Development of primary reference facilities and measurement comparison of standard artifacts for the bidirectional transmittance distribution function

The way an object looks is usually the most striking property of the object. To describe “how something looks” in a metrological way, the term visual appearance is used. Visual appearance serves as an umbrella under which different aspects are collected: color, gloss, texture, sparkle and graininess, and translucency. This paper focuses on the measurement of translucent or diffusely transmitting samples. The measurand describing this property is the bidirectional transmittance distribution function, denoted as BTDF.^1–3 Determining BTDF values accurately is important for many applications, such as satellite-based Earth remote sensing,^4,5 diffusers to tailor the light distribution in optical systems and luminaires,^6,7 computer graphics rendering,^8,9 medical materials and prosthetics,¹⁰ or food industry.¹¹ 

Despite these widespread applications of BTDF, the availability of high-quality, validated, traceable BTDF measurements is still limited. To fill in this gap, one goal of the EMPIR project “JRP 18SIB03 BxDiff–New quantities for the measurement of appearance”¹² was to develop and install new facilities for the measurement of BTDF at Physikalisch-Technische Bundesanstalt (PTB), the national metrology institute of Germany, and at Aalto University (Aalto) in Finland. Both facilities will be introduced in this paper, together with the results of a bilateral comparison of BTDF measurements for two different diffusers.

A schematic lay-out of PTB’s primary facility for laser-based, small spectral bandwidth measurement of BTDF is shown in Fig. 2. The sample (S) is mounted on a six-axis robot arm (R) in the center of a large absolute-encoded rotation stage (diameter 1.5 m). The detection system is placed on two platforms on the rotation stage. One accommodates the detection optics (L3) and an integrating sphere (intS) with a silicon photodiode (Si-PD) attached to it. On the other one, a preamplifier and a lock-in amplifier (LIA) for signal acquisition are placed. The configuration of sample positioning and detection for performing transmittance measurement in the straight-on geometry, in which both incidence and transmission are perpendicular to the sample plane, is illustrated in Fig. 3. The irradiation beam path is fixed and the combination of the (R)-controlled sample orientation and the position of the detection system on the rotation stage allow almost any bidirectional geometry to be realized. These are not restricted to in-plane geometries, spanned by the sample normal and the incident beam, but also measurements out of this plane are possible. In this setup, rigid samples with a mass up to 8 kg may be measured, with their symmetry axis mainly oriented horizontally.

For the internal comparison within PTB described in Sec. III, two narrow-band cw laser light sources have been used: a diode laser (LS 1) at 642 nm and a diode-pumped solid-state laser at 445 nm (LS 2). The spatial properties of the incident beam are controlled by a beam conditioning (BC) unit. It comprises a beam expander with two lenses (L1 and L2) and a rotating weakly scattering diffuser (D) for homogenization and laser speckle reduction. The resulting beam divergence has ∼0.1°, expressed as full width at half maximum (FWHM). The size of the irradiation beam on the sample is determined by the aperture (A1), which is interchangeable to realize beam diameters up to 30 mm. A linear polarizer (P) defines the polarization state of the irradiation. Different attenuation filters (F) can be placed in the beam path to regulate the absolute level of the detected signal. A chopper (Ch) is used to modulate the laser outputs for lock-in detection. Individual beam conditioning lines for both lasers are set up to account for different divergence and beam profiles. The mirrors M1-1, M1-2, M2-1, and M2-2 are used to steer the beam onto the center of the sample. Mirrors M2-1 and M2-2 are exchanged depending on the laser source used. Also, the chopper, the attenuation filters, and the rotating diffuser are moved to the beam line in use.

The detection optics consists of an achromatic lens and a diaphragm placed directly in front of the lens. At a nominal distance of 652.2 mm from the sample back side to the diaphragm, the detection angular resolution can be varied from 0.6° to 3.1° by applying diaphragms with different diameters. This corresponds to detection solid angles ranging from 9.1 × 10⁻⁵ to 2.3 × 10⁻³ sr. This imaging detection system allows for measurements to be carried out either in under-irradiated or over-irradiated mode, depending on the size of the irradiation and the detection areas. The detection area is given by the size of the interchangeable aperture (A2) mounted at the entrance of the integrating sphere, which is imaged on the sample back surface by the achromatic lens. With a magnification of 1.4, the largest achievable detection area has a diameter of 30 mm. Controlling the hardware settings and collecting the measurement data are done using an in-house developed LabVIEW program. Once the different beams are aligned, measurements can be carried out fully automated.

The primary BTDF facility at Aalto University is based on the 3D gonioreflectometer for spectral BRDF measurements. A detailed description of the 3D gonioreflectometer and its uncertainty budget, which can be at least partly applied on BTDF measurements, can be found elsewhere.¹⁴ The 3D gonioreflectometer is calibrated using a reference material whose BRDF is traceable to Aalto’s reference gonioreflectometer.¹⁵  Figure 4 shows the 3D gonioreflectometer setup in its configuration for transmittance measurements. The Aalto approach allows also non-rigid samples to be measured. The sample is mounted on a horizontally aligned sample holder (6), while three motorized arms are used to set the bidirectional geometry [(2) for irradiation polar angle θ_i, (3) for detection or viewing azimuth angle φ_t, and (4) for detection polar or zenith angle θ_t]. A supercontinuum laser is used for irradiation. To select the wavelength, laser-line tunable filters are used. The irradiation optics (1) includes an SMA fiber collimator, order-sorting filter, a polarizer, beam expanding and steering optics, the monitor detector, and an adjustable iris for beam size. After impinging on the sample, the transmitted radiation is collected via an off-axis parabolic mirror (5) and fiber coupled to the detector box. Depending on the wavelength, either a Si- or InGaAs photodiode is used for detection. Transimpedance amplifiers convert the current signals for voltage measurement. Motion control of the facility and data acquisition are achieved by using a LabVIEW program run on personal computer (PC).

A standard measurement procedure of a test sample, using the 3D gonioreflectometer, includes adjustments of the sample holder height by using a linear translator micrometer. Thus, the geometric center of the instrument can be set to different heights for samples of different thicknesses. The sample surface facing the incident beam is used to define the center point. To ensure accurate alignment, the reference face of the test sample is adjusted with a self-leveling multi-beam laser, enabling a repeatable alignment within 0.1 mm. Furthermore, to obtain the BTDF result of the test sample, a reference sample is measured both in the reference gonioreflectometer for its BRDF and in the 3D gonioreflectometer for its reflected signal. The ratio of both instruments’ results allows for BTDF measurements of test samples in any geometry at pre-measured wavelengths.

Irradiation of the test sample and detection of the signal is performed by three motorized arms. The irradiation polar angle can be varied in a range of 0°–90° with irradiation azimuth angle at 0° and 180°, and by using an iris, a beam size at the sample from 8 to 20 mm in diameter can be provided. During the measurements, an 8 mm beam size was used, which follows a Gaussian beam profile. The detector is equipped with a two-axis motorized arm to scan the half-sphere below the sample plane. The first arm controls the viewing polar angle, which can be adjusted within the range of 0°–90°. The second arm sets the viewing azimuth angle, allowing variations from 0° to 180°. Both arms enable in- and out-of-plane measurements of non-rigid samples. The detection has an angular resolution of 2.89°. The angular resolution corresponds to a solid angle of ∼0.0022 sr, determined by the off-axis parabolic mirror housing aperture diameter (Ø 10.85 mm) and the detector aperture-to-sample distance (204.7 mm).

The irradiation is provided by a combination of a supercontinuum laser and a laser-line tunable filter. The system provides a collimated beam in the wavelength range from 400 to 2400 nm, which has a bandwidth of 4 nm. The optical power can be adjusted in the supercontinuum laser power source to optimize the irradiation according to the sample type, with an average power of 0.3 mW. Polarization of the beam is controlled by inserting polarizers, which have extinction coefficients of 1000:1, in the cage system and in the beam path. The stability of the laser power is monitored by using a beam splitter and a two-color monitor detector, with sensitivity in the wavelength range from 400 to 1700 nm, before the iris. Transmitted light is collected by using an optical fiber that directs the light to a detector housing, which includes a silicon and an InGaAs photodiode. A transimpedance amplifier provides amplification in the dynamic range from 10² to 10⁹ that covers signal ranges for Lambertian and more transparent samples, such as frosted glass samples.

To compare the BTDF scales of the measurement facilities at Aalto and PTB, two different samples were chosen. One sample made of a 0.25 mm thick PTFE foil with a Lambertian scattering characteristic, denoted sample E, and one sample made of bulk NK7 glass with a sandblasted active surface, possessing a Gaussian scattering distribution with FWHM of 16°, denoted sample B. The BTDF for sample E has been determined in an in-plane geometry, and for sample B, both in-plane and out-of-plane geometries have been realized. The details can be found in Table I. The geometry (0°, 0°) for both incidence and detection implies the direction perpendicular to the sample plane. The measurements were performed at four wavelengths.

Completion of PTB’s primary BTDF facility was delayed due to delivery problems of some vital components. Thus, the measurements for the comparison, which had to be performed within the schedule of the BxDiff-project, were carried out on PTB’s primary facility for the measurement of regular transmission and reflection, which has been modified accordingly¹⁶ (abbr. “modified NaNoRef”). Subsequent measurements have shown that the results from both PTB facilities agree well within their specified uncertainty. An exemplary result for sample B at 642 nm, depicting the congruence, is shown in Fig. 5.

The main contributions to the uncertainty budget for the modified NaNoRef and the new primary BTDF facility at PTB are listed in Tables II and III, respectively.

Uncertainty in the measurement signal is determined by signal noise and instability in the laser power, the latter being different for both setups. To reduce the measurement noise, each measurement was repeated nine times, and the statistics was considered as signal fluctuation. As no monitoring was performed on the laser output power, the incident signal was measured before and after the transmitted signal to eliminate any linear drift in the laser power. The residual drift was considered as the instability in the laser output power.

Neutral density (ND) filters were used to adjust the optical signal to the dynamic range of the detector when measuring the incident irradiation power. The neutral density filters used on the modified NaNoRef setup were calibrated by the national standard setup for regular transmission at PTB and have minimum relative uncertainties according to the PTB Calibration and Measurement Capability (CMC)-entry for spectral transmittance,¹⁷ whereas the filters used on the new BTDF primary setup were currently only calibrated by a commercial instrument and have a larger relative uncertainty.

The uncertainty of the detection solid angle originates from the uncertainty in the area determination of the detector diaphragm and its distance to the sample back side. The larger NaNoRef-uncertainty was due to possible dust contamination by anti-reflection coating residual. This problem was avoided for the new BTDF facility. The instrumental distance was measured by a calibrated inside micrometer multiple times and the uncertainty was 0.1 mm for the modified NaNoRef and 0.3 mm for BTDF facility. An additional distance uncertainty is accounted for sample E due to an observed non-flatness of the foil. (PTB’s measurements on sample E were corrected for this sample-specific distance error and the uncertainty was estimated to be $1./3$ mm).

The uncertainty in the detection polar angle positioning is dominated by the alignment of the detector diaphragm, as the accuracy and reproducibility of the motorized detection arm/rotation stage are small in usual applications. It was estimated to be 0.01° for the modified NaNoRef setup and 0.015° for the new primary BTDF setup. Its contribution to the combined uncertainty is dependent on both sample scattering characteristics and detection polar angle setting. This component is dominant in the measurement uncertainty of sample B since, in both measurement geometries, the detection was made at the angle where the BTDF distribution exhibits large variation.

The wavelength uncertainty is dependent on the central wavelength shift of the laser spectrum from its nominal value when the lasers are operated at different output power levels (except for 532 nm). Its influence depends on the spectral characteristics of the sample, which was measured as a function of transmission angle for perpendicular incidence at PTB,¹⁶ and on the spectral transmission of the ND-filter. For sample E, the latter one contributes mainly at shorter wavelength.

The influence of the finite detection angular resolution is an important component in the uncertainty budget for sample B due to its narrow scattering distribution. It is characterized by the so-called instrument function, which describes the angular resolution ability of the measuring system and is determined by an angle-scan without sample.¹³ The measured BTDF then is the result of convolving the true sample BTDF with the instrument function. Its impact is proportional to the second derivative of the distribution with respect to the scatter angle (⁠$∂2BTDF∂θt2)$⁠. Since the angular resolution of 1° applied on both PTB setups was sufficiently small with respect to the width of sample B’s distribution, the <0.2% difference between the measured and the true distribution is considered as relative uncertainty using a deconvolution method in analogy to CIE 214.¹⁸ For sample E, whose scattering distribution is quite flat, this influence is considered as an uncertainty of 0.01% to its BTDF.

The spatial intensity variation in the irradiation beam was considered as the uncertainty of beam nonuniformity. The beam profile was measured by a laser beam analyzer and showed a 20% intensity decrease at the outer part of the beam compared to the beam center. A simple ray-tracing simulation taking this edge reduction into account by a parabolic profile resulted in only small uncertainty contributions for all measurements reported here.

The uncertainty in polarization stems from the irradiation since the detection is unpolarized. It was determined by the extinction coefficient of the linear polarizer and the difference between the two polarized BTDF values. The contribution of this component is negligible for sample E, and for sample B this component still contributes less than 0.05% to the BTDF.

The inter-reflection between optical elements was estimated, mainly between the achromatic lens and the detection diaphragm due to the small distance. This component contributes only 0.001% to the BTDF.

The digitization error accounts for the finite resolution when the measured value was digitized by the signal reading devices. On the modified NaNoRef setup, the measured data were digitized to the fourth decimal place, which results in an uncertainty of 0.01% in the BTDF. The device on the new primary BTDF setup has a higher resolution that could digitize the measured data to the sixth decimal place. Thus, this uncertainty is negligible.

The linearity of the detector used on the modified NaNoRef setup was calibrated at PTB and the measurement results were corrected. The uncertainty of the correction has an influence of no more than 0.01% on the measured BTDF. The linearity of the detector used on the new primary BTDF setup was not yet calibrated, and thus, no information is given here. We assume that this uncertainty component would influence the measurement in a similar way, as the same type of detector was used for the measurement on the primary BTDF setup.

The straylight was estimated by performing the BTDF measurement with a beam blocker placed near the back surface of the sample. The signal of the scattered light under this condition could not be differentiated from the signal when the irradiation beam was blocked. On both PTB’s setups, the straylight reduction was supported by the use of the lock-in amplifier technique and the depth of sharpness of the imaging detection system. Due to an additional light-proof chamber, where the sample was placed separated from the light source, straylight reduction was superior on the modified NaNoRef setup. Therefore, the straylight on the modified NaNoRef setup was estimated to be 1/5 of the dark signal level and similar to the dark signal level on the new primary BTDF facility.

The uncertainty budget for the primary BTDF facility at Aalto University is given in Table IV. The third column of Table IV shows the uncertainty in BTDF for sample B. The uncertainty budget has previously been evaluated for BRDF measurements elsewhere.¹⁴ The following paragraph describes major changes in uncertainties when measuring BTDF. The reader should note that several uncertainties in BTDF are a quadratic sum of the standard uncertainties to account for the reference and test sample measurement uncertainties.

Measurement noise represents the largest component in the 3D gonioreflectometer uncertainty budget. It was evaluated by recording the scattered signal of a PTFE sample at 2-second intervals over a period of 45 min.¹⁴ This approach allows us to assess signal fluctuations beyond the normal nine measurement points used for calculating each BTDF value. Measurement points that fluctuate around the signal mean can be considered as noise. The uncertainty in measurement noise has increased by a factor of 1.4 due to the lower signal when measuring transmittance as compared to reflectance measurements. To mitigate measurement noise, multiple measurement points can be acquired, and the uncertainty can be reduced by using the standard deviation of the mean. The measurement noise uncertainty in BTDF consists of both the detector and monitor uncertainties, which have been combined quadratically.

The instrument stability was evaluated by measuring samples on different days, while removing and inserting the sample again. The repeatability had a relative standard deviation of 0.1%.

The standard uncertainty in the central wavelength was determined by scanning the collimated beam against a calibrated radiometer.¹⁹ The results show that the laser-line tunable filter has a standard uncertainty of 0.15 nm. The uncertainty in BTDF is determined from the slope of the BTDF as a function of wavelength, which is sample dependent.

Straylight uncertainty was evaluated for iso- and heterochromatic light.¹⁴ Straylight contributions are confined to scattering inside the instrument darkened compartment. Therefore, heterochromatic straylight from the supercontinuum laser is limited by its out-of-band rejection level. The heterochromatic straylight contribution in uncertainty was evaluated as less than 0.01%. The isochromatic straylight was evaluated by illuminating a diffuse white PTFE sample out of focus. The results showed that in the darkened compartment intra-scattering contribution was at the same level as the dark signal. As a result, the isochromatic straylight contribution to the uncertainty was less than 0.01%.

Detector linearity has been studied elsewhere.^20,21 The measurement conditions of the test sample match that of literature, with signal currents from 10⁻¹¹ to 10⁻⁸ and 10⁻⁸ to 10⁻⁵ A for the Si and InGaAs detectors, respectively. Therefore, the standard uncertainty in the Si detector linearity is 0.05% and 0.09% for the InGaAs detector. Similar to the case of measurement noise, the relative uncertainty in BTDF due to detector linearity is determined from the combined uncertainties of the detector and monitor detector, which are added quadratically.

Beam spatial nonuniformity uncertainty was assessed by using a scanning-slit optical beam profiler.¹⁴ The beam profiler shows the beam intensity as a function of x–y coordinates. By taking slices of the Gaussian beam profile, slight asymmetries in the beam can be detected. Different slices of the Gaussian beam profile were compared, and the largest variations showed a relative difference of 0.5%. For samples with linear spatial inhomogeneities, the beam nonuniformity translates into a relative standard uncertainty of 0.14%, which follows a rectangular probability distribution. For Lambertian samples, this standard uncertainty effect on BTDF is <0.01%.

Irradiation and detection angle uncertainty depend on the goodness of the alignment procedure for intersecting the rotational axes to the geometrical center. Thus, the uncertainty in angles consists of the cumulative error in alignment residual errors. Currently, the detection azimuth angle uncertainty skews the cumulative uncertainty, and work on improving the alignment procedure for the detection azimuth angle is ongoing to lower this uncertainty component of 1.1%. The uncertainty in irradiation and viewing angles are also sample-dependent. The uncertainty can be found from multiplying the standard uncertainty in angle with the slope of the BTDF as a function of the corresponding angle. Sample B has a large slope in its BTDF as a function of θ_t due to its Gaussian transmission distribution and shows a large uncertainty in the range from 0.02% to 0.9%. The uncertainty in BTDF as a function of azimuth angle was estimated from the relative difference in BTDF when comparing values using opposite incident polar angles, mirrored around the sample reference side normal, which should ideally be as close as possible.

The sample level uncertainty affects the solid angle of the measurement. The sample surface is aligned by using a self-leveling laser that sets the geometrical center of the goniometer axes. The alignment process is repeatable within 0.1 mm, which introduces a 0.14% uncertainty in the solid angle.

The uncertainty in polarization was evaluated from the polarizer extinction coefficients. Therefore, samples that change in BTDF as a function of polarization have an uncertainty of 0.01% due to uncertainty in polarizer state.

The uncertainty in the reference sample BRDF has been evaluated in the reference gonioreflectometer uncertainty budget.¹⁵ The uncertainty was increased for transmittance measurements due to a lower signal.

The results of the comparison between PTB and Aalto are presented in this section. The weighted mean of the reported BTDF from both labs was calculated using the inverse of the squared standard uncertainty as weighting factor and the data consistency was checked by chi-squared (χ²) test.

The results of sample E are shown in Fig. 6, together with the measurement geometry expressed in the form $θi,φi$/$θt,φt$⁠. The BTDF measured on both facilities agree within their expanded (k = 2) uncertainty and the χ² test has passed for all wavelengths. The BTDF values given by PTB are systematically larger than those by Aalto. The effect might be explained by the non-flatness of the foil as it exhibits a pre-bent form that could not be completely removed by the sample holder. In PTB’s measurements, the bending was facing toward the detection, resulting in an underestimated collection solid angle, whereas in Aalto’s measurements, it was in the opposite direction and the measured results were not corrected.

Figure 7 shows the BTDF results for sample B, together with the geometries in the form $θi,φi$/$θt,φt$ for both in- and out-of-plane measurements in the corresponding subplot. The consistency check shows that the results also agree within their expanded uncertainty for both in-plane and out-of-plane geometries. For this rigid sample, no obvious systematic deviation was found between both facilities.

Two new measurement facilities have been developed and installed at PTB and Aalto University for high-quality, traceable BTDF measurement. Their performance has been tested in a bilateral comparison for two different diffusers, one with a Lambertian and the other one with a Gaussian scattering characteristic. The results in both in-plane and out-of-plane geometries agree well within their expanded (k = 2) uncertainties for all four visible wavelengths applied. The presented bilateral comparison proved the consistency of the BTDF measurements carried out on the two primary facilities in PTB and Aalto. Main contributions to the uncertainty budget have been identified and will be considered in future improvement of the systems.

The BxDiff project (Grant No. JRP 18SIB03) has received funding from the EMPIR program co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation program. J.F. gratefully acknowledges the support of the Braunschweig International Graduate School of Metrology B-IGSM.

The authors have no conflicts to disclose.

J. Fu: Data curation (equal); Formal Analysis (equal); Visualization (equal); Writing–Original Draft Preparation (equal). T. Quast: Conceptualization (equal); Formal Analysis (equal); Visualization (equal); Writing–Original Draft Preparation (equal). E. Velke: Resources (equal). M. Esslinger: Data curation (supporting); Resources (equal). M. Pastuschek: Software (equal). A. Schirmacher: Conceptualization (equal); Formal Analysis (equal); Funding Acquisition (equal); Supervision (equal); Writing–Review & Editing (equal). R. Aschan: Data curation (equal); Formal Analysis (equal); Visualization (equal); Writing–Review & Editing (equal). F. Manoocheri: Conceptualization (equal); Funding Acquisition (equal); Supervision (equal); Writing–Review & Editing (equal). E. Ikonen: Funding Acquisition (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.