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A combined cavity ring-down (CRD) and spectrophotometry technique is developed to measure with sufficiently high accuracy the reflectance of any practically fabricated optical laser component with reflectance ranging from below 0.01% to over 99.999%. In this combined technique, a CRD configuration is employed to measure reflectance higher than 99%, and a conventional spectrophotometric configuration, which is formed by simply removing the rear cavity mirror from the CRD configuration, is applied to measure reflectance below 99%. Uncertainties below 0.0001% for reflectance over 99.99% and below 0.3% for reflectance below 99% are experimentally achieved with CRD and spectrophotometry configurations, respectively, of one single experimental setup.
© 2013 Optical Society of America
1. Introduction
Reflectance measurements of optical laser components are routine practices in optical thin film laboratories. The reflectance values vary in a wide range from less than 0.01% for high-performance anti-reflectively (AR) coated laser components to higher than 99.999% for highly reflective (HR) mirrors. The widely used technique for reflectance measurement is spectrophotometry (SP) [1], which has a typical uncertainty of approximately ± 0.1% - ± 0.3% for an arbitrary reflectance value in the theoretical 0 – 100% range. Spectrophotometers like Perkin Elmer Lambda 900/1050 or Cary 5000/7000 are equipped in most optical thin film laboratories as routine reflectance/transmittance measurement tools. To improve the measurement accuracy, accessories based on multiple reflections [2–4] were employed in standard spectrophotometers, resulted in reflectance uncertainty in the sub-0.1% level, but with disadvantages of limited angles of incidence, large diameters of optical components, and high sensitivity to optical misalignment. In addition, as a reference sample was usually required to calibrate photometry amplitude to determine the absolute reflectance value, the measurement accuracy is further influenced by the reflectance uncertainty of the reference sample. Normally, for SP, the maximum measurable reflectance is limited to 99.9%, with an uncertainty in the level of ± 0.1%.
For optical laser components, a ratiometry based technique employing a laser as the light source can also be used for reflectance measurements. In 1994, A.Voss et al [5] developed a laser ratiometry (LR) based reflectometer, in which the laser power difference with/without reflection of test sample was measured with a lock-in amplifier (LIA). By employing a highly stable laser as the light source, an uncertainty of approximately ± 0.01% for 1.06μm laser optics was experimentally achieved. Even though this technique was also an international standard for reflectance/transmittance measurements (ISO 13697) [6], it was not commercialized for routine reflectance/transmittance measurements due to its structural complexity, high sensitivity to optical misalignment and scattering of laser source, requirements on high-stability laser source and precise calibration of reference samples, and so on. For both SP and LR based techniques for reflectance measurements, the ultimate limitation to measurement accuracy is the power fluctuation of the light source, which limits the typical uncertainty for reflectance measurement to the 0.1 −0.01% ranges.
On the other hand, with the continuous improvement of coating technologies, dielectric HR mirrors with reflectance approaching unity (say, higher than 99.99%) are routinely fabricated nowadays. A cavity ring-down (CRD) technique, which was first developed in the 1980s [7, 8], is employed for such high reflectance measurements. For reflectance higher than 99.99%, the typical measurement uncertainty was approximately 0.0001% (1 ppm) or less [9, 10]. In the past, various CRD configurations employing either pulsed or continuous-wave (cw) laser sources [11–13] were used for reflectance measurements. In a typical CRD configuration, the decay time τ of the ring-down cavity (RDC), which is measured to determine the reflectance, is simply expressed as:
Where R is the reflectance of the cavity mirror, L is the length of the RDC, and c is the speed of light, respectively. The measurement uncertainty for the reflectance can be expressed as:Where u(L) and u(𝜏) are the uncertainties of the RDC length and decay time, respectively. For a typical CRD system with RDC length L = 0.8m, u(L) = 0.001m (typical error if measured with a ruler), and assume u(𝜏) = 20ns for a typical photo-detector with response time in the 10ns range, the relative uncertainty u(R)/R is approximately 0.08% for R = 99% and approximately 0.3% for R = 98%, respectively, comparable to that of SP and LR. Reflectance lower than 98% is not likely be measured by CRD due to the reduced decay time and increased measurement uncertainties. Table 1 summarizes the advantages and disadvantages of the three techniques for reflectance measurements.
Table 1. Advantages and disadvantages of spectrophotometry, laser ratiometry, and cavity ring-down techniques for reflectance measurements
From Table 1 it is clear that while spectrophotometers are preferable for routine reflectance measurements, CRD based instruments are the choice for high reflectance measurements with uncertainty in the ppm to sub-ppm level. In this paper, for the first time to our knowledge, we develop a reflectance measurement technique which combining CRD and SP techniques in one simple apparatus and measuring in principle with sufficiently high accuracy the reflectance of any optical laser component which could be practically fabricated.
2. Experiment
A schematic diagram of the experimental setup is shown in Fig. 1. For the CRD configuration, an optical feedback CRD (OF-CRD) scheme [11] is employed for the reflectance measurements, as presented in Fig. 1(a). In the OF-CRD scheme, a cw F-P diode laser (Model IQ2A09 (635-15) G2R4, Power Technologies) is used as the light source, whose wavelength is centered at 635nm. The output power of the diode laser is square-wave modulated by a function generation card (Model UF2-3012, Strategic Test, Sweden) at frequency 100Hz. The initial RDC is formed by two plano-concave mirrors R1 and R2 (called cavity mirrors) with radius of curvature of 1m and a plane mirror R3. The power fluctuation of the diode laser is monitored by a photo-detector PD2 (Model 1801, New Focus). The CRD signal which leaks out of the RDC through cavity mirror R2 is detected by a photo-detector PD1 (Model APD110A/M, Thorlabs) and acquired by a data-acquisition card (Model UF2-6021, Strategic Test, Sweden) for data processing. A variable attenuator is used to adjust the laser power for optimum signal amplitudes. The CRD signals are recorded at the negative edge of the modulation.
To measure the reflectance of an optical laser component with the CRD configuration, the decay time τ0 of the initial RDC is first measured. Then the test sample is inserted into the initial RDC with the required angle of incidence to form the test RDC, as shown in Fig. 1(a). Once the decay time τ of the test RDC is measured, the reflectance R of the test sample can be determined as
Where L0 and L are the lengths of the initial and test RDCs, respectively.On the other hand, the SP configuration for reflectance measurements can be easily implemented by simply removing the (rear) cavity mirror R2 in the CRD configuration, as presented in Fig. 1(b). In this case the reflectance R of the test sample is simply
Here PPD1 and PPD2 are the output amplitudes of the photo-detectors PD1 and PD2 in the SP configuration, respectively. M is a calibration factor, which can be easily determined with the SP configuration by a reference sample with a known reflectance R0. Practically, a HR mirror with a reflectance approaching unity and being determined by the CRD configuration can be conveniently used as the reference sample. The calibration factor M can also be determined by measuring the ratio PPD2/PPD1 when no test sample is present, as shown in Fig. 1(b).Six samples were used in the experiments for reflectance measurements at 635nm wavelength. Samples #1 to #3 were dielectric HR mirrors with reflectance higher than 99.9% at 45-degree (#1) or normal (#2 and #3) incidence. Samples #4 and #5 were enhanced Ag and Al mirrors with reflectance higher than 99% and approximately 90% at 635nm, respectively. The reflectance spectra of samples #4 and #5 were shown in Fig. 2. Sample #6 was an uncoated BK7 substrate. Samples #1 to #4 were measured with the CRD configuration. Sample #3 to #6 was measured with the SP configuration, with Sample #2 served as the reference sample to calibrate the photometry amplitudes. For comparison, the reflectance of Sample #3 to #6 was also measured with a Perkin Elmer Lambda 1050 spectrophotometer.
Fig. 2 Reflectance spectra of Samples #4 and #5 in the 500nm-700nm range measured with Lambda 1050 spectrophotometer.
3. Results and discussions
Table 2 summarizes the reflectance values measured with the CRD and SP configurations, as well as with the spectrophotometer Lambda 1050. In Table 2, the reflectance values and corresponding uncertainties determined with the CRD and SP configurations are the averages and standard deviations of ten repeat measurements. For each measurement, the test sample was re-inserted and the optical arrangement was re-adjusted for both CRD and SP configurations. For each sample, only one measurement was performed with Lambda 1050. For sample #2, the CRD measurements were repeated with 10 RDC lengths between 0.7m to 0.9m. The results are presented in Fig. 3, in which the error bar for each measurement represented the standard deviation (below 1.3ppm) of 256 decay time measurements. Since there is no “standard” sample available to verify the accuracy of the reflectance values measured with CRD, measuring the reflectance with changing RDC length is a simple way to check the reliability of the measured results [14] as in principle the reflectance is independent of the RDC length while the impact of other factors such as the diffraction loss, finite response time and nonlinearity of the detector on the reflectance measurement might be RDC length dependent.
Table 2. Comparison of reflectance values measured with CRD and spectrophotometry configurations, and Lambda 1050 spectrophotometer
Figure 4 shows the measurement results for Sample #3 with the CRD, SP configurations and Lambda 1050 spectrophotometer. The CRD, SP, and Lambda 1050 measured reflectance values are 99.9887 ± 0.0001%, 100.1 ± 0.3%, and 100.3%, respectively. Even though the results obtained with the SP configuration and Lambda 1050 are in good agreement, with the difference within the uncertainties of both instruments, these over 100% values obviously do not represent the real reflectance of the sample. On the other hand, the CRD value, with uncertainties of only 0.0001% or 1ppm, is much more accurate than the SP and Lambda 1050 values. The results presented in Fig. 4 clearly indicate that only CRD is the appropriate technique to measure the reflectance over 99.9%.
Fig. 4 The reflectance of Sample #3 measured by CRD configuration, SP configuration, and Lambda 1050.
The CRD configuration is also used to measure the reflectance over 99.999% (Sample #1), between 99.99% and 99.999% (Sample #2), and between 99% and 99.9% (Sample #4). The uncertainties for measured reflectance of 99.99912% and 99.99045% are 0.5ppm and 0.8ppm, respectively, indicating that CRD is the technique to measure reflectance over 99.99%. For reflectance of approximately 99.3%, the uncertainties of the CRD and SP values are 0.1% and 0.2%, respectively. The CRD value shows a higher accuracy than the SP value. For Sample #4, the differences between the reflectance values measured with CRD configuration, SP configuration, and Lambda 1050 are between 0.1% and 0.3%, within the uncertainties.
For reflectance well below 99%, CRD is no longer appropriate for reflectance measurement as the decay time of the CRD signal is too short to be detected. In this case the SP configuration becomes appropriate for the reflectance measurements. The reflectance of Sample #5 measured with the SP configuration, 89.1% ± 0.1%, is in good agreement with the Lambda 1050 value, 89.2%, as both are based on the spectrophotometry principle. On the other hand, the reflectance of a bare BK7 substrate measured with the SP configuration, 8.07%, is in good agreement with the literature value [15], 8.09% (calculated with the literature refractive index value by taking into account the 4-degree angle of incidence during SP measurement), as expected. Worthy mentioning that due to limited experimental availability in our laboratory, samples with reflectance below 1% (and down to 0.01%) are not measured with the combined setup in this paper. However it is understandable that in the combined experimental setup if appropriate attenuators and photo-detectors are used and the optical configuration is optimized to eliminate the influence of stray light (with background correction), the SP configuration could measure reflectance as low as 0.01%, or even lower, like commercial spectrophotometers [16].
It is also worthy to mention that even though reasonably low uncertainties of the reflectance values measured with the CRD and SP configuration are obtained, the performance of the combined experimental setup is far from optimized, especially for the SP configuration. Better accuracy could be achieved in SP configuration by employing a stable laser source, appropriate attenuators and photo-detectors, as well as proper background correction to eliminate the influence of stray light. These factors have to be taken into consideration when developing the instrument combining the CRD and SP techniques. Care has also to be taken to avoid any inter- influence when combining the two techniques in one instrument.
4. Conclusions
A combined cavity ring-down and spectrophotometry technique has been developed to measure the reflectance of optical laser components in a wide dynamic range. The reflectance from below 10% to over 99.999% has been experimentally measured with a combined CRD and SP setup. Uncertainties below 1ppm for reflectance over 99.99% and below 0.3% for reflectance below 99% have been achieved with the CRD and SP configurations of one single experimental setup, respectively. It is expected that once the optical configuration of the combined setup is optimized and appropriate attenuators and photo-detectors are used, the combined CRD and SP technique can measure with sufficiently high accuracy the reflectance of any laser optical component practically fabricated, with reflectance ranges from below 0.01% to over 99.999%.
References and links
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