The measurement setup is shown in Fig. . An Infrared Systems IR-150/301 heat plate radiator (label A in Fig. ) was used for the SSE measurements. The unit features a 304.8mm×304.8mm flat black square emitting surface, with an emissivity of ϵ=0.96±0.02 over the wavelength of range 1 to 99µm. It operates from ambient temperature up to 500°C and exhibits a short-term temporal stability of ±0.1 °C and a long-term stability of ±0.2 °C, according to the manufacturer. Temperature regulation is achieved via a PID controller (label B in Fig. ). Further details are provided in the data sheet of . Individual circular apertures (label C in Fig. ) were used to vary the area of the observed radiant surface. For the discrete method, circular patterns were cut into stainless steel sheets of 2mm thickness. Stainless steel was chosen for its high thermal conductivity, which ensures a uniform temperature distribution on the camera-facing side. To minimize the reflection of ambient radiation, this side was coated with certified paint providing ϵ>0.9 in both the long-wavelength infrared (LWIR) and mid-wavelength infrared (MWIR) ranges. Further details are provided by . The radiator-facing side was left unpainted to reflect incident infrared radiation from the plate, thus slowing the heating of the aperture side observed by the camera. The holes were laser-cut to produce smooth burr-free circles and avoid the irregular conical patterns that conventional cutting tools can create for small-diameter apertures. An example aperture is shown in Fig. a. For the continuous method, an iris diaphragm (hereafter referred to as the iris), manufactured by and featuring 18 blue tempered spring steel leaves with a pin lever actuator, was securely mounted within a 3D-printed bracket. The bracket design provides a balance between the smooth insertion of the iris and sufficient stiffness to prevent movement while adjusting the aperture size. The iris, the aperture, and the 3D-printed bracket are shown in Fig. b. The aperture diameters and measurement distances were selected based on the area of the radiant heat source captured in the image, as determined by the camera optics. To enable comparison across different optical configurations, a relative diameter, ϕrel, was defined to normalize the aperture sizes in the image. For a thermogram of an arbitrary aperture with diameter ϕ in mm, ϕrel in percent is calculated as follows: 1ϕrel=ϕpx⋅100/Vres, where ϕpx is the circle diameter in px, and Vres is the image size in the vertical direction in px. The diameter of the circle in the image ϕpx was obtained using the function HoughCircles of the library OpenCV , version 4.11 . Normalization via Vres is adopted because, due to the sensor's landscape format and aspect ratio, it constitutes the primary constraint on spatial resolution. This approach facilitates not only the assessment of the SSE for different optical systems but also its compensation. Compensation methods, such as the one presented by , address subsequent applications in practical end-user scenarios for regions of the thermograms whose dimensions are entirely contained within the image. However, it is important to note that saturation of the SSE is independent of Vres and does not necessarily occur at ϕrel=100% (ϕpx=Vres). The SSE measurements were performed using an MWIR thermal imaging camera (see Table ), which was mounted on a sliding carriage (label D in Fig. ). The carriage moves along two parallel rails fixed to an optical bench, allowing the distance between the camera and the apertures to be adjusted for measurements under different optical configurations. A multi-axis platform (label E in Fig. ) was mounted on top of the carriage in a vertical configuration to hold the camera. The platform can be precisely adjusted along both horizontal and vertical axes with a resolution of 1µm, facilitating the accurate and repeatable centering of the aperture in the image. The ambient temperature and air humidity were measured during the measurements to monitor possible drift that could affect the results. Different camera configurations were not considered, as no dependency of the measurement method on the camera technology was expected. Therefore, the results presented in this paper should be generally applicable for evaluating the measurement of the SSE in infrared thermal imaging devices, when an iris diaphragm is used to vary the size of the radiant source.

The SSE measurement was performed by first setting a radiance temperature Tset on the controller and waiting for the surface temperature of the heat plate radiator to reach steady state. The thermal imaging camera was then focused on the edge of the circular apertures, and non-uniformity correction (NUC) was performed before measuring each optical configuration.

The SSE was measured using both approaches – continuous and discrete – employing a telescopic lens at Tset=120°C and a normal lens at Tset=200°C, respectively. The results are shown in Fig. . For the optical configurations considered, the curves obtained from both measurement approaches exhibit a similar monotonically increasing behavior. The measured deviation Δθ is nearly identical across the entire range of ϕrel, resulting in an almost complete overlap of the curves in each case. These observations indicate that both approaches reproduce the SSE to the same extent.

The main differences between the two methods lie in the number of sampled points on the curve, the measurement time, and the disk space required to store the data retrieved by the camera software. A summary of these three aspects is presented in Table . The curve resolution is markedly higher when the SSE is measured using the continuous approach, which makes it possible to detect the irregularity in the discrete-method curve at ϕrel ≈ 25 % (see Fig. a). At this location, the discrete data point is displaced, possibly due to temperature drift of the heat plate radiator – an effect related to the radiator's long-term stability. The continuous approach is less affected by this, since the range of aperture diameters to be measured is covered significantly faster than in the discrete approach (see Table ). The closely spaced sampling of the continuous method clearly reveals the true progression of Δθ in this region, which aligns with the trend obtained when the outlying point in the orange curve is disregarded and agrees with the proportional relationship in this region reported by other authors . The difference of Δθ at the smallest aperture in Fig. b between both approaches could also be attributed to side effects, such as the temporal stability of the heat plate radiator or small differences in camera focus. These effects are more pronounced for small object sizes due to the resulting reduction in modulation at high spatial frequencies . The improved sampling observed with the continuous approach allows for a clearer depiction of the actual progression curve in the range where the response is not proportional. Regarding storage requirements, the disk space needed is significantly larger for the continuous approach as a natural consequence of saving a greater number of thermograms.

As stated earlier, the rate at which the image diameter changes in the thermogram sequence depends on both the iris-driving period Tiris and the camera frame rate f. To evaluate the influence of these parameters, a parametric study was carried out. The SSE was measured with the telescopic lens and the close-up lens at Tset=275°C. The camera was operated at its maximum frame rate, fmax=339Hz, and the corresponding integration time for the selected measuring range was tint=28µs. The iris was driven with three different periods, approximately Tiris = {2, 5, 10} s, corresponding to a full close-and-reopen cycle (see Fig. ). These values serve as references and are not exact since the iris adjustments were performed manually.

For the case with the highest iris dynamics (Tiris = 2s), the temporal change rate of the radius, Δtpx, during the transit time ttr between the two limits can be approximated as Δtpx=ttrΔrpx=1/2τiris1/2Δϕpx=1/2⋅2s1/2440–36px=4.95mspx-1. Since tint is significantly lower than Δtpx, each frame in the datasets collected for this experiment can be considered discrete and unaffected by blur.

The results reveal that the continuous approach captures the reduction in image contrast caused by optical limitations , as can be observed in Fig. . The difference between the minimum and maximum values of θ is linked to this phenomenon and decreases down to a value of ϕrel set by the modulation transfer function (MTF) of the optical system. The reproducibility of this measurement approach is demonstrated by these results, as the relationship between the measured temperature and the aperture diameter remains practically the same under varying conditions, across the entire range of the SSE curve. If the measurements are performed during the period in which thermal equilibrium is maintained, the SSE measurement is not significantly affected by systematic errors. For 0%<ϕrel≤2%, the ROI is comparable to the iris-aperture diameter in the image, implying that the calculated θ may include pixels from the transition zone between the hot plate and the aperture. Pixels in this zone are strongly affected by the limited optical performance at high spatial frequencies.

To further assess the effect of the camera frame rate, the SSE measurements were downsampled to create new datasets. For each Tiris, a downsampled dataset was constructed by selecting thermograms Mi at the following indices: {i⋅k∣i=0,1,2,…,Ntotal}, where Ntotal is the total number of frames in the original sequence, i is the frame index, and k is an integer defining the sampling interval. This yields an effective downsampled frame rate fsi: 3fsi=1Nsi∑is=2Nsi1tis-tis-1Hz. Nsi denotes the size of each downsampled dataset, and tis is the timestamp of each sampled thermogram, as originally recorded by the camera. In this study, the sampling steps k={2,5,9,16} were used, corresponding to fsi={169,69,38,21}Hz. These values of k ensure that the constructed subsets comprise frames sampled at different positions in the original sequence. As a result, the overlap between subsets is minimized, which in turn reduces the correlation between them. The new subsets were not filtered with a low-pass anti-aliasing filter in either the temporal or spatial domain. When the subsets were created, the frame size was not reduced, and each frame was acquired independently; therefore, their temporal characteristics remain unaltered. Figure  shows the frames sampled for SSE evaluation along Φsample, for the considered iris-driving periods Tiris and downsampled frame rates fsi. The reference number of frames, Nframes=50 (from the discrete approach), is rarely achieved; in most cases, the number of sampled frames is an order of magnitude lower. Additionally, the number of relative diameters in Φsample for which only a single frame was sampled increases as fsi and Tiris decrease. This is significant, since diameter measurements based on a single frame are insufficient for monitoring temporal noise in the measured values.

The standard deviation of θ, calculated over the sampled frames, is shown in Fig. . It can be observed that the temporal noise of θ, with Nframes=50, is similar to that obtained from thermograms of varying sizes acquired at different points in time. This suggests that, for both the discrete and continuous approaches, the temporal noise affecting the SSE measurement is comparable and primarily associated with common factors, such as the intrinsic temporal noise of the camera. It also indicates that the iris-driving period Tiris and the camera frame rate f have little influence on the temporal stability of the measurement. Consequently, both approaches can accurately reproduce the SSE, provided that the thermogram sequence is acquired during a period of thermal equilibrium.

The calculated temperature deviations Δθ for the considered iris-driving periods are shown in Fig. . Three representative values of k were analyzed, corresponding to the maximum camera frame rate, half of that rate, and a value representative of what other cameras on the market can achieve (k=1,2, and 16). In all cases, the SSE is reproduced comparably, and features of the curve, such as the change in slope between ϕrel=10% and ϕrel=15%, can be identified. It can be observed that, as the iris-driving period increases, the number of sampled measurement points across the considered ϕrel range also increases; conversely, decreasing Tiris results in fewer sampled points. Even though sparse sampling can be locally compensated by defining additional measurement points in Φsample (50%≤ϕrel≤70%), the general trend of the SSE within this range is already apparent in the results.

The measurement of the SSE is influenced by not only temporal effects arising from the experimental setup but also the optical configuration of the camera. This is the case of certain absorptive neutral density filters, which regulate the amount of irradiance reaching the detector to enable measurements at higher temperatures. In the present study, the SSE was measured using the telescopic lens with an absorption filter at Tset=500°C. Figure a shows the temporal evolution of the measured temperature within the ROI θ. It can be observed that while the change in diameter ϕrel appears approximately periodic, the measured temperature does not exhibit the same cyclic symmetry. Instead, θ displays a non-stationary baseline that shifts for the consecutive cycle. Figure c presents the distribution of Δθ as a function of ϕrel, revealing a non-closing hysteresis loop. The progression of the curves shows that the path followed during the opening of the iris does not coincide with the return path during its closure. Furthermore, the first cycle concludes at a temperature value lower than the initial state, resulting in an open-loop behavior with a residual Δθ offset. This indicates that the measured signal is coupled with the temporal history of the aperture adjustment, suggesting a thermal loading effect inherent to the absorptive optical configuration. The results in Fig. b confirm that this absorption-induced drift is reflected in the digital signal (DV) before any software post-processing, localizing the phenomenon within the optical path.

The above results raise the question of whether the SSE should be treated as a dynamic phenomenon. However, it is important to differentiate between the physical nature of the SSE, which remains an inherently static opto-geometric effect, from its experimental characterization, which in this case is intertwined with the thermal dynamics of the filter. The measurement incorporates a temporal component that ideally should converge to a steady state to isolate the true SSE. Achieving such stabilization is challenging in practice, as SSE measurements are often constrained by surface temperature perturbations of the heat plate radiator when apertures are placed in front of it for extended periods. Consequently, under these experimental conditions, the recorded response manifests as a dynamic process with a transient component. Practical aspects such as how the SSE manifests in scenarios outside the laboratory, for example when measuring a hot spot at radiance temperatures where such filters are required, how it can be accounted for in the uncertainty budget, and how the SSE can be compensated for will be addressed in future work.