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Laser power detectors with natural convective cooling are convenient to use and hence widely applicable in a power range below 150 W. However, the temporal response characteristics of the laser power detectors need to be studied in detail for accurate measurement. The temporal response based on the absolute laser power standards with natural convective cooling is studied through theoretical analysis, numerical simulations, and experimental verifications. Our results show that the response deviates from a single exponential function and that an ultimate response balance is difficult to achieve because the temperature rise of the heat sink leads to continuous increase of the response. To determine the measurement values, an equal time reading method is proposed and validated by the laser power calibrations.
© 2016 Optical Society of America
1. Introduction
The absolute measurement of laser power is generally based on thermal detectors [1–4]. The characteristic behavior of the temporal response is an important property of the detector, which determines the response speed and the signal processing method. To present, some investigations into the temporal response of laser detectors have been undertaken: West et al. analyzed the response behavior of isoperibol calorimeters in 1970 [5]. The calorimeters are typically applied in the measurement of laser energy (for a pulse laser or a continuous laser over a period of time) based on transient modes. The temporal response of a simple laser power meter has been studied [6]. The meter is a relative type with a planar absorber and a cooling time constant of 1.34 s. The temporal response of a radiometer was also studied for a laser power of 1 mW [7]. Laser detectors of different types and ranges show different response characteristics. Study on these characteristics will enhance understanding of the detectors and help to improve the measurement accuracy. While, up to now, the research works on the temporal response of laser detectors are less and can’t meet the needs of users.
In laser power measurements, an absolute laser power standard (self-calibration type) is important for value realization in a country. An electrical calibration unit for value traceability and a cavity receiver for high optical absorption at different laser wavelengths are usually integrated. When heat capacity of the energy absorber is increased, the response will consequently take longer, and the determination of the response balance becomes more difficult.
Laser power detectors that employ natural convective cooling have been widely adopted, especially for a power of less than 150 W. They are very convenient to use in practical applications because the complex cooling systems are not required. In measuring process, the thermal equilibrium between the heat sink and the environment is usually very slow due to low convective efficiency, which has a direct impact on the response performance. For a relative detector with plane absorber and fast response, the temperature of the absorber will quickly close to that of heat sink, and the influence to the response is small. However, when it comes to an absolute standard with cavity absorber and slow response, the temperature tracking of the hot end to the heat sink will has a time delay, and the temporal response will be affected seriously. Therefore, a detailed study on the temporal response of an absolute laser power standard with natural convective cooling appears more important for accurate measurement.
Our research was carried out based on our newly developed 1-100 W absolute laser power standard detectors with natural convective cooling at the National Institute of Metrology (NIM) of China. The temporal response was analyzed via signal and systems theory, and numerical simulations for the heat transfer were made using ANSYS software. The features of the temporal response and the characteristic time parameter were studied in detail in experimental tests. An equal time reading method was proposed for the determination of measured values and the method was validated through the calibration of laser power meters. The influences of different convection modes on the response were also tested.
2. Systems analysis
The structural design of our newly developed 1-100 W laser power standard detector is shown in Fig. 1. The system is primarily composed of an absorption cavity (graphite material), a thermopile sensor (1060 aluminum substrate and Sb-Bi thermopile), an electric heater (ceramic substrate) and a heat sink (6061 aluminum). In the laser power measurements, heat absorbed by the cavity flows to the heat sink through the heat conduction wall of the thermopile and then spreads to the environment through convection and radiation. T1 represents the temperature of the end of the device where the laser is absorbed. Two rings of thermocouples are located at T2 and T3 for converting the temperature difference to a voltage signal as the detector’s response. T4 and T0 are the temperatures of the heat sink and the environment, respectively.
According to the signal and systems theory [8], the detector system can be divided into four subsystems connected in series. They are T1-T2, T2-T3, T3-T4, and T4-T0. The impulse response functions (IRF) of temperature differences on heat flow for each subsystem are denoted as h△12(t), h△23(t), h△34(t) and h△40(t), respectively. The IRF of the combined systems of T2-T0 and T3-T0 can be expressed as
andrespectively.In the measurement system, the heat flow into T1 is equal to the absorbed laser power and is labeled p(t). Before this energy reaches T2, it is distributed by the subsystem T1-T2, and the input excitation of the combined system T2-T0 can be expressed as
where is the normalized IRF of the subsystem T1-T2. Similarly, the input excitation of the combined system T3-T0 can be expressed asThen, the response functions of the combined system T2-T0 and T3-T0 are obtained by a convolution of the IRFs and the excitations, which can be expressed asandrespectively.Finally, the response function of thermopile under the whole system can be calculated by subtracting Eq. (6) from Eq. (5):
It can be seen from Eq. (7) that the time domain response is related to the behavior of all the subsystems. The IRF of each subsystem contributes to the broadening of r△23(t). A larger absorbing cavity would have a higher heat capacity, and would lead to a greater width in h△12(t). The influence of h△34(t) in Eq. (7) arising from subsystem T3-T4 is small due to the enhanced thermal diffusion engendered by the structural design. The h△40(t) in Eq. (7) coming from subsystem T4-T0 represents heat transfer between the heat sink and the environment. High heat capacity and large convective thermal resistance result in a large width of h△40(t), which makes the precise balance of the response very difficult in power measurements.
3. Numerical simulation
3.1 Model and parameters
Numerical simulation is a widely used method for heat transfer analysis of laser detectors [9]. Our simulations for the model shown in Fig. 1 were carried out using ANSYS mechanical APDL. Thermal parameters of the detector materials used in the simulation are listed in Table 1. The heat flux simulating laser radiation was loaded on the conical surface of the cavity. The power calculated from the heat flux (4.3072 W/cm2) and the surface area (2.3217cm2) was 10 W. Since the heat flows to the heat sink mainly via conduction, the convection and radiation from the surface of the cavity and the sensor substrate are neglected. For the heat sink, two cases were simulated: (a) the surface in a convective cooling mode with a convective coefficient of 10 W/(m2∙K) and (b) the surface held at a constant temperature mode. The continued power loading time of 0 s to 1800 s, and the transient heat transfer time of 4000 s were simulated.
Table 1. Thermal parameters of the detector materials used in the simulation.
3.2 Simulation results
The simulated time dependence on temperature is displayed in Fig. 2. When the heat sink is in convective cooling mode, temperatures of T2, T3, and T4 continually rise and balance rather slowly during power loading. 2200 s after the stop of power loading, the temperatures tend to be consistent, but still do not return to their original values. It shows that heat transfer between the heat sink and environment is a very slow process in the convective cooling mode. In comparison, the temperatures reach balance more quickly when the heat sink is held at constant temperature mode. ΔT23 (temperature difference between T2 and T3) is equivalent to the detector response. Although the overall difference of ΔT23 is not obvious in both modes, but, after amplification, the heat balance of ΔT23 in convective cooling mode is much slower than that in constant temperature mode. Therefore, the temperature rise of the heat sink causes the slowly increasing response for the whole measurement process, which is often difficult to determine the right measurement value.
Fig. 2 Simulation results of temperature rise with time. t0 - the time for the power load on, t1 - the time for the power load stop, T2 - the temperature of the hot end of the thermopile, T3 - the temperature of the reference end of the thermopile, T4 - the temperature of the heat sink, ΔT23 - the temperature difference between T2 and T3.
4. Experimental test
4.1 Response measurement by electrical calibration
Electrical calibrations were carried out on two detectors (#1304 and #1501), incorporating natural convective cooling developed according to the design shown in Fig. 1. The key difference in the detectors was the size of their respective electric heaters; #1304 has a larger heater than #1501. A DC power supply (Agilent, E3649) was used for power input. The loading time lasted 1800 s. The response, loading voltage, and current were recorded in real time by digital multimeters (Agilent, 34410A).
The zero points are set from the mean value of the 10 seconds’ response data (output voltage) immediately before the power loading. In order to minimize the influence of power instability, the ratio obtained through the output voltage divided by the load power in real time is treated as the equivalent response. The response data are normalized to the value at the end of power loading, and the curves are shown in Fig. 3. It can be seen that, after amplification, the responses keep rising during the whole power-loading stage and can’t return to zero at the end of the 2000 s after the power load stops. This confirms the results of our numerical simulations. In addition, the response of #1304 is slower than that of #1501, which is due to a larger heat capacity of the detector’s absorber.
Fig. 3 Experimental results of the response with #1304 and #1501. t0 - the time for the power load on, t1 - the time for the power load stop.
4.2 Fall time constant measurement
The time constant can be used to evaluate the property of the temporal response. In measurement, time can be divided into a number of periods and the response in each period is equivalent to an independent exponential function. A fall stage, in which the system response will not be affected by the stability of input power, can be chose in the study of responsive time constant. The fall time constant used in our analysis is calculated by Eq. (8) in the fall stage (the response after the power input is halted):
where △t is the time interval for calculations and U(t) is the output voltage in the fall stage. The fall time constant of #1501 has been computed under conditions of △t = 10 s and 100W power levels. The fall response and the computed fall time constant are shown in Fig. 4. Within 150 s of the fall response, the time constant increases from 10 s to 300 s. The response is obviously not well described by a single exponential function, which is in agreement with the result of [7] for a radiometer under 1 mW level. According to the Eq. (7) in signal and system analysis, the temporal response is the convolution of four subsystems with different time constant. The comprehensive effect results in the response with multi exponential function. In the initial stage, the response is mainly determined by hot end and is relatively quick. However, in later stages, the influence of the temperature rise of the heat sink grows and leads to a much slower response. Based on the numerical simulation results, a slow thermal balance of the heat sink in convective cooling mode leads to a slow response equilibrium and a large time constant in later stages.4.3 Calibrations for laser power meters
According to the previous results, the ultimate response balance is difficult to achieve for detectors with natural convective cooling. Hence, how does one determine the measurement values? An equal time reading method can be adopted. In this method, responses at the same time delay are assumed to reach a consistent position in different measurements, and the measurement values should be read at the same time delay in each test. To study the feasibility of this method, experimental tests were carried out on our standard detector #3, which has been reported previously [10,11]. The responses at 420 s and 600 s were chosen for #3. The correction factor of PM150 (a relative laser power meter) was calibrated by #3. The calibrations were done under 1064 nm laser system with power stability of 0.13% (standard deviation within 600 s). The results are listed in Table 2. Though there is a difference of 3% between the responsivities of #3 at different reading times, the calibration factors of PM150 are in good agreement (0.02%). The uncertainty evaluation for the measurement consistency tests at 420 s and 600 s is shown in Table 3. The opto-electric inequivalence and the cavity absorption are not contained because they have exactly the same effect for the measurement values at different reading time. The laser power realizations of 3# with different reading time are consistent. The equal time reading method is practicable for absolute laser power detectors with natural convective cooling. The method can avoid the pitfalls inherent to the response balance, reduce the loading time, and shorten the measurement process.
Table 2. Calibration results with the equal time reading method.
Table 3. Uncertainty evaluation for the measurement consistency tests at 420 s and 600 s.
4.4 Determination of the reading time
Determination of the reading time is associated with the expected measurement accuracy, and two factors should be considered: (1) the response variation within the deviation time for reading and (2) the measurement repeatability at the specified reading time.
For the first factor, the growth rate of the response decreases with time, and the response variation within the deviation time of reading should be small enough to meet the measurement precision. In laser power calibration works at NIM, the manual reading mode is often used, and the deviation time of reading can be controlled in 10 s. Electrical calibrations were done on #1304 to measure the response variation in 10 s interval. The power loading time is 1800 s, and the measurement data are normalized to the value of 1800 s. The relative variation and the response are shown in Fig. 5. For a relative ratio of variation less than 0.02%, the time delay for reading should be greater than 200 s.
For the second factor, measurement repeatability at a specified reading time should meet the requirement of uncertainty component control. The repeatability of #1304 at different reading time has been studied through electrical calibrations. The power loading sustained 1250 s, and 10 tests were done. Relative deviation of the repeated measurements with different reading time from 30 s to 1200 s is calculated using Bessel formula. The curve of the deviation is shown in Fig. 6. When the reading time is over 50 s, the deviation is less than 0.08% and tends to be stable. When using the mean value as a result, the deviation will be reduced to be less than 0.08%.
As far as #1304 is concerned, the first factor is more sensitive to determine the reading time. The time constant is 14 s at the initial stage. According to the requirement that the response variation is less than 0.02%, the reading time should be 14.3 times more than its time constant. It is worth noting that the repeatability is also related to the stability of source. In our tests, the power stability is 0.028% within 1250 s.
4.5 Influence of convective intensity
To study the influence of convective intensity on the response, two means of convection, natural and forced, were applied to the heat sink. For forced convection, a fan was used to blow on the heat sink. The responsivity of #1304 were measured through electrical calibrations with the equal time reading method (read at 240 s).
The results are listed in Table 4. The responsivity with forced convection is 0.2% higher than that with natural convection. It indicates that the convective intensity of the heat sink has some influence on the response function of the detector. In order to ensure the stable of the response function, both the electrical calibrations (for value realization) and the laser calibrations (for value transfer) should be carried out under the same environmental conditions, and the stability of air flow should be ensured in measurements. Fortunately, the convection difference (natural and forced) in the experiments represents an extreme case. Under normal circumstance, the difference of convective intensity would be very small, and the responsivity variation would be far less than 0.2% for #1304.
Table 4. Responsivity with different convection modes.
5. Conclusion
For absolute laser power standard detectors that employ natural convective cooling, the heat transfer process was analyzed and the expression of the time domain response was deduced through signal and systems theory. Our results showed that the temporal response is induced by all IRFs of detector subsystems. The heat sink, in addition to the absorption cavity and the thermopile, affected the response. Numerical simulations on our newly developed laser power standard showed that the response increases with the temperature rise of the heat sink. However, in the cases that the heat sink maintains a constant temperature, the response achieves balance quickly. The experimental results confirm this theoretical analysis. This is due to the slow heat balance between the heat sink and environment; hence, the ultimate balance of the response becomes difficult in practical measurements.
Experimental tests on the standard detectors were carried out. The response continuously rose during the power loading stage, which is in agreement with the numerical simulations. The fall time constant increasing with time delay shows that the response deviates from a single exponential function and results the combined effects of all the subsystems.
An equal time reading method was proposed to determine the measurement values. The method was validated in the calibration of laser power meters. The responses with the same reading time were repeated in different measurements. For absolute laser power standards, the reading time should be consistent both in electrical calibrations and in laser measurements. The laser power measurement was largely independent of the specific reading time. This method can avoid the judgement of response balance and shorten the measurement process by reducing the power loading time.
It must also be noted that the measurement values will be affected by the convection intensity of the heat sink; hence, the stability of environment air flow needs to be ensured in both the electrical calibration (for value realization) and the laser measurement (for value transfer).
Acknowledgment
The authors are indebted to Dr. Zhao Yang for the useful technical discussion.
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