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Abstract
The dynamic high frequency aberration (HIFA) only emerges in the compensation process in adaptive optics (AO) systems. The static surface shape of a deformable mirror (DM), which is ensured perfectly smooth by various reported techniques, cannot be used to figure out whether the HIFA exist or not. The dynamic HIFA of the DM, which has not been studied systematically up to now, is investigated theoretically and experimentally in this paper. The mechanism of the dynamic HIFA of the DM is presented in the simulation. Analysis results indicate that the tilted actuators results in shear displacements on the DM’s surface shape and thus lead to the dynamic HIFA. The tilt mode of the DM is proposed to describe the surface shape patterns under different tilt conditions. In the experiment, the dynamic HIFA is identified and the tilt modes are exactly recognized on the manufactured DM with tilted actuators, while the correction ability and the fitting residual of this DM are verified to be much worse than that of an ideal DM. Our investigations could help researchers effectively recognize and depress the dynamic HIFA in their own DMs, which could ensure the high precision aberration control during the compensation process of AO system.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The AO system, using the DM as the critical wavefront aberration corrector, plays an important role in the Inertial Confinement Fusion (ICF) [1, 2], astronomical telescopes [3, 4], microscopy [5, 6] and high-power laser systems [7, 8], etc. However, due to the limitations of the structure and actuating mechanism, the DM is unable to correct the HIFA of the incident wavefront efficiently and only used to correct the low order wavefront aberrations [9–12]. The negative impacts of the uncorrected HIFA have been revealed in many reports [10–12]. For example, in the ShenGuang-III Facility (SG-III), which is a high power laser system for the inertial confinement fusion in China, the AO system is used to correct the wavefront aberrations [10]. However, affected by the uncorrected HIFA, the far field pattern is far from smooth with plenty of discrete minor spots in it. Similar results have been observed in the National Ignition Facility (NIF) as well, which is used for the inertial confinement fusion in the United States [11]. Besides, in a fiber laser with an extra-cavity beam cleanup AO system, the uncorrected HIFA causes the unwanted burrs to appear at the edge of the focus spot and degenerates the beam quality of the fiber laser [12]. In these AO systems, the uncorrected HIFAs could be considered as the aberrations caused by the static factors (e.g. the material uniformity, the surface shape of the optical reflectors, and the surface shape of the DM) and the dynamic factors (e.g. the air turbulence, the temperature, the dynamic aberration of the material, and the dynamic aberration of the DM) [13–18].
In order to suppress the influence of the static factors, various fine manufacture techniques [13] have been developed to ensure the smoothness of the optical surface to control the static HIFAs below a certain level. For the reduction of the dynamic HIFA, the control techniques of environment stability [14–16], including the constant temperature/humidity room and totally enclosed optical route, are widely adopted in AO systems. Moreover, some researchers have been aware that the surface shape of the DM, unlike the regular optical elements, could not be well controlled during the adhesive bonding process, even if the surface shape of the DM is polished and coated well, and some special efforts should be made to mitigate the unwanted aberrations [17, 18]. In the Laser MégaJoule Facility in France (LMJ), a thick mirror is used in the DM to filter the high frequency defects introduced during the bonding operations, and annular pads are bonded at the back of the thick mirror to act as a low pass filter for the high frequency defaults smoothing [17]. In another LMJ DM prototype, the combination of a piston clearance and an elastic connection to the glass faceplate helps to minimize the unwanted transverse stress in the faceplate [18]. However, during the compensation process of the AO system, distinct dynamic HIFA could still emerge, even if the static HIFA of the whole optical system and the environment stability of the lab are perfectly controlled. According to the working principle of the AO system, the DM is considered as the primary source of the emerging dynamic HIFA in the compensation process, as the influences of other factors could be effectively reduced by various methods mentioned above. The dynamic HIFA will determine the limitation of the correction ability of a DM (e.g. large HIFA may even result in the failure of the aberration correction). However, according to our knowledge, the dynamic HIFA of the DM has not been studied systematically up to now.
In this paper, the dynamic HIFA of the DM is investigated systematically. A simulation model is built to analyze the mechanism of the dynamic HIFA, where the concept of the tilt mode is presented to describe the dynamic HIFA patterns. The influences of the structure parameters on the correction ability of the DM with dynamic HIFA are also studied. According to the simulation results, the dynamic stretching of the tilted actuator results in the shear displacements and leads to the dynamic HIFA of the DM. An effective recognition method is presented to identify the tilted actuators and the related dynamic HIFA. In the experiment, the dynamic HIFA is clearly distinguished and the correction ability of the DM with the dynamic HIFA is verified to be much worse than that of an ideal DM. The tilt modes recognition is also experimentally carried out and four types of tilt modes are precisely recognized based on the experiment data, which coincide well with the simulation results.
2. Mechanism of the dynamic HIFA and the simulation model
In the high-power laser systems, the high density piezoelectric (PZT) DM is applied to correct the wavefront aberrations [19]. Distinguishing from other optical elements, generally, a DM consists of a well-manufactured mirror with numerous actuators bonded on the back and a rigid mechanical base [Fig. 1(a)]. During the manufacture process, the surface aberration of the mirror is minimized by high precision surface polish technique and high quality coating technique. Subsequently, by adhesively bonding the mirror to the mechanical base, an assembled DM with the perfect surface shape could be achieved. However, according to the current assembling technique, it is difficult to make all the PZT actuators bonded normally to the back of the ultrathin mirror in such a high density DM (e.g. 116 actuators within a 92mm × 92mm × 1mm mirror). The consequential actuator tilt, which occurs in the local location around the actuator, is inevitable and distinct. During the compensation process of a DM, the shear displacements provided by the tilted actuators will emerge at the contact area of the mirror with the tilted actuator. As a result, the surface shape is distorted and the dynamic HIFA of the DM is formed.
Fig. 1 Analysis model of the DM. (a) Typical structure of the DM. (b) The XZ coordinates and the normal displacement of the top surface of an actuator. (c) The XY coordinates and the shear displacements of the top surface of an actuator.
In order to analyze the dynamic HIFA of the DM, a NIF DM structure (i.e. a continuous mirror and PZT actuators) [1, 2] with one actuator tilting is selected as the analysis object in Fig. 1(a). HG denotes the thickness of the mirror, and HP is the length of the actuator. The actuators aside are perpendicular to the mirror surface, while the central actuator tilts from the ideal perpendicular position (marked in dashed lines). Figure 1(b) and Fig. 1(c) illustrate the coordinates, the normal displacements and the shear displacements of the contact center of the mirror and the actuators. The surface of the DM’s mirror coincides with the XY plane. In Fig. 1(b), point Oi represents the center of the contact area of the ith perpendicular actuator with the mirror, point Ai represents the center of the contact area of the tilted actuator with the mirror, and point Bi represents the center of the contact area of the ith actuator with the base. (xi, yi, zi) and (, , ) are the coordinates of points Oi and Ai respectively. As the mirror and the actuators are bonded rigidly, the coordinates and displacements of the top surface of an actuator equals to that of the contact area of the mirror. Ui is the total displacement along the stretching direction of the actuator, and Uzi is the normal displacement along Z-axis. φi is the pitch angle of the tilted actuator (i.e. the angle between the stretching direction of the actuator and the normal direction of the mirror surface). In Fig. 1(c), points Ci and Di are the projection of point Ai along the X-axis and the Y-axis, while Uxi and Uyi are the shear displacements of the top surface of an actuator along the X-axis and the Y-axis respectively. αi is the azimuth angle of the tilted actuator (i.e. the angle between the projection of the stretching direction of the actuator in the XY plane and the X-axis). The coordinates and the displacements of the top center of an actuator along the three coordinate axes can be expressed in Eq. (1).
Here, is the Z coordinate of the top surface of the ith actuator. Based on Fig. 1 and Eq. (1), using a finite element model built in ANSYS, the distorted surface shape caused by the actuator tilt could be calculated precisely in the simulation.
In our simulation model, the DM consists of a mirror (92mm × 92mm × 1mm full size, 80mm × 80mm clear aperture), a steel base (92mm × 92mm × 40mm full size) and hexagonally distributed 116 PZT actuators (3mm-diameter, 36mm-length and 8mm-pitch, several actuators are set tilted). As the thickness of the adhesive is usually small (100μm) and the shrinkage ratio is pretty low (less than 1%), the adhesive’s influence on the surface shape could be ignored. Thus, the adhesive is excluded in the model. The whole model is built with structural tetrahedron solid elements, each having 10 nodes. The material parameters are listed in Table 1 (the SiC material will be used in section 4). The DM’s mirror is free from any restraint, except the bonding with the actuators array. The degree of freedom (DOF) of the mechanical base is set to zero (i.e. the coordinates of the nodes on the base do not change in the simulation). The temperature influence is not considered, i.e. the working temperature is assumed uniform and equal to the mounting temperature.
Table 1. Material parameters in finite element simulation
In a manufactured DM, the surface smoothness could be well ensured by series of fine manufacture techniques. However, during the compensation operation of the DM, when the tilted actuators start working, the tilt conditions will result in the shear displacements on the surface shape of the DM and lead to the dynamic HIFAs with special patterns. In the analysis model, the initial surface shape of the mirror is set to be an ideal plane, and a 10μm piston is set as the target surface shape to reveal the dynamic HIFAs all over the mirror. In practice, the piston could be realized by the 10μm actuator’s stroke in most of the DMs. Actually, in the compensation process of the AO system, a piston displacement is always set to achieve a basic reference by applying bias voltages to all of the actuators. Obviously, similar results could be obtained, providing a 3rd Zernike mode or other aberration is used as the target surface shape. The simulation consists of two primary processes, the displacement process of the mirror and the compensation process. The displacement process is achieved by applying a 10μm stretching length on each actuator. Apparently, the surface shape after the displacement process includes a 10μm piston and a deformed surface shape on the DM. The influence function of each actuator is obtained by providing a 0.2μm displacement on the top surface of each actuator sequentially. Based on the influence functions, the compensation process could be realized by stretching or shortening each actuator using the least square method. Finally, the fitting residual of the mirror, which is the difference between the final surface shape and the target surface shape, can be obtained.
3. Dynamic HIFA and tilt mode analysis
3.1 Tilt mode
In the simulation, the tilt mode (TM), a new parameter, is introduced to describe the tilt condition and the resulted surface pattern. Under different tilt conditions, including the number, the pitch and the azimuth angles, and the relative position of the tilted actuators, different mode patterns are calculated out based on the simulation model. The characteristic of the dynamic HIFA could be precisely described by the tilt modes. Figure 2 shows the analysis results of typical TMs, including the tilt condition, the deformed surface shape and the fitting residual of the DM, setting the pitch angle as 1°. In Fig. 2, the solid circles represent the tilted actuators, while the hollow circles represent the perpendicular actuators and the red arrow represents the tilt direction in the XY plane. As a reference, in the zero tilt case in which no tilts occur at all, the surface shape does not deforms. Therefore, the fitting residual is zero all over the surface shape, which is not shown for brevity.
Fig. 2 Typical tilt modes of the DM. (a) The tilt conditions of actuators. (b) The deformed surface shape of the DM. (c) The fitting residual of the DM after compensation. Note: As to the name of each TM, the first figure after “TM” represents the number of tilted actuators, while the other two figures represent the serial number. For example, TM101 represents the first mode when only one actuator is tilted, and TM603 represents the second mode when six actuators are tilted.
In a hexagonally distributed DM, a hexagon with six actuators on the vertexes and one actuator in the center is assumed as a basic unit. Figure 2 lists the primary tilt modes from one actuator to one basic unit, which could depict the tilt mode patterns adequately and help researchers recognize the tilt modes in their own DMs. In Fig. 2, the TM101 mode represents the situation that an actuator tilts towards an adjacent actuator, while in TM102 mode the azimuth angle rotates by 90° (i.e. an actuator tilts towards the angular bisector of two adjacent actuators). In these two modes, a convexity appears in the same direction of the tilt, while a concavity appears in the opposite direction. In the TM201 and TM202 modes, a large convexity or concavity appears in the middle of the two tilted actuators, generating three extremums in the deformed surface shape and fitting residual. In the TM203 mode, two actuators tilt in the same direction. The convexity of the left actuator offsets the concavity of the right actuator, which results in a plane zone in the middle of the two actuators, while a convexity and a concavity appear in the outer side of the two actuators. In the TM301 mode, three actuators tilt towards their center, resulting in a large convexity (0.1μm amplitude) in the center and three small concavities (−0.05μm amplitude) around. The convexity amplitude decreases to 0.05μm and the concavity amplitudes are slightly smaller than −0.05μm after correction. In the TM302 mode, the actuators tilt in the opposite direction of TM301, which results in an opposite surface shape (i.e. a small concavity in the center and three large convexities around). Some TM patterns in Fig. 2 are summarized in Table 2, in which the number of tilted actuators, convexities and concavities are listed.
Table 2. Tilt mode patterns
As we can see from Fig. 2(b), a convexity and a concavity appears on both sides of the tilted actuator, which means that the tilt mode could not be effectively corrected by pulling or pushing the corresponding actuator. The peak to valley (PV) values of the deformed surface shape and the fitting residual of five typical tilt modes are listed in Table 3, in which all the non-correction ratios, (Fitting Residual PV)/(Deformed surface shape PV), are larger than 80%. Namely, more than 80% aberrations could not be corrected and remain on the surface of the DM.
Table 3. Correction ability of the DM on five tilt modes
3.2 Zernike polynomial decomposition of the tilt mode
In Fig. 3, a TM601 mode is decomposed into Zernike polynomials (the upper limit of the Zernike orders is set 48), as an example. The TM601 mode [Fig. 3(a)] and its high frequency component [Fig. 3(c)] almost have the same pattern and amplitude, while the pattern of the low frequency component [Fig. 3(b), 3(d)] is apparently different. This indicates that the tilt mode could be essentially considered as the high frequency aberration, which determines the deformed surface shape of a DM and the uncorrected residual of an AO system. Note that the fitting coefficient ratio is the ratio of the amplitude of the Zernike order to the PV value of the surface shape.
Fig. 3 Zernike polynomial decomposition of TM601 mode. (a) TM601 mode. (b) Low frequency component. (c) High frequency components. (d) The fitting coefficients ratio of the low frequency component. Note: Here, the components with the Zernike polynomial orders larger than 48 are defined as the high frequency components, and the components with the Zernike polynomial orders less than 48 are defined as the low frequency components.
3.3 Tilt mode decomposition and combination
The pattern of the tilt mode has the properties of decomposition and combination, i.e. the pattern of a tilt mode with multiple tilted actuators could be decomposed into multiple tilt modes. Conversely, multiple tilt modes can be combined into a tilt mode with multiple tilted actuators. The properties of decomposition and combination can be expressed in Eq. (2).
Here, (x, y) is the coordinate in the XY plane; i and n are the sequence number and the amount of the tilt modes to be combined respectively; Wi and Wc are the surface shape of the combined tilt modes and the combination tilt mode respectively.
As an example, Fig. 4 shows the combination of the three TM206 modes with different tilted actuators into a new tilt mode. Comparing Fig. 2(b17) and Fig. 4(d), the pattern and amplitude of the TM601 mode is almost the same with the new combination mode. The fitting coefficient ratios of the first 48 order Zernike polynomials of the new combination mode are shown in Fig. 5(a). Figure 3(d) and Fig. 5(a) indicate that the coefficient ratios of the combination tilt mode and the TM601 mode are almost the same. As the calculated ratio difference between the new combination mode and the TM601 mode is less than 10−4 [Fig. 5(b)], the new combination tilt mode and the TM601 mode could be considered exactly the same. This means that the three TM206 modes can be combined into the TM601 mode, and the TM601 mode can also be decomposed into three TM206 modes. Apparently, the decomposition and combination process are applicable to other tilt modes.
Fig. 4 Decomposition and combination of the tilt modes. (a)-(c) Three TM206 modes. (d) The combination mode.
Fig. 5 The fitting coefficients ratio of the first 48 orders Zernike polynomials of the tilt modes. (a) The new combination mode. (b) The difference between Fig. 3(d) and Fig. 5(a).
3.4 Tilt mode and dynamic HIFA recognition
The dynamic HIFA is very harmful and limits the compensation ability of the DM. However, the manufactures, researchers and users could hardly find the dynamic HIFA in the quality inspection process of the surface shape, as it only emerges during the dynamic operation. According to the analysis results above, by identifying the tilt modes, the dynamic HIFA of the DM could be effectively recognized.
The tilt mode and the dynamic HIFA recognition process of a manufactured DM consist of three major steps, including the piston realizing, the tilt mode identifying and the tilted actuators recognition. In the first step, a bias voltage is applied to all the actuators to realize a piston on the DM. In the second step, by searching the convexities and the concavities, the HIFA areas and the tilt modes are identified based on the TM pattern obtained by an interferometer. In the third step, according to the TM modes shown in Fig. 2, a convexity and a concavity will be paired to distinguish a tilted actuator and the tilt direction in the HIFA area (the actuator tilts toward the convexity). It is notable that a convexity or a concavity could be shared to form a pair to recognize a tilted actuator. Finally, the tilt mode and the dynamic HIFA of the DM are successfully figured out. Figure 6 shows an example of the dynamic HIFA recognition. In the identified HIFA area, three pairs of convexity and concavity, sharing the common convexity, are recognized as the TM301 mode. From the pattern shown in Fig. 6, three actuators can be distinguished tilting towards their center.
Fig. 6 Three pairs of convexity and concavity, sharing a common convexity in the TM301 mode. Each colored ellipse represents a pair of convexity and concavity.
4. Influence of the structure parameters
The influences of structure parameters on the correction ability of an ideal DM, including the mirror thickness [19], the number and distribution of the actuators [20], have been studied in some researches. Considering the tilt mode and the dynamic HIFA in the actual DM, more structure parameters should be taken into account. These parameters include the material and the thickness of the mirror, the pitch angle (defined in section 2), the stretching length of the actuators, and the contact area diameter. Note: In the following discussion, the TM101 mode is selected as the analysis object.
4.1 Pitch angle of the actuator
Figure 7(a) and 7(b) show the influence of the actuator pitch angle on the deformed surface shape and the fitting residual. As the PV values and root mean square (RMS) values increase linearly with the pitch angle, the correction ability could be improved and the dynamic HIFA could be suppressed, by decreasing the pitch angle of the actuator. For large pitch angle (e.g. φ = 6°), the PV value of the fitting residual is almost half of the original, which indicates that the low order of the aberration caused by the large tilt could be corrected by the DM.
Fig. 7 PV/RMS values of the deformed surface shape and the fitting residual. (a)–(b) The influence of the mirror materials and the actuator pitch angle. (c) The mirror thickness. (d) The actuator stretching length. (e) The contact area diameter (between the PZT actuator and the mirror).
4.2 Material and thickness of the DM’s mirror
Figure 7(a) and 7(b) also indicate that the mirror material (BK7, SiC) do not affect the correction ability of a DM with dynamic HIFA. Figure 7(c) shows the correction ability does not increase monotonically with the mirror thickness, while the variation of the PV value is less than 7% and the RMS values almost stay unchanged when the thickness improved from 1mm to 2mm. The maximum PV value appears at around 1.4mm mirror thickness. It could be concluded that both the material and the thickness only have slight influence on the correction ability of a DM with dynamic HIFA.
4.3 Stretching length of the actuator
In order to compensate the aberrations in AO systems, the actuators are required to stretch in different lengths to generate the conjugated surface shape. With the increase of the stretching length, both the deformed surface shape and the fitting residual will be strongly affected. In Fig. 7(d), the longer the actuator stretches, the larger the fitting residual, and the worse the dynamic HIFA emerges. When the actuator stretches to the length of 60μm, the fitting residual achieves as large as 0.5μm, even at the small pitch angle of 1°. In AO systems, the actuator stretching length is proportional to the amplitude of the aberration to be compensated, providing it could be realized by the actuator’s stroke. Accordingly, the HIFA is also in proportion to the amplitude of the aberration. Namely, the larger the aberrations to be corrected are, the worse the dynamic HIFA and the correction ability of the DM will turn. It indicates that the HIFA of the DM is not static, but dynamic, which is closely related to the aberrations to be corrected. Based on this notable analysis result, for different aberrations, a DM will present relevant different HIFA in different AO systems, or even in the same AO system.
4.4 Contact area diameter
Figure 7(e) shows the influence of the contact area diameter (between the PZT actuator and the mirror) on the deformed surface shape and the fitting residual. With the contact area diameter increasing from 1mm to 5mm, the PV value of the deformed surface shape decreases monotonically (i.e. larger contact area diameter introduces smaller deformation to the surface shape with tilted actuator). Also, the contact area diameter has influence on other factors, including the influence function and the coupling value. For the simulation model with 1mm thick mirror and 8mm pitch, Fig. 7(e) shows a minimum fitting residual PV value is achieved with a contact area diameter of 3mm.
4.5 Number of the tilted actuators
Table 4 lists the simulation results for two kinds of tilt situations. Situation I represents that the DM has multiple adjacent tilted actuators, while situation II only one tilted actuator. All of the tilted actuators in situation I are set inclining to the center of the tilted actuators. The pitch angle in situation II varies from 1° to 5°.
Table 4. PV value and RMS value of the two situations
As shown in Table 4 and Fig. 8, in situation I, when the number of tilted actuators is less than three, the PV value of the deformed surface shape and the fitting residual increase with the number of tilted actuators. When the number of tilted actuator is more than three, the PV and RMS values will stay stable. For the situation I with five 1° tilted actuators, the PV values of the deformed surface shape and the fitting residual are 0.1856μm and 0.1577μm respectively, which is three time of that of the perpendicular situation (0.054μm). In situation II, the PV values of the deformed surface shape and the fitting residual increase linearly with the pitch angle. For the situation II with only one 5° tilted actuator, the PV values of the deformed surface shape and the fitting residual are 0.5071μm and 0.2792μm respectively, which are almost two times of that in situation I. Obviously, the pitch angle of the actuator contributes much more HIFA to the DM, comparing with the number of tilted actuators.
As we know, HIFAs will not be observed when the DM does not work, as the surface shape of a DM is well manufactured by series of fine manufacture techniques. The static surface shape could not be used to figure out whether the HIFA exist or not. According to the above analysis, our methods indicate that the tilted actuators and the related dynamic HIFA could be clearly distinguished by applying a piston on the mirror and checking the tilt modes from the consequential surface shape of the DM. In order to depress the dynamic HIFA of a DM, the pitch angle of the actuator should be controlled as small as possible. If the pitch angle could not be changed, it is recommended that the DM should be remade to eliminate the dynamic HIFA and achieve the best correction ability, by adjusting the recognized tilted actuators and making them perpendicular to the top surface of the mechanical base. Otherwise, in order to avoid the emergency of the HIFA, the DM should be restricted only in the AO systems with small aberration. For instance, for a DM with only one actuator recognized 2° tilted, the PV value of the compensated aberration should be smaller than 10μm, if the target fitting residual is 0.2μm [Fig. 7(a)].
5. Experiment
In the experiment, two DMs with the same structure were manufactured in our lab [Fig. 9]. The structure of the DMs in the experiment is similar to the simulation model described in section 2. Each DM consists of a mirror plate, a PZT actuator array with mounting posts, and a mechanical base. One of the two DMs is manufactured without any tilted actuator (DM1), while some actuators are specially set tilted (totally 45 actuators are set tilted and the pitch angles are set 1° to 5° randomly) in the other DM (DM2). The clear aperture of the mirror is 80mm × 80mm. The total 116 actuators (P885.91, Physik Instrumente GmbH) are set in hexagonal distribution and the distance between two adjacent actuators is 8mm. The parameters are listed in Table 5. In our experiment, in order to achieve the accurate results, the effects of other factors are designed to be minimized. First, the two mirrors for the DMs are chosen to have almost the same quality. Second, the environment stability is well controlled throughout all the experiments (22°C temperature and 40% humidity). Third, only the DMs are replaced in the contrast experiments, without any other setup elements moved. Under this condition, the air turbulence could be considered the same in the measurements of the two DMs.
Table 5. Parameters of the DMs in the experiment
In the experiment, the deformed surface shape of the DMs is measured by an interferometer (ChengDu TYGGO photoelectricity Co., Ltd, INF100-LS, 632.8nm wavelength), after a 10μm piston. The correction ability and the fitting residual of the DMs are inspected by a Shack-Hartmann close-loop AO system, using a 1030nm wavelength fiber laser source. Figure 10 shows the measurement result of the two DMs. For the DM1 (without any tilted actuator), the deformed surface shape is excellent without any distinct HIFA, the PV value of which is as low as 0.36μm [Fig. 10(a) and 10(b)]. When the DM1 works in a Shack-Hartmann close-loop AO system, the system aberration can be corrected well and the PV value of the fitting residual is only 0.28μm [Fig. 10(c)]. The DM1 without any tilted actuator shows the fine deformed surface shape and the excellent correction ability. For the DM2 (with some actuators specially set tilted), the deformed surface shape is not flat enough with a 0.94μm PV value [Fig. 10(d) and Fig. 10 (e)]. As we can see from Fig. 10(e), the interference fringes are not straight and full of tiny curves, which indicate the emerging HIFA. When this DM2 with the HIFA works in an AO system, the system aberration could not be well corrected and the PV value of the fitting residual is as high as 1.05μm [Fig. 10(f)], which is fairly larger than that of the DM1 [0.28μm, Fig. 10(c)]. Due to the emerging HIFA on the surface shape, the correction ability of the DM2 is strongly limited.
Fig. 10 Experiment results of the DMs. (a) The color temperature diagram of the deformed surface shape the DM1. (b) The interference fringes the DM1. (c) The Shack-Hartman closed-loop correction result of the DM1. (d) The color temperature diagram of the deformed surface shape the DM2. (e) The interference fringes the DM2. (f) The Shack-Hartman closed-loop correction result of the DM2.
In the experiment, detailed explorations were further taken to investigate the tilt modes recognition in the DM2. The experiment results are shown in Fig. 11, where the dashed circles represent the tilted actuators, and the arrows represent the tilt directions of the actuators. In Fig. 11(a), a TM101 mode is observed at the position where one actuator tilts towards its adjacent actuator. A convexity appears between the tilted actuators and an adjacent actuator along the tilt direction, while a concavity appears between the tilted actuator and another adjacent actuator in the opposite direction simultaneously. The experiment data exactly agree with the simulated TM101 mode in Fig. 2(b1). In most cases, the convexity and the concavity locate right at the center of the two adjacent actuators. In Fig. 11(b), a TM202 mode is observed at the position where two adjacent actuators tilt in the opposite direction. Two convexities appear between the tilted actuators and their adjacent non-tilted actuators along the tilt directions respectively. Two concavities superpose with each other and result in one larger concavity between the two tilted actuators. The mode shown in Fig. 11(b) with three local extremums coincides well with the simulated TM202 mode shown in Fig. 2(b4). In Fig. 11(c), a TM203 mode is observed at the position where two adjacent actuators tilt in the same direction. A convexity appears between the left tilted actuator and its adjacent non-tilted actuator along the tilt direction, while a concavity appears between the right tilted actuator and its adjacent actuator in the opposite direction. As the concavity by the left tilted actuator offsets the convexity by the right tilted actuator, a flat zone comes into being at the position between the two tilted actuators. The mode shown in Fig. 11(c) coincides well with the simulated TM203 mode shown in Fig. 2(b5). In Fig. 11(d), a TM301 mode is observed at the position where three adjacent actuators tilt towards their center. Three concavities appear between the tilted actuator and its adjacent actuator opposite to the tilt direction. Three convexities superpose to build a large convexity in the center among the three actuators. The mode shown in Fig. 11(d) coincides well with the simulated TM301 mode shown in Fig. 2(b9).
Fig. 11 Experiment result of the tilt modes recognition. The color temperature diagram of the TM101 mode (a1), the TM202 mode (b1), the TM203 mode (c1) and the TM301 mode (d1). The interference fringes of the TM101 mode (a2), the TM202 mode (b2), the TM203 mode (c2) and the TM301 mode (d2). The dashed circles represent the tilted actuators. The arrows represent the tilt directions of the actuators.
6. Conclusion
In conclusion, the dynamic HIFA of the DM is investigated theoretically and experimentally in this paper. In the AO system, the dynamic HIFA significantly reduces the compensation ability of the DM. The static surface shape cannot be used to figure out whether the dynamic HIFA exist or not in a DM, as it only emerges during the dynamic compensation process. A simulation model based on a high density DM is built to analyze the mechanism of the dynamic HIFA. Analysis results indicate that the stretching of the tilted actuators results in the shear displacements on the DM’s surface shape and lead to the dynamic HIFA. The tilt mode of the DM is presented to describe the tilt condition and its resulted surface pattern. The primary tilt modes of a hexagonally distributed DM are calculated. According to the analysis results, the tilted actuators and the related dynamic HIFA could be clearly distinguished from the consequential surface shape by applying a piston on the mirror and checking the tilt modes. Comparative experiments are carried out to verify the simulation results. In the DM with tilted actuators, the dynamic HIFA is clearly distinguished by the tiny curves in the interference fringes. The correction ability and the fitting residual of the DM with the dynamic HIFA are verified to be much worse than that of a DM without tilt. In the experiment, the tilt modes recognition process is also successfully carried out and four types of tilt modes are precisely recognized from the experimental pattern, which coincide well with the simulation results. Simulation and experiment results shows, in order to reduce the dynamic HIFA of a DM, the pitch angle of the actuator should be as small as possible. If the pitch angle could not be changed, it is recommended that the DM should be remade to eliminate the dynamic HIFA and achieve the best correction ability, by adjusting the recognized tilted actuators and making them perpendicular to the top surface of the mechanical base. Otherwise, the DM should be restricted only in the AO systems with small aberration to avoid the emergency of the HIFA.
Funding
National Natural Science Foundation of China (NSFC) (Grant No. 61775112).
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