Open Access
Add to BibSonomy
Abstract
Time-of-flight method was adopted to measure the distance between two parallel precision apertures utilized in a vacuum chamber for cryogenic radiometry. The diameters of the apertures are 9 mm and 8 mm, respectively. A 1550-nm femtosecond pulse laser, a 70-GHz photodetector, and a 30-GHz oscilloscope were used to measure the round-trip flight time difference between the flat front surfaces of the two precision apertures. The distance between the apertures was analyzed to be 0.36423 m with a relative standard uncertainty of 0.004%. The non-contact distance measurement method is useful for applications such as low background infrared radiance measurement system based on an absolute cryogenic radiometer.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Absolute cryogenic radiometers (ACRs) were first invented by scientists at the National Physical Laboratory of UK [1]. The ACRs work at a cryogenic temperature of 5 K and demonstrated milliwatt optical radiation measurement capability with an uncertainty of 4 parts in 105, which is much smaller than the electrical substitution radiometers (ESRs) working at ambient temperature. ESRs normally consist of a receiver cavity made from thermally conductive material such as pure copper for high heat diffusivity and coated with black paint for nearly 100% absorptivity, a resistor heater for efficient electrical power substitution, a carefully tailored thermal link for optimal temperature rise and response time, a sensitive and linear temperature sensor, a low-noise heat sink, and a temperature-stabilized background with insignificant stray light. ACRs achieve significantly better performance because the greater heat diffusivity and the lower thermal capacitance of the pure-copper receiver at cryogenic temperature may result in improved electrical substitution equivalence and heat sensitivity, respectively.
ACRs have been widely studied and adopted as the primary standards for optical radiant power realization [2–8]. They can be naturally employed as absolute radiometers for irradiance measurement with one precision aperture applied to define the effective detection area [3,9]. Absolute radiance measurement can also be conducted using two precision apertures to define both the effective detection area and the field of view in terms of a solid angle [10–13].
Recently, ACRs have been successfully built to measure optical radiant power at ∼1 pW level with 0.1% uncertainty, owing to the breakthroughs in the development of sub-1-Kelvin cryocoolers and extremely thermal sensitive superconducting transition edge sensors (TESs) [14]. Meanwhile, advanced coating materials with high optical absorptivity and thermal conductivity were studied to enable optical radiant power measurement over a wide spectral range into the far infrared and terahertz spectral region, which can further expand the ACR working wavelength range [15,16]. Such technical achievements can dramatically enhance the capabilities of the ACR-based radiance characterization system for the light sources such as sub-room-temperature blackbody emitters.
Radiance (L) can normally be calculated based on the measurement results of the optical power (Φ), the projected detector area (Ap), and the solid angle of the radiation source extended to the center of the projected detector area (Ω), using the following equation:
For a typical radiance measurement system based on an ACR, as illustrated in Fig. 1, the aperture diameters are usually small compared to the distance between the apertures (d). The radiance can then be evaluated using
Fig. 1. The schematic view of the principle of the optical radiance measurement based on an ACR featuring two parallel concentric precision apertures.
The areas of the apertures can be measured at 20°C using contact or non-contact methods with a relative standard uncertainty of less than 0.005% [17]. Invar is normally a good choice to make the small-sized apertures to be used in cryogenic systems owing to its well-studied small thermal expansion/contraction coefficients [18,19]. Corrections would help reduce the measurement uncertainty significantly. The areas of the apertures can certainly be directly measured at desired cryogenic temperature for high precision but requires complicated measurement systems [20,21].
The distance between the apertures can also be measured at room temperature and then corrected for cryogenic temperature applications. For instance, a relative standard uncertainty of 0.14% at 30.77 cm were reported for a low-background infrared measurement system [10]. However, the relative standard uncertainty is more than one order higher than those of optical radiant power or aperture areas measurement results and hence should be improved for better optical radiance characterization capabilities.
2. Experiment setup
Time-of-flight methods have been widely employed for non-contact distance measurement with high precision [22–27]. It is a convenient option to measure the distance inside a vacuum chamber through an optical window. In this work, time-of-flight method was adopted to measure the distance between two precision apertures mounted inside an ACR vacuum chamber in their working positions under the same conditions of cryogenic optical radiance measurement. The schemes of the measurement of the distance between the precision apertures and the radiance characterization of a blackbody infrared emitter are illustrated in Figs. 2(a) and 2(b), respectively.
Fig. 2. The schematic view of the time-of-flight distance measurement setup (a) and the ACR system for blackbody radiance characterization (b).
An all-fiber femtosecond mode-locked laser (FML-15-B, Optilab) with a repetition rate of 30 MHz and a pulse width in the range of (300∼600) fs was used for the measurement. 5% of the energy of the femtosecond pulse was applied to generate a trigger voltage signal using an 18.5-ps IR photodetector (1444, New Focus). The rest of the pulse was coupled into a circulator and then collimated to probe the aperture surfaces. The two optical pulses reflected from the aperture surfaces were then collected by the collimator, guided through the return channel of the circulator, and delivered onto a 70-GHz IR photodetector (XPDV3120R, Finisar) to generate two voltage pulse signals.
The voltage signals of the trigger photodetector and the receiver photodetector were transmitted via 2.4-mm 50-Ohm inputs to a 30-GHz digital communications analyzer (Infiniium DCA-J 86100C, Keysight) in oscilloscope mode with fs-level timing resolution. The response time of the photodetectors were measured to be ∼10 ps using an electro-optic sampling measurement facility [28–30].
Two cylindrical precision apertures were machined from Invar with inner diameters of 9 mm and 8 mm, respectively. The outer diameters are 25 mm and the non-flatness of the front surfaces facing the light source are ∼5 µm. The two precision apertures were mounted in the ACR vacuum chamber as illustrated in Fig. 3(a) and the front view of the real installed units from the light source side is shown in Fig. 3(b). The two precision apertures were mounted concentrically with <0.1 mm central displacement inside the two terminals of a metal/plastic tube and the tube was installed on a stress-relieving and thermally-isolated holder supported by an Invar post rooted from the room-temperature base of the cryocooler. The first aperture was thermally linked to the 35 K shield and the second aperture to the 5 K stage of the cryocooler, respectively, both via soft pure copper belts. The ACR receiver cavity with an entrance diameter of 10 mm was placed closely after the second precision aperture for full acceptance of transmitted light.
Fig. 3. The schematic view of the precision apertures installed in an ACR vacuum chamber (a) and the front view of the installed precision apertures (b).
3. Measurement results
The collimator was mounted on a multi-axis translation stage capable of X-Y scanning plus horizontal/vertical tilting and adjusted to observe two voltage pulse signals with similar peak magnitude on the sampling oscilloscope. The timing jitter to measure one single voltage pulse on the sampling oscilloscope can be improved to ∼90 fs from ∼1.45 ps when the averaging number was increased from 1 to 256 (Fig. 4). The time difference between the two voltage pulses from the receiver photodetector can be directly measured using the ΔTime mode (Fig. 5). The standard deviation of the measurement can be better than the 90-fs timing jitter because certain correlated effects may cancel out for the two voltage pulses. The Gifford-McMahon cycle cryocooler has a horizontal vibration magnitude of ∼30 µm and the relative vibration between the two precision apertures may be as high as ∼3 µm, corresponding to a distance light travels for ∼10 fs in vacuum. Hence, the averaging number was not further increased beyond 256 for both simplicity and efficiency.
Fig. 4. The receiver photodetector signal obtained on the sampling oscilloscope: (a) number averages = 1; and (b) number averages = 256.
Fig. 5. The time difference of the two electrical pulses from the receiver photodetector resulted from the two femtosecond pulses reflected by the precision apertures.
A fiber-optic tunable attenuator was applied before the trigger photodetector and the peak of the trigger voltage signal was adjusted to be ∼20 mV. In the advanced trigger setup of the sampling oscilloscope, the high sensitivity mode was used for hysteresis and the trigger attenuation factor was set 1.000:1.
The trigger level of the trigger photodetector was adjusted from 1 mV to 16 mV with an increment of 1 mV and the time difference of the two voltage pulse signals as well as the standard deviation were measured for each trigger level. The results were plotted and displayed in Fig. 6. When the trigger level approached to the 20-mV peak magnitude, the standard deviation of the measurement became significantly large. Optimal trigger level with minimal standard deviation was decided to be 7 mV. The time difference of a round trip in vacuum between the two precision apertures was 2.4299 ns, with a standard uncertainty of 30 fs.
Multiple measurements were conducted at different positions of the apertures as illustrated in Fig. 7. The time difference results were 2.4298 ns, 2.4299 ns, 2.4299 ns, and 2.4300 ns, respectively. The average time difference (ΔtAvg) was calculated to be 2.4299 ns with a standard deviation of 82 fs. The averaged distance between the precision apertures, dAvg, can then be calculated to be 0.36423 m using dAvg=cΔtAvg/2, where c is the speed of light.
The time-of-flight distance measurement result was traced to length using a motorized linear translation stage calibrated by a standard optical interferometer. The two precision apertures were again used for the calibration except that the second precision aperture was mounted on the linear translation stage so the distance between the two precision apertures can be adjusted. The standard uncertainty of the timing difference was evaluated to be ∼42 fs for the interested displacement. The overall uncertainty of the measurement of the distance of 0.36423 m (corresponding to a light flight time of 2.4299 ns in vacuum) was then evaluated to be (corresponding to a light flight time of 97 fs in vacuum) 15 µm and the relative standard uncertainty can be calculated to be 0.004%.
4. Analysis and discussion
As shown in Eq. (2), the radiance can be evaluated based on the measurement results of the absolute optical power, the effective area of the precision apertures, and the distance between precision apertures in an ideal case.
The absolute optical power measurement uncertainty can be achieved as low as tens of ppm at a power level of ∼1 mW [1]. However, the uncertainty increases significantly as the incident optical power decreases. When working with a blackbody infrared emitter with a working temperature of ∼300 K, the optical power incident received on the ACR cavity detector may get close to the ACR equivalent thermal noise at ∼nW level so the measurement uncertainty would be limited to be ∼0.1% using a conventional ACR apparatus. Ultra-sensitive superconducting TESs would be helpful to improve the performance but other relevant issues such as the dynamic range of the TES working temperature needs to be carefully studied [14].
The relative standard uncertainty for the measurement of aperture area at ambient temperature is 65 ppm. The Invar shrinks by 0.040% from 293 K to 40 K [18]. The actual coefficient of thermal expansion (contraction) measurement results below 40 K was rather loose [19]. However, a shrinkage ratio of 0.042% with an uncertainty of 0.002% at 4 K may be deducted from the data at 100 K, 77 K, and 40 K. The areas of the precision apertures after correction (A1 and A2) can then be applied for cryogenic applications.
For a practical radiance measurement system based on blackbody infrared emitters with a relatively large output port diameters, the radiance is uniform near the normal direction [31,32]. Integrating sphere light sources can also have good radiance spatial distribution [33]. Such light sources and the ACR cavity detector can be considered insensitive to the orientation within a small solid angle near the normal axis. However, the geometric properties of the two-aperture ensemble consisting of the projected source area, the projected detection area, and the distance between the centers of the projected areas should be carefully examined. As explained in Fig. 8, the actual projected source and detection areas and the distance between the centers of the precision apertures could deviate significantly from the ideal case. Since the femtosecond mode-locked laser can always be adjusted to be perpendicular to the flat front surface of the first precision aperture, only the relative position of the second precision aperture to the first needs to be studied. There are two simple types of non-ideal cases to be discussed: (1) cases with only non-concentricity problem and (2) cases with only non-parallelism problem. The actual cases may contain both non-concentricity and non-parallelism problems but the effects can be analyzed independently.
For the cases with only non-concentricity problem, the distance between the centers of the precision apertures (d) is larger than the measured distance (dAvg) and the effective projected source and detection areas (A1,p and A2,p) are less than A1 and A2, respectively. Since the outer ring radius of each precision aperture was machined with ±10 µm accuracy and the center of the aperture deviates by ±10 µm from the center of the outer ring, the displacement of the center of the aperture is within 20 µm from any edge of the outer ring. The two precision apertures were mounted inside the two terminals of a metal/plastic tube, where (1) the metal part was used to fix the aperture position and to cool the mounted aperture and (2) the plastic part was used to isolate the heat between 35 K and 5 K. The tube was mounted on a stress-relieving holder so the centers of the precision apertures would not shift as much as the total expansion/contraction. The non-concentricity was estimated to be less than 0.1 mm and would not cause significant error on the projected areas and distance. For a measured distance of ∼0.364 m, a non-concentricity displacement of as large as 1 mm could only result in a 4-ppm error from the actual distance. The errors of the projected areas to the areas of the precision apertures can be evaluated to be negligible in a similar way.
For the cases with only non-parallelism problem, the measurement data obtained in this work (Fig. 7) were analyzed. The tilt across the 8-mm aperture diameter can be calculated to be 0.015 mm, the error between the projected detection area A2,p and the area of the second precision aperture A2 is evaluated to be only 3.5 ppm. However, one issue worth attention is that, as shown in Fig. 9, certain extent of non-parallelism may compromise the time-of-flight measurements when the fiber-optic collimator is installed too far to receive the tilted reflection pulses. A bad tilt could only be found after being measured and the situation could hardly be improved without in situ adjustment devices. Therefore, the components would best be carefully designed, machined, and assembled.
5. Conclusion
Time-of-flight method using femtosecond mode-locked laser and high-speed photodetectors was employed to measure the distance between two precision apertures applied in vacuum for a cryogenic optical radiance characterization system. The relative standard deviation was evaluated to be 0.004%. The apertures’ non-concentricity and non-parallelism effects on the distance and consequently radiance measurement results were estimated to be negligible. The time-of-flight method can be useful to measure the distances with high precision and consequently improve the accuracy of low-background infrared radiance measurement systems.
Funding
Ministry of Science and Technology of the People's Republic of China (2016YFF0200301); National Institute of Metrology of China (AKY1602, AKY1603, AKYZD1909).
Acknowledgments
Authors thank Weimin Wang, Yike Xiao, Yinuo Xu, Yongjie Lin, Xufeng Jing, Changyu Shen, and Huaping Gong from China Jiliang University for helpful technical discussions.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. J. E. Martin, N. P. Fox, and P. J. Key, “A cryogenic radiometer for absolute radiometric measurements,” Metrologia 21(3), 147–155 (1985). [CrossRef]
2. T. Varpula, H. Seppä, and J. M. Saari, “Optical power calibrator based on a stabilized green He-Ne laser and a cryogenic absolute radiometer,” IEEE Trans. Instrum. Meas. 38(2), 558–564 (1989). [CrossRef]
3. P. V. Foukal, C. Hoyt, H. Kochling, and P. Miller, “Cryogenic absolute radiometers as laboratory irradiance standards, remote sensing detectors, and pyroheliometers,” Appl. Opt. 29(7), 988–993 (1990). [CrossRef]
4. R. U. Datla, K. Stock, A. C. Parr, C. C. Hoyt, P. J. Miller, and P. V. Foukal, “Characterization of an absolute cryogenic radiometer as a standard detector for radiant-power measurements,” Appl. Opt. 31(34), 7219–7225 (1992). [CrossRef]
5. T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, and A. C. Parr, “National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35(7), 1056–1068 (1996). [CrossRef]
6. K. D. Stock and H. Hofer, “Present state of the PTB primary standard for radiant power based on cryogenic radiometry,” Metrologia 30(4), 291–296 (1993). [CrossRef]
7. S. P. Morozova, V. A. Konovodchenko, V. I. Sapritsky, B. E. Lisiansky, P. A. Morozov, U. A. Melenevsky, and A. G. Petic, “An absolute cryogenic radiometer for laser calibration and characterization of photodetectors,” Metrologia 32(6), 557–560 (1995). [CrossRef]
8. H. Gan, Y. He, X. Liu, N. Xu, H. Wu, G. Feng, W. Liu, and Y. Lin, “Absolute cryogenic radiometer for high accuracy optical radiant power measurement in a wide spectral range,” Chin. Opt. Lett. 17(9), 091201 (2019). [CrossRef]
9. J. E. Martin and N. P. Fox, “Cryogenic solar absolute radiometer (CSAR),” Metrologia 30(4), 305–308 (1993). [CrossRef]
10. R. U. Datla, M. C. Croarkin, and A. C. Parr, “Cryogenic blackbody calibrations at the National Institute of Standards and Technology low background infrared calibration facility,” J. Res. Natl. Inst. Stand. Technol. 99(1), 77–86 (1994). [CrossRef]
11. E. Theocharous, N. P. Fox, V. I. Sapritsky, S. N. Mekhontsev, and S. P. Morozova, “Absolute measurements of black-body emitted radiance,” Metrologia 35(4), 549–554 (1998). [CrossRef]
12. A. C. Carter, R. U. Datla, T. M. Jung, A. W. Smith, and J. A. Fedchak, “Low-background temperature calibration of infrared blackbodies,” Metrologia 43(2), S46–S50 (2006). [CrossRef]
13. H. Gan, N. Xu, X. Liu, Y. He, H. Wu, G. Feng, W. Liu, and Y. Lin, “Total and spectral radiance measurements of blackbody radiation sources based on an absolute cryogenic radiometer,” Proc. SPIE 11338, 127 (2019). [CrossRef]
14. A. C. Carter, S. I. Woods, S. M. Carr, T. M. Jung, and R. U. Datla, “Absolute cryogenic radiometer and solid-state trap detectors for IR power scales down to 1 pW with 0.1% uncertainty,” Metrologia 46(4), S146–S150 (2009). [CrossRef]
15. Y. Deng, Q. Sun, J. Yu, Y. Lin, and J. Wang, “Broadband high-absorbance coating for terahertz radiometry,” Opt. Express 21(5), 5737–5742 (2013). [CrossRef]
16. J. Lehman, C. Yung, N. Tomlin, D. Conklin, and M. Stephens, “Carbon nanotube-based black coatings,” Appl. Phys. Rev. 5(1), 011103 (2018). [CrossRef]
17. M. Litorja and J. Fowler, “Report on the CCPR-S2 supplementary comparison of area measurements of apertures for radiometry,” http://www.bipm.org/utils/common/pdf/final_reports/PR/S2/CCPR-S2.pdf (Jan. 4, 2007).
18. J. E. Ekin, “Experimental techniques for low-temperature measurements: cryostat design, materials properties, and superconductor critical-current testing, Oxford University, 2006”.
19. S. Roose and S. Heltzel, “High-precision measurements of the thermal expansion at cryogenic temperature on stable materials,” Macroscale2011, [CrossRef] .
20. R. Schodel, A. Walkov, M. Zenker, G. Bartl, R. Meeb, D. Hagedorn, C. Gaiser, G. Thummes, and S. Heltzel, “A new ultra precision interferometer for absolute length measurements down to cryogenic temperatures,” Meas. Sci. Technol. 23(9), 094004 (2012). [CrossRef]
21. T. Middlemann, A. Walkov, and R. Schodel, “State-of-the-art cryogenic CTE measurements of ultra-low thermal expansion materials,” Proc. SPIE 9574, 95740N (2015). [CrossRef]
22. 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]
23. 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]
24. H. Wu, F. Zhang, S. Cao, S. Xing, and X. Qu, “Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser,” Opt. Express 22(9), 10380–10397 (2014). [CrossRef]
25. H. Wu, F. Zhang, J. Li, S. Cao, X. Meng, and X. Qu, “Intensity evaluation using a femtosecond pulse laser for absolute distance measurement,” Appl. Opt. 54(17), 5581–5590 (2015). [CrossRef]
26. H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015). [CrossRef]
27. X. Lu, S. Zhang, C.-G. Jeon, C.-S. Kang, J. Kim, and K. Shi, “Time-of-flight detection of femtosecond laser pulse for precise measurement of large microelectronic step height,” Opt. Lett. 43(7), 1447–1450 (2018). [CrossRef]
28. J. Li, N. Xu, H. Gan, J. Li, and Z. Zhang, “70GHz photodetector’s pulse waveform measurement at NIM,” Appl. Mech. Mater. 644-650, 1027–1030 (2014). [CrossRef]
29. J. Li, H. Gan, and N. Xu, “Test System of 100GHz Photodetector Time Response at NIM,” Proc. CLEO-PR (Optical Society of America, 2015), paper 25F1_3 (2015).
30. J. Li, N. Xu, H. Gan, Z. Zhang, and M. Zhang, “Use test system of 100GHz photodetector waveform calibrate rise time of oscilloscope,” Proc. SPIE 9677, 96771A (2015). [CrossRef]
31. P. W. Nugent and J. A. Shaw, “Large-area blackbody emissivity variation with observation angle,” Proc. SPIE 7300, 73000Y (2009). [CrossRef]
32. S. P. Morozova, A. Y. Dunaev, A. A. Katysheva, V. I. Sapritsky, N. A. Parfentyev, S. A. Ogarev, and D. N. Karpunin, “Facility for measuring the spatial uniformity of the radiation power of the surface of the large-area blackbody,” Int. J. Thermophys. 38(5), 74 (2017). [CrossRef]
33. Y. He, P. Li, G. Feng, Y. Wang, Z. Liu, C. Zheng, H. Wu, and D. Sha, “Computer modeling of a large-area integrating sphere uniform radiation source for calibration of satellite remote sensors,” Optik 122(13), 1143–1145 (2011). [CrossRef]
