# Line-Shaped Illumination: A Promising Configuration for a Flexible Two-Photon Microscopy Setup
## 3 Overview of Applications
### Two-Photon Spectral Measurements  
Several procedures have been devised for the measurement of TPA spectra. The technique exploiting the LSTPM setup belongs to the class of the so-called indirect methods [7,20]. The use of a line-shaped excitation light beam enables to obtain a high signal level, which is usually very difficult to obtain in two-photon fluorescence measurements ([PERSON]). Here, we recall the basic steps of the proposed technique, while details of TPA spectra measurements by LSTPM are listed and discussed in [13]. The nonlinear fluorescence emission is measured for different values of the excitation wavelength. The TPEF optical power, \(P_{F}(\lambda)\), as a function of the illumination wavelength, \(\lambda\), is given by [1,2]:  
\[P_{F}(\lambda)\propto\frac{\sigma(\lambda)}{\tau_{p}f_{p}}\left(\frac{\lambda }{hc}\right)^{2}l_{av}^{2} \tag{1}\]  
where \(\sigma(\lambda)\) is the TPA cross-section, \(\tau_{p}\) is the pulse duration, \(f_{p}\) is the laser repetition rate, \(NA\) is the numerical aperture of the optical system focusing the laser beam on the sample (e.g., a microscope objective), \(h\) is the Planck constant, \(c\) is the speed of light in the vacuum, while \(l_{av}=l_{av}(x,y)\) is the time-averaged illumination intensity distribution in the focal plane. If \(l_{F}=l_{F}\) (\(x,y\)) is the fluorescence intensity distribution in the sample and \(A\) is the fluorescing area, the fluorescence emission, \(P_{F}\), will be written as:  
\[P_{F}=\int_{A}I_{F}(x,y)dxdy \tag{2}\]  
Figure 4: Adapted from [13]. (**a**) Two-photon fluorescence emission generated by illumination lines at 765 (**A**) and 770 nm (**B**). (**b**) Two-photon fluorescence emission profile in \(y\) direction generated by 765 (**A**) and 770 nm (**B**) excitation wavelengths: measured intensity (blue crosses) and relative Gaussian fit (pink lines). In both panels, each pixel corresponds to 0.214 μm. Reproduced with permission from the authors, [PERSON]; published by Wiley, 2018. The use of the LSTPM in order to measure TPA spectra is based on the calculation of the fluorescence response, \(P_{F}=P_{F}\left(\lambda\right)\), as provided by Equation (2). In our approach, the fluorescence emission pattern \(I_{F}=I_{F}\) (\(x\), \(y\)) is detected by a CCD camera. \(P_{F}\) can then be retrieved from the geometry of the optical setup. Finally, \(\sigma(\lambda)\) is obtained, except for a numerical constant, so that a relative TPA spectrum is obtained. Great care has to be taken about the spectral behavior of the optical components of the setup in order to minimize errors arising from wavelength-dependent properties. The spectral response of each element has thus been systematically tested by means of an optical spectrum analyzer (Ando AQ-6315). The response has proven to be flat for the wavelength range of the measurements with an error of 0.5%. Actually, this technique has been validated with dyes whose TPA spectra are available in the literature, i.e., fluorescein isothiamate (FITC) and Alexa 488 [13; 14]. Comparisons between the spectra measured by LSTPM and those reported in the literature are shown in Figures 5 and 6, highlighting the very good performance of our novel technique in providing relative measurements. We note that this method has the advantage of the intrinsic high selectivity on the TPA signal, which is a specific feature of the fluorescence-exploiting techniques. Moreover, a line-shaped beam allows to excite a large volume of the specimen, thus generating a strong two-photon fluorescence signal, which does not require a photon counter device to be recorded. Therefore, we can conclude that this approach has the advantage of employing an  
Figure 5: Adapted from [13]. Comparison between the two-photon absorption spectrum of FITC dextran from measurements (blue curve) and from the literature (fuchsia curve). Reproduced with permission from the authors, J. Micros. : published by Wiley, 2018. Figure 6: Adapted from [14].