## 1 Introduction  
In the United States, the average annual age-adjusted incidence rate of patients diagnosed with a tumor of the central nervous system (CNS) is 24 per 100,000 [1]. Particularly, infiltrative gliomas have a poor prognosis. Median survival ranges from about 8 to 15 months for glioblastoma multiforme (GBM) compared to 3 to 10 years for low-grade gliomas (LGG) [1, 2]. Maximizing the extent of resection while prioritizing neurological function in cytocrudective surgery is one of the most decisive prognostic factors and essential in the initial treatment of gliomas, meningiomas (MNG) and brain metastases (MET) [3, 4, 5, 6, 7, 8, 9]. Protoporphyrin IX (PpIX) fluorescence guidance was first established for intraoperative visualization of high-grade gliomas (HGG) [10,11] and was afterwards investigated in MNG [12] and MET [13], with promising results. Presurgical administration of the non-fluorescent precursor 5-aminolevulinic acid (5-ALA) leads to tumor-specific metabolization of PpIX [14]. Surgical microscopes can be equipped with optical filters to visualize the red fluorescence of PpIX and thereby detect tumorous tissue. Conventional PpIX-guided surgery, however, is limited for lower-grade gliomas or low concentrations of PpIX in tumor infiltrated brain, where endogenous tissue fluorescence and parts of the blue excitation light outweigh the PpIX fluorescence [3,15,16]. Particularly, the vast majority of pure LGG lack fluorescence during resection [3,16,17,18,19], and visible fluorescence in these tumors was mostly observed in anaplastic foci [17,20,21]. Phase fluorescence lifetime imaging in frequency-domain (FD-FLIM) has shown promise for delineating low PpIX concentrations from competing fluorophores due to differences in their respective decay dynamics [15,22,23,24,25,22]. As excited-state populations of PpIX have a slower depopulation rate (native lifetime \(\tau\approx 16.4\) ns [26]), PpIX accumulation in tissue entails increased fluorescence lifetimes with respect to the approximately 1 ns to 2 ns found in physiological brain parenchyma [15,24,25,27]. When PpIX fluorescence and tissue autofluorescence are on the same order of magnitude, the measured lifetime depends on the relative PpIX and autofluorescence signal contributions [15]. The average FD-FLIM phase lifetime \(\tau_{\phi}\) for \(i\) fluorophores contributing to a multiexponential decay is given by  
\[\tau_{\phi}=\frac{\sum\limits_{i}\alpha_{i}\tau_{i}^{2}/(1+(2\pi f_{mod})^{2} \tau_{i}^{2})}{\sum\limits_{i}\alpha_{i}\tau_{i}/(1+(2\pi f_{mod})^{2}\tau_{ i}^{2})}\,, \tag{1}\]  
with \(f_{mod}\) being the modulation frequency, \(\alpha_{i}\) the intensity contribution and \(\tau_{i}\) the fluorescence lifetime of each fluorophore \(i\)[28]. In contrast, the average fluorescence lifetime measured in time-domain is given by  
\[\tau=\frac{\sum\limits_{i}\alpha_{i}\tau_{i}^{2}}{\sum\limits_{i}\alpha_{i} \tau_{i}}\,. \tag{2}\]  
As a result, fluorophores with shorter lifetimes are weighted more strongly for frequency-domain measurements of the phase when compared to the average lifetime in time-domain FLIM [28]. For delineating weak concentrations of PpIX in tissue, it is therefore of particular interest to reduce autofluorescence contributions and maximize the PpIX signal within the detection band of the emission filter.  
In our previous work, we employed a detection band from 590 nm to 740 nm for capturing the tissues' fluorescence response [15,22,23,24,25]. We hypothesize that adjusting the spectral detection band to optimize the PpIX to autofluorescence ratio further increases the overall measured lifetime, thus enhancing the contrast to the autofluorescence background of physiological brain parenchyma. To substantiate our hypothesis, both FD-FLIM and spectroscopic fluorescence data were acquired ex vivo on a set of 130 brain tumor specimens. We then evaluated both FD-FLIM and combined time- and spectrally resolved fluorescence data to verify the adjustments made to the detection band.