A deformable mirror with actuators of thermoelectric coolers (TECs) is introduced in this paper. Due to the bidirectional thermal actuation property of the TEC, both upward and downward surface control is available for the DM. The response functions of the actuators are investigated. A close-loop wavefront control experiment is performed too, where the defocus and the astigmatism were corrected. The results reveal that there is a promising prospect for the novel design to be used in corrections of static aberrations, such as in the Inertial Confinement Fusion (ICF).
© 2015 Optical Society of America
As the core device in adaptive optics system, the deformable mirror (DM) is being under investigation for many years, multiple actuating mechanisms have been developed. The piezoelectric actuating mechanism is largely used in astronomy and laser engineering, where the quick response and adequate stroke can be achieved [1, 2]. However, the cost of the piezoceramic DM is high, and the wavefront control suffers from the intrinsic hysteresis of piezoceramics . The electrostatic force and electromagnetic force are also used as the actuating power in DMs that fabricated by micro-electromechanical-system (MEMS) technology, the MEMS DM are normally used in imaging of minute structures [4, 5]. Compared with the piezoelectric actuating mechanism, the actuating power of electrostatic force or electromagnetic force is weaker, but the resolution of the actuators is much higher, hundreds or thousands actuators can be integrated into one DM of a diameter of several centimeters [6, 7]. The thermal deformation is another actuating mechanism for DM . Recent years, DMs of thermal actuators are used in the interferometer gravitational wave detectors, where the noise in the detection must be effectively suppressed. The heating effect can be achieved by different means, such as ring heaters , external pump beams , radiative heaters  or thermal resistance . Combining the thermal effect with the piezoelectric effect, the thermal-piezoelectric deformable mirror is reported recently . The slow response of the thermal actuator is a main disadvantage of thermal DM, which limits its use in applications that ask for quick response. However, the thermal DM can be used in the ICF systems, such as the National Ignition Facility of America , or the ShenGuang Project of China . The aberration of each laser beamlet in the ICF system is nearly the same when the pump power is fixed, thus the control parameters can be determined in advance, the comparatively slow response of the thermal actuator is not a barrier for the wavefront correction of the laser beamlet. Besides, the simple structure of the thermal actuating DM can bring about better stability and robustness. Finally, the low cost of the thermal actuating DM is quite appealing in systems of multiple laser beamlets, where hundreds of DMs are used. The thermal actuating DM that is design to be used in the high power laser has been proposed in , where the thermo-field bimetal effect is used to control the surface shape of the mirror. Further research on controlling the thermal response functions can be seen in , where a water channel is designed to shape the response function, as well as limit the cross-talk between actuators. Different from the single-heating thermal actuating DM, the DM with TEC actuators is presented in this paper, the bidirectional thermal actuating property of the TEC can perform both upward and downward surface control of the mirror. The structure of the DM is introduced at first. Then the configuration of the wavefront correction system is presented. In the experimental study, the response functions of the actuators were investigated. Finally, a close-loop wavefront control experiment was performed.
2. Structure of the bidirectional thermal actuating DM
In order to realize both upward and downward surface control of the mirror, the thermoelectric coolers (TECs) are chosen as the thermal actuators. According to the polarity of the applied electric current, the TEC actuator pumps the heat from one side to the other. By shifting the polarity of the current, both the heating and refrigerating thermal actuation can be applied. Different from the DM actuated by thermo-field bimetal effect , the thermal actuator presented in this paper has direct thermal contact with the mirror. The fabrication procedure of the DM is shown in Fig. 1. In order to keep the surface quality of the mirror, a standard flat mirror of a large aperture is set to be the reference surface. In the first step, the mirror is put on the standard flat mirror to get a “plane transfer”. In the second step, a water channel is glued to the backside of the mirror, which is used to dissipate the heat when dealing with continuously running high power laser. Each actuator is surrounded by a squared water flow when turning on the water pump. In the third step, the copper pillars are directly glued to the backside of the mirror with the smaller ends, where the wider ends of the pillars are pre-glued to the TEC actuators. Then the heating or refrigerating actuation of the TEC is conducted to the mirror via the copper pillar. Finally, a heat sink is put on the TECs to extract the thermal power and keep the TECs work within appropriate temperature range.
A photo of the prototype is presented in Fig. 2. The square mirror has a dimension of 82 mm × 82 mm × 2.5 mm, the material is BK7 glass. There are 25 actuators arranged as a 5 × 5 square array. The working aperture is defined by the 5 × 5 square array as the dash line indicates. The interval between adjacent actuators is 13 mm. The size of the thermal contact is decided by the smaller end of the copper pillar, which is 3 mm in diameter. The maximum driving current for the TEC is 3.3A, and the maximum temperature difference between the two sides of the TEC is more than 67°C.
As shown in Fig. 2, the number of the 25 actuators starts from the upper left corner and ends at the bottom right corner line by line. The wires of the 25 TECs are connected to a direct current supply driver through an air plug connecter. Some material parameters of the mirror and the copper pillar are summarized in Table 1.
Two mechanisms mainly account for the actuation of the TEC actuator. The first mechanism of the actuation is the thermal expansion of the cooper pillar. According to the parameters in Table 1. However, the elongation of the pillar does not completely transfer to the deformation of the mirror since part of the elongation of the pillar would be absorbed by the soft glue layer. The glue turned into a gel-like structure after solidification and formed a cushioning between the pillar and the faceplate, which would reduce the stress at the contact and alleviate the “print-through” effect.
The second mechanism of the actuation is the deformation of the faceplate itself. The copper pillar has a large thermal conductivity, the temperature distribution within the pillar is nearly uniform. The heating or refrigerating effect of the TEC is conducted to the faceplate via the cooper pillar, and the temperature gradient is formed around the thermal contact of the faceplate. The expansion of the glass material itself contributes to the deformation of the faceplate too. The water channel is glue to the faceplate, which applies constrains on the faceplate. Besides, a thermal exchange wall is formed around each actuator due to the powerful water convection, which limits the temperature gradient within certain area. Thus the response function will not be too wide, and the cross-talking among actuators can be controlled. More details of controlling the response functions of the actuators by adjusting the convection condition can be seen in .
When the TEC heats the copper pillar, the elongation of the pillar gives the faceplate an upward actuation on one hand. On the other hand, the heated faceplate would bend itself to a biconvex shape considering the constraints applied around the thermal contact. The two mechanisms add up to an upward actuation to the faceplate. Similarly, a downward actuation is expected when the TEC refrigerates the copper pillar.
3. Configuration of the wavefront correction system
The researches of the DM are carried out via an adaptive optics system with Shack-Hartman wavefront sensor. The configuration of the system is shown in Fig. 3. The Shack-Hartman wavefront sensor consists of a high performance camera and a microlens array. The CCD is produced by Basler, with a resolution of 1004 × 1004 pixels, the dimension of the photosensor is about 7.43mm × 7.43mm. The microlens array has a dimension of 10mm × 10mm, the pitch of the microlens array is 300μm, which is made by Edmund Optics Inc. A 1053nm fiber laser is chosen as the spot light source, the fiber has a 9μm core and a 125μm cladding. The collimation lens and the relay lens form a telescopic system. The focal length of the collimation lens and the relay lens is 1.5m and 100mm respectively, thus the scaling factor is 15 times. The fiber laser is first collimated by the collimation lens and then reflected by the DM. After passing through the telescopic system, the re-collimated light is focused by the microlens array and detected by the camera. A current supply driver is used to provide the electric power to the TEC actuators, the maximum driving current of the current supply driver is 3.5A, and the polarity can be switched. In the wavefront control, the S-H Unit transfers the measured light intensity into digital data and performs the wavefront reconstitution, as well as generating the control currents of the 25 actuators to correct the measured wavefront.
4. Experimental investigation of the DM
The experiments were carried out in our thermostatic laboratory, where the environment temperature is set to be 20°C. The cooling water of the water channel and the heat sink is also set to be 20°C. The surface shape of the mirror after fabrication is checked by an interferometer at first, where the wavelength of the interferometer is 632.8nm. Since the 5 × 5 actuator array covers just part of the faceplate, the working aperture of the DM is defined as the square area of 52 mm × 52 mm. The interference pattern of the working aperture of the faceplate is showed in Fig. 4(a), where the Peak-Valley (PV) value is 0.92μm, the Root Mean Square (RMS) value is 0.18μm.
In order to have a general understanding of the actuation of the DM, an open-loop experiment of flattening the mirror was carried out first. We changed the current and the polarity of the TEC and observed the deformation of the faceplate via the interferometer. Just as expected, when applying a positive current, the TEC heated the copper pillar and produced an upward actuation to the faceplate. On the contrary, when applying a negative current, the TEC refrigerated the copper pillar and produced a downward actuation to the faceplate. By adjusting the driving current one by one, we tried to adjust the surface shape of the mirror to be a flat surface. After the open-loop adjustment, the PV and RMS were reduced to 0.38μm and 0.09μm respectively, the interference pattern of the flattened mirror is shown in Fig. 4(b).
After knowing basic features of the actuation, the DM was put in the wavefront correction system to carry out further investigation. According to the 15 times scaling of the telescopic system, the 52mm × 52mm working aperture of the faceplate corresponds to an aperture of about 3.5mm × 3.5mm at the entrance of the Shack-Hartman sensor. Theoretically, a 12 × 12 focused dot matrix on the camera can cover the working aperture, however, a 14 × 14 focused dot matrix was used in the test of response functions to guarantee all response functions were covered.
Among different actuating mechanisms, the thermal actuation has a comparatively slow response. The curve of stroke over time is presented in Fig. 5. Two different driving currents were applied on the actuator 8. The time to reach 90% stroke cost about 25s when the driving current is 1A positive, while the time for 90% stroke cost 5 more seconds when the driving current is 2A positive. When the thermal equilibrium state of the DM formed, the actuator showed a quite good stability in the stroke.
The response functions of the 9 actuators on upper left quarter of the mirror are shown in Fig. 6, where the response functions were measured when applying 2A positive current. The TEC produced heating actuation when applying positive current, the upward deformations of the faceplate were observed. It is interesting to see that there is a slight upward displacement observed in the opposite direction of the actuator on the faceplate, and this phenomenon is observed in response functions of nearly all actuators. From the PV values listed in Fig. 6, we can know that the strokes of the actuators were not uniform, the stronger stroke is more than 2 times larger than the weaker stroke.
By shifting the polarity of the current supply driver, the actuator 13 was applied driving current of positive 2A and negative 2A respectively, the comparison of the two response functions is presented in Fig. 7. The stroke of the upward stroke is 4.29μm and the downward stroke is 1.35μm. When applying the same driving current, the heating effect obviously brings about larger deformation of the mirror than the refrigerating effect.
The results from Fig. 6 and Fig. 7 showed that the uniformity of the stroke is not very good, there are actuators have obviously stronger or weaker response functions than the average level, however, there seems to be no pattern for the positions where the stronger or weaker response function appears. The actuator stroke over the driving current was measured. The measuring range of the current is set to be −3A to 3A with measuring points at −3A, −2A, −1A, −0.5A, −0.25A, 0A, 0.25A, 0.5A, 1A, 2A and 3A. We applied the maximum driving current 3A to the 25 actuators, the average upward stroke is around 5-6μm and the average downward stroke is around 1.5-2μm. By attaching a thermistor to the copper pillar with conductive grease, the temperature of the copper pillar at the measuring points was obtained. Stroke curves of three actuators over the temperature of the copper pillars are presented in Fig. 8, where the actuator 13 represents a medium stroke level of the response function, actuator 8 and actuator 17 represent a stronger and weaker stroke level of the response function respectively.
Obviously, the temperature of the three copper pillars are not uniform when the same current is applied. The copper pillar temperature of actuator 8 covers from −0.3°C to 95.8°C, while the temperature ranges of actuator 13 is 3.8°C~76.9°C and actuator 17 is 7.2°C~71.9°C. In the bonding of the TECs and the heat sink, the TECs may not lie on the same plane, the gaps between the TECs and the heat sink are different. The thickness of the glue is nonuniform for different TEC, thus the thermal conductivity is nonuniform too, which causes the difference in the temperature of the copper pillars. Besides, the glue thickness between the faceplate and the cooper pillars, the thermal transfer efficiency of the thermal contacts all account for the difference stroke among actuators. Therefore, the same temperature of the copper pillars did not bring about an identical stroke.
Compared with the refrigerating actuation, the heating actuation has a much stronger capacity in temperature control. In the medium stroke of actuator 13, the same 3A current can provide 56.9°C temperature rise while only 16.2°C temperature drop is achieved. The comparison in actuator 17 is 51.9°C to 12.8°C, and actuator 8 is 75.8°C to 20.4°C. On average of the three actuators, the heating actuation is 3.76 times more powerful than the refrigerating actuation.
As a consequence, a larger elongation of the copper pillar, as well as a larger thermal deformation of the mirror can be achieved when the heating actuation is applied, thus a larger upward stroke is observed in the experiment. For instance, the upward stroke of actuator 8 already exceeds the higher limit of the measuring range of the Shack-Hartman sensor when the positive current is larger than 2A. According to the linear relation of the temperature-stroke curve, a stroke larger than 10μm can be predicted when the maximum 3A positive current is applied, where the temperature of the copper pillar reaches 95.8°C. However, when the maximum 3A negative current is applied, the temperature of the copper pillar is −0.3°Cand a downward stroke of only 2.44μm is achieved. The maximum upward stroke and downward stroke of actuator 13 are 5.95μm and 1.60μm respectively. For actuator 17, the maximum upward stroke and downward stroke are 4.60μm and 0.93μm respectively.
Based on the change of the response slope, the stroke curve can be divided into two stages. In the stage where the temperature difference between the copper pillar and the environment is within 10°C, the response slope is better, but the linearity is poor. While in the stage where the temperature difference is beyond 10°C, a drop in the response slope is observed, but the stroke keeps a better linear relation with the temperature of the copper pillar.
According to the measured response functions, a close-loop wavefront correction was performed to test the wavefront correction ability of the DM. As two typical aberrations, the defocus and the astigmatism were chosen as the target aberrations to be corrected. There were four aberrations corrected in the experiment, which were a convex defocus, a concave defocus, a 45° astigmatism and a 90° astigmatism. The PV value of the four target aberrations were all set to be 3.5μm. In the correction of each aberration, the target aberration is introduced in the wavefront correction system and set to be the reference of the system, the S-H unit is responsible for analyzing the input wavefront and generating the control current to compensate the target aberration. Theoretically, when the surface shape of the mirror is in a conjugate relation to the target aberration, the target aberration is fully corrected. The theory of the wavefront correction is based on the least square method, the close-loop correction method used in the experiment is described in .
The measuring area is a 12 × 12 focused dot matrix of the Shack-Hartman sensor, which corresponds to the 52mm × 52mm area of the DM. Depending on the increments of the control currents, the time for reaching the thermal equilibrium state ranges from 40 to 60 seconds during each loop. After a dozen loops of corrections, the PV values of the residue aberrations descended to below 0.5μm, the driving currents of the four close-loop correction are recorded.
Considering the measurement error of the wavefront correction system, the results of the close-loop corrections need to be verified by the interferometer. Since the driving currents of the close-loop corrections have been recorded, the surface shape of the faceplate should be in a conjugate relation to the target aberration when the recorded driving current is applied. The verification experiment was carried out on the interferometer. By applying the corresponding currents obtained from the close-loop correction to the DM, we acquired the surface shape of the faceplate which was conjugate to the target aberration. The results of the verification experiment is summarized in Fig. 9. The first column is the target wavefront that needs to be corrected. The second column is the measured interference pattern of the faceplate when the recorded driving current is applied. The interference patterns were in good accordance with the close-loop correction results, the faceplate presented a conjugate shape to the target aberration. Compared with the target wavefronts, the relative errors of PV and RMS are listed out too. The maximum relative error of PV is 11.1%, which appeared in the correction of the convex defocus. The maximum relative error of RMS is 19.9%, which appeared in the correction of the concave defocus. On average, the relative error of PV and RMS is 5.9% and 13.4% respectively in the corrections of the four target aberrations.
From the results of the close-loop experiment, the DM showed a good correction ability to typical aberrations, which indicated a promising application prospect for the DM to be used in the wavefront correction of the high power laser, where the target aberration is normally static.
In conclusion, a DM with TEC thermal actuator is introduced in this paper. Both heating and refrigerating driving power are available for the TEC actuator, thus the upward and downward surface shape control of the mirror can be performed. The correction ability of the mirror was first tested by an open-loop flattening experiment. Then the details of the response functions were investigated. The average upward stroke is around 5-6μm and the average downward stroke is around 1.5-2μm when the maximum 3A driving current is applied. However, the stroke uniformity of the actuators is not good enough. With better bonding technology, we believe a more uniform response function with larger than 10μm stroke can be achieved. Finally, a close-loop wavefront correction experiment was performed, where the correction of the defocus and the astigmatism were completed. Though the response of the thermal DM is comparatively slow, tens of seconds are needed to reach a thermal equilibrium state, there is still a promising prospect for the design to be used in occasions that are dealing with static aberrations.
This study is sponsored by the National Natural Science Foundation of China (Grant No. 61178055).
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