront sensor operating on an extended source. This paper describes and justifies the design of the infrared wavefront sensor, while defining and characterizing the Shack-Hartmann wavefront sensor camera. Performance and illustration of field tests are also reported.
© 2012 Optical Society of America
High resolution imaging with adaptive optics and numerical image restoration processing are now operational for ground-based telescopes. It provides a real-time compensation for turbulence degraded images. However, these correction techniques are only effective in a limited field of view due to anisoplanatism. For endoatmospheric applications, strong intensity fluctuations may also limit the degree of correction, depending on the wavelength range.
ONERA was given responsibility for building and testing an adaptive optics (AO) demonstrator for ground-to-air imaging. The need for night and day operation led to the choice of the mid-infrared band II, observation being performed with a 35 cm diameter telescope. The AO system included a Shack Hartmann wavefront sensor (SH WFS) to measure wavefront perturbations on extended objects. The issue of endoatmospheric wavefront sensing has been previously discussed especially regarding anisoplanatism. Analytical analysis of the error terms, including anisoplanatism and differential scintillation, has been presented in Refs. [1, 2]. Wavefront sensing on extended sources has been analyzed theoretically in [3, 4]. However it had to be addressed from a practical standpoint .
This paper focuses on the most crucial aspect, that is, the Shack Hartmann wavefront sensor’s design in mid-IR (3.4– 4.2 μm) and its behavior. Contrasting with uncooled SH WFS predecessors, in the visible  or in the infrared range for aberration metrology [7, 8], we work at low signal-to-noise ratio like in astronomy. To our best knowledge, our mid-IR SH WFS incorporates the detector and optics accurately in a cryostat like the successful near-IR SH WFS , but without mobile parts and without adjustment. Main characteristics of the SH WFS include an array of 5 × 5 subapertures, a field of view of 1.3 mrad and a frame rate of 500 Hz. Wavefront sensor design was made by ONERA and high know-how in cryogenic detectors and mechanics was entrusted to SOFRADIR.
This paper is divided into four sections. The first sets out design of the SH WFS in detail; the second defines the major optical component, i.e. microlens array, opto-mechanical technology and a brief description of readout electronics. The third presents the characterizations and lab tests. The fourth presents expected performance for extended object wavefront sensing and illustrates the field tests. Finally, we draw conclusions as to perspectives for working with the SH WFS.
2. Overall design of the Shack-Hartmann wavefront sensor
2.1. Application parameters
At wavelength 4 μm, the angular resolution of an imaging system for airplanes in the 10 – 15km range is 10 μrad with a 35 cm diameter telescope. The typical Fried diameter is r0 = 7 cm at λ = 4 μm for a terrestrial slant path observation, and a SH WFS with 5x5 subapertures is well suited. In such conditions, the isoplanatic length equals 2 m at 10 km and it limits the size of the extended source. The sensor FoV is of 1.3 mrad, corresponding to 13 m at 10 km as we want to study anisoplanatism effects. The wavefront coherence time is about 2 ms with a wind speed 10 m/s, and that drives the camera frame rate to roughly 500 Hz. The simulated performance of the AO system leads to a Strehl ratio of 30 % in these conditions.
2.2. Detector design
Spectral band of the wavefront sensor spans between 3.4 and 4.2 μm. The image sampling equals fNyquist /2 at the central wavelength 3.7 μm. This under-sampling is found to be sufficient in paragraph 5.1. The sampling and field of view led to the choice of a focal plane array (FPA) using a region of interest at 125 × 125 pixels, i.e. (5 × 25)2. Since the flux detected from the scene could range between 3 104 and 106 photons, the chosen detector was a MCT . Its other essential characteristics are its well capacity of 1.38 Me− and a noise level ≤ 250 e− with a 440 Hz frame rate. Fixed pattern noise was negligible as opposed to temporal noise, after 2-point correction. Detector matrices were selected to present a very low number of dead pixels, minimizing their presence on the microlens optical axis.
2.3. Optical design
Classical Shack-Hartmann architecture was used for the optical design. All optical components and the detector needed to be cooled in the same dewar (see justification in paragraph 3.3). Figure 1 gives an overall view of the SH WFS optical scheme. The dewar’s internal envelope comprises a field stop installed at the AO system’s focal plane; a collimation lens and a 5 × 5 microlens array, both in silicon are inside and referred to as the light unit including the field stop. Cooling the dewar’s light unit prevents emissivity from the field stop and the optics. A cold pupil is incorporated onto the microlens array plane face, delimited using a centrally-obscured mask. The cold filter is set on the cold pupil. Owing to the optical component’s thermal properties (see paragraph 3.3), design was Zemax-simulated. The entire SH WFS optical length was 64 mm, that is rather compact.
Positions for all SH WFS components were set within a certain tolerance to specify the mechanics and the mounting. The relative transverse positions of the center of the optical components were at ± 50 μm. Tolerance on the longitudinal position of the optical components was ± 60 μm. Orientation of the microlens array in relation to the detector pixel grid was specified with an absolute precision of 5 mrad.
2.4. Scattered light reduction
According to the optical design, only parasitic external radiation is scattered or reflected on the dewar’s mountings and mechanical surfaces. Stray light impact was simulated using Zemax. To reduce stray light, we considered the following elements: a mechanical conical shell between the field stop and the collimator lens, a cylindrical shell between the collimation lens and the microlens, two annular diaphragms after the collimation lens and above the cold pupil, and finally the detector with its baffle blocking light from around the cold table. The carry-field-stop was blackened on both faces with an IR-absorbent coating.
The same IR-absorbent material covered the internal dewar surfaces, including the mechanical optic support. We set a broad optical scattering indicatrix with the diffusion coefficient of 4 % and an absorption of 96 %. The coating BRDF influence was neglected. Not fewer than 104 rays were projected from the field diaphragm radiating at 2π steradians. At the detector, most stray light came from reflections on the collimation lens or on the pupil mask; it proved essential to have lens and microlens coatings with an anti-glare reflexion coefficient under 1%, in addition to employing two absorbent diaphragms.
3. Realization of the Shack-Hartmann wavefront sensor
3.1. Cryogenic microlens array
Great care was taken in the microlens array component. It indeed served three crucial purposes: focusing with the microlenses, limitation of the aperture with a cold pupil and reduction of the detection spectral bandwidth. The microlens array features are presented in Fig. 2. The cold pupil is circular with a central obscuration. It is made of a chromium opaque mask 1 μm thick. The cooled band-pass filter having a transmission between 3.4 and 4.2 μm is made with a multi-dielectric coating and is environmentally resistant to thermal shocks, with no degassing. SILIOS realized the microlens array with the mask, the coating being deposited separately. The design of the microlens array is presented in Fig. 3 with squared lenslets (filling factor of 100%). The curvature of the lens was made of 64 levels etched in the silicon substrate by a plasma process. The manufacturer used a Reactive Ion (dry) Etcher with an SF6/O2 gases. The main interest of this technique is the high degree of control of lens shape. The basic principle for encoding 2N etched levels was proceeding by N individual steps (here N = 6). The pattern for each etching step was defined by a photo-lithography process. The N patterns were aligned one to another with an error margin of less than 1 μm. We checked by numerical simulation that the discretization of the shape did not affect the image quality. A nearly perfect Strehl Ratio of SR=99.8% is obtained.
3.2. Opto-mechanical technology
Figure 4 shows the entire SH WFS assembled inside the dewar. The optical section comprises the light unit and the window on the dewar’s external envelope. From top to bottom can be recognized the square field stop, collimation lens and microlens array. The cryostat contains the light unit and the cold finger on which the detector is placed. SOFRADIR realized high-precision mechanics to meet the tolerances requirements. INVAR material was used as the mechanical support to minimize constraints on the silicon optics. The optics were joined at their periphery with epoxy glue, validated on models. Alignment of the detector in relation to the light unit was possible during the cryostat integration phase by reversible mounting of the detector. The photograph on Fig. 5 shows the SH WFS mounted with its Stirling cooler as it was delivered. At left one can see the the cryostat containing the light unit and below a thin capillary that propagates the cold from the cooler to the right.
3.3. Thermal analysis
A complete simulation of the thermal behavior of optics in the cryostat was performed on the basis of the mechanical and optical design brief, and then the thermal gradient inside the cryostat was delivered (see Fig. 6). The longitudinal gradient is along the optical axis and the radial gradient is transverse to it. The radial gradient is negligible due to the low conductivity of the silicon optics, but the longitudinal gradient is wide. The detector being placed on a cold table at a temperature of 90 K, the microlenses were at 100 K, the collimation lens at 120 K and the field stop at 124 K. The thermal gradient from the detector to the field stop helped the specifications of all elements at their working temperature. This knowledge was exploited in the Zemax model of cold optics for the SH WFS. Final optics positions were found using the cryogenic SH WFS model. In particular the focal length of the microlenses at room temperature was calculated at 100 K in order to place the detector correctly. Finally, the thermal background internal to the SH WFS had to be significantly lower compared to the blue sky and to the AO bench background at an outdoor temperature of 20 °C. A temperature of the field-stop lower than 190 K means the internal background is a tenth of that of the blue sky. Note this temperature is 124 K, guaranteeing that the internal thermal background was negligible.
3.4. Readout electronics
A classical readout integrated circuit was used based on silicon CMOS technology. Organization of the readout integrated circuit permitted the FPA to simultaneously integrate information from the diodes (coupled with a Capacitance Trans-Impedance Amplifier) to store the data, multiplex it by row, multiplex row information and finally, sample and hold it. The readout integrated circuit design provides users with snapshot operation, integrate-while-read mode and programmable integration time. The digital proximity electronics provides analog-to-digital conversion and multiplexing of the detector’s four analog outputs. These low-noise electronic boards drive the detector and interface with the computer. The delay these electronics and dead-pixel Real Time computer (RTC) correction produces is significantly less than the temporal latency of the AO loop.
4. Characterization of the Shack-Hartmann wavefront sensor
4.1. Microlens focal images
The first images obtained with the SH WFS are presented on Fig. 7 after 2-point correction. At left, the focal plane array of high quality with 125 × 125 pixels without dead pixels on the optical axis of the microlenses, in addition to good alignment. The spots are images of a marginally-resolved source centered in the field of view. In each sub-image, signal and background are proportional to the effective subaperture surface. We measured the alignment of the focal plane array relative to the microlens array, by using the position of the four farthest spots on the vertical and horizontal column crossing the FPA center. We measured a rotation angle of 3 mrad, better than the specification (see paragraph 2.3).
4.2. Spectral band and quantum efficiency
We measured spectral response including spectral transmission and quantum efficiency using a special bench with a Fourier transform interferometer in a 3 to 5 μm band. The spectral responses of adjacent 2 × 2 diodes were measured. The resulting mean spectral response is presented on Fig. 8. Wavelengths delimiting the SH WFS spectral bandwidth were 3.38 μm for the cut-on and 4.22 μm for the cut-off.
The SH WFS was then installed on a bench, in front of a black body set at two temperatures successively to get the detector quantum efficiency averaged on the spectral bandwidth. The fluxes impinging on the detector were estimated based on optics transmission and spectral response, leading to continuous volt levels at the photodiodes: respectively 1.7 V and 2.2 V for black body temperatures of 303 K and 318 K. These voltages are equivalent to filling 40% and 60% of well capacity (1.38 Me−). The factor of proportionality between the number of electrons per second in the equivalent diode capacitance (0.107 pF) and the delta of flux per pixel gave an averaged quantum efficiency of 88%, knowing the transmission of the optics of 82 %.
4.3. Camera linearity, noise and calibration
This section reports the measurements of the detector linearity, noise and calibration of the SH WFS camera which is not commercial. Linearity was measured by plotting the signal at different exposure times, and assessing the camera’s level of saturation at the largest exposure time. The photometric calibration consisted of measuring the correspondence between the digitized signal in ADU (Analog to Digital Unit) and detected photo-electrons. To do so we plotted the signal variance as a function of the signal.
The entire SH WFS field of view was evenly lit by a black body source. For each exposure time, we recorded two consecutive images, I1 and I2, we shall refer to as “bi-frame”. The exposure times were successively texp = 1, 10, 100, 500, 1000, 2500, 5000, 7500, 10000, 12500, 15000, 17500, 20000 μs. For each bi-frame, the image was cut into 25 regions of interest drawn by the fields of the 5 × 5 sub-apertures. Each region’s size contained in fact 24 × 24 pixels since the image of the square field stop corresponded to 24.5 pixels. We then calculated the signal average and variance in ADU on each subaperture. The flux averaged over the bi-frame is:
This method amounts to simply computing the temporal mean and variance of each bi-frame pixel and then spatially averaging the two maps obtained.
Figures 9 and 10 show respectively the linearity and calibration. We decided to restrict illustrations to nine sub-pupils, including eight sub-pupils inside the pupil and one hidden by central obscuration. The previous eight sub-pupils were evenly lit since they were not obscured. Note the results were the same whether or not non-uniformity was corrected. In Fig. 9, the signal linearity range is between 3170 ADU (texp = 1 μs) and 13200 ADU (texp = 15 ms). Saturation is at 13200 ADU reaching the detector well’s maximum capacity. Note that the central sub-pupil (with No. 13) presents a completely linear variation of the signal flux since it was reduced by the central obscuration. In Fig. 10, we plot signal variance in relation to the signal. Two regimes are visible on these graphs, namely a zone corresponding to linearity and a saturation zone where the signal variance collapses. By removing the last 2 measurements in saturation, the linear regime fits a straight line according to the “least squares” criterion. The line slope is G = 0.0075 on average. The saturation level is therefore (13200 – 3170)/0.0075 = 1.33Me− to be compared to the announced full well capacity of 1.38Me−. The camera calibration equation is therefore
Readout noise (RON) is estimated by the signal variance when the exposure time is minimal. On Fig. 10 and for subaperture No. 13, we read . This noise value was also measured at the factory. Note that digitalizing noise is negligible when compared to RON.
4.4. Camera vibration
The Stirling cooler causes vibrations at 50.075 Hz that propagate via the capillary and the mechanical structure. We used mechanical simulation to study vibrations the cooler caused and the effect on the optics and detector. All predicted movements are below 1 μm RMS; nevertheless we built a mechanical structure for the Stirling cooler and cryostat. The mechanical isolation between the cooler and cryostat enclosure has joint shocks at the interface (see Fig.11). The top section supporting the compressor is in stainless steel; the bottom section supporting the cryostat is in steel to get a high mass ratio between the two parts. To decrease AO bench vibrations, we added stops, firmly fixing the mechanical housing in place on the plate control.
We checked expected vibration levels, by installing the SH WFS with its objective and a source on the bench; it was set at focus. We measured vibrations transmitted to the spot image onto the detector by centroids. The residual wavefront should be smaller than 0.2 rad RMS, corresponding to a spot displacement on the FPA smaller than 1 μm RMS. Measurements for a specific subaperture image are shown on Figs. 12 and 13. The two graphs represent the power spectral density (PSD) of the spot motion projected on axis x and y. PSD causes a vibrational peak at approximately 50 Hz as expected. Along x axis (resp. y), the total centroid standard deviation is equal to 0.25 μm (resp. 0.32 μm), the component restricted around 50 Hz equals 0.16 μm (resp. 0.22 μm). These measurements were conducted on the 20 subaperture images, that the cold pupil did not obscure. The results summary is given in terms of WFE over the pupil. The standard deviation of the tip and tilt Zernike coefficients are: σtip = 0.04 rad RMS and σtilt = 0.05 rad RMS. The quadratic sum of these values gives the WFE, which is well below the specification, thereby validating our mechanical housing.
4.5. Modulation transfer function
Wavefront measurement accuracy depends on spot image width. We first had to measure the focal spot’s optical quality. To do so we therefore measured the modulation transfer function (MTF) from several images of a slightly inclined razor blade, illuminated by a black body. Optical conjugation was performed with a high-quality lens, working at the anti-nodal point. We considered the lens did not limit measurement of the modulation transfer function of the WFS subapertures, since the optical aperture was that of the SH WFS. Images were recorded with a non-uniformity correction of the pixel response. Each sub-image was handed as follows: we defined an area of interest i(x, y) around the blade which included both a bright and a dark area. The image is the Edge Spread Function ESF resulting from convolution of the Line Spread Function LSF and a Heaviside heav that represents the razor blade:Fig. 14. We show only the nine sub-pupils that are unmasked. The measured MTF (solid line), the theoretical MTF (dashed) and the MTF of a pixel are represented in the Figure. The theoretical MTF was calculated from the pixel MTF and the average of the optical MTF of a diffraction limited square sub-pupil, its cutoff frequency varying by wavelength between 3.4 – 4.2 μm. We see that both theoretical and measured MTF are very close. For these 8 sub-pupils, the average Strehl ratio is 92 ± 4 %. Such optical quality is excellent even if scattered.
5. Expected and real performances of the Shack-Hartmann wavefront sensor
5.1. Position-finding algorithms for an extended scene
An illustration of noisy subaperture images sampled at Shannon/2 is provided in Fig. 15. The extended source has either a high contrast of 0.4 or a low contrast of 0.04 corresponding respectively to target temperatures of 455 K and 305 K. Indeed, the simulated SH image includes photon, thermal, detector noise and residual turbulence. The noise induced by background sky amounts to 118 e− RMS, thermal noise is 122 e− RMS and the dominant RMS noise detector is 250 e−. The noise induced by sky background is given at the 7 cm subapertures focal plane and Shannon/2 sampling. It corresponds to the frame rate 500 Hz used for performance simulations. Measuring the wavefront slope in a Shack-Hartmann subaperture relies on the object’s position measurement. Cross-correlation allows both to detect and locate a signal on a background, even with low contrast and noise. This method was chosen for its better detectivity on a structured background, its good noise resistance and image under-sampling.
By simulations we studied the slope measurement error expressed as a phase at the subaperture edge. This error in rad2 was the sum of the variance and the squared bias. We note that measurement noise was filtered by the AO loop. Given depreciation, we set the maximum slope measurement noise to 0.5 rad2. In any event, this contribution remains well below other errors (i.e. anisoplanatism, temporal and fitting errors).
In practice the correlation was performed between a reference image from an unmasked sub-pupil (i.e. the template) and an image from any other sub-pupil, partially obscured or not, for example by pupil mask or telescope spider. Once cross-correlation performed, several algorithms to find its peak with sub-pixel accuracy were implemented: the “parabolic fit” and two in-house variants of “ center of gravity”. The “parabolic fit” calculates the peak position by interpolating with a parabola the cross-correlation in a window of 3 × 3 pixels centered on the maximum. The “center of gravity” calculates the position of the peak by applying a threshold which is either a fraction of the cross-correlation maximum (version 1), or the minimum of the cross-correlation seen in a window centered on the maximum (version 2). These algorithms had been tested as equally accurate in term of positioning the peak under certain simulation conditions . However the tests were done using a Gaussian spot image sampled at Shannon. Here, the correlation methods calculated the cross-correlation map with under-sampled images . These methods were compared to the one proposed in  which deals properly with under-sampling. We call below this method the maximum likelihood estimator (ML). We note that the ML is equivalent to a correlation, if the source has a compact support and stationary Gaussian noise. However, ML is more complex and hence cannot be easily implemented with a 440 Hz RTC.
Yet we studied in simulation the error of the slope measurement, including its bias. We compared the strength of the algorithms in presence of the two object contrasts. We also evaluated their ability to deal with differences in sub-aperture illumination between the unmasked template and a given subaperture may be obscured in its middle by thin vertical stripe. Figure 16 presents slope wavefront errors (squared bias plus variance) as a function of the subaperture obscuration in fraction of “spider” width. From top to bottom we present estimations with: ML, “center of gravity” (version 1), “center of gravity” (version 2), “parabolic fit”. Two object contrasts of 0.04 (squares) and of 0.4 (triangles) were considered. Error along x and y are displayed respectively in left and right columns.
The first result was that, for the low-contrast object, slope measurement errors reached the same level regardless of the method considered. From Fig. 16 the error levels obtained in all cases were compatible with the operation of an AO system since they were less than 0.1 rad2 at high contrast and less than 0.5 rad2 at low contrast. All methods met the given requirement of the measurement noise (0.5 rad2). In particular, the cross-correlation methods are slightly nonlinear but ML. This is not a problem since they can be calibrated. Further, we could rank the correlation methods for a high-contrast object. The best in terms of accuracy is the ML estimator. Both versions of “center of gravity” have a comparable performance in terms of slope measurement error. In detail, version 1 of “center of gravity” is slightly less noisy than version 2. Both require nevertheless adjustment of the threshold or window size. For example, with a high-contrast object, we use a window of 15 × 15 pixels. At low contrast, the window is to be reduced to 3 × 3 pixels. The method of “parabolic fit” doesn’t require such an adjustment, but it is lightly less accurate than “center of gravity” because of its greater non-linearity. Finally “center of gravity” has been implemented in the RTC and used in operation of the closed-loop AO in field trials.
The second result is that all methods employed with a “spider” subaperture obscuration are biased up to 0.3 rad. In fact, the bias depends on the subaperture obscuration, that is difficult to calibrate and therefore not acceptable. This result led to the specification of a very thin spider on the telescope which was not necessary on the SH WFS cold pupil.
5.2. Field tests
Two test campaigns were conducted in June and October 2008 in Verdon (France) with the full AO bench. The bench used a telescope 35 cm in diameter, a tip and tilt mirror and 6 × 6 actuators on a deformable mirror for the high order wavefront correction, the RTC, the mid-IR SH WFS for the wavefront sensing and finally a mid-IR camera for full pupil imagery at fNyquist/2 sampling. The optical bench observed fixed thermalized sources 10 cm in diameter at temperatures ranging from 40 °C and 100 °C. They were located on top of a mountain at an altitude of 700 m above the observation point and at a distance of 11.5 km. Sources being much smaller than SH WFS pixel, these temperatures are still representative of an IR target. These source temperatures relate to contrasts of 0.04 and 0.4 taken in the expected-performance WFS study (see previous paragraph 5.1). The ability of the AO bench to make the full pupil images sharper is illustrated on Fig. 17 at high contrast. The source used as a reference by the SH WFS is the full structure of 3 m x 2 m, each spot being separated by 50 cm from one to another. The structure size is smaller than correlation length since we had D/r0 = 2 during the field tests. Indeed we are not in the limit of a very large structure with respect to the correlation length. In addition, data from the SH WFS recorded in open loop with a point source were treated with the method SCO-SLIDAR . They helped to retrieve the profile along the optical axis of the 11.5 km between the source and receiving telescope. This profile compared favorably with data obtained from measurements at both ends of the line of sight and to the terrain profile. Actually we detected a rise of along the sight line that corresponded to a greater proximity of ground at a certain point of propagation. These results are the first experimental validation of the method. Details of this work are presented in a recent communication . The knowledge of the profile led us to estimate the performance of the AO demonstrator showing correlation of the error budget obtained in simulation with that of the experience.
6. Conclusion and perspectives
This paper has presented the development of a SH WFS working on extended source in the mid-IR band. The SH WFS meets the requirements of an AO system in terms of accuracy, sensitivity and frame rate. It fulfilled the mid-IR constraints that are optics and FPA being at cryogenic temperature, and vibrations due to the cooler. This device was to our best knowledge a world first by incorporating optics accurately in a cryostat without adjustment. This device was implemented on a AO bench. Performances have been demonstrated in laboratory and the behavior in the AO system was checked during a field experiment. We closed the loop on the AO system in 2007 in the laboratory. During the field experiment in 2008, the entire AO system provided an endoatmospheric demonstration by raising the spatial resolution of the telescope images. Agreement between simulated and experimental performance was found. Furthermore, the mid-IR wavefront sensor was used also to remotely sense the turbulence profile along the line of sight.
Perspectives of using this SH WFS are foreseen in other campaigns such as to study heat flux close to the ground in the agronomy domain. Mid-IR spectrum is interesting to enlarge the range by delaying the saturation of scintillation. Other applications could be monitoring the on top of buildings in ground-based telecoms.
Advanced know-how on wavefront sensor design combined with cryogenic detectors and mechanics is useful in developing an IR WFS in the field of astronomy. Galactic and extragalactic star-forming regions have to be observed in the near-IR band with adaptive optics. AO ultimate performance relies on a key element: the wavefront sensor working at near-infrared wavelengths in order to catch the few photons coming from embedded regions obscured by dusty clouds. For current AO systems, not using LGS, a SH WFS in the infrared could be a valuable equipment to enlarge their sky coverage in the short term. For planned systems with laser guide stars, such a device could be envisaged for low order aberration wavefront sensing on IR natural guide stars. Hence the need for low noise (a few e- RMS per pixel) and high speed (up to 1.5 kHz) for a large detector array (typically a few tens of thousand pixels) is critical. Noiseless amplification in pixel is provided using avalanche photodiodes (APD) with electrons multiplication. A Shack-Hartmann wavefront sensor with such a MCT APD array is currently in development in the framework of the RAPID project .
This work was supported by the French Délégation Générale de l’Armement and ONERA. The authors thank Francis Mendez and Joseph Montri for technical support in mounting and servicing the SH WFS. The authors also thank Luc Veyssire and Mathieu Geldof for testing the SH WFS and the entire ONERA team participating in the field tests. The authors thank Franck Lefvre and Jean-Baptiste Moullec for the fruitful exchanges they have had with them, and are very grateful to Jean-Marc Conan for his contribution in reading the draft and sharing his insightful commentary.
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