# Spectra Prediction for WLEDs with High TLCI
## 1 Introduction  
In recent years, white light-emitting diodes (WLEDs) have been increasingly used in lighting environments to shoot films and television due to them having a long service time, good reliability, vibration resistance, environmental protection, small size, bright color, fast response, etc. [1; 2; 3; 4; 5]. One of the essential properties of a light source is color rendering. There are various metrics to quantify the color rendering performance of light sources, such as the color rendering index (CRI) [6], color quality scale (CQS) [7], fidelity index (Rf), gamut index (Rg) [8], etc. However, even if the measured values are very good, the abovementioned evaluation system cannot fully reflect the true colors of image materials due to the mismatch between the spectral component and the color characteristics of the camera's photosensitive chip when one is evaluating the color rendering of light sources used to shoot films and television. The minimum requirements for the color rendering of light sources to shoot films and television are that the grey scale must appear grey, and the actors' skin color must be reproduced correctly. In addition, consistency is also important [9]. Although color rendering deviations can be moderately corrected through post-grading, it usually consumes a lot of time and money, and the results are often unsatisfactory. To this end, many scholars have studied whether the light source can accurately reproduce color in films and television [10; 11], and they aim to constantly improve the color rendering index calculation. In November 2011, Mr. [PERSON], an engineer and optical expert of the British Broadcasting Corporation (BBC) and the European Broadcasting Union (EBU), proposed the television lighting consistency index (TLCI) [12]. The TLCI cannot only correctly represent the human eye's perception of light color but also the camera's reception of light color and color restoration [13]. The TLCI mimics a television camera and display using specific features that affect color performance [13], with the only input condition being the spectral power distribution of the luminaire. Therefore, accurately predicting the spectrumis crucial for designing WLEDs with a high TLCI, and until recently, no general design method other than trial and error has been used. Traditional phosphor-converted LEDs use yellow phosphors to convert the blue light emitted by the chip into yellow light to obtain white light. White light with various correlated color temperatures (CCTs) can be obtained by adjusting the proportion of phosphor [14; 15; 16; 17]. However, these packages have a poor CRI and have subsequently been improved upon by using a variety of phosphors with different emission spectra [18; 19; 20], which makes the prediction of the LED spectrum more difficult. [PERSON] et al. [21] experimentally measured the excitation spectra of seven red phosphors and the emission spectra of two green phosphors and selected two green phosphors and one red phosphor with less resorption than that of the two phosphors. Then, the LEDs were optimized by measuring the luminescence spectra of LED chips coated with different mass ratios of phosphors, reducing the trade-off between luminous efficiency and the color rendering index. Although experiments can achieve satisfactory results, the experiments often require a lot of time and effort, and environmental interference cannot be eliminated. [PERSON] et al. [22] proposed different models to predict the spectrum of a WLED with multiple phosphors, but [PERSON] et al. [23] considered that the excitation spectrum of one phosphor overlaps with the emission spectra of other phosphors in LEDs with multiple phosphors, and the final spectrum could not be estimated by superimposing the emission spectra of phosphors. They successfully predicted the emission spectrum of WLEDs with multiple phosphors by considering the mixing weight ratio of the phosphors, reabsorption, and re-emission.