Multimode fibers have recently been demonstrated to be a promising candidate for ultrathin and high resolution endoscopy. However, this method does not offer depth discrimination for fluorescence imaging and the numerical aperture of the fiber limits its resolution. In this paper we demonstrate optical sectioning and enhanced resolution using saturated excitation and temporal modulation. Using a continuous wave laser excitation, we demonstrate improved resolution in all three dimensions and increased image contrast by rejecting out of focus light.
© 2015 Optical Society of America
Optical scanning microscopy is an important tool in biology and other sciences. Unfortunately, scattering materials, such as biological tissue, deteriorate the focusing capability of an optical scanning imaging system as well as the collection of the generated signal (i.e. fluorescence), which restricts the imaging depth. Various techniques have recently been investigated to focus light [1–7] and image through scattering media [8–10], but the depth limit remains a few mm at best. An alternative to these techniques is fiber-based endoscopy, bypassing the scatterer altogether. Fiber-based endoscopes are typically constructed with fiber bundles. Alternatively, they consist of a single-mode fiber (SMF), a lens, and an actuation system to scan a focused spot. The number of pixels of the images obtained with the fiber bundle approach is generally limited by the number of fibers in the bundle and the resolution tends to be poor. The single mode fiber approach can have higher resolution but at the cost of an actuation housing at the distal end [11,12].
Multimode fibers (MMFs) have been recently investigated as a potential solution for high performance endoscopes [13–16]. The MMF yields higher resolution imaging compared to the fiber bundle due to the very dense information that can be transmitted by the modes into the small cross section of its core. Never-the-less, the resolution of the MMF image is limited by the relatively small numerical aperture of the fiber (NA typically between 0.2 and 0.5) [16,17]. The numerical aperture of the multimode fiber endoscope system can be increased by using a thin layer of scattering material [18,19] or with micro-fabricated optics  in front of the fiber.
To discriminate structural features in a thick sample, the ability to reject out of focus light is also important. Fiber-based endoscopic sectioning has been obtained by implementing multi-photon imaging using scanning endoscopes  and fiber bundles . Lensless, digital scanning two-photon endoscopy was also demonstrated with thin, custom-made bundles [23,24]. The images in ref . and  had a limited field of view (FOV) of about 50 μm and the imaging plane was 500 μm away from the fiber facet, which reduced the collection efficiency. Endoscopic sectioning can also be obtained by implementing confocal filtering. Confocal microendoscopy using a fiber bundle was demonstrated in 1996 . In the case of coherent imaging through MMFs, it has recently been demonstrated that modal scrambling can be compensated. A virtual pinhole was applied to obtain a digital confocal endoscope . This method relies on the coherence of light, and thus cannot be used in fluorescence endoscopy.
Multi-photon excitation is widely used in microscopy to obtain depth sectioning. Multi-photon excitation is difficult with MMFs since the focusing of femtosecond pulses through MMFs requires modal and chromatic dispersion compensation as demonstrated recently . In this paper, we use saturated excitation (SAX)  a nonlinear method used for high resolution microscopy and we harness it to imaging through MMF. As in two-photon microscopy, the nonlinearity of the fluorescence response induced by SAX improves spatial resolution and introduces optical sectioning [28–30]. Furthermore, SAX is well matched to MMF imaging since it uses a continuous wave (CW) laser with narrowband temporal modulation instead of femtosecond pulses, thereby bypassing the problem of modal and chromatic dispersion. Hence, using fluorescence saturation with CW excitation, we demonstrate ultrathin endoscopic imaging with an improved resolution compared to linear imaging. We also demonstrate that the depth discrimination provided by SAX can improve the contrast of thick sample images.
This paragraph aims at recalling the principle of resolution improvement and depth discrimination in SAX imaging. We also show that the geometry of MMF endoscopy by phase conjugation is compatible with SAX. In this paper, we record fluorescence scanning image through a MMF. The fluorescence collected is integrated at every scanning position, so, at low power, the effective intensity point spread function (PSFfiber) is equal to the illumination intensity point spread function (PSFexc):
At higher excitation intensity, saturated excitation of fluorescence molecules induces a nonlinear relationship between illumination and fluorescence intensities. By sinusoidally modulating the excitation intensity and demodulating the fluorescence signal, the harmonics created by fluorescence saturation can be isolated. The fluorescence signal obtained by demodulation at the nth harmonic frequency is proportional to the nth power of the excitation intensity (at the condition that the illumination intensity is low enough in order to not saturate the nth harmonic) [28–31]:Fig. 1a, the effective excitation point spread function (PSFfiber,SAX) is sharpened at the region around the peak where the saturation is maximum. The resolution of the contribution proportional to the nth power of the excitation intensity improves the linear imaging resolution by a factor of √n [28,29].
Extracting the nonlinear fluorescence signal also provides depth discrimination . This can be visualized by calculating the signal emitted as a fluorescent plane is scanned axially through the PSF (Fig. 1b). Because of energy conservation, in the linear case (blue plot on Fig. 1b), the signal is constant as a function of the axial position, illustrating the absence of sectioning. In contrast to the linear case, the integrated intensity of the SAX demodulated signal exhibits a peak in the focal plane (red and green plots in Fig. 1b). This is the origin of optical sectioning capability with SAX. In consequence, demodulated saturated fluorescence signal can be recorded to obtain both improvement in resolution and optical sectioning. We detail in the next section how we implemented it for MMF endoscopic imaging.
3. Experimental setup
The schematic diagram of our experimental apparatus is shown in Fig. 2. It is a modified version of the one presented previously by Papadopoulos et al. . The focused spot produced by the multimode fiber is obtained by digital phase conjugation of the field recorded previously on the opposite side with the off-axis holographic setup. The sample is scanned to produce a fluorescence image. The light is modulated sinusoidally in time. At low excitation level, the fluorescence response depends linearly on the excitation. When the excitation intensity increases, the fluorescence response saturates and modifies the temporal response of the fluorophores. This leads to the formation of harmonics of the carrier frequency.
In the experiment the beam was sinusoidally modulated in time at ω = 2 kHz with an acousto-optic modulator (AOM). The AOM is placed at the very beginning of the setup so that the induced Doppler shift does not affect the hologram acquisition. To detect the saturated contribution, it is critical that the excitation modulation is a perfect sinusoid in order not to induce any signal at the harmonics frequency. To do so, we calibrated the acousto-optic modulator response and drove it with a radio frequency generator able to envelop the 80 MHz sound wave with an arbitrary kHz modulation (AFG 3102C, Tektronix). A substantial intensity (about 100 kW/cm2) is necessary to obtain fluorescence saturation (See Appendix A), so a high power source (Verdi-V10, Coherent) is used and the losses are minimized. The phase only spatial light modulator is placed in the image plane of the facet of the fiber, but on a different optical path than the one used to record the hologram. This separation avoids the 75% loss of light induced by the (50/50) beam splitter in the previous arrangement . Two (90/10) beam splitters are used to maximize the light sent onto the SLM which is used during the scan. The possibility of digitally scanning the beam by using a set of saved patterns has been demonstrated elsewhere [14,16]. Here we keep a single phase conjugated excitation spot and we scan the sample with a piezoelectric stage. For each scanning position, the temporal response is recorded during 20 ms. The time trace for each scanning position is saved and by taking the Fourier transform, the value of the harmonics for each pixel is extracted off-line on a computer. By averaging over several periods, the narrow band harmonic signals buried into the noise (spread over a wider spectrum) can be recovered.
We use fluorescent nanodiamonds (120 nm diameter) as imaging probe . They contain nitrogen vacancies defects that exhibit fluorescence that peaks at 670 nm and do not bleach even under high excitation intensity.
In order to characterize the improvement in resolution given by this technique we recorded the PSF by scanning a single nanodiamond into the focused spot produced by the fiber with different excitation intensities.
It can be observed in Fig. 3 that both the lateral and axial FWHM decrease with higher harmonics demodulation. We measured the linear lateral FWHM to be 850 nm (the diffraction limit is 700nm for a 0.39 NA fiber). From the profiles on Fig. 3(d) and 3(e), the gain both in lateral and axial resolution is estimated to be about 1.6 with the third harmonic demodulation, close to the theoretical √3 expectation. The images and the plots on Fig. 3 are normalized. The higher harmonic frequency components have a signal intensity one to two orders of magnitude lower than the fundamental frequency component and the background that appears on the Fig. 3(c) is due to shot noise (see Appendix A).
In Fig. 4, we illustrate the gain in resolving power due to SAX by imaging clusters of nanodiamonds immobilized on a glass slide. The fluorescent nanodiamonds were observed by extracting the third harmonic component. Comparison of the image formed at low light power at the fundamental frequency with the SAX image, confirms the improvement of the spatial resolution in SAX microscopy. Some details (arrows on Fig. 4) of the nanocrystals assembly, invisible with linear imaging are resolved in the demodulated image. The resolution for the third harmonic is about 500 nm and it opens the path for micro-structure observation with MMFs.
As shown in Eq. (2) and Fig. 1b, SAX also achieves significant suppression of out-of-focus light in a similar manner as two-photon fluorescence microscopy . Measuring the axial edge response [31,32] of our system confirms this depth-discrimination property (Appendix B). Figure 5(a) shows axial edge response which is the fluorescence signal collected from a thick dye layer (Rhodamine 6G) while it is scanned along the optical axis. The linear response (blue plot) shows the absence of sectioning in the system but the demodulated signal (green plot) at the second harmonic exhibits the edge transition when the focus is entering the dye layer.
For a given fluorophore, the illumination wavelength is shorter in SAX (by a factor of 2 roughly) than in two photon excitation imaging. As a result the excitation PSF is narrower because of the shorter wavelength. Correspondingly, the light used to form the image comes from a thinner section when we extract the second harmonic of the modulation in SAX. Furthermore the sectioning performance is not altered by the Stokes shift (Appendix B). It can be observed on the curve of Fig. 5(a), that the slope of the transition with second harmonic demodulation is similar to the one given in a confocal microscope with a 0.4 NA objective and an infinitely small pinhole. However, the out of focus light rejection mechanism takes place in the digital domain and as we will detail in the discussion section is bound to the available SNR.
We demonstrated that the image contrast can be improved with this method by scanning a sample composed of two layers of nanodiamonds separated by 30μm. Background fluorescence light is generated by the out of focus layer but is not saturated. It can be observed on Fig. 5(b) and 4(c) that the background light is filtered out in the second harmonic demodulated signal and that the contrast of the image is improved. As with the edge response measurement, only the second harmonic demodulation could be recorded.
We have demonstrated that saturated excitation in MMF scanning fluorescence microscopy can lead to resolution increase in all three dimensions. We measured an improvement in resolution by a factor of 1.6, which is close to the theoretical factor of resolution gain of 1.73. The available improvement in resolution can in principle be improved indefinitely by using higher harmonics of the modulation frequency, but the improvement is practically restricted by the available signal to noise ratio. As shown on Fig. 6 (Appendix A), the third harmonic signal is about 30 times lower than the DC component. With nonbleaching probes, the SNR could be improved by increasing the acquisition dwell time and improving detected signal, but this comes with the cost of imaging speed.
We also demonstrated that besides the resolution improvement, the advantage of saturated excitation imaging method is the ability to remove out of focus light. However, this property suffers from its inability to physically reject out-of-focus light before it reaches the detector. As opposed to two-photon absorption, saturated excitation creates fluorescence signal throughout the entire thickness. Then, the out of focus light rejection is obtained by isolating digitally the harmonics generated by the saturation. Thus, in the presence of out of focus light, the level of the high harmonics compared to the fundamental frequency signal is reduced. As the system is shot noise limited (see Appendix A), the stronger the out of focus signal is, the more severe the SNR conditions are for extracting the harmonics signals. Because of this limitation we demonstrated background rejection only with the second harmonic in the result section.
In the case of biological imaging, the staining is usually made of fluorescent proteins or anti-bodies, which are subject to photobleaching. For a typical dye, hundreds of kW/cm2 excitation intensity is required to observe the saturation with the SAX method [29–31]. Therefore, the main issue is whether the number of photons obtained at each pixel is large enough to probe the high demodulated harmonics. On optimized SAX microscope systems, high excitation intensity has been shown to be compatible with various biological samples [30,31]. In this proof of concept experiment, we bypassed the problem by both using nonbleaching nanodiamonds and scanning the sample with a fast piezoelectric stage. In a real endoscope based on phase conjugation through multimode fiber, the limiting element in terms of scanning speed is the phase modulating element. The use of a digital micro-mirror device would allow modulation at kHz rates and would achieve the required speed . The MMF collection efficiency here is also limited compared to microscope objectives. So, for biological imaging with this method, only the second harmonic demodulation is realistic.
In conclusion, we have shown how fluorescence saturation can improve imaging through MMF. The resolution of endoscopic imaging through MMF is limited by the relatively low NA of the fiber. In SAX mode, we demonstrated resolution improvement in all three dimension. We obtained 500nm lateral resolution, well below the limit of diffraction in conventional imaging. In linear imaging, the contrast of thick sample images is limited by the absence of optical sectioning. We demonstrated that out of focus light elimination by SAX can improve the image contrast in the limit given by the available SNR in the chosen experimental conditions. Thus, the use of SAX in MMF endoscopy by phase conjugation provides better image quality for photostable, fluorescent samples.
Appendix A Saturation curve of the NDs
We present here the nonlinear response of a single 120 nm nanodiamond containing about 1000 nitrogen vacancies. From this curve the level of excitation intensity necessary to demodulate high harmonics and get high resolution imaging can be determined. The noise is measured as the average value over all the frequencies apart from the modulation frequencies and its harmonics. The slope of the noise signal (yellow curve α√I), indicates that shot noise was the main source of noise in the detection of nonlinear fluorescence signals. As reported previously , around 100 kW/cm2, the saturation of the fluorescence response becomes significant enough to allow the extraction of the high harmonic signals. In order not to saturate the harmonic signal and to maximize the level of nonlinear signal compare the fundamental, we used about 60 kW/cm2 for the second harmonic signal and 250 kW/cm2 for the third harmonic signal.
Appendix B Theoretical expression of the impulse response (point spread function) and edge response of the system
This paragraph aims at deriving the Point Spread Function and the edge response obtained by temporal modulation of the excitation beam and demodulation of the fluorescence response in order to make clear how the method benefits from saturated excitation. All the equations presented here can be found in [30,32]. The point spread function (PSF) of a confocal microscope can be written as:
The same considerations can be made to evaluate the sectioning performances. If we consider edge response of the fiber imaging:
In the first case (blue curve in Fig. 7), the fluorescence response is linear to the excitation. Assuming an infinitely thick dye layer, the edge response is constant. The red and the green curve in Fig. 7 represent the edge response for SAX and two photon microscopy respectively. In both cases the Equation 6 applies, illustrating that SAX and two photon microscopy can perform sectioning. The better performance in SAX microscopy is given by the shorter excitation wavelength (as long as a sufficient SNR can be maintained).
In conclusion, because the imaging through the fiber is a purely scanning technique it benefits maximally from the SAX demodulation compared with confocal imaging where some gain in resolution and some sectioning are already provided by the spatial filtering with the pinhole.
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