To observe the details of thick volumetric specimens with high-spatial resolution and image contrast, background rejection capability is significantly important because thick samples produce strong out-of-focus fluorescence signals. For the evaluation of the depth discrimination properties in SAX microscopy, we estimated the optical transfer functions (OTFs) with different pinhole sizes and compared them with those used in typical confocal microscopy. The effective point-spread function (PSF) of confocal microscopy is given by multiplying the excitation PSF with the detection PSF.43 When the same objective lens is used for both excitation and fluorescence detection, the detection PSF is given by the 2-D convolution of the excitation PSF and the pinhole aperture function, if the wavelength of the fluorescence is similar to the wavelength of the excitation.44 The effective PSF for SAX microscopy is also given by the product of the detection and the excitation PSF, which can be estimated as the spatial distribution of the fluorescence signal that is detectable after harmonic demodulation.39,45 Equations (1) and (2) show the effective PSFs for typical confocal microscopy and for SAX microscopy with the ’th harmonic demodulation . Display Formula
(2)where and denote the excitation PSFs for confocal and SAX microscopies, respectively. In addition, and are the detection PSF and the aperture function for a detection pinhole, respectively. The OTFs were calculated by applying Fourier transforms to the effective PSFs. Figure 1 shows the OTFs of the axial frequency calculated for different pinhole sizes that correspond to 0.17, 0.25, 0.5, 0.83, and 1.66 Airy units at the pinhole. We assumed that Rhodamine 6G was excited at 532 nm through an objective lens with an numerical aperture (NA) of 1.49. For SAX microscopy, the frequency of the excitation modulation was assumed to be 10 kHz, and the fluorescence signal was demodulated at the second- and fourth-harmonic frequencies.