## 1 Introduction  
Accurate photometric measurements require the calibration of photometric meters. According to [1], for this procedure, a light source characterized by the spectrum of an CIE illuminant A is required, which is a blackbody radiator at a temperature of 2856 K. Incandescent illuminants provide predictable spectral output, stable if correctly supplied, but are inefficient and have limited spectral capabilities [2]. The rapid advancement of LEDs in optical power and wavelength range makes LED-based spectrally tunable light sources (LSTLSs) promising for replicating an approximate illuminant A spectrum [3], addressing challenges from the discontinuation of incandescent standard lamps. Recently, multi-emitter LED systems have become a compelling retrofit solution for traditional light sources, offering enhanced performance, energy efficiency, and, most of all, spectral tunability with stable and adjustable light levels [4; 5; 6]. A unique feature of LED technology is the modulation of their emission by forward current [7] and junction temperature [8]. Careful thermal consideration is required regardless of how it is perceived--as an advantage or disadvantage. Researchers have explored LSTLSs as a potential calibration alternative since the early 2000s [9; 10; 11; 12]. The main benefit of an LSTLS is its ability to generate different spectral power distributions (SPDs) and illuminances with a single system, eliminating the need to exchange the light source or add optical filters [13; 14]. Initially, LSTLs utilized multiple LEDs within specific wavelength bands, primarily limited to the visible range [15]. Further, the advancements in LED technology have enabled high-power LEDs to emit sufficient optical power across broader wavelengths, including ultraviolet and infrared regions, which is especially useful for testing photovoltaic modules [16]. The goal of research on LSTLSs has always been to accurately reproduce various SPDs, particularly CIE standard illuminants, with high flexibility and luminous efficacy [6; 15]. Current research efforts primarily focus on increasing the number of channels (wavelengths of LEDs) and the number of emitters in each channel to extend emission ranges and enhance the precision and speed of spectral matching through advanced algorithms [15]. Although several papers have focused on the spectral matching of CIE illuminants for various applications, for example, calibration of illuminance meters [9], colorimetry [11; 12; 13; 15], testing photovoltaic modules [16; 17], calibration of optical sensors [18], general lighting [19; 20; 21], vision research [22], textile industry [23], or medical illumination and imaging [6; 24; 25], only a few have addressed selecting the optimal set of LEDs for simulations [17; 26; 27]. This is crucial because, with a few dozen LEDs available from manufacturers, there are many possible combinations for adjusting their performance. The National Institute of Standards and Technology (NIST) and Philips [27] have developed an LSTLS luminaire for general lighting that utilizes 22 different LED wavelengths (channels) and provides nearly 100,000 lumens, generating a comprehensive range of CIE daylight sources and other SPDs. [PERSON] et al. [13] proposed a 35-LED channel LSTLS and integrating sphere (30 cm diameter). They used a spectral matching algorithm with an iterative convergence procedure based on partial derivatives. To evaluate the quality of the obtained SPD, the ratio of the integrated absolute difference between test and target source distributions to the integrated target source distribution (standard illuminants) was applied. [PERSON] et al. [22] used a minimization algorithm to avoid lengthy convergence procedures, allowing each LED's linear and repeatable luminance adjustment. Their system included a one-meter integrating sphere and six spectrally programmable light sources, though the number of spectral channels was insufficient for precise matches to real illuminants.