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Abstract
We present the design of a radiometer that can simultaneously measure both centroid wavelength and irradiance of a light source without recording its spectrum, when the light source has a finite spectral bandwidth. It consists of two photodiodes separated with a beam splitter in its basic construction, which can be referred to as a dual-photodiode radiometer. This radiometer is calibrated by measuring the spectral responsivities of two photodiodes against the spectral irradiance at the input aperture. The concept of the simultaneous measurement is valid under the condition that the spectral responsivities are linear against wavelengths within the spectral bandwidth of the source to be tested. The feasibility and expected accuracy are analyzed by numerical simulations and experimentally tested for the realization of a UVA irradiance meter, which shows an agreement within 0.2 nm and 0.6% for centroid wavelength and irradiance, respectively, with other reference instruments.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
A radiometer denotes, in the most general sense, an instrument that measures optical radiation [1]. The major application of a radiometer is to characterize a source of radiation by measuring or monitoring optical radiation emitted from the source. Commonly, radiometers are assigned to a group of instruments measuring a spectrally integrated quantity within a specific bandwidth, while instruments capable of the spectrally resolved measurement of optical radiation are classified as spectro-radiometers. The detailed design, term, and calibration method for a radiometer can vary depending on the quantity to be measured. For example, a UVA irradiance meter is a radiometer measuring optical radiation of a broadband ultraviolet source in a quantity of irradiance defined as radiant power per unit area integrated in a wavelength range from 320 to 400 nm [2].
For an accurate measurement of a spectrally integrated quantity, a radiometer ideally should have a rectangular shape of spectral responsivity, i.e., a spectrally flat response within a specified wavelength range and a zero response at other wavelengths. In practice, this condition is difficult to realize for radiometers based on a photodiode sensor, as a specially designed filter is required to make the spectral responsivity of photodiodes flat against a wavelength. Various errors of a radiometer are related to the spectral and spatial properties of the filter [3]. In particular, when a photodiode-based radiometer needs to be used for a light source having spectral distribution different from that of its calibration source, one needs to perform the spectral mismatch correction based on the measured spectral distribution of the sources and the measured spectral responsivity of the radiometer [2,3]. The error due to spectral mismatch of a radiometer can be significant for light sources such as light-emitting diodes (LEDs) and organic light-emitting diodes (OLEDs) whose spectral distributions are variable. In addition, realization of a filter for a flat response in a wide wavelength range is challenging, as the spectral transmittance of the filter should be specifically matched to the spectral responsivity of the used photodiode. Consequently, photodiode-based spectrally integrating radiometers so far are commonly used in a limited wavelength range, e.g., for UVA irradiance meters, and often had to be supplemented by a spectro-radiometer when a light source with unknown spectrum was to measure.
In this work, we propose a new design of a photodiode-based radiometer, which can measure the spectrally integrated irradiance of light sources without need of the spectrally flat response. We refer to the new design as a dual-photodiode radiometer, as its basic configuration consists of two photodiodes and one beam splitter or one filter. From the dual-photodiode signals, the new radiometer is capable of measuring both the irradiance and the centroid wavelength of the source simultaneously, which is of great advantage for testing and comparing light sources such as LEDs and OLEDs of different colors. The requirements for the spectral property of the beam splitter or of the filter are much more relaxed compared with the case of the spectrally flat response, which can be realized, more easily in our opinion, in a wider wavelength range. We note that a similar concept based on dual-photodiode signals was reported for a laser wavelength meter [4,5]. The dual-photodiode concept in this work is more versatile, as it can also be used for measurement of radiometric quantities of spectrally extended sources. In the following, we describe the working principle of the dual-photodiode radiometer and show its expected performance based on numerical simulations. We finally present an experimental realization of the new design for a UVA irradiance meter and test its feasibility by comparing with other reference instruments [6].
2. WORKING PRINCIPLE
A. Basic Design
Figure 1 schematically shows a construction example of the dual-photodiode radiometer for simultaneously measuring irradiance and centroid wavelength of light sources with finite spectral bandwidth. The light source to be measured irradiates the surface of a diffuser with the area defined by a precision aperture, which builds the input aperture of the radiometer. Inside the light-tight enclosure of the radiometer, two photodiodes, #1 and #2 in Fig. 1, are installed to detect the light transmitted through the input aperture. The amount of light detected by each photodiode is determined by the reflectance or transmittance of the beam splitter placed in the middle of the beam path. A light trap and two baffles are used to avoid stray light caused by multiple reflections inside the enclosure.
Fig. 1. Schematic construction of a dual-photodiode radiometer for simultaneous measurement of irradiance and centroid wavelength of light sources with finite spectral bandwidth.
B. Measurement Equations
Let the irradiance $E$ at the position of the input aperture be the quantity to be measured, we can express it as an integral of spectral irradiance ${E_\lambda }$ ($\lambda $) over wavelength $\lambda $ within the spectral bandwidth $\Delta \lambda $ of the light source:
The readout signals of the radiometer shown in Fig. 1 are the photocurrents ${i_1}$ and ${i_2}$ from photodiodes #1 and #2, respectively. We can model these signals by introducing the spectral irradiance responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ of the photodiodes #1 and #2, respectively, against spectral irradiance ${E_{\lambda}}(\lambda )$ at the input aperture:The main concept of the new radiometer design is to construct the photodiodes and the beam splitter in such a way that the spectral responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ should be a linear function against the wavelength within the spectral bandwidth of the source to be measured:
In the following, the discussions are continued based on the assumption that the linear model of Eq. (3) is valid in a specific wavelength range between ${\lambda _{\min}}$ and ${\lambda _{\max}}$, which should be broader than the spectral bandwidth $\Delta \lambda $ of the light source to be measured:
It is important to note that the source to be measured must have zero flux outside the range between ${\lambda _{\min}}$ and ${\lambda _{\max}}$ so that the dual-photodiode radiometer concept is only applicable to sources with a finite spectral bandwidth such as LEDs and spectrally filtered lamps.Applying Eq. (3) to Eq. (2), we can rewrite the photocurrent signals as
C. Practical Realization
For realizing the dual-photodiode radiometer in practice, the most important issue is whether the two conditions of the theoretical model can be fulfilled: the first was that the spectral responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ of two photodiodes against the spectral irradiance at the input aperture are linear against wavelength as described in Eq. (3). The second was that the ratio $r(\lambda )$ of the responsivities defined in Eq. (4) is a monotonic function against the wavelength. Note that these conditions are critical only in a wavelength range from ${\lambda _{\min}}$ to ${\lambda _{\max}}$, which is larger than the spectral bandwidth $\Delta \lambda $ of the light source under test [see Eq. (5)].
From the basic construction of Fig. 1, we can model the spectral responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ as products of the properties of different components:
For the numerical simulation in Section 3, we test the feasibility of the concept based on a simplest construction model. Here, we can assume a diffuser whose spectral transmittance ${t_d}(\lambda )$ is practically wavelength-independent in the range of interest as described in the commercial product catalogue [7]. Also, the geometrical collection efficiencies ${g_1}$ and ${g_2}$ can be simply set to an arbitrary constant. Then, the spectral dependence of the responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ is mainly determined by the photodiodes and the beam splitter according to the model in Eq. (11). For the choice of the beam splitter, one should consider that the difference between two responsivities becomes large enough so that the function $r(\lambda )$ of their ratio has a large slope against wavelength. We note that this slope is related to the uncertainty for the determination of the centroid wavelength according to Eq. (9).
In practice, the model of Eq. (11) is useful in the construction stage to predict the expected spectral responsivities based on the selected components. Once the radiometer instrument is constructed, the spectral responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ should be measured in the unit of ${\rm A}/({{\rm Wm}^{ - 2}})$ at each wavelength by using a comparator setup based on a tunable monochromatic uniform source.
D. Alternative Design
The concept of the dual-photodiode radiometer in its basic construction of Fig. 1 can be applied to other designs of a radiometer. For example, by modifying the input aperture suitable for a beam incidence in the underfilled condition, one can construct a radiometer measuring spectrally integrated radiant flux or, simply, a power meter. When the radiometric quantity to be measured is changed, the spectral responsivity of each photodiode should be recalibrated against that quantity at the input aperture. Note, however, that the measurement of the centroid wavelength is not affected from such a change because its measurement, based on Eq. (9), relies only on the ratio, i.e., on the relative values of both the spectral responsivities.
The dual-photodiode radiometer can also be constructed without a beam splitter, as shown in Fig. 2 for an integrating-sphere-based construction. Instead of a beam splitter, the inner wall of the integrating sphere delivers the same fraction of the incident light to the two photodiodes by producing a uniform spatial distribution of light through multiple reflections. The baffles are used to avoid the direct illumination of the photodiodes from the incident light, which causes a deviation from the uniform distribution. For this construction, the factors ${t_d}(\lambda ) \times {{g}_1}$ and ${t_d}(\lambda ) \times {{g}_2}$ in Eq. (11) are replaced with the spectral throughput of the integrating sphere. The difference of spectral responsivity between two photodiodes is produced by using a filter attached to one of the photodiodes. The measurement equations of the dual-photodiode radiometer remain the same for this alternative construction. The integrating-sphere-based design of Fig. 2 can be a solution, for example, when the improved angular and spatial uniformity of the radiometer is required.
Fig. 2. Integrating-sphere-based construction of a dual-photodiode radiometer for simultaneous measurement of irradiance and centroid wavelength of light sources with finite spectral bandwidth.
3. NUMERICAL SIMULATION
For testing the feasibility of the dual-photodiode radiometer concept, we first performed numerical simulations for a test device based on the basic construction of Fig. 1. The test device corresponds to a simple realization model with commercially available photodiodes and a beam splitter with a calculable spectral reflectance. Figure 3 shows a typical example of spectral power responsivity for a commercially available Si photodiode (Hamamatsu, model S1339-1010BQ). Assuming that the same model of photodiode is used for #1 and #2, we can identify Fig. 3 as ${s_1}(\lambda ) = {s_2}(\lambda )$ in Eq. (11). We see that from 400 to 900 nm, the spectral power responsivity $s(\lambda )$ is close to a linear function. For the beam splitter, we consider a silver thin film coated on glass. Figure 4 shows the calculated results of spectral reflectance and transmittance for the Ag coating with a thickness of 10 nm under the condition of unpolarized light input at an angle of 45° [8,9]. Similar to Fig. 3, the spectral shape of both ${r_{BS}}(\lambda )$ and ${t_{BS}}(\lambda )$ is close to a linear function in a range from 400 to 900 nm.
Fig. 3. Example of spectral power responsivity of a commercial Si photodiode, which can be used for the dual-photodiode radiometer.
Fig. 4. Spectral transmittance and reflectance of a beam splitter based on Ag film coating on glass (thickness of 10 nm, angle of incidence 45°, unpolarized).
Combining Figs. 3 and 4, we obtain the spectral irradiance responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ as well as their ratio $r(\lambda )$ of the radiometer, as shown in Fig. 5. For this calculation, we assumed ${t_d}(\lambda ) = {1}$ and ${g_1} = {g_2} = {1\,\,{\rm m}^2}$ in Eq. (11) for simplicity. In Fig. 5(a), we see that the spectral responsivity ${s_{E,1}}(\lambda )$ of photodiode #1 is close to a linear function in a range from 400 to 900 nm, while ${s_{E,2}}(\lambda )$ of photodiode #2 shows a slowly varying deviation from a linear function. The ratio of two responsivities in Fig. 5(b) shows that the function $r(\lambda )$ is monotonic in a range from 400 to 900 nm. In conclusion, we confirm that the conditions of the theoretical model of the dual-photodiode radiometer are generally fulfilled for the simple realization model. However, we also notice deviations of the practical realization from the theoretical requirements of Eq. (3). The errors expected from these deviations are determined by numerical simulations with various input spectra of test light source.
Fig. 5. Spectral irradiance responsivity data calculated from the data of Figs. 3 and 4 for the simple realization model of the dual-photodiode radiometer. (a) Spectral irradiance responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ for the photodiodes #1 and #2, respectively. (b) Ratio $r(\lambda ) = {s_{E,1}}(\lambda )/{s_{E,2}}(\lambda )$.
Fig. 6. Spectral irradiance of a spectrally filtered source used for the numerical simulation, which has a Gaussian function at a centroid wavelength of 550 nm. The spectral bandwidth in FWHM is varied from 5 to 25 nm.
Fig. 7. Differences of centroid wavelength in (a) absolute and in (b) relative between the reference and test values resulted from the numerical simulation for a spectrally filtered source of Fig. 6, which are plotted as a function of the reference centroid wavelength at different values of spectral bandwidth in FWHM.
Supposing different types of light sources with known spectral irradiance illuminate on the test device, the centroid wavelength and the irradiance are calculated based on the device data of Fig. 5 according to the measurement Eqs. (9) and (10). The numerical simulations are performed by using the in-house developed software codes (Visual Basic) with a wavelength resolution of 0.05 nm. The results of the simulations, i.e., the centroid wavelength ${\lambda _c}$ and the irradiance $E$, are compared with the values calculated from the preset spectral irradiance of the source. For convenience, we refer to the values obtained from the test radiometer via numerical simulation and the values calculated from the source spectral irradiance as the “test” and “reference” values, respectively.
A. Simulation with Spectrally Filtered Sources
The first source used for the numerical simulation is a spectrally filtered source providing spectral irradiance with a Gaussian profile. Such a spectrally filtered source corresponds to a light source transmitted through a bandpass filter or through a grating monochromator, which is often used for calibration and characterization of radiometers. We numerically generated the spectral irradiance ${E_\lambda }(\lambda )$ of the source by using the Gaussian function at a preset centroid wavelength with the peak value normalized at ${1\,\,{\rm W/m}^2}$, as shown in Fig. 6. The spectral bandwidth in FWHM of the function is varied from 5 to 25 nm in a step of 5 nm.
The results of the numerical simulation for a spectrally filtered source are summarized in Figs. 7 and 8 for centroid wavelength and irradiance, respectively. In Fig. 7(a), the wavelength differences between the reference value and test values of the centroid wavelength, defined as $\Delta {\lambda _c} \equiv {\lambda _{c[{\rm ref}]}} - {\lambda _{c[{\rm test}]}}$, are plotted against the reference centroid wavelength of the Gaussian light source with different spectral widths in FWHM. Figure 7(b) shows the relative differences $ {{\Delta {\lambda _c}} \mathord{/ {\vphantom {{\Delta {\lambda _c}} {{\lambda _c}}}} } {{\lambda _c}}} $ of the centroid wavelength. Figure 8 shows the analogous plot for the relative differences between the reference and test irradiance values: $\Delta {E_{\rm rel}} \equiv ( {{E_{[{\rm ref}]}} - {E_{[{\rm test}]}}} )/{E_{[{\rm ref}]}}$. The symbols indicate the result data from the simulation, while the connecting lines are only for better visibility.
Fig. 8. Relative differences of irradiance between the reference and test values resulted from the numerical simulation for a spectrally filtered source of Fig. 6, which are plotted as a function of the reference centroid wavelength at different values of spectral bandwidth in FWHM.
Fig. 9. Spectral irradiance of (a) colored LEDs in red/green/blue/yellow. (b) Colored OLEDs in red/green/blue, which are used for the numerical simulation.
Table 1. Results of the Numerical Simulation with the Simple Realization Model of the Dual-Photodiode Radiometer for Colored LEDs and OLEDs of Fig. 9
In Fig. 7, we see that the wavelength errors in the measurement of the centroid wavelength are less than 0.6 nm or 0.15% in the range from 400 to 1000 nm, when the spectral width of a source is less than 10 nm in FWHM. The error increases as the spectral bandwidth increases and is especially strong at wavelengths near 400, 440, 490, and 620 nm. In contrast, we also find some wavelengths, at which the errors of centroid wavelength remain small regardless of spectral bandwidth, for example, at 420, 590, 650, and 840 nm. We identified that the wavelengths with small or large errors of centroid wavelength coincide with those at which the slope of the spectral responsivity ${s_{E,2}}(\lambda )$ shown in Fig. 4 has negligible or severe deviations from a constant, respectively, within the spectral bandwidth of the test source. Note that the working principle of the dual-photodiode radiometer relies on the linear shape of the spectral responsivities within the spectral bandwidth of the source as modeled in Eq. (3). Therefore, the results in Fig. 7, with the errors correlated with the linear shape of the spectral responsivity, not only validate the working principle of the concept but also evaluate the tolerance of the realization model of Fig. 4.
The errors of irradiance are relatively small, as shown in Fig. 8, compared with those of the centroid wavelength. The dependence of relative errors for irradiance is only significant near 400 nm, where the deviation of the spectral responsivity ${s_{E,2}}(\lambda )$ from a linear function is most significant. For other wavelengths, the relative error of irradiance is less than 0.5% in the wavelength range shorter than 500 nm and less than 0.2% in the range longer than 500 nm.
Fig. 10. Spectral irradiance of (a) white LEDs with a correlated color temperature (CCT) of 3000 and 6500 K and (b) white OLEDs with a CCT of 3000, 4000, and 5500 K, which are used for the numerical simulation.
Table 2. Results of the Numerical Simulation with the Simple Realization Model of the Dual-Photodiode Radiometer for White LEDs and OLEDs of Fig. 10
In conclusion, for a spectrally filtered Gaussian source with a spectral bandwidth of less than 10 nm (FWHM), the dual-photodiode radiometer is capable of measuring the centroid wavelength and the irradiance with an error of less than 0.6 nm and 0.3%, respectively, in a wavelength range from 400 to 900 nm. As the spectral bandwidth increases, the errors of centroid wavelength and irradiance proportionally increase at the wavelengths where the spectral responsivities of the radiometer show a large deviation from a linear function within the spectral bandwidth. The maximum errors of centroid wavelength and irradiance for a spectral bandwidth of 25 nm (FWHM) are 2.0 nm and 1.3%, respectively, at a wavelength of 400 nm. In contrast, at the wavelengths where the linear-shape condition of spectral responsivity is fulfilled for the realization model, the errors are nearly independent on the spectral bandwidth, which confirms the validity of the working principle of the dual-photodiode radiometer.
B. Simulation with Colored LEDs and OLEDs
As the next test source for the numerical simulation, we used LEDs and OLEDs of different colors with spectral irradiances ${E_\lambda }(\lambda )$ shown in Fig. 9. The data of Fig. 9 correspond to the experimentally measured values by using a spectro-radiometer for the typical LED and OLED products available in the market. Note that the data set of LEDs and that of OLEDs in Fig. 9 is presented in the separate plots as they are obtained in different measurement conditions.
Fig. 11. Spectral transmittance of a SCHOTT BG7 glass filter at the normal incidence, which is used as a beam splitter in the dual-photodiode UVA irradiance meter.
Measurement of LEDs and OLEDs is one of the important applications, in which the dual-photodiode radiometer has the particular advantages. LEDs and OLEDs are the light sources with finite spectral bandwidth, suitable for the concept of the dual-photodiode radiometer. The dual-photodiode radiometer can measure both centroid wavelength and irradiance simultaneously in a single photocurrent reading, which combines the advantages of both a photodiode-based radiometer and a spectro-radiometer. Moreover, the concept of the dual-photodiode radiometer can be realized in a wide wavelength range covering the whole visible range, which was challenging for the photodiode-based radiometers with a filter making the spectrally flat response. Therefore, testing the performance of the simple realization model on various colored LEDs and OLEDs in the visible range is of particular interest.
Fig. 12. Spectral irradiance responsivity data measured for the dual-photodiode UVA irradiance meter. (a) Spectral irradiance responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ for the photodiodes #1 and #2, respectively. (b) Ratio $r(\lambda ) = {s_{E,1}}(\lambda )/{s_{E,2}}(\lambda )$.
The results of the numerical simulation for colored LEDs and OLEDs are summarized in Table 1. For colored LEDs, the largest errors of centroid wavelength and irradiance are 1.41 nm and 0.7%, respectively, resulting for the blue LED. These results are comparable with the results for the spectrally filtered sources with a spectral bandwidth of 25 nm in FWHM, to which the bandwidth of colored LEDs are similar. For colored OLEDs, which have larger spectral bandwidths than LEDs, the errors are generally larger: the errors of centroid wavelength and irradiance can be as high as 2.85 nm and 0.96%, respectively, for the OLEDs. However, for all the colored LEDs and OLEDs, the maximum relative errors of centroid wavelength and of irradiance do not exceed 0.5% and 1%, respectively. We note that these errors expected for the dual-photodiode radiometer are smaller than the typical relative uncertainty level expected for the LED illuminance measurement with a spectro-radiometer [10].
C. Simulation with White LEDs and OLEDs
Finally, we used white LEDs and OLEDs as the test source for the numerical simulation. The white LEDs and OLEDs are of interest in the field photometry, and a radiometer such as an irradiance meter is rarely applied for these products. Nevertheless, we performed the simulation for these sources to test the accuracy limit of the concept.
Two types of white LEDs with a correlated color temperature (CCT) of 3000 and 6500 K, and three types of white OLEDs with a CCT of 3000, 4000, and 5500 K are used, whose spectral irradiances ${E_{\lambda}}(\lambda )$ are shown in Fig. 10. Similar to Fig. 9, the data of Fig. 10 correspond to the experimentally measured values by using a spectro-radiometer for the typical products available in the market.
Table 2 shows the summary of the simulation results for the white LEDs and OLEDs. As we expected from the previous results, the errors are large compared with the filtered or colored sources as the spectral bandwidths of the white sources are significantly large. For such a large spectral bandwidth, the linear-shape condition of the spectral responsivities is hardly fulfilled. Nevertheless, the relative errors of the centroid wavelength and irradiance shown in Table 2 are still within 2% and 3%, respectively, which are yet useful in practice, e.g., for a fast monitoring purpose. The results also provide the information for the tolerance of the device against the realization of the spectral responsivities required for the accurate operation of the dual-photodiode radiometer.
Fig. 13. Spectral distribution of four sources used for experimentally testing the validity of the dual-photodiode UVA irradiance meter.
Table 3. Results of the Experimental Validity Test of the Dual-Photodiode UVA Irradiance Meter for UV Sources of Fig. 13
4. EXPERIMENT FOR UVA IRRADIANCE METER
As the first device of a dual-photodiode radiometer under experimental test, we constructed an irradiance meter that can be operated in the UVA range [6]. The basic construction is the same as in Fig. 1 with the commercial Si photodiode (Hamamatsu, model S1339-1010BQ, see Fig. 3). The integrating-sphere-based design of Fig. 2 is not used, as the sphere coating is generally known to be unstable for the UV radiation. A fused-silica diffuser is used behind a precision aperture with a diameter of 2 mm. For the beam splitter, we used a colored glass filter (SCHOTT BG7) installed at an angle of 45°. Figure 11 shows the spectral transmittance of the filter measured at the normal incidence condition. We note that the exact values of the spectral transmittance and reflectance of the beam splitter are not necessary for the operation of the radiometer because the spectral irradiance responsivities of two photodiodes, which include these parameters according to Eq. (11), are directly measured in the calibration. The absorption of the beam splitter does not influence the operation of the radiometer unless it changes with time from the condition of the initial calibration.
The irradiance responsivity of two photodiodes of the radiometer is experimentally measured in the following procedure. First, the relative spectral responsivities of both channels are measured by using a lamp-monochromator-based spectral responsivity comparator setup, where the beam diameter was slightly larger than the aperture size. Then, the absolute power responsivity is measured at one laser wavelength of 404 nm by using a calibrated photodiode. For the absolute measurement, the diameter of the laser beam was as small as 1 mm. Finally, the area of the precision aperture is separately measured by using a calibrated 3D profiler. Combining the measured data of the three steps, the absolute irradiance responsivities ${s_{E,1}}(\lambda )$ and ${s_{E,2}}(\lambda )$ for each photodiode of the radiometer were calibrated in the unit of ${\rm A}/({{\rm mW\cdot {\rm cm}}^{ - 2}})$ against the irradiance unit commonly used in the UV radiometry. Figure 12 shows the measured responsivities together with their ratio $r(\lambda )$. We note that, for this device, we interchanged the numbering of the photodiodes in Fig. 1 to obtain the clear monotonic function of $r(\lambda )$, i.e., the photodiode #1 corresponds to the photodiode detecting the transmitted light from the beam splitter. From the results of Fig. 12, we confirm that the conditions of the theoretical model of the dual-photodiode radiometer are fulfilled for this device from 330 to 450 nm.
As the test source, we selected four UV sources with a finite spectral bandwidth: a high-pressure Hg lamp filtered at 365 and 405 nm with a bandwidth of approximately 15 nm, and UV LEDs with peak wavelengths at 365 and 385 nm. Figure 13 shows the measured spectral distribution of the test sources. To test the validity of the dual-photodiode UVA irradiance meter, we measured the centroid wavelength and irradiance of these sources by using the test device and compared the results with those measured with the reference instruments. For the centroid wavelength, a spectroradiometer was used as the reference instrument, which is calibrated by using the spectral irradiance standard lamp and the wavelength standard lamps [10]. For the irradiance, an electrically calibrated pyroelectric radiometer (ECPR) was used, which is the transfer standard for the UVA meter calibration at KRISS [11].
Table 3 shows the summary of the experimental validity test for the dual-photodiode UVA irradiance meter. The values measured with the test device show an agreement with those measured with the reference devices within 0.2 nm and 0.6% for centroid wavelength and irradiance, respectively. These differences are smaller than the typical uncertainties of the reference values, which are evaluated to be 0.2 nm and 0.7% ($k = {1}$) for centroid wavelength and irradiance, respectively, of a UV source at 365 nm with a bandwidth of 10 nm [11]. The differences in Table 3 are also smaller than the uncertainties, which are preliminarily evaluated for the dual-photodiode UVA irradiance meter [6].
5. SUMMARY AND DISCUSSION
We presented a new design of a radiometer, which can measure in a single reading both centroid wavelength and irradiance of a light source having a finite spectral bandwidth. The basic construction consists of two photodiodes separated with a beam splitter, and it is calibrated by measuring the spectral responsivity of each photodiode against the spectral irradiance at the input aperture. We derived the measurement equations of this dual-photodiode radiometer, which are valid under the following conditions: first, the spectral responsivities of both detectors should be a linear function of wavelength within the spectral bandwidth of the light source to be measured. Second, the ratio of the two spectral responsivities should be a monotonic function so that its inverse function can exist.
The feasibility of the design is first tested by numerical simulations for a simple realization model with the components available in practice. From the simulation results for a spectrally filtered source with a Gaussian shape, we confirmed the validity of the measurement equations at wavelengths where the linear-shape condition for the spectral responsivities is fulfilled. At the wavelengths where the spectral responsivities have deviations from a linear function, we could observe the increasing errors in the centroid wavelength and irradiance measurements as the spectral bandwidth of the source increases. We also performed the simulation for colored and white LEDs and OLEDs. For measurement of colored LEDs and OLEDs, we obtained the relative errors of centroid wavelength and irradiance to be less than 0.5% and 1%, respectively, which is promising for a practical instrument. For white LEDs, however, the relative errors are as high as a few percent, as the deviation of the spectral responsivities from a linear function became significant for the wide spectral bandwidth of white sources.
Experimentally, we realized a dual-photodiode UVA irradiance meter as a test device, which can be used for finite-bandwidth sources in a range from 330 to 450 nm. The validity of the device is tested by comparison with a calibrated spectro-radiometer and an ECPR as the reference instruments at various light sources. An agreement of less than 0.2 nm and 0.6% for centroid wavelength and irradiance, respectively, was confirmed, which were less than the uncertainties of the reference instruments.
In conclusion, we showed that the concept of the dual-photodiode radiometer is best suitable for light sources with a relatively narrow spectral bandwidth such as colored LEDs/OLEDs and filtered lamps. For such sources, the condition of the linear spectral responsivity within the spectral bandwidth can be easily realized in a wide wavelength range with an accuracy that is comparable with the best practice by using both a photodiode and a spectro-radiometer together. For a broadband source such as a white LED/OLED, a more careful fabrication of the beam splitter is required to fulfill the condition in a wider wavelength range.
For practical application of the concept to field instruments, additional issues need to be investigated. The uncertainty of the dual-photodiode radiometer is primarily determined by the uncertainty of the spectral irradiance responsivities of the two detectors, when the condition of the linear function of wavelength is fulfilled. Any deviation from this condition, however, would add an extra component of measurement error, which generally depends on the spectral distribution of the source. For practical instruments, therefore, we are developing an effective method to estimate the maximum uncertainty expected for a dual-radiometer with the calibrated spectral responsivities by simulating all the possible spectra under test. Other remaining issues regarding the practical instruments are the stability and the environmental sensitivity of the calibrated spectral irradiance responsivities. These could be primarily affected by a long-term variation of the beam splitter or filter coating, which needs to be experimentally tested by repeated calibrations. Experimental tests to produce the full uncertainty budget, including the stability components, are in progress for the UVA and visible ranges, which will be reported in a separate publication.
REFERENCES
1. A. C. Parr, R. U. Datla, and J. L. Gardner, Optical Radiometry (Elsevier, 2005).
2. G. P. Eppeldauer, C. C. Cooksey, H. W. Yoon, L. M. Hanssen, V. B. Podobedov, R. E. Vest, U. Arp, and C. C. Miller, “Broadband radiometric LED measurements,” Proc. SPIE 9954, 99540J (2016). [CrossRef]
3. T. C. Larason and C. L. Cromer, “Sources of error in UV radiation measurements,” J. Res. Natl. Inst. Stand. Technol. 106, 649–656 (2001). [CrossRef]
4. S. Roy, S. Chaudhuri, and C. S. Unnikrishnan, “A simple and inexpensive electronic wavelength-meter using a dual-output photodiode,” Am. J. Phys. 73, 571–573 (2005). [CrossRef]
5. COHERENT, User Manual WaveMate Wavelength Meter.
6. D.-J. Shin, S. Park, K. Jeong, and D.-H. Lee, “Reference radiometer in a dual-photodiode design for calibration of UVA irradiance meters,” in Proceedings of the 29th session of the CIE, CIE x046:2019 (2019), pp. 1243–1248.
7. See, for example, UV fused silica ground glass diffusers provided by Thorlabs Inc., https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6337.
8. N. Ahmad, J. Stokes, N. A. Fox, M. Teng, and M. J. Cryan, “Ultra-thin metal films for enhanced solar absorption,” Nanoenergy 1, 777–782 (2012). [CrossRef]
9. Calculation software available athttps://www.filmetrics.com/reflectance-calculator.
10. S. Park, D.-H. Lee, Y.-W. Kim, and S.-N. Park, “Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity,” Appl. Opt. 46, 2851–2858 (2007). [CrossRef]
11. G. Xu, X. Huang, and Y. Liu, “APMP.PR-S1 comparison of irradiance responsivity of UVA detectors,” Metrologia 44, Tech. Suppl. 02001 (2007). [CrossRef]
