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Abstract
The spatial uniformity of the spectral radiance by four commercial flat-field sources relying on white Light-Emitting Diode (LED) technology were investigated in the 400–800 nm spectral range using a hyperspectral radiometer. Results showed that for most of the flat-fields the spatial non-uniformity defined by the standard deviation of radiance differences across the source area in a given spectral interval, is typically lower than 1% within 5 cm from the center of the source and not exceeding 5% within 10 cm. The corresponding impact on radiance spectral distribution indicated non-uniformity values generally lower than 1.5% within 5 cm from the center of the sources, but increasing to several percent beyond the 5 cm distance. Finally, the spectral noise of radiance measurements defined by the variation coefficient across repeated acquisitions of the same target area on the sources exhibited mean values between 0.02% and 0.1% for most of the flat-fields in the 420–700 nm interval, but reached several percents outside such a spectral region as a result of the low flux from white LEDs. The above non-uniformity features of white LED-based flat-fields were shown to generally outperform those of a custom flat-field built of a lamp illuminating various diffusers. These findings indicate that flat-fields based on white LED technology may be suitable radiance sources for applications whose measurement requirements are satisfied by the spectral distribution of the radiant flux by white LEDs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Reflectance plaques illuminated by 1000 W quartz-halogen tungsten coiled filament (FEL) lamps are commonly used as the main source for both absolute radiometric calibration and relative characterizations of optical radiance sensors. While calibrated sources (both plaque reflectance and lamp irradiance) are required for the determination of the responsivity of sensors, relative sources support sensor characterizations. Specifically, a spatially uniform source (see Fig. 1), would be required for the characterization of radiance sensors for non-linearity, immersion factor, temperature response and polarization sensitivity [1]. To be noted that the normal view of the sensor with respect to the source, minimizes requirements on the isotrophic distribution of radiance and would simply require the radiance is uniform within the field-of-view of the sensor. Recent studies [2] have shown the relevance of flat-field sources based on white Light-Emitting Diode (LED) technology [3,4] for the determination of the immersion factor of radiance sensors (i.e., the factor quantifying the change of in-water with respect to in-air sensor responsivity).
Fig. 1. Radiance sensor normally looking at a flat-field source (a) exhibiting a uniform spatial radiance distribution across most of its active area (b).
White LEDs rely on single blue LED chips with phosphor powder suspended in epoxy resin covering the LED dies. Due to this specific design, the emitted radiant flux exhibits a bichromatic spectral distribution with a first broad band due to LED electroluminescence peaked at approximately 460 nm and an additional broad band generally peaked at 560 nm due to phosphor re-emission of a fraction of the absorbed blue light [5]. Motivated by the potentials of white LED based technology to support radiometric applications [6,7] and specifically by the use of withe LED-based flat-fields for laboratory characterizations of optical sensors, this study investigates the spatial uniformity of the radiance field by various commercial products. The measurement setup and methods are described in section 2. Results are presented in section 3 and discussed in section 4. Lastly, the main conclusions are outlined in section 5.
2. Materials and methods
2.1 Flat-field sources and characterization method
The four white LED-based flat-field sources whose radiance spatial uniformity and spectral features were investigated in this study are a 15$\times$15 inches (approximately 38$\times$38 cm) Spike-a (Fitchburg, WI) Flat Fielder hereafter identified by the acronym SP, a 8$\times$8 inches (approximately 20$\times$20 cm) Advanced Illumination (Rochester, VT) Edge-lit Backlight identified by the acronym AI, a 9$\times$16 inches (approximately 23$\times$41 cm) Metaphase (Bristol, PA) series FR-BL identified by the acronym M-BL, and a 12$\times$12 inches (approximately 30$\times$30 cm) Metaphase series MB-CBL identified by the acronym M-CBL. These flat-field sources rely on diverse manufacturing solutions, still not comprehensively disclosed. In particular SP, AI, and M-BL are built of an optical diffuser edge-lit by one (M-BL) or alternatively two (SP and AI) LED arrays fixed on the inner walls of the devices. Contrarily, M-CBL consists of a white LED matrix normally illuminating an optical diffuser covered by two light-collimating films [8]. Schematic of both designs are shown in Fig. 2(a) for SP, AI, M-BL, and Fig. 2(b) for M-CBL. These different designs, which combine the effects of light spectral and angular distribution by white LEDs varying with LED technologies [9,10], spatial arrangement of the individual LED sources [11], diffuser-LEDs geometries, and also the use of additional optical elements such as light-collimating films, suggest diverse spatial non-uniformity of the output radiance of the various sources. In view of comprehensively supporting the evaluation of results from the analysis of the non-uniformity of LED-based flat-fields, the radiance obtained with a custom-made flat-field source (CM) was also analyzed. This specific source, previously applied for the determination of the immersion factor of radiance sensors [12], is built of four 25 cm diameter and 5 mm thick optical glass diffusers by Schott AG (Grünenplan, Germany), illuminated by a 1000 W quartz-halogen lamp positioned at a distance of approximately 100 cm.
Fig. 2. Schematic of SP, AI and M-BL (a), and M-CBL (b) LED-based flat-field sources. It is specified that M-BL relies on a single LED array.
All the measurements included in this study were performed with a TriOS (Rastede, Germany) RAMSES-ARC hyperspectral radiance sensor. RAMSES-ARC has a nominal full-angle field-of-view, of approximately 7$^{\circ }$ and provides radiance measurements in the 320–950 nm interval with spectral sampling and resolution of approximately 3.3 nm and 10 nm, respectively. The integration time varies automatically between 4 and 8192 ms depending on the target radiance.
The spatial uniformity of each white LED-based flat-field was investigated by measuring the radiance at various positions $p$ along the main $X$- and $Y$-axis by keeping the sensor normal to the source. The distance $h_0$ between the optical window of the sensor and the outer surface of the flat-field sources was kept constant during measurements. Specifically, the minimum measurement distance was applied: these varied between 1.7 cm and 2.6 cm across the different sources as a function of their mechanical construction. This produced sensor footprints on the sources ranging between 1.2 and 1.3 cm diameter determined by the pupil of approximately 1 cm diameter and the 7$^{\circ }$ full-angle field-of-view of the RAMSES-ARC radiance sensor. It is recalled that for a uniform source, the radiance measured by the sensor would not depend on $h_0$. On the contrary, when the uniformity requirement is not met, radiance measurements exhibit a dependence on the distance from the source. Thus, measurements performed at the minimum working distance $h_0$ ensure a radiometric characterization with a higher spatial resolution than that obtainable at wider distances.
For each source, repeated series of measurements were performed to assess the radiance spatial non-uniformity. Each series of measurements was performed with constant integration time $\tau$ at positions $p$ spaced by 2 cm along the $X-$ and $Y-$ axis. In view of restricting the analysis to those regions of the flat-fields suitable for radiometric applications, the first 3 cm from the edge of the active areas were excluded from the analysis to minimize the impact of reflection and shading from any mechanical component framing the sources. The total number of measurements performed for each LED-based and custom-made source is reported in Table 1 together with the measurement distance $h_0$ and the integration time $\tau$ of the RAMSES-ARC sensor. The number of measurement positions $p$ along the $X$- and $Y$-axis is indicated by $N$ and $M$, respectively. A schematic of the measurement setup is shown in Fig. 3.
Table 1. Parameters identifying the measurements performed for the evaluation of the spatial uniformity of radiance by the flat-fields. Symbols $h_0$, $\tau$, $N$, and $M$ indicate the distance of the radiometer from the source, integration time, and the number of measurements at positions $p$ along the $X$- and $Y$-axis, respectively.
Fig. 3. Measurement setup applied to characterize the spatial non-uniformity of the flat-field sources.
The various sources were powered in agreement with manufacturers’ instructions and assumed stable during each characterization lasting 20 to 40 minutes as a function of the area of the flat-fields. Average radiance spectra in physical units and alternatively in digital counts, are shown in Fig. 4 for the SP, AI, M-BL, M-CBL, and CM sources. The spectral radiance in units of mW m$^{-2}$ nm$^{-1}$ sr$^{-1}$ displayed in Fig. 4(a) provides information on the actual spectral distribution and intensity of each source. The counts in Fig. 4(b) highlight the spectral regions (i.e., tentatively below 420 nm and beyond 700 nm) going to be affected by higher measurement noise as a result of the very low counts produced by the sensor due to the low radiance from the LED-based sources. The spectral differences between Fig. 4(a) and 4(b) are explained by the shape of the sensor spectral responsivity
Fig. 4. Radiance spectra determined for the SP (blue), AI (green), M-BL (red), M-CBL (orange), and CM (black) flat-field sources in physical units (a) and digital counts (b).
2.2 Data reduction
Each measurement $DN_C(p,\lambda )$ in digital counts, identified by the specific position $p$ on the source and the sensor center-wavelength $\lambda$ (i.e., the mid-point of each spectral band), results from the averaging of 50 consecutive acquisitions. Individual acquisitions were corrected for the radiometer dark signal as detailed in [13]. The spatial non-uniformity of the radiance was quantified from:
where $DN_{C}(0,\lambda )$ indicates the measurement corresponding to the center of the source and the subscript $C$ the measurements performed along the $X$- or $Y$-axis, respectively.It is mentioned that literature provides alternative methods to quantify the spatial non-uniformity of light sources [14]. The one applied here aims at discussing radiance non-uniformity with respect to the reference value corresponding to the geometric center of each source.
3. Results
Results from the spatial uniformity assessment of SP are comprehensively illustrated in Fig. 5. Specifically, the values of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ are displayed in Figs. 5(a) and 5(b) as a function of the distance of the measurement position $p$ from the center of the source, and in Figs. 5(c) and 5(d) as a function of wavelength.
Fig. 5. Uniformity values $\varepsilon _X(p,\lambda )$ (a) and $\varepsilon _Y(p,\lambda )$ (b) determined for SP as a function of the distance from the center of the source along the $X$- and $Y$-axis, and additionally $\varepsilon _X(p,\lambda )$ (c) and $\varepsilon _Y(p,\lambda )$ (d) determined as a function of wavelength.
Results indicate a significant spatial variability combined with an appreciable spectral dependence (i.e., a change in the spectral distribution with the distance of $p$ from the center). In view of minimizing the impact of these factors, the analysis for the various flat-fields was restricted to measurement conditions satisfying requirements for radiance sources relevant to radiometric applications: radiances well above the noise level of the sensor and additionally, regions of the active areas of the sources exhibiting the highest spatial uniformity. Because of this, results for the various LED-based flat-fields are summarized through: $i.$ the mean values $E_{X,\Lambda }(p)$ and $E_{Y,\Lambda }(p)$ of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ displayed in Figs. 6(a) and 6(b) as a function of the distance of the measurement position $p$ from the center of the sources, but restricted to the spectral interval $\Lambda _{ref}=$ [500 nm, 600 nm] exhibiting high radiance values; and $ii.$ the mean values $E_{X,P}(\lambda )$ and $E_{Y,P}(\lambda )$ of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ displayed in Figs. 6(c) and 6(d) as a function of wavelength, but restricted to distances lower than 5 cm from the center of the sources where, heuristically, the spatial uniformity is higher. It is mentioned that alternative analysis showed equivalent results for $E_{X,\Lambda }(p)$ and $E_{Y,\Lambda }(p)$ when extending the spectral interval from 500–600 nm to 400–800 nm, but larger values of $E_{X,P}(\lambda )$ and $E_{Y,P}(\lambda )$ when including measurements performed at distances larger than 5 cm from the center of the source.
Fig. 6. Spectrally averaged values $E_{X,\Lambda }(p)$ (a) and $E_{Y,\Lambda }(p)$ (b) of ${\varepsilon }_X(p,\lambda )$ and ${\varepsilon }_Y(p,\lambda )$ in the interval $\Lambda _{ref}$, displayed as function of the distance from the center of the flat-field along the $X$- and $Y$-axis, and additionally geometrically averaged values $E_{X,P}(\lambda )$ (c) and $E_{Y,P}(\lambda )$ (d) of ${\varepsilon }_X(p,\lambda )$ and ${\varepsilon }_Y(p,\lambda )$ for distances lower than 5 cm from the center of the flat-field displayed as a function of wavelength.
Results shown in Fig. 6 for the various flat-fields are largely explained by the different manufacturing solutions (e.g., side- or normal-lit, one or two LED arrays) and size of the flat-field active area. Most of $E_{X,\Lambda }(p)$ and $E_{Y,\Lambda }(p)$ exhibit values varying between +1% and -5% up to 5 cm from the center of the sources. Exception is M-BL, with values of $E_{X,\Lambda }(p)$ and $E_{Y,\Lambda }(p)$ exceeding -10 % at approximately 5 cm from the center of the source. Remarkable is the symmetry and higher spatial uniformity along both the $X-$ and $Y-$axis exhibited by M-CBL, which is explained by the use of a LED matrix normally illuminating the diffuser coupled to light-collimating films, opposite to LED arrays providing side-lit to the diffuser. The systematic decrease in radiance towards the edges of the active area shown in Figs. 6(a) and 6(b) by M-CBL relying on normal-lit by a LED matrix, is explained by the finite extension of the LED matrix itself (i.e., the outermost regions do not benefit of equal flux contributions from nearby elementary areas).
The spectral values of $E_{X,P}(\lambda )$ and $E_{Y,P}(\lambda )$ restricted to distances lower than 5 cm from the center of the active area of the sources, show values well within $\pm$1% except for M-BL exceeding -4% on the $X$-axis and approaching -2% on the $Y$-axis.
Results from the analysis of data from the various sources are also presented in Figs. 7(a) and 7(b) through the standard deviation $\sigma _{X,\Lambda }(p)$ and $\sigma _{Y,\Lambda }(p)$ of spectrally averaged $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ in the $\Lambda _{ref}$ spectral interval. Specifically, $\sigma _{X,\Lambda }(p)$ and $\sigma _{Y,\Lambda }(p)$ are applied as spatial non-uniformity indices for the sampled positions $p$ in a spectral region relevant for laboratory applications. Excluding M-BL, $\sigma _{X,\Lambda }(p)$ and $\sigma _{Y,\Lambda }(p)$ exhibit values of the spatial non-uniformity lower than 1% within 5 cm from the center of the sources. The same indices exhibit values generally lower than 1.5 % within 10 cm from the center.
Fig. 7. Standard deviation $\sigma _{X,\Lambda }(p)$ (a) and $\sigma _{Y,\Lambda }(p)$ (b) of spectrally averaged $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ in the $\Lambda _{ref}$ interval, determined at each measurement position $p$ on the $X$- and $Y$-axis for SP (blue), AI (green), M-BL (red), and M-CBL (orange).
The former results are complemented by the quantification of changes in the spectral radiance distribution across the sampled positions $p$. Results, displayed in Figs. 8(a) and 8(b) and given by the standard deviations $\sigma _{X,P}(\lambda )$ and $\sigma _{Y,P}(\lambda )$ of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ restricted to distances lower than 5 cm from the center of the sources, exhibit values generally lower than 1.5%, but largely increase when determining $\sigma _{X,P}(\lambda )$ and $\sigma _{Y,P}(\lambda )$ beyond the 5 cm distance. It is recalled that AI has the smallest active area among those considered in this study. Thus, it is characterized by the shorter distance between the two LED arrays installed on the inner walls underneath the diffuser plate (see Fig. 2(a)), which certainly improves the spatial uniformity of the radiance field. Lastly, in correspondence of the spectral regions characterized by the lowest radiance (see Fig. 4), the fluctuations of both $\sigma _{X,P}(\lambda )$ and $\sigma _{Y,P}(\lambda )$ exhibit larger values.
Fig. 8. Standard deviation $\sigma _{X,P}(\lambda )$ (a) and $\sigma _{Y,P}(\lambda )$ (b) of the spatially averaged $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ determined at each sensor center-wavelength $\lambda$ across distances of the measurement position $p$ lower than 5 cm from the center of the source (dashed lines) or across the entire $X$- and $Y$-axis (continuous lines) for SP (blue), AI (green), M-BL (red), and M-CBL (orange).
4. Discussion
4.1 Spatial uniformity of the radiance by a custom flat-field source
In view of having an independent term of comparison, the analyses performed for the LED-based flat-fields were repeated for the custom-made flat-field (CM) built of multiple optical glass diffusers illuminated at 100 cm distance by a 1000 W quartz-halogen lamp. An effort was made to ensure symmetry of the system (i.e., making the lamp aligned with respect to the center of the diffusers) together with a careful shielding of the ambient light. Results on spatial uniformity, which are summarized in Fig. 9, exhibit values of both $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ reaching 15% at 5 cm from the center of the source and well exceeding 25% at 10 cm.
Fig. 9. Uniformity values $\varepsilon _X(p,\lambda )$ (a) and $\varepsilon _Y(p,\lambda )$ (b) determined for CM as a function of wavelength and of the distance from the center of the source along the $X$- and $Y$-axis, respectively.
The spatial non-uniformity indices displayed in Fig. 10 given by the standard deviations $\sigma _{X,\Lambda }(p)$ and $\sigma _{Y,\Lambda }(p)$ of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ over the $\Lambda _{ref}$ interval, exhibit values that may approach 1.5% for measurements performed within distances lower than 5 cm from the center of the diffusers, and do not appreciably change when relaxing the distance limits.
Fig. 10. Standard deviation $\sigma _{X,\Lambda }(p)$ (a) and $\sigma _{Y,\Lambda }(p)$ (b) of spectrally averaged $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ in the $\Lambda_{ref}$ interval, determined for CM at each measurement position $p$ on the $X$- and $Y$-axis.
The changes in the spectral radiance distribution displayed in Fig. 11 and quantified by the standard deviations $\sigma _{X,P}(\lambda )$ and $\sigma _{Y,P}(\lambda )$ of $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ determined at each center-wavelength $\lambda$ from measurements performed with distances lower than 5 cm from the center of the source, exhibit values of approximately 5%. Definitively, these results indicate that the spatial uniformity of most LED-based flat-fields (i.e., M-CBL, SP and AI) exceeds that of CM.
Fig. 11. Standard deviation $\sigma _{X,P}(\lambda )$ (a) and $\sigma _{Y,P}(\lambda )$ (b) of spectral $\varepsilon _X(p,\lambda )$ and $\varepsilon _Y(p,\lambda )$ determined for CM at each sensor center-wavelength $\lambda$ from measurements performed at distances of the measurement position $p$ lower than 5 cm from the center of the source (dashed lines) or across the entire $X$- and $Y$-axes (continuous lines).
4.2 Impact of the source noise and sensor sensitivity on radiance measurements
The overall analysis performed for the various sources benefitted of 50 successive acquisitions for each individual measurement at each position $p$ along the $X-$ and $Y-$axis (see section 2.2). This solution aimed at diminishing the effects of the low signal-to-noise ratio characterizing the LED-based sources below approximately 420 nm and beyond 700 nm (see Fig. 8), amplified by the low RAMSES-ARC sensor sensitivity in the blue spectral region. The impact of such a noise has been quantified through the mean of the variation coefficients $CV(\lambda )$ defined by the ratio of the standard deviation to the average of the 50 acquisitions contributing to each of the $N$ and $M$ independent measurements performed on the X- and Y-axis, respectively. It is mentioned that 50 was heuristically chosen as trade-off between acquisition-time and number of acquisitions warranting a significant reduction of random noise. Results are displayed in Fig. 12 as a function of wavelength for both the LED-based and custom-made sources. Consistently with the spatial uniformity results, with exception of M-BL, the LED-based sources show two different regimes: one exhibiting mean $CV(\lambda )$ values generally lower than 0.2% in the the spectral range between approximately 420 nm and 700 nm; and the other showing mean $CV(\lambda )$ values increasing up to approximately 5% outside the previous spectral interval. M-BL, still exhibiting spectral shape of $CV(\lambda )$ similar to those of the other LED-based sources, shows much higher values. Notable, the custom-made flat-field source shows mean $CV(\lambda )$ values varying between 0.13% and 0.10% through the entire 400–800 spectral range.
Fig. 12. Mean variation coefficients $CV(\lambda )$ of the 50 acquisitions contributing to each of the $N$ and $M$ individual measurements along the X- and Y-axis, respectively, performed for the quantification of the spatial non-uniformity of SP (blue), AI (green), M-BL (red), M-CBL (orange) and CM (grey). The vertical error bars indicate the standard deviation of the $CV(\lambda )$ values.
5. Conclusions
LED-based flat-fields can be convenient radiance sources for laboratory activities, provided they satisfy radiance spatial uniformity requirements. In view of investigating such a potential, the uniformity of the radiance field of four commercial LED-based flat-fields has been evaluated in the 400–800 nm spectral range with a hyperspectral radiance sensor.
Results show an obvious dependence of the spatial uniformity of radiance on both the applied manufacturing solution and size of the source. Specifically, the poorest spatial uniformity is displayed by M-BL characterized by the largest active area and relying on a single side-lit LED array. Conversely, the best performance is shown by M-CBL built on a LED-matrix normally illuminating a diffuser plate coupled to light-collimating films. Intermediate results are shown by SP and AI relying on 2 side-lit LED arrays. Quantitatively, the spatial non-uniformity indices $\sigma _{X,\Lambda }(p)$ and $\sigma _{Y,\Lambda }(p)$ determined for M-CBL exhibit values typically lower than 1% within 5 cm from the center of the source. The corresponding changes in the spectral radiance distribution given by $\sigma _{X,P}(\lambda )$ and $\sigma _{Y,P}(\lambda )$ show values generally lower than 1.5 % with the same geometric constrains (except for M-BL along the $X$-axis). These findings indicate that the uniformity features of LED-based flat-fields generally outperform those of a custom-made flat-field built of multiple diffusers illuminated by a 1000 W quarts-halogen lamp at 100 cm distance.
Finally, the spectral noise affecting the individual measurements applied for the analysis shows values varying from 0.02% to 0.1% for most LED-based flat-fields in the 420–700 nm interval (i.e., SP, AI, M-CBL), but it can reach several percents outside such a spectral region.
Overall results suggest that white LED-based flat-fields may support radiometric applications in spectral regions exhibiting radiance levels and spatial uniformity satisfying sensors sensitivity and characterization needs. Drawback of white LED-based sources is the limited and uneven flux distribution across the spectrum. Still, out of the scope for this work, the temporal stability of white LED-based flat-fields should be verified to warrant applications requiring a long-term stability of the source.
Funding
Joint Research Centre.
Disclosures
The authors declare no conflicts of interest.
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