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Abstract
Inner surface defects of inertial confinement fusion (ICF) capsule are a key factor leading to ignition failure; however, there are still no effective and non-destructive detection methods available. To solve this problem, we propose the first interferometric microscope with confocal focusing (CFIM). CFIM first uses confocal technology to achieve accurate axial positioning of both capsule and the camera, thereby ensuring that the inner surface of the capsule is precisely and clearly imaged at the camera. Then, phase-shifting interferometry based on a short-coherence source and a spherical reference is applied to obtain inner defects result from null inner surface interferograms. In addition, in-situ focusing is realized by the axial adjustment of camera, but not by the capsule, to ensure that the outer defects and the fake inner defects caused by it have the same pixel coordinates, thereby solving the confusion of fake inner defects. The comparative experimental results of the CFIM and the scanning electron microscope (destructive detection) prove the feasibility of the proposed method. With unique precision confocal focusing and in-situ focusing ability, CFIM provides the first approach for non-destructive detection of inner surface defects of ICF capsule to the best of our knowledge.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Inertial confinement fusion (ICF) is not only an ideal technological means to obtain clean energy in the future, but also provides strong support for the research into condensed matter physics and astrophysics under extreme high-temperature and high-pressure conditions [1–3]. In ICF device, high-energy laser beams are focused precisely on a small hollow spherical capsule filled with deuterium-tritium (DT) fuel; then the capsule shell implodes instantly and uniformly compresses the DT fuel inside to the state of high temperature and high pressure, thus achieving fusion ignition. The capsule is the core component of the ICF device [4–7]. According to a Nature study [5], a small change in topography on the inner surface of the capsule can lead to ignition failure. The inner surface defects are the key factors in determining the quality of the inner surface, which leading to asymmetrical compression and Rayleigh–Taylor instability during implosion. Therefore, it is necessary to know clearly whether there are inner surface defects, how convex and concave they are, and their size during the entire process of manufacturing, screening, assembly, and final inspection of the capsule. Obviously, the realization of accurate and non-destructive detection of inner defects of the capsule is a key challenge in ICF research with important scientific significance and application value.
Existing methods for capsule surface quality characterization can be divided into contour line methods and wide-field methods. However, the non-destructive inner surface defect detection of ICF capsule is not yet realized.
Contour line measuring methods are based on stylus scanning or shadowgraph. The stylus scanning method, including laser differential confocal (LDC) scanning [6–8] and atomic force microscopy (AFM) scanning [9,10], which utilizes a non-contact LDC probe or a contact AFM probe to scan the entire equator line of the capsule. Thus, the profile of this equator is obtained with high spatial resolution. Shadowgraph illuminates the capsule with visible light [11,12] or X-ray [13,14], and the backlit shadowgraph generated is used to obtain the contour line of the section of the capsule. Scanning is unnecessary in shadowgraph; therefore, the measuring speed is relatively high. The above methods can effectively measure the inner surface profile (except for AFM), but only one contour line can be obtained by one measurement, which implies that the isolated defects are easily omitted between two adjacent contour lines. Therefore, the above contour line methods cannot effectively detect inner surface defects.
In contrast, wide-field methods can obtain the surface topography with a certain field of view (FOV), so that defects in the FOV can be detected efficiently and without omissions. Wide-field methods include microscopy and interferometry. Microscopy methods, including digital holographic microscopy (DHM) [15], confocal microscopy [16] and scanning electron microscopy (SEM) [17], are both mature microtopography measurement techniques, and good results have been obtained for the detection of outer surface defects. However, it is difficult for the above microscopes to accurately detect defects on the inner surface through the spherical outer surface. Interferometry methods include phase-shifting diffraction interferometry (PSDI) [18] and null interferometric microscope (NIM) [19,20]. A short-coherence light source is adopted in both PSDI and NIM to avoid parasitic fringes, and phase-shifting interferometry (PSI) is used to retrieve the wavefront and then outer surface defects. The outer surface is not imaged at the camera in PSDI, and the surface topography is calculated indirectly by propagating the wavefront from the detector surface to the capsule surface numerically. However, such an indirect approach is both time consuming and inaccurate [16]. To address this problem, the NIM images the outer surface of the capsule at the camera; thus, the defects result can be obtained directly and clearly from the interferograms. In fact, NIM is believed to be the first approach for direct and large-field surface defects detection on ICF capsules [19].
However, it is still difficult for NIM to detect inner surface defects directly. The key problem is that it is difficult to achieve accurate focusing of the inner surface. Although NIM can capture inner surface interferograms owing to the short-coherence source, it cannot obtain clear defects result directly because the inner surface is defocused [21]. Furthermore, the traditional interferometric microscopy typically moves the sample axially to visually find a clear image, such focusing approach is not only ex situ but also lacks accurate and objective criteria. As a result, it is difficult to focus the inner surface quickly and accurately. In addition, the pixel-to-pixel correspondence of the inner and outer results is destroyed by ex situ focusing, which leads to the confusion between the real inner defects and the fake ones caused by the outer surface defects.
In this paper, the first interferometric microscope with confocal focusing (CFIM) is proposed to solve the above problems through its unique precision confocal focusing and in-situ focusing ability. CFIM provides accurate and objective criteria for the axial position of the capsule and camera, ensuring that the inner surface of the capsule is precisely imaged. The camera is axially adjusted to realize inner and outer surface in-situ focusing, ensuring the in-situ correspondence of outer defects and the fake inner defects caused by them. PSI is used to obtain inner and outer defects result from inner and outer null interferograms, and the fake inner defects are in situ marked according to the position of the outer defects.
2. CFIM principle
2.1 Basic principle of CFIM
The principle of CFIM is shown in Fig. 1. The light emitted from the short-coherence source is collimated and then split by a polarized beam splitter (PBS). The S-polarized beam is focused by the reference objective (RO) and then reflected by the reference surface (R) along the original path. The reference light passes through the quarter-wave plate (λ/4) twice and then passes through the PBS. Axially adjusting the entire reference arm (Ref. arm) will change the optical delay of reference light, as well as introduce phase shift for the implementation of PSI. The P-polarized beam is focused by the measuring objective (MO) at the center of the ICF capsule and then reflected along the original path. After passing through λ/4 the second time, the measuring light is reflected by PBS. After passing through or being reflected by PBS, measuring light and reference light then enter the detecting arm, which includes the PSI-confocal detection system, the confocal detection system, and the beam splitter (BS).
The lights passing through BS enter the confocal detection system. The reference beam is filtered out by a S-direction polarizer P2, then the measuring light passes through a narrow bandpass filter F and a convergent lens CL. The intensity of the measuring light is finally detected by detector D, which is placed after a confocal pinhole PH. The sample scanning confocal curve ILC-S can be recorded when axially scanning the capsule, of which the peak point can be used for axial positioning of the capsule.
The light reflected by the BS enters the PSI-confocal detection system, after passing through a 45°polarizer P1, the reference light and measuring light have the same polarization state. Then the reference light and measuring light can get interference if we scan the Ref. arm in order to make the optical path difference (OPD) is close to zero. The interferogram is captured by CCD after passing through the tube lens (TL) and collimating-imaging lens (CIL). Optical coherence tomography (OCT) intensity curve IOCT can be obtained by monitoring the gray value of the center pixel in the interferogram when scanning the Ref. arm, thereby the inner and outer coherent peaks can be distinguished.
The deep red beam, which is finally focused on CCD, indicates the conjugate relationship between the measured surface and CCD. If the real conjugate light emanates from one single point of measured surface, the detector scanning confocal curve ILC-D can be recorded when axially scanning the CCD, of which the peak point can be used for axial positioning of CCD.
2.2 Relationship between confocal and interferometric optical path
The relationship between confocal and interferometric optical path is shown in Fig. 2. As shown in Fig. 2(a) the confocal curve ILC-S(zShell) is used to accurately position the center of ICF capsule at the focus point of MO. In Fig. 2(b), the peaks of two confocal curve ILC-D(zCCD) corresponding to the conjugate position of inner and outer surface of the shell, which can be used to position CCD accurately. The detailed principle will be introduced in section 3. In Fig. 2(c), the two coherent peaks corresponding to inner and outer surface interferograms respectively, according to the axial coordinate of coherent peaks, the Ref. arm is accurately positioned at zero OPD positions of the inner and outer surfaces of the ICF shell. As shown in Fig. 2(d), when the outer surface is focused on CCD and the Ref. arm is position at outer coherent peak, phase shifted interferograms of outer surface can be captured by stepping the Ref. arm. Similarly, when the inner surface is focused on CCD and the Ref. arm is position at inner coherent peak, phase shifting interferograms of inner surface can be captured by stepping the Ref. arm.
In simple terms, confocal technology is used to position the capsule and CCD in order to focusing clearly, interferometric technology is used to position the Ref. arm and capture phase shifting interferograms. Then PSI technology is applied to obtain the inner and outer surface topography respectively.
As shown in Fig. 2(e), the inner measuring light is modulated by the outer defects, this modulation finally causes fake defects which are coupled in inner result. The fake defects can be removed according to the position and height of outer surface topography.
2.3 inner and outer surface topography calculation and decoupling
The strict intensity formula of short coherent interference can be found in [22]. If the broadened Gaussian envelope caused by group dispersion and the chirp phase term are ignored, the captured inner and outer interferograms can be written as
where (x, y) denotes the pixel coordinate, n is the index of the phase-shifting interferograms, δ(n) is the phase shift value, A and B are the background and modulation, φi and φo are the phases of the measuring wavefront reflected by the inner and outer surfaces, respectively. The reference arm is driven step by step for phase shifting, and then the phase results can be obtained by PSI algorithm [23] and phase unwrapping algorithm. It’s worth to note that the interested defects are submerged by low frequency topography fluctuation in the phase results, which might be produced by the defocus and tilt of both capsule and Ref, non-common path error of Twyman Green Interferometer, as well as the low frequency surface topography of measured surface itself. Therefore, it’s necessary to fit the low frequency surface topography by Zernike polynomial and then remove it. The phase results after Zernike fit removal are written as φi and φo, then we have :The decoupling model of fake defects is shown in Fig. 3, in which the spherical term of capsule surface and wavefront is removed for clarity. The original incident wavefront φi0 is considered as ideal spherical wave, after passing through outer surface, φi0 is modulated by outer defect Ho and become φi1. Then, φi1 is reflected to be φi2 by inner surface. Finally, φi2 is modulated by outer defect Ho for the second time and become φi3, which is the finally measured phase φi shown in formula (3). The multiple inner-boundary reflections are not shown in Fig. 3 since they are background light and don’t influence the phase results obtained by PSI. Besides, please note that the actual imaging beam is separated but not travels forward like Fig. 3. However, a separated marginal ray of imaging beam theoretically has the same optical path length as the forward-propagating principal ray in the condition of clearly imaging, therefore we only analyze the principal ray here.
In general, the slope of defects is small (science the transverse size is much larger than its height), which means that we can just consider the OPD introduced by the height of defect but ignore the deflection of light. Based on above assumption we have:
Based on formula (4), fake defects can be decoupled by the following equation:
2.4 Automatic defects detection based on digital image processing algorithm
The interested defects in surface topography result might be obvious for naked eyes, but it’s neither easy to identify nor obtain its dimensions and position automatically. To deal with this problem, we use digital image processing algorithm for the automatic defects detection. The principle of detection algorithm is shown in Fig. 4.
First, the inner surface result Hi is segmented and converted into a global binary image according to a global threshold εg, which should be higher than the noise or the residual fake defects, as shown in Fig. 4(a).
Based on formula (6), all the defects that higher than εg can be identify.
Second, the center height ht of all the identified defects can be calculated by :
where the subscript t is the index of defects, CR denotes for the connected region of binary image, which can be find by blob analysis algorithm.Finally, the full width at half maximum FWHMt can be calculated as shown in Fig. 4(b). A local threshold εt is set to be equal to ht/2, L and R are the left pixel and the right pixel of which the height just below εt. Two linear equations can be fitted using the height and location of L and L-1 pixel, R and R-1 pixel:
3. Inner and outer surface focusing based on BFSC
Bilateral fitting subtracting confocal (BFSC) technology is applied in CFIM to provide accurate and objective criteria for the axial positioning of the capsule and camera, thereby realizing accurate inner and outer focusing shown in Fig. 2(a) and (b).
3.1 theoretical model of confocal technology and BFSC
Figure 5(a) shows the basic principle of confocal technology, in which the point source, focus of MO and detection point (pinhole PH) are conjugate. When the sample S is scanned and the PH as well as detector D remain stationary, S-scanning confocal curve ILC-S(uS) can be recorded:
When the PH as well as D are scanned and S remain stationary, D-scanning confocal curve ILC-D(uD) can be recorded:
where uS and uD denote for the normalized axial displacement of S and D. The peak points of ILC-S and ILC-D accurately corresponding to the focus of MO and the detection point, thereby the axial coordinates of these two peaks can be used as the criteria for accurate positioning of S and D respectively.Figure 5(b) shows the principle of BFSC, which is used to precisely obtain the axial coordinate of the peak point P of confocal curve [24]. The axial coordinates uP is the criteria for positioning the camera or capsule in the CFIM. Data points with relative intensity between 0.45-0.65 on both sides of the confocal curve are selected to fit two straight lines $l_{A}(u) = k_{A}u+T_{A}$ and $l_{B}(u) = k_{B}u+T_{B}$, where kA and kB are the slopes of lA and lB, and kA≈- kB, TA and TB are intercepts of the two fitting lines. By subtracting lA and lB, the difference confocal line lc is obtained as follows:
The slope of lc is approximately equal to 2kA, while the slope near the peak of I is zero, therefore BFSC has higher sensitivity and noise immunity compare to traditional confocal technology. In Eq. (10), if lc is set to be 0, then the coordinate uP can be obtained and further used as the positioning criteria.
3.2 Inner and outer surface focusing based on BFSC
The basic idea of inner and outer surface focusing is positioning CCD axially in two special position, making it coincide with the conjugate plane of inner and outer surfaces respectively. During the focusing procedure from outer to inner surface, the size of interferogram remain the same since the focal planes of TL and CIL coincide. The principle and procedure is shown in Fig. 6.
Figure 6(a)-(b) shows the principle of outer surface focusing. In Fig. 6(a), a flat mirror is placed in the position of Ro/2 and the reflected beam converge at Vo point. The distance between Vo and O is just the outer radius of capsule Ro, O is the focus point of MO as well as the center of capsule. The reflected light pass through the CFIM imaging system and finally converge at CPo point, which means the conjugate plane of outer surface of capsule. D-scanning confocal curve can be recorded by scanning the CCD (zCCD) as well as recording the intensity ILC-D based on virtual pinhole technology, then BFSC is applied to obtain the axial coordinate of the peak point. In Fig. 6(b), CCD is placed at CPo point, the capsule is placed at confocal position according to S-scanning confocal curve and BFSC, then the vertex of outer surface Vo is conjugate with CCD, which means the outer surface focusing is realized.
Figure 6(b) - (c) shows the principle of inner surface focusing. Under the condition of outer surface focusing is realized, the capsule keep still and CCD is move dCCD to CPi point, then the inner surface focusing is realized. The distance dCCD can be calculated by optical ray tracing model of both the CFIM imaging system and the capsule shell. Note that the outer radius, thickness and refractive index of the capsule shell must be known in advance, and the error of these parameters would lead to CCD positioning error, thereby affect the focusing accuracy and the resolution of defect detection.
4. Experiments
4.1 Experimental system
Based on the CFIM principle, the CFIM system is built up as shown in Fig. 7. The short-coherence source is a super-luminescent diode (SLD) with 850 nm center wavelength and about 50nm spectrum width, and the minimum measurable thickness is greater than 20μm (when n=1.5), which is basically limited by the coherence length of SLD. MO and RO are two identical microscope objectives (20X,0.45 NA, WD 3.1 mm). The reference surface is a fused silicon sphere with a radius of 12 mm and a PV of λ/20 (@632.8nm). The focal lengths of TL and CIL are 100 mm and 200 mm, respectively. The optical size of CCD1 is 1/2"(5.427 mm × 6.784 mm, 1024×1280 pix).
In the reference arm, RO and R are fixed on the PZT for phase shifting, while PZT is fixed on the delay stage for optical delay adjustment. In the measuring arm, the capsule was fixed to a rotary stage and a three-dimensional axial manual stage. The rotary stage was used to rotate the capsule during the experiment to find defects, and the manual stage was used to adjust the position of the capsule with a minimum axial scale of 10 μm. The light reflected by the BS enters the PSI-confocal detection system. CCD1 is fixed on the CCD stage driven by the open-loop mode, and its axial position is converted by the pulse number. The light transmitted by the BS enters the confocal detection system, in which the airy disk is imaged at CCD2 by a 4X finite-conjugated microscopic objective. Virtual pinholes are both set on CCD1 and CCD2. The computer is used for motion control and data acquisition.
4.2 Experimental result
The inner defects of a semitransparent capsule with an outer diameter of 948.7 μm and shell thickness of 79.9 μm were detected. The refractive index of the capsule shell is approximately 1.55 (@850nm).
A flat mirror is placed at Ro/2 position from the focus of MO, then CCD1 is driven to axial scan, and the recorded confocal response curve ILC-D is shown in Fig. 8(a). The axial coordinate of the peak is 11.04 mm obtained by BFSC, then CCD1 is placed in this coordinate, namely the CPo position. After that, the mirror is removed and the ICF capsule is placed at confocal position based on BFSC again (ILC-S). At this time, the outer focusing is completed.
The delay stage is moved to adjust the optical delay of the reference arm. When the interference fringes appear in CCD1 and the contrast reaches the maximum value for the first time, OPDo is approximately equal to 0. The PZT is used to drive the reference arm to carry out a phase shift. The first frame phase-shifting interferogram is shown in Fig. 9(a). The phase is extracted using the PCA algorithm. The outer surface defects obtained after phase unwrapping and Zernike fit removal are shown in Fig. 9(b), in which the unwrap error in the margin of field of view might be caused by the large height of the defect and the off-axial aberration of imaging system.
Please note that the point-like patterns in Fig. 9(a) are caused by the backward-reflecting beams from the objective or the bull's eye rings caused by dust, they are background light and therefore disappears in PSI result of Fig. 9(b). Some small defects on the edge are not clearly observed in Fig. 9(a) but “appear” in Fig. 9(b), this is limited by the low brightness on the edge and visual sensitivity.
Keeping the capsule still, CCD1 is moved from the CPo to CPi point by a distance of d2 to achieve accurate inner focusing. The distance d2 is calculated using ZEMAX software, the optical model established, and the calculation process are shown in Fig. 10. The accuracy of lens distances (MO and TL, TL and CIL) are ensured by mechanical machining, then the nominal values can be directly used for modeling since its influence can be ignored. In the ZEMAX model, the axial position coordinate of MO is 0, the distance between the vertex of the outer surface of the capsule and MO is -8.52565 mm, the ideal image surface position is 64.6543 mm in the case of the outer focusing, and 59.1168 mm in the case of the inner focusing. Therefore, dCCD=5.5375 mm can be obtained by subtraction.
Delay stage is used again to adjust the optical delay. When the contrast of interference fringes reaches the maximum value for the second time, OPDi can be considered to be approximately 0. The PZT is used to drive the reference arm to carry out a phase shift. The first frame phase-shifting interferogram and inner defect results are shown in Fig. 11(a) and Fig. 11(b). The fake defect is marked by a red rectangle according to the pixel position of the outer defect shown in Fig. 9(b). There are a large number of convex inner defects with heights not exceeding 70 nm and transverse dimensions not exceeding 3 μm.
Fig. 11. Inner surface (a) interferogram, (b) surface form, and (c) close-up view of inner defects after high-pass filter.
According to the outer/inner defects results shown in Fig. 9 and Fig. 11 and the decoupling model shown in formula (5), the result of fake defects decoupling is shown in Fig. 12(a). It’s obvious that the fake defects are conspicuously eliminated, except for some residual error caused by diffraction and phase unwrap error. Based on the decoupled inner defects result, the automatic defects detection algorithm is applied. A total of 12 inner defects higher than 45nm are detected, and the close-up of No.9 defect is shown in Fig. 12(b). Based on the algorithm shown in formula (8), the FWHM in x and y direction are 2.8 and 2.6 μm.
4.3 Comparative experimental results of SEM
To verify the feasibility, the CFIM results were compared with the results obtained by SEM (destructive detection). The same capsule was cut open and a ZEISS SEM was used to observe the inner surface directly, as shown in Fig. 13(a) and Fig. 13(b). A large number of small convex defects were also observed on the inner surfaces of both hemispheres under 2000-3000X magnification, as shown in Fig. 13(c) and Fig. 13(d). Their transverse dimensions were estimated to be no more than 1 μm.
Fig. 13. SEM results of the same capsule, (a) hemisphere 1 and (b) hemisphere 2, inner defects found on (c) hemisphere 1 and on (d) hemisphere 2. Some of the defects are marked by arrows for clarity.
The detected inner surface defects are small in size and large in number, and the cutting angle of the capsule are extremely difficult to control. Therefore, it is difficult to match the defect results of CFIM and SEM one by one. However, both CFIM and SEM have detected a large number of convex inner surface defects, and the transverse dimensions of defects are approximately consistent (the transverse dimensions measured by CFIM are wider due to diffraction), thus proving the feasibility of CFIM in detecting inner surface defects non-destructively.
5. Conclusion
In this study, a CFIM with accurate and in-situ focusing ability is proposed, and the non-destructive detection of inner surface defects is realized. CFIM uses BFSC technology to provide an objective and accurate criterion for the adjustment of the axial position of the detection surface and the measured surface, thus ensuring the accuracy of inner focusing and defect detection. Owing to in-situ focusing, the outer defects and the fake inner defects caused by them have the same pixel coordinate, thus solving the problem of fake defect misjudgment. The practical experiment proves the feasibility of this method. To the extent that we know, CFIM provides the first effective way for non-destructive detection of inner surface defects of capsule with its unique accurate focusing and in-situ focusing ability, which has important theoretical and application value for ICF research.
Funding
National Key Research and Development Program of China (2017YFA0701203); National Science Fund for Distinguished Young Scholars (51825501).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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