Recent advances and perspectives in photometry in the era of LED lighting

Photometry contributes to our understanding how the world is perceived by the human visual system, where a specific example is an early study of photographic plates. Nowadays photometry has an important role in measurement of lighting, particularly in the transition from incandescent lighting to LED lighting. In the context of sustainability and energy efficiency, updated photometric methods are needed that address the spectral, color, geometrical, and temporal characteristics of LED light sources. Highlights of the recent advances in these measurement methods are reviewed. Furthermore, challenges and achievements are described in the measurement of optical power, particularly related to the definition of the photometric SI base unit, the candela. These achievements are based on progress in the development of underpinning optical measurement standards, with a focus on technologies like the electrical substitution radiometer and the predictable quantum efficient detector. As a conclusion, the importance of ongoing research and development in photometry is emphasized considering its crucial role in supporting the advances of LED lighting technology and sustainable development goals of lighting industry.


Introduction
Photometry aims to characterize the world around us in the same way as it is sensed by the human visual system.One of the early studies by Bull and Mills Cartwright [1] was measurement of photographic density of negatives, where the brightness matching of a human observer was essential for a reliable result.The needs of printing industry have changed, but the quality of printed and displayed images is still of their utmost importance.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
The method used in [1] was similar as employed at the same time for determining the photopic luminous efficiency function [2][3][4][5] and later standardized by the International Commission on Illumination (CIE) with a symbol V(λ) [6].Those works are important for the lighting industry contributing to the sustainable development by reducing energy consumption.Sustainable development goals are addressed by transition from incandescent lighting to LED lighting [7,8] which has brought up new measurement needs and emphasized the significance of reliable photometry for ensuring the high quality of lighting.
As lighting is nowadays based on LEDs, it is appropriate to revise the photometric methods from use of incandescent lamps to those of LED light sources.For example, CIE has recently published a LED Reference Spectrum for Photometer Calibration [9], largely based on research concerning the advantages of LED based calibration sources for photometers used with LED lighting [10].Future work in photometry may take full advantage of the new reference spectrum and related LED based calibration sources when they start to become widely available.
Many features of lighting change with LEDs, such as spectral, color, geometrical and temporal characteristics.Lighting industry needs reliable measurements on all these features which forms a continuing challenge for research laboratories aiming to develop measurement methods with low uncertainties.Finally, the underpinning scales of optical power measurements are needed to quantify the energy savings gained by LED lighting as compared with earlier types of lighting.It is noteworthy that there has been a simultaneous development of optical power measurements during the past 100 years, which is reflected in the gradually changing definitions of the photometric base unit of the SI system-the candela [11][12][13].

LEDs for lighting
Technologies for artificial lighting have been under significant development.The history of incandescent lighting dates back to the early 19th century when inventors began experimenting with electric light.Thomas Edison's groundbreaking invention revolutionized the way of illuminating homes and cities, gradually replacing gas and oil lamps.Following the prolonged dominance of incandescent lighting throughout much of the 20th century, the growing demand for environmentally sustainable and economically viable alternatives prompted the emergence of new lighting technologies.Compact fluorescent lamps gained popularity as an energy-efficient replacement for incandescent bulbs [8].These lamps utilized a combination of gas and phosphors to produce light, offering significant energy savings.Additionally, halogen bulbs were introduced, providing improved efficiency and longer lifespans compared to traditional incandescent bulbs.These developments marked a transition towards more sustainable lighting options, laying the groundwork for further advancements in lighting technology and the eventual rise of even more efficient alternatives.
The true breakthrough came with the advent of LED technology [14].LED lighting offers exceptional energy efficiency, long lifespan, and versatile design possibilities.Rapid advancements in LED technology have resulted in increased brightness, improved color accuracy, and reduced costs, making it the preferred choice for residential, commercial, and outdoor lighting applications today.LED lighting has revolutionized the lighting industry, leading in many cases to adapted measurement and characterization methods as compared with those of traditional incandescent lighting.

Spectral characteristics
LED light sources offer unique spectral characteristics that distinguish them from other lighting technologies.One key aspect is their ability to emit incoherent light in a narrow range of wavelengths, resulting in a more specific color output.With fluorescent materials, LEDs can be engineered to emit light across the whole visible spectrum.Moreover, LED light sources have exceptional color consistency and accuracy, providing a high color rendering index (see appendix for further details) and enabling accurate representation of objects' true colors [15].The spectral control makes LED light sources ideal for various applications, including lighting design, photography, and horticulture.
In all these applications it is important to quantify the useful amount of light obtained from the LED light sources.Photometers measure light weighted by the V(λ) function corresponding to the sensitivity of human eye (see appendix for further details).Photometer responsivities have been traditionally calibrated by observing their signal from a known light source whose spectrum resembles CIE Standard Illuminant A [16], a Planckian radiator at the temperature of 2856.5 K.This method works well with measurements of incandescent lighting, but for LED lighting the spectral mismatch and related uncertainties increase, because the spectral shape of white LEDs is different from Illuminant A.
The photometer calibration for LED lighting applications would improve, if the known light source used for calibration would have a spectrum resembling the usual spectra in LED lighting applications, instead of a spectrum resembling Illuminant A. For this purpose, the spectra of a large number of LED products have been studied and used to calculate representative spectral power distributions (SPDs) for LED sources of different correlated color temperature categories [10].It was found that in general, when compared with Standard Illuminant A, all potential LED calibration spectra reduced spectral mismatch errors when measuring LED products.The white phosphor-converted LED spectrum with correlated color temperature of about 4100 K was found to be most suitable to complement Illuminant A in luminous responsivity calibrations of photometers.It was used as the basis of spectrum L41 (figure 1), defined as the CIE reference spectrum for photometer calibration [9].It is noteworthy that a light source resembling L41 works well as a calibration source also with photometers intended for use in daylight applications.
Practical LED light sources [18][19][20], with spectral irradiance resembling the L41 spectrum, have been developed.Even if their spectra would somewhat deviate from the reference spectrum L41, they would reduce the spectral mismatch error in photometer calibration relative to calibrations using incandescent lamps.The LED light sources [18][19][20] have also other promising features, such as robustness and stability, which make them attractive as complementary standard lamps, working standards, and comparison artefacts.Their performance will be tested in a forthcoming international comparison measurement with global coverage of participants.
The SPD of a light source determines the emissive tristimulus values, such as X, Y, Z and color coordinates defined as ratios of tristimulus values (see appendix for further details).Spectroradiometers are commonly employed devices that analyze the SPD of light emitted by LEDs.To measure color accurately, calibration is crucial [21][22][23][24][25][26].Calibration ensures that the measurement results correspond to true spectral shapes across different LED light sources.In addition to spectral analysis, colorimeters are another commonly used tool for color measurement with LEDs.These devices assess color by comparing light intensity across different color filters.Colorimeters offer ease of use and are suitable for various applications such as display calibration and ambient lighting control.
Calibration of spectroradiometers is nowadays based on known incandescent light sources whose spectral irradiance is traceable to black body radiator following Planck radiation law [27][28][29][30].The incandescent working standard lamps are very convenient to transfer the primary calibration from a Planckian radiator to spectroradiometer user.The challenge here is that the use of incandescent lamps for lighting reduces, implying that the availability of incandescent working standard lamps may also reduce.LED light sources designed as new type of working standard are a promising candidate for spectroradiometer calibration in the visible wavelength range, meeting the demands of color measurements.However, research in this area is still at early stages [31,32] and it is not yet clear that the uncertainties and convenience of use of the earlier incandescent standard lamps are achieved.
Color coordinates are quantities defined in terms of ratios of spectral integrals.They are further used as a basis for calculating other important color quantities.Reliable uncertainty estimation is difficult for ratios of spectral integrals because uncertainty components which are the same at all wavelengths, like aperture area, cancel out and the contribution of noise-like components approaches zero when the number of wavelengths used in the measurement increases.This problem of colour coordinate uncertainty evaluation has been addressed by analyzing partial correlations at neighboring wavelengths through a basis function method [33].The need for further work in estimating uncertainties of spectral integrals has been recognized [34][35][36], which is anticipated to yield more reliable uncertainties in colorimetry with LED lighting [37,38].

Geometrical characteristics
LED light sources offer directional lighting, with the ability to emit light in specific directions without the need for additional reflectors or diffusers.This directional nature reduces wasted light and enables focused illumination, making LEDs highly efficient for task lighting and spotlighting applications.Furthermore, the small size of LEDs allows for easy integration into different lighting fixtures and applications.LEDs can be designed to emit light in specific directions, resulting in efficient light distribution and reduced light pollution.
The lighting designer needs information on the angular distribution of light intensity, but such information is also essential for measurement purposes.Figure 2 shows examples of angular distributions of LED light sources.Such data are needed when the absolute integrating-sphere method is used for luminous flux measurements of LED lamps [39][40][41][42].Integrating spheres are also widely used in industry where their calibration is traceable to transfer standard lamps or more advanced artifacts [43].In goniometric setups for luminous flux measurements, the detector or spectroradiometer is moved at known angles relative to the light source [44,45].This motion is necessarily slow and such measurements of angular distributions take a long time.An alternative, fast way of obtaining the angular intensity distribution is that the light source illuminates a Lambertian reflecting screen at a large distance and the screen is imaged by a camera [46][47][48].Knowing the geometric relation between the system components, it is possible to calculate the intensity distribution within the angular range of the screen or construct the full intensity distribution by rotating a light source with wide angular pattern.The extreme case of this method is to use a 2π camera (fisheye) on the wall aperture of an integrating sphere [49].
The fisheye method was originally developed for spatial non-uniformity corrections in luminous flux measurements with integrating spheres, but it can be also used for fast measurement of light source angular distributions [42,49].The method needs to be calibrated for the angular responsivity of the sphere with a light source of known angular distribution, determined by the goniometric measurement (see figure 3).However, it may be possible to make the fisheye method independent of the goniometric measurements by using a narrowbeam light source in the middle of the sphere [39,50] and raster-scanning the sphere responsivity in all directions, in a similar way as has been done in accurate optical aperture area measurements [51].Furthermore, if a 2π hyperspectral camera is used in the sphere wall aperture, combined angular and spectral information may be obtained with the fisheye method.

Temporal characteristics
The lifetime of LED lamps is very long as compared with alternative technologies, making a significant contribution to sustainability, in addition to energy efficiency.Natural aging monitoring on a time scale of many years is challenging and may lead to intolerable delay in obtaining the results.However, ageing of LED light sources can be accelerated by increasing the junction temperature of the LEDs [52][53][54][55][56].In extending the LED lamp lifetime, care should be taken to ensure that the driver electronics is not the limiting factor.It has also been found that LEDs operating at higher junction temperatures are more often damaged [57].
LED lights have instant on/off capabilities, providing immediate illumination without any warm-up time.This feature is particularly beneficial in applications where instant lighting is required, such as security lighting or emergency situations.LEDs also excel in dimming capabilities, offering smooth and flicker-free dimming across a wide range of light levels.The LED lamps are quite resistant to frequent switching, ensuring consistent performance and reliability over time.In fact, the first definite observation of reduced lifetime due to switching was observed only recently in natural ageing conditions [58].
Significant energy and cost savings can be obtained with LED lighting when light is used only when needed in buildings, pedestrian areas, and streets [59][60][61].Figure 4 shows a comparison of streetlamp ageing results, when one lamp group has natural ageing while another cycled group of lamps has been switched between 20% and 100% power with 30 s interval [58].Although after 10 000 h of ageing the cycled group shows a few percent lower luminous flux, the switching frequency is about ten times the average switching frequency which would occur in real traffic conditions with smart lighting.Thus, the effect of smart control in energy savings exceeds the increase of maintenance costs due to the decreased lifetime of switched streetlamps [58].
Certain LED lighting installations may exhibit visually harmful temporal effects [62].In some cases, LEDs operating with poor driver circuitry can cause perceptible flicker, leading to eye strain, headaches, and discomfort.Rapid on/off switching or irregular pulse-width modulation can result in noticeable strobing, which can be distracting and disrupt visual perception.Addressing these issues through proper design, highquality components, and adequate measurements is crucial to minimize visually harmful temporal effects and ensure a comfortable and visually pleasing lighting experience.
Figure 5 shows examples of light waveforms with different types of LED driver electronics.The new EU Ecodesign regulation set requirements for lighting equipment on the European market starting September 2021.This regulation defined restrictions for two temporal light artefact (TLA) metrics, short-term flicker severity index (P st LM ) and stroboscopic visibility measure (M VS ): P st LM < 1 and M VS < 0.4, to limit TLA effects.For both metrics, the value 1 means that an average observer has 50% chance to perceive these TLAs.When these values are less than one, they are not visible on the average.Measurement methods for the above parameters with LED lighting have been improved recently [63][64][65][66].
By comparing the TLA results obtained from the older (before 2017) and newer (after 2021) LED lamps, it can be concluded that the luminaire manufacturers have taken the EU Ecodesign regulation into account.This has been done by favoring better LED driver types, which in general results in lower P st LM and M VS values [67].

Underpinning optical measurement standards
Energy efficiency of LED light sources is one of their key advantages.Quantitative determination of this characteristics in units of lm W −1 requires measurement of the produced luminous flux and electrical input power of the LED lamp.Although measurement of electrical power sounds simple, the variable AC power line impedance may be a considerable challenge in the case of practical LED lighting [68,69].However, here we focus on the luminous flux measurements which are closely related to improvements in the definition of the SI base unit candela.

Definition of the candela
The definition of the candela, the SI unit for luminous intensity, has undergone significant changes over the years.Historically, the candela was defined as the luminous intensity of a specific type of candle flame.In 1930s, developments started in order to define the candela in terms of blackbody radiation at a specific temperature.This line of development resulted in 1967 in the final form of the 'source-based'  candela where the candela was the luminous intensity, in the perpendicular direction, of a surface of 1 / 600 000 m 2 of a black body at the temperature of freezing platinum under a pressure of 101 325 N m −2 [11].But the difficulties still continued in carrying out easy measurements with this kind of material artifact.Meanwhile, improved absolute detectors were under development [70,71] which suggested another approach in the definition of the candela.In 1979, the candela was defined as the luminous intensity in a given direction of a source that emits monochromatic radiation with a frequency of 540 THz and has a radiant intensity of 1/683 watt per steradian [12].This definition removed the dependence on specific light sources and allowed underpinning optical power measurements for the realization of the definition of the candela [72][73][74].The frequency of 540 THz corresponds to a wavelength of 555 nm of optical radiation, which is at the peak of the photopic luminous efficiency function V(λ).With light sources containing wavelengths other than 555 nm, the luminous intensity is obtained by weighting with the V(λ) function.
In 2019, the SI system underwent a redefinition that further refined the definition of the candela.It is now defined in terms of a fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 THz, which is 683 lm W −1 , exactly [13].These changes in the definition of the candela reflect the progress in metrology and the quest for more precise and universal standards in the field of light measurement.Accurate measurement of optical power or detector spectral responsivity continues to be the starting point of traceability for measurement of luminous intensity and luminous flux.The mise-en-pratique for the definition of the candela [13] specifies two detector-based methods as primary standards of optical power: cryogenically cooled electrical substitution radiometer [72][73][74] and predictable quantum efficient detector (PQED) [75,76].

Measurement of optical power
The electrical substitution radiometer (ESR) in a cryostat has become the most important optical power standard in metrology laboratories [77], often used with monochromatic laser radiation.The radiation absorber is positioned within the cold cavity of the cryostat at a temperature slightly above the boiling point of helium (figure 6).The cold cavity is alternately heated by electrical wiring and incoming radiation providing traceability of optical power to measured heating current and voltage.Cooling below 10 K significantly enhances the heat diffusivity of copper, allowing large-size absorption cavity and effectively reducing the non-equivalency between optical and electrical heating [72].Furthermore, superconducting current leads to the heating wires of the cavity reduce parasitic heating [73].The ESRs operated at cryogenic temperatures [72][73][74] thus have significant advantages as compared with room-temperature ESRs [70].The former devices, capable of measuring absolute optical power with a relative uncertainty of 0.01% or below, are commonly referred to as absolute cryogenic radiometers (ACRs).
An alternative to ACRs is provided by absolute detectors based on induced-junction silicon photodiodes [78][79][80][81][82], where each incoming photon is converted to an exactly one electronhole pair.The measured photocurrent accurately quantifies the incoming optical power, provided that the vacuum wavelength of the laser radiation is known and the effects of reflectance, absorption, charge-carrier recombination losses and quantum yield can be eliminated or estimated with a relative uncertainty of 0.01% or below.In the PQED [75,76,83], all these conditions can be met at the visible wavelength range and relative measurement uncertainties at least as low as with ACRs can be achieved.
Reflectance losses can be reduced with the wedge trap structure of the PQED photodiodes as shown in figure 7 [84].Furthermore, the correction due to the remaining reflection out of the PQED is easy to measure or calculate within a relative uncertainty of 0.001% in responsivity when the thicknesses and refractive indices of the SiO 2 coating layers are known [85].The absorption of SiO 2 at visible wavelengths has been estimated to be negligible [81].Recently, a method for very accurate determination of the correction due to chargecarrier recombination losses was introduced [86].The method is based on measurement and analysis of the photocurrent as a function of reverse bias voltage of the PQED photodiodes [87].Fitting of a 3D simulation model of charge-carrier recombination losses to the photocurrent-voltage data allows to determine the critical parameters of bulk and surface recombination losses.The developed fitting method makes the PQED an independent primary standard of spectral responsivity at the relative uncertainty level of 0.003%.Finally, models have also been developed to account for the effects of quantum yield at short visible wavelengths with sufficient accuracy for the needs of photometry [88,89].
The PQED photodiodes with SiO 2 coating were originally manufactured from low-doping p type silicon [75].It is also possible to make PQED photodiodes from low-doped n type silicon, but then Al 2 O 3 has been used as the coating material to produce the induced junction [90,91].The charge-carrier recombination losses of n type photodiodes appear to be somewhat larger than those of p type photodiodes.A new invention of nitride coating on top of a thin SiO 2 layer has been developed for p type PQED photodiodes [92].The performance of the nitride coated photodiodes is at least as good as that of the original p type PQED photodiodes [75].This is an important achievement because it demonstrates that PQED photodiodes with very good characteristics can be produced by professional photodiode manufacturers and thus PQED photodiodes can be made widely available.
Operation of a PQED at room temperature is as easy as operation of Hamamatsu-photodiode-based trap detectors, widely employed as spectral responsivity working standards in photometry.Gas flow through the detector aperture is used to protect the PQED photodiodes from dust in ordinary laboratory room and such protection should actually be used with all accurately calibrated detectors.In irradiance mode measurements, where incident light enters close to the aperture edge, synthetic dry air should be used as flowing gas to avoid formation of a gas lens in front of the aperture [93].Besides simplicity of use and maintenance, another significant advantage of PQED photodiodes is their stable spectral responsivity over long time periods.Comparison between PQEDs and ACRs did not reveal any change of spectral responsivity within approximately 10 years, including measurements at short visible wavelengths [94].
For direct realization of photometric units, the PQED offers an interesting possibility of determining luminous intensity or illuminance of a white LED light source without the V(λ) filter [95], which is often the most problematic component in ordinary photometers.For a LED lamp resembling L41 [9], the main uncertainty component would then come from the relative spectrum of the lamp influencing the spectral mismatch correction factor, where the relative spectral responsivity of the PQED would be known within a relative uncertainty of 0.01% or better.Such a PQED photometer without a physical filter would allow all types of photometric weighting to be taken into account numerically, for example scotopic, mesopic [96][97][98] or any new photometric weighting function based on cone fundamentals [99].

Conclusions and outlook
Photometry continues to be an important field of research.LED lighting offers significant energy-saving possibilities compared to traditional lighting technologies.LEDs consume much less electricity to produce the same level of brightness as incandescent bulbs or fluorescent lamps.This translates to substantial energy savings, reducing electricity bills and environmental impact.Furthermore, LEDs have long lifespans, lasting significantly longer than conventional bulbs.Additionally, LED lighting can be easily integrated with smart lighting controls, allowing for customized scheduling, occupancy sensing, and dimming, maximizing energy efficiency by adapting to specific needs and usage patterns.All these developments of LED lighting should be supported by appropriate measurement methods of photometry, described above for the different characteristics of LED light sources.
The changes in the definition of the photometric base unit-the candela-reflect the developments in photometry and metrology demonstrating the importance of the underpinning optical power measurements.During the past decades it was experienced that parallel development of lighting technology and photometry is a continuous source of interesting research topics and it is expected to be so for the foreseeable future.

Color rendering index
Color rendering index (CRI) serves as a metric to assess a light source's capacity to depict the true colors of objects when compared to a source which is spectrally identical to daylight.Light sources with a high CRI are desirable in color-critical applications.Numerically, a CRI value can reach a maximum of 100, aligning with a source whose spectrum closely resembles that of a black body, like incandescent lamps.In contrast, low-pressure sodium lighting yields a negative CRI, while fluorescent lights typically range from approximately 50 for basic types to about 98 for the best multi-phosphor types.Common white-color LEDs often have a CRI of 80 or higher, while some LEDs can achieve a CRI of up to 98.

Photopic luminous efficiency function V(λ)
Photopic luminous efficiency function V(λ) represents the average spectral sensitivity of human visual system in brightly lit conditions.Derived from subjective assessments of which among a pair of variously colored lights appears brighter, it serves to illustrate the relative responsiveness to light of differing wavelengths.It is not an absolute reference to any individual.The values of V(λ) function are tabulated by CIE and the function attains a maximum value of 1 at the wavelength of 555 nm and smoothly decreases to zero when decreasing (increasing) the wavelength to 360 nm (830 nm).

Tristimulus values X, Y, Z and color coordinates x, y
Much of quantitative colorimetry is based on tristimulus values X, Y, Z and color coordinates x = X/ (X + Y + Z) and y = Y/ (X + Y + Z).Emissive tristimulus values are spectral integrals, such as X = ˆLe (λ)x (λ) dλ, and corresponding equations for Y and Z.In the above equation, L e (λ) is the spectral radiance and x (λ) as well as related ȳ (λ) and z (λ) are defined CIE standard observers [6].Function ȳ (λ) is the same as V(λ).Reflective tristimulus values are defined with the aid of sample reflectance and normalization by SPD of the illuminant.

Figure 3 .
Figure 3. (a) Photograph captured by the fisheye camera inside an integrating sphere with spotlight LED source.(b) Processed photograph for determining the angular intensity distribution of the LED light source.For image processing, a reference photograph is needed where the sphere is illuminated by a light source with an angular intensity distribution as uniform as possible.The seam between the sphere halves, the lamp holder socket at the bottom, and the baffle in the center are visible in (a), but removed in the processed image (b) [49].(a) and (b) Reproduced from [49].© The Author(s).Published by IOP Publishing Ltd.CC BY 4.0.

Figure 5 .
Figure 5. Normalized light waveforms of four LED lamps, each with different driver type A, B, C or D [63].Reproduced from [63].CC BY 4.0.

Figure 6 .
Figure 6.Block diagram of the first cryogenic radiometer for laser power measurement from 1985 [72].Reproduced from [72].© IOP Publishing Ltd.All rights reserved.