## 1 Introduction  
Freeze-drying is a highly appropriate methodology for drying thermally labile products and matrices. Due to its relatively high operational cost, it is mainly used for drying products with high intrinsic values such as pharmaceutical products, e.g., drugs, proteins and vaccines, as well as food commodities [1, 2]. For monitoring the product's temperature during a freeze-drying cycle, a few probes are in most cases directly placed in the materials undergoing drying. The types of probes used in this work were a Pt100 sensor to measure temperature and a LyoRX sensor to measure resistivity _and temperature_ in the material (integral parts of the freeze-drying instrument) [3]. Pt100 sensors are resistance thermometers that normally have a resistance of 100 ohm at 0 \({}^{\circ}\)C, whereas the LyoRX measures resistance between two pin-electrodes (The LyoRX is a brand name of [PERSON], Osterode, Germany). This is the main feature of this sensor, although it also incorporates a Pt100 sensor to measure temperature. A value of 100% resistivity is indicative of a frozen material in which no current can flow between the pins. The direct contact between the probes and the material has certain drawbacks. First, it is a single-point measurement, and second, the presence of the probe itself affects the drying process [4]. In two previous articles from 2014 and 2022, [PERSON] et al. described the coupling of an IR camera to a freeze-dryer, thereby measuring the product temperature contact-free and with superior spatial resolution [5, 6]. The work from 2014 described the first application of this kind [5]. Additional papers were subsequently published by other authors, who also made use of infrared cameras to monitoring the freeze-drying processes using a variety of configurations of IR cameras and freeze-dryers. For example, some of the reports described operating the IR camera inside the freeze-drying chamber and others reported measuring directly onto glass surfaces that are not transparent to IR radiation [7; 8; 9; 10; 11; 12; 13; 14]. The first two publications by [PERSON] made use of an IR camera with a microbolometer limited to 320 \(\times\) 240 pixels and a 25 mm wide-angle lens that covered a field of view of approximately 30 \(\times\) 40 cm, which corresponds to the size of a freeze-drying trap [5; 6]. The references [5; 6] contain detailed schematics of the experimental setup used in this work. The second article from 2022 specifically addressed a shortcoming of the first work, namely, that only the surface temperature could be monitored. The new development allowed monitoring along depth profiles (e.g., a side view) using custom-made cuvettes with a Ge-window [6]. Limitations of the spatial resolution of the IR camera's sensor and its lens were nonetheless apparent as only 84 pixels could be used for monitoring the side and 64 pixels for monitoring the surface view of the cuvettes. Despite its relatively low spatial resolution, it is still superior to the Pt-100 probes, which provide only one measurement point that, additionally, is not contact-free. [PERSON] and [PERSON] established a long time ago that the presence of probes in the material increases the ice-nucleation temperature as well as the primary drying speed. Vials with probes consequently finished primary drying earlier than similar vials without probes [4]. Other contact-free approaches have been reported; for instance, [PERSON] et al. published a paper about the monitoring of temperature along depth profiles whereby strips with five sensing elements were attached on the outside of glass vials during freeze-drying [15]. However, when using this approach, the temperature readouts are compromised by an averaged temperature as the temperature is measured on the outside of the glass vials. This effect also prevails when IR cameras are used for measurements of temperature on the outside of glass vials, although IR-thermography clearly provides superior spatial resolution [8].