- Email: [email protected]
Measurement of electron beam moire fringes with pulsed-dilation framing camera using different lasers
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Measurement of electron beam moire fringes with pulsed-dilation framing camera using different lasers
T
⁎
Yanli Baia, , Rongbin Yaoa, Haiying Gaoa, Xun Wangb, Dajian Liua a Guilin University of Electronic Technology, National Demonstration Center for Experimental Education of Mechanical and Electrical Engineering Training, Guilin 541004, China b Guilin University of Electronic Technology Institute of Information Technology, Guilin 541004, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Ultrafast diagnostic techniques Electron beam moire fringe Pulse-Dilation framing camera Wavefront curvature radius
The electron beam moire fringe (EBMF) is generated by using a pulse-dilation framing camera. Its characteristics are measured via a nanosecond- and a femtosecond-laser. The wavefront curvature radius of the two lasers is calculated based on the measurement of the EMBF rotation angle and this result is discussed in detail. The experiments show that the EBMF rotation angles measure 31.9° and 16.6°, while the wavefront curvature radii are 12.5 mm and 21.1 mm, when the ns-laser and the fs-laser are used, respectively. This study greatly contributes in the development of EBMF-based technologies and proposes novel application directions for the use of pulse-dilation framing cameras.
1. Introduction The moire fringe is an interference pattern, which can be generated by optical phenomena or by electrons. The optical moire fringe is produced by the beating of the spatial frequencies of two superimposed layers, which leads to the generation of a low frequency fringe pattern in the space. Due to its high sensitivity to the slightest displacements and/or distortions in the structure of the layers, the moire fringe has been widely investigated and it is currently used in a vast number of applications in various fields [1]. The electron beam moire fringe (EBMF) was initially proposed by Kishimoto [2]. In his work, a fine grating prepared via electron beam lithography was used as a specimen grating. A primary electron beam generated by a scanning electron microscope (SEM) was used as a reference grating for the microscopic measurements. An EBMF is measured by employing a framing camera, which makes use of a framing camera with image converter [3,4]. This technique has contributed to further improve and extend the EBMF application in the electron-optics field. A framing camera is a practical ultrafast diagnostic technology. This device is widely used in inertial confinement fusion (ICF) experiments, due to its performances that allow one to obtain a high two-dimensional spatial resolution and a picosecond (ps) temporal resolution [5]. Typically, an ICF implosion lasts around 100 ps [6,7] but the detailed time-history of the burn phase of the implosion cannot be captured via traditional micro-channel plate (MCP) framing cameras. Therefore, pulse-dilation framing cameras with temporal resolution higher than 10 ps have been widely investigated and developed [8,9]. A pulse-dilation framing camera consists of a photocathode (PC), a mesh, a drift area, an imaging system, and a MCP framing camera [10,11]. The PC and the mesh form the accelerating area via the generation of a time-dependent electric field gradient. In this work, the incoming laser beam is converted into photoelectrons (PEs) at the interface with the photocathode. Due to the time-
⁎
Corresponding author. E-mail address: [email protected] (Y. Bai).
https://doi.org/10.1016/j.ijleo.2019.163149 Received 6 May 2019; Accepted 23 July 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
Fig. 1. Schematic diagram of the pulse-dilation framing camera used in this work.
dependent nature of the electric field intensity, PEs which are generated at an earlier point in time transit faster through the drift area compared to those generated later, producing a gradually increasing temporal width of the PE beam. The MCP framing camera, situated at the end of the drift area, captures a slice of the PE time-dilation, achieving a higher temporal resolution compared to that of traditional framing cameras. This imaging system, which makes use of magnetic lenses, ensures two-dimensional imaging. Since the PC and the mesh behave as two specimen gratings, this camera can be used to produce electron beam moire fringes. In this work, an EBMF produced via a pulsed-dilation framing camera based on the one developed by Liao and Lei [3,4] and several factors which influence its characteristics, such as the structure of PC and the mesh angle, are investigated. These results only scratch the surface of the possible applications of EBMF pulsed-dilation framing cameras, further investigations have to be carried out to completely characterize these devices and their potential. In this paper, EBMF imaging was carried out by employing two different lasers. Furthermore, the wave-front curvature of the lasers was investigated via the analysis of the rotational angle of the fringes. These results open the doors towards the further development and novel applications of EBMF-based pulse-dilation framing cameras. 2. Experimental setup The schematic diagram of the pulse-dilation framing camera used in this work is shown in Fig. 1. It consists of a pulse-dilation system, an imaging system, and a MCP framing camera. The pulse-dilation system includes an Au-PC, a mesh, and a drift area. The Au-PC is a microstrip-line structure designed via the fabrication of an ultraviolet(UV) ray mask, which is composed of several squares separated at various nominal spatial frequencies [12] by regular slits. The PC mesh is made of nickel and its spatial frequency is 10 L P/mm. The distance between the PC and the mesh is ˜1.6 mm. Since the spatial frequency of the camera is ˜10 L P/mm and the pulse width of the nanosecond- and femtosecond-laser is narrow, the EBMF can only be observed with a PC spatial frequency of 15 L P/mm. Fig. 2 shows the photomicrographs of the PC slits (15 L P/mm) and of the mesh (10 L P/mm). The period of the 15 L P/ mm slits (Fig.2a) of the PC measures 75.75 μm and the spacing between two consecutive gratings is 43.98 μm. Adjacent gratings are alternated with a 31.77 μm-wide wire. The period of the mesh (Fig.2b) measures 106.34 μm and the spacing between two consecutive gratings is 91.34 μm. Moreover, two gratings are separated by a 15 μm-wide wire. The drift space, which covers the distance from the mesh to the MCP framing camera, measures 500 mm. The imaging system consists of an axis-symmetrical magnetic lens with an inner diameter of 160 mm, a gap of 4 mm, and axial length of 100 mm, mounted in the center of the drift area. To ensure the imaging of moire fringes, the camera was set to generate a 1:1 magnification of the electron image. 3. Experimental results and analysis In the experiment, a ns-laser and a fs-laser were used to excite the photoelectrons. The Au-coated slits of the photocathode were maintained at -1.5 kVdc, while the mesh was held at ground. The signal-bearing photoelectrons transit through the drift area and are imaged onto the MCP framing camera via the magnetic lens with a 1:1 magnification level. The MCP framing camera includes a MCP and a phosphor screen (PS). The MCP is biased to -700 Vdc and it is used to multiply the photoelectrons; the PS is biased to 3.4 kVdc
Fig. 2. Photomicrographs: (a) the slits of 15 L P/mm in the PC; (b) the 10 L P/mm of mesh. 2
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
Fig. 3. EBMF images using different lasers: (a) ns-laser; (b) fs-laser.
and it converts the photoelectrons into a visible light image by the application of a potential difference between the MCP and the PS. The image is then recorded via a charge-coupled device (CCD) with the dimensions of 1392 × 1040 pixels and interval between adjacent pixels of ˜20 μm [12]. Additionally, the imaging rotation angle (40°) was measured via the magnetic lens and its values is consistent with previous experiments [13]. To enable the overlap between the PC imaging and the MPC microstrip, the grating angle between the photocathode and the mesh was then set to 45°-line. The EBMF measurements are reported in Fig.3. Due to pulse difference between the ns-laser and the fs-laser, the imaging process presents three main differences between the image obtained with the ns-laser (Fig.3a) and the one obtained with the fs-laser (Fig.3b): 1) The intensity of the image recorded with the fs-laser is higher than the one captured with the ns-laser; 2) The pulse width of the nslaser is longer than the fs-laser’s one and this results in a variation of the image uniformity; 3) The EBMF rotation angle presents a variation, due to the aforementioned differences between the ns-laser and the fs-laser and it can be calculated by the CCD coordinates. The EBMF rotation angles in the ns-laser experiment and in the fs-laser experiment measure approximately 31.9° and 16.6°, respectively. Based on these results, the ns-laser and fs-laser wavefront curvature radius (R) of 12.5 mm and 21.1 mm, respectively, can be calculated via Eq. (1) [14].
R=d+
d | cos θ + sin θ tan ϕ − 1|
(1)
Here, d is the distance between PC and the mesh and it measures 1.6 mm; θ is the grating angle between PC and the mesh and it measures 45°, while ϕ is the EBMF rotation angle. 4. Conclusion The EBMFs of a pulse-dilation framing camera are experimentally recorded by using two different laser sources. Due to the differences in the laser characteristics, the moire fringes present different features in their intensity pattern, uniformity, and rotation angle. The variation of the rotation angle is caused by the wavefront curvature radius of the laser and the results presented in this work show that the EEBMF rotation angle of the ns-laser and the fs-laser measure 31.9° and 16.6°, respectively. Based on the distance and on the grating angle between the PC and the mesh, the wavefront curvature radius of the ns-laser and the fs-laser are be calculated and their values are 12.5 mm and 21.1 mm, respectively. This work proposes a novel direction for the application of pulsedilation framing cameras and shows their potential for the investigation of curved surfaces. Moreover, it enables the first steps towards the development of EBMF-based cameras with even higher spatial performances. Declaration of conflict interest statement The authors declare no competing financial interest. Acknowledgments This work was supported by a grant from the National natural science foundation of China (Nos. 11865007 and 61863008). Natural science foundation of Guangxi (No. 2018GXNSFAA281073). The key project of Guilin University of Electronic Technology (No. JGA201806). 3
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
References [1] A.T. Shepherd, 25 years of moire fringe measurement, Precis. Eng. 1 (2) (1979) 61–69. [2] S. Kishimoto, M. Egashira, N. Shinya, Microcreep deformation measurements by a moire method using electron beam lithography and electron beam scan, Opt. Eng. 32 (3) (1993) 522–526. [3] Y. Liao, Y. Lei, H. Cai, et al., Electron beam moiré fringes imaging by image converter tube with a magnetic lens[J], J. Appl. Phys. 119 (21) (2016) 35–38. [4] Y. Lei, Y. Liao, J.H. Long, et al., Observation of electron beam moiré fringes in an image conversion tube[J], Ultramicroscopy 170 (2016) 19–23. [5] J.D. Kilkenny, High speed proximity focused X-ray cameras[J], Laser Part. Beams 9 (01) (1991) 49. [6] P.A. Jaanimagi, D.K. Bradley, Neutron streak and framing camera diagnostics for ICF implosions. 20th International Congress on High Speed Photography and Photonics, International Society for Optics and Photonics Proc. SPIE 1801 (1993) 710–717. [7] S.A. Voss, C.W. Barnes, J.A. Oertel, et al., Gated X-ray framing camera image of a direct-drive cylindrical implosion, Ieee Trans. Plasma Sci. 27 (1) (1999) 132–133. [8] T.J. Hilsabeck, J.D. Hares, J.D. Kilkenny, et al., Pulse-dilation enhanced gated optical imager with 5 ps resolution, Rev. Sci. Instrum. 81 (10) (2010) 10E317. [9] Yanli Bai, Jinhua Long, Houzhi Cai, et al., Demonstration of 11-ps exposure time of a framing camera using pulse-dilation technology and a magnetic lens, Opt. Eng. 54 (12) (2015) 124103. [10] S.R. Nagel, T.J. Hilsabeck, P.M. Bell, et al., Dilation x-ray imager a new/faster gated x-ray imager for the NIF, Rev. Sci. Instrum. 83 (10) (2012) 10E116. [11] H. Cai, W. Fu, D. Wang, et al., Dilation x-ray framing camera and its temporal resolution uniformity, Opt. Express 27 (2019) 2817–2827. [12] Y. Bai, R. Yao, H. Gao, et al., Achieving a large detector sensitive area of short magnetic focusing pulse-dilation framing tube using a combination lens, Opt. – Int. J. Light Electron. Opt. (178) (2019) 1097–1101. [13] Bai Yanli, Long Jinghua, Houzhi Cai, Simulated and measured spatial resolution of framing converter using short magnetic focusing[J], J. Shenzhen Univ. Sci. Eng. 32 (2) (2015) 178–182. [14] G. Hechenblaikner, Measurement of the absolute wavefront curvature radius in a heterodyne interferometer[J], J. Opt. Soc. Am. A Opt. Image Sci. Vis. 27 (9) (2010) 2078–2083.
4
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Measurement of electron beam moire fringes with pulsed-dilation framing camera using different lasers
T
⁎
Yanli Baia, , Rongbin Yaoa, Haiying Gaoa, Xun Wangb, Dajian Liua a Guilin University of Electronic Technology, National Demonstration Center for Experimental Education of Mechanical and Electrical Engineering Training, Guilin 541004, China b Guilin University of Electronic Technology Institute of Information Technology, Guilin 541004, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Ultrafast diagnostic techniques Electron beam moire fringe Pulse-Dilation framing camera Wavefront curvature radius
The electron beam moire fringe (EBMF) is generated by using a pulse-dilation framing camera. Its characteristics are measured via a nanosecond- and a femtosecond-laser. The wavefront curvature radius of the two lasers is calculated based on the measurement of the EMBF rotation angle and this result is discussed in detail. The experiments show that the EBMF rotation angles measure 31.9° and 16.6°, while the wavefront curvature radii are 12.5 mm and 21.1 mm, when the ns-laser and the fs-laser are used, respectively. This study greatly contributes in the development of EBMF-based technologies and proposes novel application directions for the use of pulse-dilation framing cameras.
1. Introduction The moire fringe is an interference pattern, which can be generated by optical phenomena or by electrons. The optical moire fringe is produced by the beating of the spatial frequencies of two superimposed layers, which leads to the generation of a low frequency fringe pattern in the space. Due to its high sensitivity to the slightest displacements and/or distortions in the structure of the layers, the moire fringe has been widely investigated and it is currently used in a vast number of applications in various fields [1]. The electron beam moire fringe (EBMF) was initially proposed by Kishimoto [2]. In his work, a fine grating prepared via electron beam lithography was used as a specimen grating. A primary electron beam generated by a scanning electron microscope (SEM) was used as a reference grating for the microscopic measurements. An EBMF is measured by employing a framing camera, which makes use of a framing camera with image converter [3,4]. This technique has contributed to further improve and extend the EBMF application in the electron-optics field. A framing camera is a practical ultrafast diagnostic technology. This device is widely used in inertial confinement fusion (ICF) experiments, due to its performances that allow one to obtain a high two-dimensional spatial resolution and a picosecond (ps) temporal resolution [5]. Typically, an ICF implosion lasts around 100 ps [6,7] but the detailed time-history of the burn phase of the implosion cannot be captured via traditional micro-channel plate (MCP) framing cameras. Therefore, pulse-dilation framing cameras with temporal resolution higher than 10 ps have been widely investigated and developed [8,9]. A pulse-dilation framing camera consists of a photocathode (PC), a mesh, a drift area, an imaging system, and a MCP framing camera [10,11]. The PC and the mesh form the accelerating area via the generation of a time-dependent electric field gradient. In this work, the incoming laser beam is converted into photoelectrons (PEs) at the interface with the photocathode. Due to the time-
⁎
Corresponding author. E-mail address: [email protected] (Y. Bai).
https://doi.org/10.1016/j.ijleo.2019.163149 Received 6 May 2019; Accepted 23 July 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
Fig. 1. Schematic diagram of the pulse-dilation framing camera used in this work.
dependent nature of the electric field intensity, PEs which are generated at an earlier point in time transit faster through the drift area compared to those generated later, producing a gradually increasing temporal width of the PE beam. The MCP framing camera, situated at the end of the drift area, captures a slice of the PE time-dilation, achieving a higher temporal resolution compared to that of traditional framing cameras. This imaging system, which makes use of magnetic lenses, ensures two-dimensional imaging. Since the PC and the mesh behave as two specimen gratings, this camera can be used to produce electron beam moire fringes. In this work, an EBMF produced via a pulsed-dilation framing camera based on the one developed by Liao and Lei [3,4] and several factors which influence its characteristics, such as the structure of PC and the mesh angle, are investigated. These results only scratch the surface of the possible applications of EBMF pulsed-dilation framing cameras, further investigations have to be carried out to completely characterize these devices and their potential. In this paper, EBMF imaging was carried out by employing two different lasers. Furthermore, the wave-front curvature of the lasers was investigated via the analysis of the rotational angle of the fringes. These results open the doors towards the further development and novel applications of EBMF-based pulse-dilation framing cameras. 2. Experimental setup The schematic diagram of the pulse-dilation framing camera used in this work is shown in Fig. 1. It consists of a pulse-dilation system, an imaging system, and a MCP framing camera. The pulse-dilation system includes an Au-PC, a mesh, and a drift area. The Au-PC is a microstrip-line structure designed via the fabrication of an ultraviolet(UV) ray mask, which is composed of several squares separated at various nominal spatial frequencies [12] by regular slits. The PC mesh is made of nickel and its spatial frequency is 10 L P/mm. The distance between the PC and the mesh is ˜1.6 mm. Since the spatial frequency of the camera is ˜10 L P/mm and the pulse width of the nanosecond- and femtosecond-laser is narrow, the EBMF can only be observed with a PC spatial frequency of 15 L P/mm. Fig. 2 shows the photomicrographs of the PC slits (15 L P/mm) and of the mesh (10 L P/mm). The period of the 15 L P/ mm slits (Fig.2a) of the PC measures 75.75 μm and the spacing between two consecutive gratings is 43.98 μm. Adjacent gratings are alternated with a 31.77 μm-wide wire. The period of the mesh (Fig.2b) measures 106.34 μm and the spacing between two consecutive gratings is 91.34 μm. Moreover, two gratings are separated by a 15 μm-wide wire. The drift space, which covers the distance from the mesh to the MCP framing camera, measures 500 mm. The imaging system consists of an axis-symmetrical magnetic lens with an inner diameter of 160 mm, a gap of 4 mm, and axial length of 100 mm, mounted in the center of the drift area. To ensure the imaging of moire fringes, the camera was set to generate a 1:1 magnification of the electron image. 3. Experimental results and analysis In the experiment, a ns-laser and a fs-laser were used to excite the photoelectrons. The Au-coated slits of the photocathode were maintained at -1.5 kVdc, while the mesh was held at ground. The signal-bearing photoelectrons transit through the drift area and are imaged onto the MCP framing camera via the magnetic lens with a 1:1 magnification level. The MCP framing camera includes a MCP and a phosphor screen (PS). The MCP is biased to -700 Vdc and it is used to multiply the photoelectrons; the PS is biased to 3.4 kVdc
Fig. 2. Photomicrographs: (a) the slits of 15 L P/mm in the PC; (b) the 10 L P/mm of mesh. 2
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
Fig. 3. EBMF images using different lasers: (a) ns-laser; (b) fs-laser.
and it converts the photoelectrons into a visible light image by the application of a potential difference between the MCP and the PS. The image is then recorded via a charge-coupled device (CCD) with the dimensions of 1392 × 1040 pixels and interval between adjacent pixels of ˜20 μm [12]. Additionally, the imaging rotation angle (40°) was measured via the magnetic lens and its values is consistent with previous experiments [13]. To enable the overlap between the PC imaging and the MPC microstrip, the grating angle between the photocathode and the mesh was then set to 45°-line. The EBMF measurements are reported in Fig.3. Due to pulse difference between the ns-laser and the fs-laser, the imaging process presents three main differences between the image obtained with the ns-laser (Fig.3a) and the one obtained with the fs-laser (Fig.3b): 1) The intensity of the image recorded with the fs-laser is higher than the one captured with the ns-laser; 2) The pulse width of the nslaser is longer than the fs-laser’s one and this results in a variation of the image uniformity; 3) The EBMF rotation angle presents a variation, due to the aforementioned differences between the ns-laser and the fs-laser and it can be calculated by the CCD coordinates. The EBMF rotation angles in the ns-laser experiment and in the fs-laser experiment measure approximately 31.9° and 16.6°, respectively. Based on these results, the ns-laser and fs-laser wavefront curvature radius (R) of 12.5 mm and 21.1 mm, respectively, can be calculated via Eq. (1) [14].
R=d+
d | cos θ + sin θ tan ϕ − 1|
(1)
Here, d is the distance between PC and the mesh and it measures 1.6 mm; θ is the grating angle between PC and the mesh and it measures 45°, while ϕ is the EBMF rotation angle. 4. Conclusion The EBMFs of a pulse-dilation framing camera are experimentally recorded by using two different laser sources. Due to the differences in the laser characteristics, the moire fringes present different features in their intensity pattern, uniformity, and rotation angle. The variation of the rotation angle is caused by the wavefront curvature radius of the laser and the results presented in this work show that the EEBMF rotation angle of the ns-laser and the fs-laser measure 31.9° and 16.6°, respectively. Based on the distance and on the grating angle between the PC and the mesh, the wavefront curvature radius of the ns-laser and the fs-laser are be calculated and their values are 12.5 mm and 21.1 mm, respectively. This work proposes a novel direction for the application of pulsedilation framing cameras and shows their potential for the investigation of curved surfaces. Moreover, it enables the first steps towards the development of EBMF-based cameras with even higher spatial performances. Declaration of conflict interest statement The authors declare no competing financial interest. Acknowledgments This work was supported by a grant from the National natural science foundation of China (Nos. 11865007 and 61863008). Natural science foundation of Guangxi (No. 2018GXNSFAA281073). The key project of Guilin University of Electronic Technology (No. JGA201806). 3
Optik - International Journal for Light and Electron Optics 195 (2019) 163149
Y. Bai, et al.
References [1] A.T. Shepherd, 25 years of moire fringe measurement, Precis. Eng. 1 (2) (1979) 61–69. [2] S. Kishimoto, M. Egashira, N. Shinya, Microcreep deformation measurements by a moire method using electron beam lithography and electron beam scan, Opt. Eng. 32 (3) (1993) 522–526. [3] Y. Liao, Y. Lei, H. Cai, et al., Electron beam moiré fringes imaging by image converter tube with a magnetic lens[J], J. Appl. Phys. 119 (21) (2016) 35–38. [4] Y. Lei, Y. Liao, J.H. Long, et al., Observation of electron beam moiré fringes in an image conversion tube[J], Ultramicroscopy 170 (2016) 19–23. [5] J.D. Kilkenny, High speed proximity focused X-ray cameras[J], Laser Part. Beams 9 (01) (1991) 49. [6] P.A. Jaanimagi, D.K. Bradley, Neutron streak and framing camera diagnostics for ICF implosions. 20th International Congress on High Speed Photography and Photonics, International Society for Optics and Photonics Proc. SPIE 1801 (1993) 710–717. [7] S.A. Voss, C.W. Barnes, J.A. Oertel, et al., Gated X-ray framing camera image of a direct-drive cylindrical implosion, Ieee Trans. Plasma Sci. 27 (1) (1999) 132–133. [8] T.J. Hilsabeck, J.D. Hares, J.D. Kilkenny, et al., Pulse-dilation enhanced gated optical imager with 5 ps resolution, Rev. Sci. Instrum. 81 (10) (2010) 10E317. [9] Yanli Bai, Jinhua Long, Houzhi Cai, et al., Demonstration of 11-ps exposure time of a framing camera using pulse-dilation technology and a magnetic lens, Opt. Eng. 54 (12) (2015) 124103. [10] S.R. Nagel, T.J. Hilsabeck, P.M. Bell, et al., Dilation x-ray imager a new/faster gated x-ray imager for the NIF, Rev. Sci. Instrum. 83 (10) (2012) 10E116. [11] H. Cai, W. Fu, D. Wang, et al., Dilation x-ray framing camera and its temporal resolution uniformity, Opt. Express 27 (2019) 2817–2827. [12] Y. Bai, R. Yao, H. Gao, et al., Achieving a large detector sensitive area of short magnetic focusing pulse-dilation framing tube using a combination lens, Opt. – Int. J. Light Electron. Opt. (178) (2019) 1097–1101. [13] Bai Yanli, Long Jinghua, Houzhi Cai, Simulated and measured spatial resolution of framing converter using short magnetic focusing[J], J. Shenzhen Univ. Sci. Eng. 32 (2) (2015) 178–182. [14] G. Hechenblaikner, Measurement of the absolute wavefront curvature radius in a heterodyne interferometer[J], J. Opt. Soc. Am. A Opt. Image Sci. Vis. 27 (9) (2010) 2078–2083.
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