近红外大口径波长移相干涉仪关键技术及应用研究
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摘要
大口径平面光学元件在天文、航天、强激光等领域有着重要且广泛的应用,例如在我国神光Ⅲ高功率固体激光装置的重大项目中使用了大量高精度的大口径平面光学元件,这些光学元件在加工与使用过程中需要能够对其面形和光学均匀性进行高精度检测的近红外大口径干涉仪。针对神光Ⅲ的研制需求,本论文开展了基于波长移相方式的近红外大口径干涉仪的研制工作。尽管波长移相方式比硬件移相方式更适合应用于大口径光学元件的干涉测量中,但波长移相干涉时移相量大小不仅与波长变化量有关,还与干涉腔长有关,且随着腔长增大,对波长分辨率的要求越高。而根据应用需求,某些大口径光学元件需在布儒斯特角或小角度下进行测量,此时,干涉腔长过长,无法实现移相量的准确标定。因此需解决短腔长测量时不同腔长下的移相量标定问题和长腔长测量时的相位计算问题。此外,工作波长近红外、测量孔径Φ600mm,需具备足够的中频段传递能力、能够在测量区域非连通和长腔长下进行测量等条件对干涉仪的相位计算、光学系统设计和光路调校等方面提出了更高的要求。本文围绕以上几个关键技术及其应用展开了研究。
移相量的精度直接关系到相位计算精度,为了解决在不同干涉腔长下测量时的移相量实时标定问题,本文提出了基于李萨如图技术和基于一维时域傅立叶变换的移相量标定方法,前者通过李萨如图拟合技术实现移相量的计算,精度较高。该方法不要求移相量相等,且在超短腔长(腔长为0.01m左右)时仍能使用,但其对于干涉图的对比度要求较高,同时参与计算的两个点的相位差不能是π的倍数。后者通过对空间某点不同时刻的光强值进行一维傅立叶变换等处理得到移相量,该方法没有前一种方法的缺点,但要求移相量相等。将该方法应用于波长移相干涉仪中,其测量结果与Zygo GPI移相干涉仪的测量结果偏差在λ/50(PV值)范围内。结果表明,两种方法均能够实现波长移相干涉测量时的移相量标定,且后者计算性能更稳定。
在长干涉腔长下测量时,由于移相步进量分辨率受限导致偏离π/2,给波面计算带来了误差。针对此情况,首先,研究了波长调谐随机移相算法,该算法不标定移相量,采用最小二乘原理和迭代计算,在适合的收敛条件下实现相位的计算。在长腔长下测量时,该方法的测量结果与短腔长下的测量结果偏差约λ/70(PV值)。然后,提出了自适应相位筛选法,该算法对多幅移相干涉图进行筛选得到移相步进量为π/2的干涉图。在长腔长下测量时,该方法的测量结果与短腔长下的测量结果偏差约λ/300(PV值)。结果表明,这两种方法都可以很好地解决长腔长测量时移相量标定的技术问题,且后者比前者计算精度高。
针对非连通区域的相位解包问题,提出了基于离散余弦变换算法的种子点相位解包方法。该方法利用种子点法对各分离区域进行解包,再利用离散余弦变换算法求得的干涉级次,将各分离区域的解包相位进行统一。实验验证了该方法的正确性和精度。该方法能够快速准确地实现非连通区域的相位解包。
针对干涉仪的研制需求,光路设计时采用单片双凸非球面作为准直物镜、成像系统采用双远心光路、去除旋转毛玻璃等措施来满足要求。针对波长调谐激光器的输出波长分辨率与激光器控制器的分辨率相关的特性,研制了高精度的电压驱动源,从硬件上保证了激光器能够实现高精度地波长调谐。针对干涉光路不可见的特点,采用可见光辅助调校技术实现了系统的调校。并对系统的光学质量、重复性和测量不确定度进行测量和分析,干涉仪系统的测量不确定度优于λ/15。
最后研究了近红外大口径波长移相干涉仪的应用。首先研究了波长移相干涉仪测量平行平板的光学参数。测量时,只需要平行平板放入测量和空腔测量两个步骤,采用傅立叶变换算法实现多表面干涉条纹的分离。通过模拟仿真和实验验证了该算法的正确性和精度。该方法可用于测量平行平板的前后表面面形及光学均匀性,且测量步骤简单、精度较高,尤其适用于大口径平行平板的测量。然后研究了近红外大口径干涉仪在大口径光学元件以及长腔长下的测量。实验结果表明,该干涉仪可以高精度地实现大口径光学元件和长腔长下光学元件的面形测量。
The planar optical elements with large aperture have found wide applications in the fields of astronomy, aerospace, high power laser and others. One example is the Shenguang III high power solid-state laser facility in which a large number of optical elements with large aperture and high quality are employed. An interferometer that has capability of measuring the surface shapes and optical homogeneity of the elements with large aperture during the process of manufacturing and applications is then required. To this end, a wavelength tuning-based phase-shifting interferometer with a diameter of600mm has been developed, which is illuminated by a source in the near-infrared wavelength range. Although wavelength tuning-based method has the advantage of measuring elements with large aperture over hardware shifting methods, the required value of wavelength tuning is a function of both the changes of the wavelength and the length of the cavity between the transmission flat and the reflective flat. And the wavelength resolution increases with the increasing of the length of the cavity. Second, the measurements of large optical elements have to be performed at the Brewster angle or a small angle in some applications in which the cavity length is very large, which makes it difficult to accurately calibrate the phase shifts. It is therefore necessary to find methods of calibrating the phase shifts at small cavity lengths and calculating the phase at large cavity lengths. In addition, the interferometer developed is illuminated by the near-infrared wavelength range with clear aperture size of600mm, enough transmission in mid-spatial frequency and capability of calculating the phases of discontinuous regions and performing measurements at a large cavity length, which lead to more strict requirements to phase calculation, optical design, and system alignment. In this thesis, these key techniques and their applications are investigated.
The precision of calculated phase is directly determined by the precision of phase shifts. In this thesis, two methods are proposed to calibrate the phase shifts for measurements at different cavity lengths. The first method is based on the Lissajous figures in which phase shifts are obtained by fitting of Lissajous figure with high precision. In this method, no equal phase shifts are required and it can work at a small cavity length (about0.01m). However, it has the limitations of requiring interferograms with high contrast and the phase difference between two points should not be multiples of π. These limitations are overcomed by the second method in which phase shifts are found by Fourier transform of the intensities captured at one point at different time. This method requires equal phase shifts and can be used in the wavelength tuning-based phase-shifting interferometer. Two groups of measurement experiments were carried out with both the wavelength tuning interferometer and the Zygo GPI interferometer. The results show the difference of the PV values is less than λ/50, which demonstrated that the phase shifts can be calibrated by both methods at high precision with the latter method of higher stability.
Compared with measurements at small cavity lengths, the phase shifts will deviate from π/2due to the limitation of the phase shift step resolution when measuring at large cavity lengths, which results in error in final phase calculation. In order to solve the problem, the random phase-shifting algorithm with wavelength tuning is analyzed, in which the phase shifts are assumed to be unknowns and the phases are calculated through iterative spatial and serial least-squares fitting. The difference between the PV values of the wavefronts obtained at a large cavity length and a small cavity length is less than λ/70. An adaptive phase selecting method is then proposed, in which several interferograms with a phase shift π/2are chosen from a large number of interferograms. It is found that the difference between the PV values of the wavefronts obtained at a large cavity length and a small cavity length is less than λ/300. The results show both methods can be employed in measurements at large cavity lengths with the latter method of higher precision.
A seed point unwrapping algorithm based on Discrete Cosine Transform (DCT) algorithm is proposed to unwrap the wrapped phases in discontinuous regions, in which the phases in discontinuous regions are unwrapped with the seed point algorithm respectively and they are then unified with the interferometric orders obtained by DCT algorithm. The phases of discontinuous regions can rapidly and correctly unwrapped by the method which demonstrated the validity and the precision of the method.
To meet the requirements of the interferometer developed, a single aspherical lens was used for collimation, and double telecentric configuration for imaging and a rotating diffuser is removed in the image system. Based on the resolution of the output wavelength and the controller of the laser, a voltage driver with high precision is developed, in which the wavelength can be tuned by the driver with high precision. Due to the invisibility of the near-infrared light, the adjusting method with visible light is proposed. The optical quality and the measurement repeatability of the interferometer were evaluated and it was found that measurement uncertainty of the interferometer was better than λ/15.
Finally, the potential applications of the interferometer are discussed. The parallel plates were first measured in only two steps:first with and second without the parallel plate in the cavity between transmission flat and reflective flat. The Fourier transform algorithm was used to separate several groups of the fringes. Both the numerical simulation and the measurement experiments demonstrate the validity of the presented method. The method is characterized by its high precision and simplicity and can be used for measuring the parallel plates with large aperture. The interferometer was then employed to measure the optical elements with large aperture and at a large cavity length with data of high precision.
移相量的精度直接关系到相位计算精度,为了解决在不同干涉腔长下测量时的移相量实时标定问题,本文提出了基于李萨如图技术和基于一维时域傅立叶变换的移相量标定方法,前者通过李萨如图拟合技术实现移相量的计算,精度较高。该方法不要求移相量相等,且在超短腔长(腔长为0.01m左右)时仍能使用,但其对于干涉图的对比度要求较高,同时参与计算的两个点的相位差不能是π的倍数。后者通过对空间某点不同时刻的光强值进行一维傅立叶变换等处理得到移相量,该方法没有前一种方法的缺点,但要求移相量相等。将该方法应用于波长移相干涉仪中,其测量结果与Zygo GPI移相干涉仪的测量结果偏差在λ/50(PV值)范围内。结果表明,两种方法均能够实现波长移相干涉测量时的移相量标定,且后者计算性能更稳定。
在长干涉腔长下测量时,由于移相步进量分辨率受限导致偏离π/2,给波面计算带来了误差。针对此情况,首先,研究了波长调谐随机移相算法,该算法不标定移相量,采用最小二乘原理和迭代计算,在适合的收敛条件下实现相位的计算。在长腔长下测量时,该方法的测量结果与短腔长下的测量结果偏差约λ/70(PV值)。然后,提出了自适应相位筛选法,该算法对多幅移相干涉图进行筛选得到移相步进量为π/2的干涉图。在长腔长下测量时,该方法的测量结果与短腔长下的测量结果偏差约λ/300(PV值)。结果表明,这两种方法都可以很好地解决长腔长测量时移相量标定的技术问题,且后者比前者计算精度高。
针对非连通区域的相位解包问题,提出了基于离散余弦变换算法的种子点相位解包方法。该方法利用种子点法对各分离区域进行解包,再利用离散余弦变换算法求得的干涉级次,将各分离区域的解包相位进行统一。实验验证了该方法的正确性和精度。该方法能够快速准确地实现非连通区域的相位解包。
针对干涉仪的研制需求,光路设计时采用单片双凸非球面作为准直物镜、成像系统采用双远心光路、去除旋转毛玻璃等措施来满足要求。针对波长调谐激光器的输出波长分辨率与激光器控制器的分辨率相关的特性,研制了高精度的电压驱动源,从硬件上保证了激光器能够实现高精度地波长调谐。针对干涉光路不可见的特点,采用可见光辅助调校技术实现了系统的调校。并对系统的光学质量、重复性和测量不确定度进行测量和分析,干涉仪系统的测量不确定度优于λ/15。
最后研究了近红外大口径波长移相干涉仪的应用。首先研究了波长移相干涉仪测量平行平板的光学参数。测量时,只需要平行平板放入测量和空腔测量两个步骤,采用傅立叶变换算法实现多表面干涉条纹的分离。通过模拟仿真和实验验证了该算法的正确性和精度。该方法可用于测量平行平板的前后表面面形及光学均匀性,且测量步骤简单、精度较高,尤其适用于大口径平行平板的测量。然后研究了近红外大口径干涉仪在大口径光学元件以及长腔长下的测量。实验结果表明,该干涉仪可以高精度地实现大口径光学元件和长腔长下光学元件的面形测量。
The planar optical elements with large aperture have found wide applications in the fields of astronomy, aerospace, high power laser and others. One example is the Shenguang III high power solid-state laser facility in which a large number of optical elements with large aperture and high quality are employed. An interferometer that has capability of measuring the surface shapes and optical homogeneity of the elements with large aperture during the process of manufacturing and applications is then required. To this end, a wavelength tuning-based phase-shifting interferometer with a diameter of600mm has been developed, which is illuminated by a source in the near-infrared wavelength range. Although wavelength tuning-based method has the advantage of measuring elements with large aperture over hardware shifting methods, the required value of wavelength tuning is a function of both the changes of the wavelength and the length of the cavity between the transmission flat and the reflective flat. And the wavelength resolution increases with the increasing of the length of the cavity. Second, the measurements of large optical elements have to be performed at the Brewster angle or a small angle in some applications in which the cavity length is very large, which makes it difficult to accurately calibrate the phase shifts. It is therefore necessary to find methods of calibrating the phase shifts at small cavity lengths and calculating the phase at large cavity lengths. In addition, the interferometer developed is illuminated by the near-infrared wavelength range with clear aperture size of600mm, enough transmission in mid-spatial frequency and capability of calculating the phases of discontinuous regions and performing measurements at a large cavity length, which lead to more strict requirements to phase calculation, optical design, and system alignment. In this thesis, these key techniques and their applications are investigated.
The precision of calculated phase is directly determined by the precision of phase shifts. In this thesis, two methods are proposed to calibrate the phase shifts for measurements at different cavity lengths. The first method is based on the Lissajous figures in which phase shifts are obtained by fitting of Lissajous figure with high precision. In this method, no equal phase shifts are required and it can work at a small cavity length (about0.01m). However, it has the limitations of requiring interferograms with high contrast and the phase difference between two points should not be multiples of π. These limitations are overcomed by the second method in which phase shifts are found by Fourier transform of the intensities captured at one point at different time. This method requires equal phase shifts and can be used in the wavelength tuning-based phase-shifting interferometer. Two groups of measurement experiments were carried out with both the wavelength tuning interferometer and the Zygo GPI interferometer. The results show the difference of the PV values is less than λ/50, which demonstrated that the phase shifts can be calibrated by both methods at high precision with the latter method of higher stability.
Compared with measurements at small cavity lengths, the phase shifts will deviate from π/2due to the limitation of the phase shift step resolution when measuring at large cavity lengths, which results in error in final phase calculation. In order to solve the problem, the random phase-shifting algorithm with wavelength tuning is analyzed, in which the phase shifts are assumed to be unknowns and the phases are calculated through iterative spatial and serial least-squares fitting. The difference between the PV values of the wavefronts obtained at a large cavity length and a small cavity length is less than λ/70. An adaptive phase selecting method is then proposed, in which several interferograms with a phase shift π/2are chosen from a large number of interferograms. It is found that the difference between the PV values of the wavefronts obtained at a large cavity length and a small cavity length is less than λ/300. The results show both methods can be employed in measurements at large cavity lengths with the latter method of higher precision.
A seed point unwrapping algorithm based on Discrete Cosine Transform (DCT) algorithm is proposed to unwrap the wrapped phases in discontinuous regions, in which the phases in discontinuous regions are unwrapped with the seed point algorithm respectively and they are then unified with the interferometric orders obtained by DCT algorithm. The phases of discontinuous regions can rapidly and correctly unwrapped by the method which demonstrated the validity and the precision of the method.
To meet the requirements of the interferometer developed, a single aspherical lens was used for collimation, and double telecentric configuration for imaging and a rotating diffuser is removed in the image system. Based on the resolution of the output wavelength and the controller of the laser, a voltage driver with high precision is developed, in which the wavelength can be tuned by the driver with high precision. Due to the invisibility of the near-infrared light, the adjusting method with visible light is proposed. The optical quality and the measurement repeatability of the interferometer were evaluated and it was found that measurement uncertainty of the interferometer was better than λ/15.
Finally, the potential applications of the interferometer are discussed. The parallel plates were first measured in only two steps:first with and second without the parallel plate in the cavity between transmission flat and reflective flat. The Fourier transform algorithm was used to separate several groups of the fringes. Both the numerical simulation and the measurement experiments demonstrate the validity of the presented method. The method is characterized by its high precision and simplicity and can be used for measuring the parallel plates with large aperture. The interferometer was then employed to measure the optical elements with large aperture and at a large cavity length with data of high precision.
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