Design and Manufacture of a Stand for Measuring the Illuminance Differences of Semi-Transparent Materials Used in Additive Manufacturing

Additive manufacturing by fused deposition modeling (FDM), also known as fused filament fabrication (FFF), has transitioned from rapid prototyping to functional production of components for consumer, lighting, and optical applications. A growing subset of applications exploits translucent FDM parts, e.g., lampshades, diffusers, light covers, and housing, where controlled light transmission and scattering are central to performance rather than an incidental byproduct of the process [1-3]. For such components, designers require quantitative knowledge of visible‑range light transport: not only spectral transmittance, but also luminous transmittance, haze, and the balance between regular (collimated) and diffuse transmission.

In conventional polymer optics, these quantities are routinely characterized with spectrophotometers equipped with integrating spheres under standards such as ASTM D1003 and ISO 13468. These standards prescribe measurement geometry, wavelength range, sphere design, and sample preparation for transparent and translucent plastic sheets. Recent metrology work has refined and critiqued these procedures, highlighting the importance of integrating‑sphere geometry, port fraction, and measurement mode (single‑ vs double‑beam; single‑ vs. double‑compensation) for accurate and traceable measurements of total luminous transmittance and haze [4-6]. Parallel efforts in color and appearance science have leveraged integrating‑sphere data to infer intrinsic optical parameters—absorption and scattering coefficients, phase functions, and refractive index—of translucent polymers using radiative‑transfer models and machine‑learning inversion [7-9].

These established approaches cannot, however, be transferred naively to FDM‑produced translucent parts. FDM microstructure is highly heterogeneous and anisotropic: extruded filaments form roads with inter‑road and inter‑layer voids, partial coalescence zones, and surface stair‑stepping, all embedded in a semi‑crystalline or amorphous polymer matrix. The resulting refractive‑index fluctuations and void distributions generate strong multiple scattering, often dominating bulk absorption in determining the overall transmittance and appearance of the part. Hamp et al. demonstrated that transmittance of 3D‑printed materials as a function of thickness departs markedly from simple Beer–Lambert behavior due to multiple scattering, even for relatively simple multithickness specimens measured in a direct‑beam geometry [3]. This indicates that standard homogeneous‑slab assumptions, underlying much of traditional optical characterization, are at best approximate for typical FDM plaques.

Only a small number of studies have directly addressed the optical characterization of FDM‑printed translucent parts using sphere‑based methods. Wang and Zhou [1] printed flat polylactic acid (PLA) plaques intended for lampshade applications and measured their spectral transmittance and haze with a commercial UV–Vis spectrophotometer equipped with an integrating sphere, explicitly referencing ISO 14782:2021 for haze determination. They systematically investigated the influence of color (milky vs. colorless PLA), wall thickness, and layer height, showing that milky PLA acts as a stronger diffuser with better luminous uniformity, and that increasing wall thickness reduces transmittance while increasing haze [1]. Vochozk et al. [2] used an integrating sphere with a luxmeter to quantify the “translucency” (essentially luminous total transmittance) of PLA plaques as a function of six FFF processing parameters—orientation, layer height, nozzle temperature, fan speed, extrusion multiplier, and print speed—across 32 parameter combinations and ten replicates each. All investigated factors were found to significantly affect the measured luminous transmittance, underscoring the sensitivity of optical behavior to FDM process settings [2].

These FDM‑focused works, however, do not yet amount to a comprehensive, standards‑like methodology for visible‑range total transmittance of FDM translucent parts. Instrument geometry and port fractions are only partially documented [1, 2], and there is limited discussion of how deviations from the flat, polished, homogeneous sheets assumed in ISO/ASTM methods—e.g., surface relief from layer lines, internal porosity, and anisotropic road patterns—should be handled in sample preparation, alignment, and data interpretation. At the same time, the broader metrology literature makes clear that integrating‑sphere design and operating mode can introduce systematic biases in total transmittance and haze. Shahpaski et al. demonstrated, with a flexible custom integrating‑sphere bench, that different illumination/collection geometries (0°/d, d/d, d/0°), port arrangements, and detector fields‑of‑view produce measurable shifts in total transmittance and haze compared to commercial instruments and provided detailed design guidelines for achieving comparability with ASTM D1003‑type measurements [4]. Hwang and Baek [5] recently showed analytically and experimentally that standard single‑beam sphere methods, as recommended in ASTM and ISO standards, retain multiplicative factors from multiple reflections in the sphere, whereas a double‑beam configuration can cancel these factors and reduce bias in luminous transmittance and haze. An inter‑laboratory pilot comparison coordinated within the Asia Pacific Metrology Programme further confirmed that double‑beam and double‑compensation methods provide more consistent total and diffuse transmittance than conventional ASTM D1003 implementations, even for high‑transmittance artefacts [6].

In parallel, appearance‑oriented research on 3D‑printing materials has advanced the use of standard reflectance/transmittance spectrophotometers, often with integrating spheres, to recover intrinsic optical properties rather than just phenomenological transmittance values. Simonot et al. [7] combined sphere measurements of slightly scattering polymer sheets with an extended two‑flux radiative‑transfer model to separate regular and diffuse components and to predict the reflectance and transmittance of stacked layers. More recently, Pranovich et al. [9] proposed printing collections of slabs with different thicknesses, measuring their sphere‑based reflectance and transmittance, and fitting analytic or Monte Carlo radiative‑transfer models to estimate scattering and absorption coefficients for appearance prediction of 3D‑printed parts. Abu Rmaileh et al. [8] extended this idea by modelling the light paths inside a commercial reflectance/transmittance spectrophotometer via Monte Carlo simulation and training machine‑learning models to invert measured R/T spectra to absorption, scattering, phase function, and refractive index of printing materials, demonstrating agreement with independent laboratory‑grade measurements.

Taken together, these strands of research suggest both an opportunity and a need. On the one hand, FDM studies show that process parameters can be tuned to achieve specific levels of luminous transmittance and scattering in translucent parts [1-3]. On the other hand, integrating‑sphere metrology and appearance modeling provides the tools to rigorously quantify total transmittance, diffuse/regular components, and even intrinsic optical coefficients in translucent polymers [4-10]. Yet there is, to date, no unified, FDM‑specific framework that adapts sphere‑based standards, bench design, and inversion methodologies to the particular microstructural realities of FDM‑printed translucent components.

In recent years, additive manufacturing (3D printing) has seen a marked increase in its use for the rapid and straightforward production of functional prototypes. The manufacturing process is distinguished by the wide array of materials used, as well as their specific properties and characteristics. A significant corpus of scientific studies is dedicated to the mechanical and geometric properties of the materials utilised in this production, as well as to the technological factors influencing the production process. However, research on the light transmittance of semi-transparent materials for additive printing remains scarce. The purpose of this article is to present a designed and manufactured stand for measuring the permeability of translucent materials used in additive manufacturing. The design of the test stand arose from the idea of researching translucent materials and their potential applications in various industries (automotive manufacturing, advertising, and lighting fixture production). The low cost of additive manufacturing and the availability of components (sensors, microcontrollers, and other parts) made it possible to build the stand shown here. The test samples and their holders are manufactured according to the needs of the research.

ASTM D1003 is a standard method for measuring the light transmittance of plastics. Typically, open-type measuring instruments are used for this method (ASTM, 2019). ISO 13468 is a standard for measuring total light transmittance in the visible spectrum. The proposed stand utilises the measurement concept outlined in these standards; however, it has been designed as a closed-type system, thereby eliminating the influence of external light noise. A laboratory stand is developed using additive printing technology based on the materials and methods presented in Figure 10. The basic principles presented in Figure 1 are followed during its construction. A special holder is created for each sample size, ensuring precise positioning between the light source, sample, and light sensor.

Figure 10. The stand in a laboratory environment

The stand comprises: (1) a base; (2) a light‑sensor cover with a concealed sensor; (3) a holder for the test specimen; (4) a movable cover for enclosing the specimen during measurement; (5) a cooler assembly with an integrated light source; (6) temperature sensors; (7) a cooling fan for the light source; and (8) auxiliary holders and accessories.

The stand is controlled by an ESP32 controller. Measuring modules for optical and electrical quantities, temperature sensors, and PWM control modules are interfaced with the controller. The electronic components of the stand are operated and measurement data is collected through a program code developed specifically for this purpose in the Arduino IDE environment. Additionally, the automated acquisition reduces operator‑dependent variability and enhances the reproducibility of measurements [27]. The measurement workflow follows the block diagram shown in Figure 11.

Figure 11. Measurement procedure block scheme

Figure 12. Normal distribution plot, 200 lx

The process begins with booting the system and loading the main software and the necessary libraries for the peripheral modules. Then, while monitoring and controlling the operating temperature of the source and the electrical parameters, the procedure for measuring and calibrating the stand begins. Calibration is performed with no test sample in the stand. The calibration steps are repeated each time the sample or the light intensity received from the source changes. The light source intensity is controlled by monitoring the electrical parameters. Once the calibration process is complete and the measured values are stable, the transmittance of the samples under investigation can be measured. The selected test detail is placed in the holder (Figure 12) and then in the stand. The movable cover is closed, and the measurement procedure (Figure 11) is performed. The obtained data is entered into tables, and the results are presented graphically. Due to the specificity and short duration of the measurement, multiple measurements are performed. The measurement data is checked for compliance with the normal distribution law using the Anderson–Darling (AD) test, the Shapiro–Wilk test, or another similar method. A test for gross errors (Grubbs' test) is also performed. If the data follow the normal distribution law and there are no gross errors, the transmittance and light attenuation are calculated according to the test sample. Transmittance is calculated as the difference between the illuminance during calibration and the illuminance obtained from the measurement with the test sample in place, as shown in Eq. (1). The unit of measurement used for transmittance is lux (lx).

$\Delta T=T_c-T_m$     (1)

where,

∆T: Transmittance difference;

T_c: calibration Transmittance;

T_m: measured transmittance with a test element in place.

Attenuation is calculated as the ratio between transmittance and calibration value, with the results expressed as a percentage (%).

$\delta_{l a}=\frac{\Delta E}{E c} \cdot 100 \%$    (2)

where,

δ_la: light attenuation;

∆E: transmittance;

E_c: calibration illuminance.

To validate the stand and demonstrate its capabilities, data from measurements of samples with thicknesses of 1 mm, 1.5 mm, 2 mm, 2.5 mm, 3 mm and 3.5 mm are presented. All test samples are produced using the same printing parameters; only the thickness of the sample varies. Tests are performed on test samples of the aforementioned thicknesses at calibration illuminance levels ranging from 200 lx to 10,600 lx in increments of 800 lx. Due to the large volume of data, only the results at the following calibration illuminance levels are presented: 200 lx, 2,600 lx, 6,600 lx and 10,600 lx. Table 2 shows the results of measuring samples with thicknesses of 1 mm and 1.5 mm at 200 lx, with 30 measurements taken for each sample. The values of voltage (V), current (A), and light (lx) are also indicated. During the measurements, the temperature sensors do not detect any change in the temperature of the light source. The measured temperature of the light source is 25 degrees. The standard deviation, repeatability error, and measurement uncertainty were calculated for the presented data (see Table 3).

Table 2. 1 mm and 1.5 mm light measurements data

Table 3. Statistical check

The results presented in Table 2 show insignificant changes in the voltage and current values, as well as identical light measurement values. Figure 12 shows the data distribution, as shown in the graph; all the data is grouped in a straight line. Based on these results, only the average values from the remaining measurements are shown, since the fluctuations in the data are similar. Table 4 shows the measurement data for all sample thicknesses at calibration light levels of 200 lx, 2,600 lx, 6,600 lx and 10,600 lx. Transmittance is calculated using Eq. (1).

Table 4. Light transmittance data of all tested objects

Table 5. Light attenuation

Table 5 shows the light attenuation calculated using Eq. (2).

The results obtained for light attenuation show very similar values (less than 2% difference) for each of the samples at different light intensities.

To make the results easier to understand, three graphs showing the relationship between attenuation and illuminance (Figure 13), illuminance and sample thickness (Figure 14), and illuminance and sample thickness (Figure 15) are presented.

Figure 13. Attenuation to illuminance

Figure 14. Illuminance to thickness

Figure 15. Attenuation to thickness

According to the obtained results, the transmittance of the sample decreases as its thickness increases. This condition is valid for all the presented measurement conditions. The attenuation percentage is independent of illuminance. As shown in Figure 13, the relationship between attenuation and illuminance is linear. The differences in attenuation values at various light levels are minimal, never exceeding 2%. This indicates that lighting has little impact on attenuation percentages. This confirms that the material being measured exhibits stable optical properties within the considered light range. Figure 14 shows the relationship between illuminance and the thickness of the test samples. A step change in the relationship between thickness and detail is observed at 1.5 mm. After a sample thickness of 2 mm, the relationship becomes linear. At the lowest illuminance, the step is least pronounced; as the illuminance increases, however, this relationship becomes increasingly pronounced. The occurrence of this specific zone can be attributed to the attainment of a critical thickness, at which the internal structure of the material begins to exert a more substantial influence on the propagation of light. This phenomenon warrants further in-depth research to establish this dependence. Figure 15 shows the attenuation with respect to the thickness of the details. It shows that attenuation depends strongly on the thickness of the test detail. The curves for different illuminances practically overlap, which once again confirms the hypothesis that attenuation is mainly a function of thickness rather than illuminance. Increasing the thickness of the material results in an increased optical path length, which consequently leads to higher losses due to absorption and scattering.

The authors would like to thank the Research and Development Sector at the Technical University of Sofia for the financial support.