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Abstract
Precise determination of the refractive index and surface spacing in multi-lens system is essential for ultra-precision system performance, such as lithography objectives with strict requirements for each lens fabrication and assembly position. Generally, the nominal value of the refractive index at a given wavelength must be known before resolving the geometric thickness of multi-lens using conventional methods, which leads to inaccurate and inconvenient measurements. We propose a method to simultaneously measure the refractive index and surface spacing in multi-lens system based on dual-comb ranging method. The precision of the thickness measurement is better than 0.18 µm, and the refractive index is better than 1.6 × 10−4. This study provides a potential solution for realizing the real-time, fast, and precise measurement of the geometric thickness and assembly position of multi-lens in lithography objectives.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Thickness is a significant physical parameter, which is highly relevant to length and is usually defined as the distance between two parallel surfaces. Thickness measurement has a wide range of applications, such as semiconductor manufacturing, ultra-precision manufacturing equipment, and aerospace research [1]. The common optical system consists of multiple lenses, and the geometric thickness between adjacent lens surface spacing determines each lens assembly position along the optical axis, which is essential to be measured precisely, especially for high-precision optical systems such as lithography objectives and professional camera lenses. For instance, lithography objectives, which are the core components of a lithography machine, have more than 30 lenses. To ensure the performance of the lithography machine, the deviation of the lens surface spacing, including the lens center and airgap thickness, is required to be within 5 µm. In addition, it is necessary to obtain the lens surface spacing in the assembly process of every lens in real time because the obtained results can be used to compensate for potential errors in the manufacturing process, tolerance testing, and quality control. Therefore, it is critical to precisely and rapidly measure the lens surface spacing to guarantee assembly quality and improve the performance of the optical system.
Recently, the non-contact thickness measurement methods have attracted attention due to the practical advantages of non-destructive inspections compared with contact ones. The optical method is one of the most commonly used non-contact methods because of its high precision and measurement speed. It is noted that the direct measurement result of the optical method is the optical path length, so determining the refractive index simultaneously is the key to resolving the geometric thickness. Various measurement methods of the refractive index and geometric thickness based on spectral-domain interferometry have been reported [2–4], but these methods are not suitable for the large-scale multi-lens system measurements due to the limitation of the optical spectrum analyzer resolution.
There are some optical methods for measuring the geometric thickness of multi-lens surface, which include the confocal image method [5], the confocal chromatic method [6,7], and the low coherent interference method [8–10], etc. However, these methods could also only obtain the optical path length so that it is inevitable to refer to the nominal value of the refractive index to resolve the geometric thickness of the lens. Usually, the nominal value of the refractive index can be obtained in the material refractive index table or calculated by the Sellmeier equation with the known Sellmeier coefficient of the material. However, these methods will lead to the geometric thickness resolving error with using the nominal refractive index because they could not give the real refractive index value under the current environmental conditions. Therefore, realizing the measurement of refractive index in real-time is also of great importance when measuring multi-lens system.
In addition, there is mechanical movement in the measurement process of both the confocal method and low coherence interferometry, which is sensitive to environmental vibrations. Moreover, if the number of lenses to be measured increases in the lens group, the scanning time also increases, which is time-consuming. Due to the limitations of the system and material, the confocal chromatic method has a limited measurement range, and the curvature and material of the lens should be used as a priori knowledge. Under these circumstances, the confocal chromatic method is not suitable for large-scale multi-lens structure measurements.
Over the past few decades, optical frequency comb (OFC) has become a powerful and indispensable tool in optical metrology, especially for ranging systems [11–22]. An OFC consists of a series of ultrashort femtosecond pulses in the time domain and has provided discrete and equally spaced optical modes over broad spectra, which is ideal for large-scale, high-precision, and real-time absolute distance measurements [23,24]. The dual-comb based ranging (DCR) system uses two OFCs with slightly different repetition frequency. Because of the advantage of interferogram signals separation in time-domain, the DCR could realize the simultaneous measurement of multi-layer spacing thickness without mechanical scanning. There has been some reports of the simultaneous determination of geometric thickness and refractive index using dual-comb spectroscopy [25,26]. However, these methods may not be able to realize multi-lens measurements when only analyzing spectral-domain information or the multireflected echo signals are overlapped in the time domain because the optical path length of these signals can be the same in the transmission-type measurement.
Combined with time domain analysis, a method was proposed for measuring the multi-lens surface. This method locks the optical cross-correlation signal to a zero datum using a dual-comb system, realizing a total of 12 lens surfaces being assessed simultaneously with a positioning accuracy of 1.0 µm [27]. However, this scheme can only directly obtain the optical path length, and after referring to the nominal refractive index, the geometric thickness of the lens can be obtained. In addition, it is not industrially friendly for practical applications because the periodically poled potassium titanyl phosphate crystal (PPKTP) is easily disturbed by the external environment.
In this study, we propose and demonstrate a method to simultaneously measure the surface spacing and refractive index in a self-made multi-lens system based on dual-comb ranging. Using this method, each lens surface spacing can be resolved quickly and precisely without referring to any prior knowledge, such as the nominal refractive index of the lens. The experimental results show a precision of 0.18 µm and 1.6 × 10−4 in determining the lens surface spacing and refractive index, respectively. Our method has the potential to assist the assembly and adjustment of high-precision optical systems, such as lithography objectives.
2. Experimental setup and measurement principles
2.1 Principle of DCR method
The time-of-flight (TOF) method is one of the typical methods in the DCR system which achieves a meter-scale measurement range and micrometer-level precision. A pulse train from the signal laser (repetition rate fr1) can be divided into measurement and reference signals, and the time interval between the two signals is expressed as Δτ. The local oscillator laser (repetition rate fr2) beats the signal laser, which produces an interferogram [28,29]. As shown in Fig. 1, based on the multi-heterodyne of the tooth-by-tooth basis, optical longitudinal mode lines are down-converted to the radio frequency (RF) domain, forming an RF longitudinal mode with an interval of Δfr = fr1- fr2, and the measurement result updating time is 1/Δfr. The distance to be measured can be calculated by the time delay (Δt) between the measurement interference signal and the reference interference signal. Owing to linear optical sampling, the time delay Δt is magnified by fr1/Δfr times compared with Δτ. By performing the Fourier transform on the interference signals of the measurement and reference arms, the phase difference of each longitudinal mode in the RF domain and the time delay Δt = dΔφRF(k)/dfRF(k)/2π can be calculated, then the distance can be expressed as Eq. (1) [30,31].
Fig. 1. (a) The description of optical longitudinal mode in the optical frequency domain, (b) The description of RF longitudinal mode in the radio frequency domain, (c) The phase information of the RF longitudinal mode after performing the Fourier transform. fopt: optical frequency, fRF: the radio frequency.
2.2 Experimental setup
Figure 2(a) shows the schematic of the experimental setup. Two repetition frequency locked femtosecond lasers (MenloSystems ASOPS TWIN 250) are used as signal laser (fr1 = 250.010030 MHz) and local oscillator (fr2 = 250.000000 MHz) respectively with the repetition frequency difference Δfr 10030 Hz and ∼0.1 ms update time. The lasers are with 1560 nm center wavelength and ∼75 mW average output power. The signal laser is incident into free space using an adjustable focus collimator (AFC: Throlabs CFC11P-C) after passing through a circulator (Circ) and is then divided into the reference and measuring arms using a beam splitter (BS: Throlabs BS030). The beam reflected by mirror M1 is denoted as S1, and the other beam entering the measuring arm passes through every lens (L1: Throlabs LA1050, L2: Throlabs FA1417, L3: Throlabs LC1611) of the lens group. The lens group is mounted in a cage system to guarantee the alignment of the optical axis. Theoretically, the beam will be reflected on the front and rear surfaces of each lens, and the reflected beams are denoted as S2, S3, S4,…, Si respectively. By adjusting the focus of the collimator, we can ensure that the light reflected from each surface of the measured target has sufficient energy for interference. Mirror M2 was placed at the end of the measurement path. The geometric thickness of each lens or air gap is expressed as d1, d2,…, di. After all reflected beams pass through the circulator and combine with local oscillator at the coupler (CP), interferograms generated by the asynchronous sampling of the dual-comb method can be collected by the InGaAs photo detector (PD: 500-MHz bandwidth) and digitized using a data acquisition card. A low-pass filter (∼50 MHz) is employed in the data acquisition module to avoid spectrum aliasing. The time delay Δt between different interferograms can be determined from the slope of the phase-frequency spectra after Fourier transformation. Therefore, the optical length Li of each spacing can be calculated by the time-of-flight method and expressed as
Fig. 2. (a) Schematic of the experimental setup, (b) The pulses sequence corresponding to the reflecting beam from six lens surfaces and two mirrors respectively.
As shown in Fig. 2(b), the interference signals reflected from each surface are arranged sequentially in the time domain. For example, the spacing between S2 and S3 corresponds to the thickness of the first lens, while the spacing between S3 and S4 corresponds to the thickness of the first air gap. Measurements must be conducted when placing and removing the lens group from the system to simultaneously obtain the refractive index of the lens and the geometric thickness of the lens surface spacing in a lens group. When the lens group is placed, the reflected signal S8 from M1 will move in the time domain compared to the reflected signal S8’ from M1 when the lens group is not placed. For practical applications, the lenses in the group are generally fabricated using the same material; therefore, the lens refractive index can be defined as n, and the air refractive index n0 is a known quantity. Taking three lenses in the lens group as an example, the geometric thickness of each lens surface spacing and refractive index can be obtained from Eq. (3) and (4).
3. Experiments and results
To verify the performance of this method, we used a self-made lens group containing three lenses. The nominal thickness of the three lenses is 9.7 ± 0.1 mm (L1), 7.3 ± 0.1 mm (L2), and 4.0 ± 0.1 mm (L3) respectively. Figure 3(a) shows the interferograms generated by the corresponding surface-reflecting light. The signal-to-noise ratio (SNR) of a single-shot measurement is low because of the low reflectance of each lens surface. Simultaneously, due to the curvature of the lens surface, the signal intensity reflected by each surface is quite different. Hence, the SNR of different interferograms differs, and the measurement precision is affected. Here, we can adjust the focus of the collimator to balance the intensity and SNR of each interferogram to ensure high measurement precision for each optical surface. We discuss the minimum distinguishable spacing between adjacent lens surfaces without overlapping between echo pulses. As shown in Fig. 3(b), the full-width of the interferograms obtained is around 0.65 microseconds, corresponding to 2.6 mm in geometric thickness difference. To measure optical systems with thin lenses, we can use a broader spectrum that is still within the available spectral range, limited by the band-pass sampling theorem of dual-comb ranging method, as it generally generates narrower interferograms.
Fig. 3. (a) The measured interferogram signals corresponding to different reflecting surfaces. (b) Normalized interferogram signal of S5, with 0.65 µs full-width in time-domain.
When the lens group is placed in the system or removed from the system, we conduct measurements and obtain a series of interference signals. After the Fourier transform of the interference signals, we can obtain the time delay Δt between different interferograms that are determined by the slope of the phase-frequency spectra so that we can get the optical thickness between each adjacent lens surface (i.e., L1, L2, L3, L4, and L5). In addition, we obtained Lr by comparing the optical thickness change between S8 and S1 in the two measurements. The refractive index of the lens was solved using Eq. (4), which is 1.5215. Table 1 shows the thickness measurement results of the three lenses and two air gaps in the lens group according to Eq. (3), based on the interferograms obtained in Fig. 3(a) after 1s average. The d1-d5 are 9.6480 mm, 56.8051 mm, 7.3437 mm, 26.6435 mm, and 4.0487 mm, respectively. It can be observed that the measurement results of the lens thickness are consistent with the nominal values.
Table 1. Measured thickness by the proposed method and the nominal value of the lens thickness
To further verify the measurement accuracy of this method, we experimented to compare the results of the proposed method to the “standard results” provided by a commercial inductance meter. The probe of the inductance meter was placed at one lens (L3) outer frame, and we translated L3 along the optical axis so that d4 changed accordingly with a total of approximately 2 mm using nine steps. Figure 4(a) shows that the ranging results of the proposed method conform with those of the commercial inductance meter. The fitting slope and correlation coefficient (R2) are 0.99923289 and 0.99999416, respectively. The comparison residuals are kept within −2.28 µm to 2.15 µm after an averaging time of 1 s.
Fig. 4. (a) Ranging results of the proposed method versus the ranging system results from commercial inductance meter. The data length is 1s with 42000 pairs of interferograms, and their ranging average was used for the comparison. (b) The measurement repetition precision of thickness and the refractive index measured value when the lens (L3) is at different positions.
After obtaining the geometric thickness value of each adjacent lens surface spacing when L3 is placed at ten different positions, the lens refractive index can also obtain ten results. Theoretically, the measured refractive index does not change due to the different lens positions. As shown in Fig. 4(b), the repeatability precision of the thickness measurement was better than 0.18 µm, and that of the refractive index was better than 1.6 × 10−4 after an averaging time of 1 s, demonstrating the excellent repeatability of this experimental setup.
4. Discussion and conclusion
Theoretically, the number of lenses that can be measured by this system only depends on the intensity of the light source, ensuring that the reflecting light on each surface can be obtained. Moreover, the intensity of the reflecting light can be adjusted by the adjustable focus collimator to meet the measurement requirements. In addition, in order to make each interferogram in the time domain corresponds to the lens surface, the maximum measurement range should be limited to the non-ambiguity range, which is 0.6 m in this experiment. However, the non-ambiguity range of the dual-comb method can be extended to a large size [32,33], so this is not the critical factor for limiting the measurement range.
In this study, we only considered that the lens group was fabricated with the same material. If the lenses are composed of different materials, the refractive indices of all lenses are different. Under these circumstances, the geometric thickness and refractive index value of each lens can also be solved using this method. As shown in Fig. 5, we consider a lens group containing three lenses with different refractive indices as an example. The measurement process was divided into four steps. We conducted measurements when no lens was placed in the system. In the first step, we insert the first lens (L1) into the system and perform measurements. The change of optical path difference between S8 and S1 due to the insertion of the lens can be expressed as Eq. (5).
Fig. 5. The measurement schematic when each lens of the lenses group is fabricated by different materials
In the second step, we insert the second lens (L2) into the system. Similarly, the change of optical path difference between S8 and S1 due to the insertion of the second lens can be expressed as Eq. (6)
Finally, the third lens (L3) is inserted into the system, and we can obtain equations similar to Eq. (3). That is,
The refractive index of each lens can be calculated by combining the above equation,
In summary, we propose a method to simultaneously measure the thickness and refractive index of multiple lenses based on dual-comb ranging. Using this method, the lens surface spacing in optical systems, including lens thickness and the air gap, can be measured with a precision of 0.18 µm. Simultaneously, the refractive index of the lens material can be determined at a precision of 1.6 × 10−4. The comparison result between our proposed method and commercial distance measurement equipment demonstrates an accuracy within 2.28 µm. The measurement result updating time can reach 0.1 ms or even faster, which depends on the Δfr between the two combs. In short, this study provides a solution to realize real-time, fast, and precise measurement of the lens surface spacing in a lens group, which has the potential to assist the assembly process of high-precision optical systems such as lithography objectives.
Funding
National Natural Science Foundation of China (92150104).
Acknowledgments
The authors thank Shijun Peng at Changchun National Extreme Precision Optics Co., Ltd. for the fruitful discussion and comments on the work.
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.
References
1. J. Park, J. A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf 20(3), 463–477 (2019). [CrossRef]
2. J. Park, H. Mori, and J. Jin, “Simultaneous measurement method of the physical thickness and group refractive index free from a non-measurable range,” Opt. Express 27(17), 24682–24692 (2019). [CrossRef]
3. D. J. Bang, Y. Kim, Y. Kim, M. Kim, and K. Kim, “Simultaneous measurement of group and phase refractive indices and physical thickness of transparent plates with low coherence Fabry–Perot interferometry,” Appl. Opt. 57(16), 4428–4433 (2018). [CrossRef]
4. H. Park and K. Joo, “High-speed combined NIR low-coherence interferometry for wafer metrology,” Appl. Opt. 56(31), 8592–8597 (2017). [CrossRef]
5. A. V. Goncharov, L. L. Bailón, N. M. Devaney, and C. Dainty, “Optical testing of lens systems with concentric design,” Proc. SPIE 7389, 738912 (2009). [CrossRef]
6. M. Kunkel, J. Schulze, M. Kogel-Hollacher, and S. Sprentall, “Non-contact measurement of central lens thickness,” ICALEO® 2005: 24th International Congress on Laser Materials Processing and Laser Microfabrication (2005). [CrossRef]
7. W. Zhao, R. Sun, L. Qiu, L. Shi, and D. Sha, “Lenses axial space ray tracing measurement,” Opt. Express 18(4), 3608–3617 (2010). [CrossRef]
8. A. Courteville, P. Slangen, C. Cerruti, R. Wilhelm, and F. Garcia, “A novel low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy,” Internation. Soc. Optics Photonics 6341, 63411Q (2006). [CrossRef]
9. P. Langehanenberg, A. Ruprecht, D. Off, and B. Lueerss, “Highly accurate measurement of lens surface distances within optical assemblies for quality testing,” Proc. SPIE 8844, 88440F (2013). [CrossRef]
10. R. Wilhelm, A. Courteville, and F. Garcia, “Dimensional metrology for the fabrication of imaging optics using a high accuracy low coherence interferometer,” Proc. SPIE 5856, Optical Measurement Systems for Industrial Inspection IV, (2005).
11. N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011). [CrossRef]
12. T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef]
13. Y. S. Jang and S. W. Kim, “Distance measurements using mode-locked lasers: a review,” Nanomanuf. Metrol. 1(3), 131–147 (2018). [CrossRef]
14. J. Lee, Y. J. Kim, K. Lee, S. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010). [CrossRef]
15. K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000). [CrossRef]
16. N. R. Doloca, K. Meiners-Hagen, M. Wedde, F. Pollinger, and A. Abou-Zeid, “Absolute distance measurement system using a femtosecond laser as a modulator,” Meas. Sci. Technol. 21(11), 115302 (2010). [CrossRef]
17. G. Wu, M. Takahashi, H. Inaba, and K. Minoshima, “Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement,” Opt. Lett. 38(12), 2140 (2013). [CrossRef]
18. G. Wang, Y. S. Jang, S. Hyun, B. J. Chun, H. J. Kang, S. Yan, S. W. Kim, and Y. J. Kim, “Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser,” Opt. Express 23(7), 9121 (2015). [CrossRef]
19. Y. S. Jang, G. Wang, S. Hyun, H. J. Kang, B. J. Chun, Y. J. Kim, and S. W. Kim, “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep. 6(1), 31770 (2016). [CrossRef]
20. K. N. Joo and S. W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954 (2006). [CrossRef]
21. K. N. Joo, Y. Kim, and S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799 (2008). [CrossRef]
22. S. A. Van den Berg, S. T. Persijn, G. J. P. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012). [CrossRef]
23. A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012). [CrossRef]
24. S. W. Kim, “Combs rule,” Nat. Photonics 3(6), 313–314 (2009). [CrossRef]
25. A. Asahara, A. Nishiyama, S. Yoshida, K. Kondo, Y. Nakajima, and K. Minoshima, “Dual-comb spectroscopy for rapid characterization of complex optical properties of solids,” Opt. Lett. 41(21), 4971–4974 (2016). [CrossRef]
26. K. Sumihara, S. Okubo, M. Okano, H. Inaba, and S. Watanabe, “Ultra-precise determination of thicknesses and refractive indices of optically thick dispersive materials by dual-comb spectroscopy,” Opt. Express 30(2), 2734–2747 (2022). [CrossRef]
27. W. Kim, J. Jang, S. Han, S. Kim, and S. W. Kim, “Absolute laser ranging by time-of-flight measurement of ultrashort light pulses,” J. Opt. Soc. Am. 37(9), B27–B35 (2020). [CrossRef]
28. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009). [CrossRef]
29. Z. Zhu and G. Wu, “Dual-comb ranging,” Engineering 4(6), 772–778 (2018). [CrossRef]
30. S. Zhou, V. Le, S. Xiong, Y. Yang, K. Ni, Q. Zhou, and G. Wu, “Dual-comb spectroscopy resolved three-degree-of-freedom sensing,” Photonics Res. 9(2), 243–251 (2021). [CrossRef]
31. S. Zhou, C. Lin, Y. Yang, and G. Wu, “Multi-pulse sampling dual-comb ranging method,” Opt. Express 28(3), 4058–4066 (2020). [CrossRef]
32. J. Lee, S. Han, K. Lee, E. Bae, and S. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013). [CrossRef]
33. X. Zhao, X. Qu, F. Zhang, Y. Zhao, and G. Tang, “Absolute distance measurement by multi-heterodyne interferometry using an electro-optic triple comb,” Opt. Lett. 43(4), 807–810 (2018). [CrossRef]
