We report a non-axial-scanning second harmonic imaging technique, in which the chromatic aberration of a Fresnel lens is exploited to focus different wavelengths of a fundamental beam into different axial positions to effectively realize axial scanning. Since the second harmonic signals at different axial positions are generated by different fundamental wavelengths and hence accordingly have different center wavelengths, they can be resolved and detected in parallel by using a spectrometer without axial mechanical scanning. We have demonstrated a system capable of achieving about 8 μm effective axial scanning range. Proof-of-concept imaging results are also presented.
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The merging of nonlinear optics and microscopy has created new paradigms for optical imaging. Laser-scanning second harmonic generation (SHG) imaging [1–5], amongst an array of emerging nonlinear optical imaging modalities, has been extensively investigated in recent times. SHG imaging is unique in that it utilizes the second order nonlinear susceptibility χ(2) as an imaging contrast mechanism. It can be used to image samples possessing second order nonlinearity, or the surfaces of specimens with inversion symmetry in which χ(2) vanishes in bulk (under electric dipole approximation) . Some significant advantages of SHG imaging include no photobleaching effect, which is a major limitation of fluorescence microscopy (one- or multi-photon excitation ), non-blinking steady signal, inherent optical sectioning ability, and minimum photodamage [8,9]. Despite all these advantages, conventional SHG imaging requires three-dimensional (3D) point-by-point scanning, which can significantly limit the 3D or the x-z and y-z (x, y: lateral directions; z: axial direction) cross-section imaging speed. To address this challenge, here we explore a chromatic SHG imaging technique, which can eliminate mechanical axial scanning by exploiting the chromatic aberration of the Fresnel lens.
The chromatic scanning technique was previously applied to epi-reflection confocal microscopy [10–13]. Our group has recently extended it to two-photon fluorescence imaging [14,15]. To illustrate the underlying principle, let us consider focusing a pulsed fundamental beam by a Fresnel lens. The focal length F of the Fresnel lens is a function of wavelength and satisfies the relationship [16,17]
2. Experimental results
The schematic diagram of our experimental setup is shown in Fig. 1 . It is similar to that used in our prior chromatic two-photon imaging work. Briefly, femtosecond laser pulses from a Ti:Sapphire mode-locked laser (KMLabs, pulse width ~50 fs, repetition rate ~100 MHz, center wavelength ~820 nm) were delivered to our experimental system through a 40-cm-long photonic crystal fiber (Thorlabs, ESM-12-01). The fiber output was collimated by an objective (20 × , numerical aperture NA 0.4) and subsequently expanded with an imaging system consisting of two lenses with focal lengths of 75.6 mm and 250 mm respectively. A Fresnel lens (design wavelength: λ0 = 821 nm, design focal length: f0 = 100 mm) was then utilized to focus the beam. As aforementioned, due to the chromatic aberration different wavelengths of the laser beam were focused to different axial positions, effectively realizing axial scanning. To achieve desired axial and lateral resolutions, the beam was re-collimated by a lens (focal length: 38.1 mm), reflected by a dichroic mirror (Thorlabs DMLP505), and focused by an objective lens (60 × , NA 0.85) onto a sample. The second harmonic signal generated in the sample was then collected in the forward direction by another objective lens (20 × , NA 0.4). After passing through a band-pass filter (Chroma Tech. 405/40BP), which was used to eliminate the fundamental beam, the second harmonic signal was coupled into a five-meter-long multimode fiber. Finally, the output signal from the multimode fiber was detected by a spectrometer (PI/Acton SpectraPro 2500 with a liquid nitrogen cooled charge coupled device detector PI/Acton Spec-10).
We characterized the effective chromatic scanning range of the system. To this end, we air-dried a thin layer of BaTiO3 nanocrystal (Nanostructured & Amorphous Materials Inc., Average Particle Size: 200nm, Morphology: Spherical) solution (suspended in water) on a microscope cover slide (VWR Micro Cover Glass). A single cluster of nanocrystals (c.f., the microscope image shown in Fig. 2(a) inset) was identified and placed near the focal plane of the objective L2 (c.f., Fig. 1) as a second harmonic probe. The cover glass and hence the nanocrystal cluster was scanned vertically by using a computer-controlled motorized translational stage. The generated second harmonic signal was then collected and coupled into a five-meter-long multimode fiber, and detected by the spectrometer. Figure 2 shows our measured results. Each row of the figure represents a spectrum of the second harmonic signal generated by the BaTiO3 nanocrystal cluster placed at a corresponding axial position as indicated in the vertical axis. As the nanocrystal was moved away from the objective, the center wavelength of the second harmonic signal shifted towards shorter wavelength, as expected from the focal length-wavelength relation of the Fresnel lens (c.f., Eq. (1). This clearly demonstrates the chromatic scanning behavior. An effective chromatic scanning range of about 8 μm in the sample plane is obtained. For each wavelength, we found the corresponding depth position that yielded the maximum second harmonic signal (i.e., where the fundamental wavelength is focused). The obtained depth position (z)-wavelength (λ) relationship is shown in Fig. 2(b), which can be fitted with a linear curve with a slope of about 1.1 µm/nm.
To demonstrate the chromatic imaging capability, we utilized our system to image the surface of a LiNbO3 crystal, which was purposely scratched by silicon carbide sandpaper. An optical microscope image of the crystal is shown in Fig. 3(a) , in which the region of interest (30 µm × 30 µm) is overlaid with a pseudo-color SHG image. Two-dimensional point-by-point lateral scanning of the crystal sample was performed with a scanning step of 1 µm by using computer-controlled translational stages (Newport ESP300 3-Axis Motion Controller with motorized actuator). At each point a second harmonic spectrum was recorded, from which the axial image information is obtained. Figure 3(b) shows a series of second harmonic images at wavelengths from 404 nm to 413 nm with an interval of 0.52 nm. The “X’ shaped grooves on the crystal surface can be observed. The vertical cross section of the grooves can be better visualized in Fig. 3(c), in which the x-λ (z) cross-section images at three different positions (i.e., y = 20 µm, 26 µm, and 30 µm respectively) are shown. It appears that the grooves are tilted with respect to the crystal surface, which is not unexpected considering that the surface was randomly scratched.
In addition, we also imaged a LiNbO3 microcrystal created by using the same scratching method. A microscope image of the microcrystal is shown in Fig. 4(a) . Similarly, a two-dimensional lateral scan of the sample over an area of 40 µm × 40 µm was performed. The obtained SHG images at wavelengths from 404.2 nm to 410.0 nm with an interval of 0.52 nm is shown in Fig. 4(b). Figure 4(c) shows three x-λ (z) cross-section images at y = 10 µm, 26 µm, and 28µm respectively. Although due to the limited axial scanning range and spatial resolutions the quality of these images needs further improvement, these preliminary proof-of-concept results have clearly demonstrated the 3D imaging capability of the chromatic SHG technique.
3. Discussion and conclusion
In the current work, a multimode fiber was used to collect the SHG signal and deliver it to the spectrometer. Since the second harmonic beam had large chromatic aberration and hence was launched into multiple spatial modes, significant amount of signal power was lost when coupled through the entrance slit of the spectrometer. To improve the overall SHG signal collection efficiency, here we propose a method to collimate the chromatically aberrated second harmonic beam by using chromatic material dispersion. Qualitatively, a shorter-wavelength SHG signal (corresponding to a shorter fundamental wavelength) is nearer to the collecting lens, which implies that the chromatic aberration of the collecting lens should be opposite to that of the Fresnel lens in order to collimate the second harmonic beam. Note that for a singlet lens, the focal length f is given by 1/f = (n − 1)(1/R1 − 1/R2)  where n is the index of refraction and R1 and R2 are the radius of curvatures of the two facets. For lens material with normal dispersion, the shorter the wavelength the larger the index of refraction is (hence a shorter focal length). Therefore, chromatic material dispersion can compensate for the chromatic aberration produced by the Fresnel lens and result in a better-collimated second harmonic beam. Figure 5(a) shows a schematic diagram of such a chromatic SHG imaging system with improved collection efficiency. For simplicity we assume that lenses L1 and L4 are achromatic and have the same focal length, and so do lens L2 and L3 (c.f. Fig. 5(a)). Note that the change of focal length of the Fresnel lens as a function of wavelength satisfies
The chromatic aberration can be largely compensated in the example shown in Fig. 5(b) if the lens material is N-SF11  glass and a ratio f/F = 3.37 is chosen. One can also use other highly dispersive lens materials and adjust the focal lengths of the two pairs of objectives to optimize the system design.
In summary, we have investigated the feasibility of chromatic second harmonic imaging, in which mechanical axial scanning is eliminated by utilizing the chromatic aberration caused by a Fresnel lens. In our proof-of-concept experiment, an approximately 8μm effective chromatic scanning range (measured in the air) has been achieved. It should be noted that the chromatic scanning range inside a medium differs from that in the air. One can utilize a second harmonic probe buried inside the medium to directly calibrate the system or calculate it from the wavelength-depth mapping relationship measured in the air (e.g., the scanning range in the medium is scaled by the average refractive index). We believe that this new technique has the potential to significantly improve the speed of SHG imaging and therefore useful for real-time applications such as monitoring dynamic biological processes in three dimensions.
This work is supported by the National Science Foundation (Award# DBI0649866, ECCS0547475, DMR-0820404 and DMR-0908718). The Fresnel lens used in our experiments was acquired through the OIDA Photonics Technology Access Program sponsored by the National Science Foundation and the Defense Advanced Research Projects Agency.
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