Second-harmonic generation (SHG) microscopy, featuring high resolution, high contrast, noninvasive, and photobleaching-free properties, has been widely applied in various fields such as biomedicine, material science, and nanotechnology^[1–3]. SHG microscopy utilizes high-energy beams to focus on samples with non-centrosymmetric structures, including certain crystals^[4,5], muscle fibers^[6], collagen fibers^[7,8] and other biological tissues, which can generate a second-harmonic signal under laser irradiation. Quantification facilitates the extraction of more structural information and sensitive changes in collagen fiber organization due to various diseases and damage. Breast cancer with different pathologies was distinguished by quantifying the changes of collagen fibers at the cellular and molecular scales using SHG^[9]. Pixel-based SHG microscopy has also been used to study the arrangement of collagen fibers and the acquisition of molecular helix angles in different ovarian cancer tissues without the previous requirement of having well-aligned fibers and is more widely applicable to tissues^[10,11]. Collagen fiber alterations with skin aging are detected by SHG^[12] to point out that delicate alterations lead to a more ordered structure of collagen molecules due to oxidative damage, and orientation indices were obtained to analyze the difference between burn-damaged skin and control skin^[13]. In addition to studying the properties of collagen fibers, SHG microscopy can also be combined with other imaging methods to characterize sarcomere length, distribution, and myosin filaments, a key structure for the production of the second harmonic^[14,15].

However, the pixel-by-pixel scanning method mentioned above is limited by the imaging speed. Wide-field illumination takes less time compared to pixel-by-pixel scanning to obtain the resulting image at a large field of view with high resolution, but it is limited by the weaker intensity of the generated signal compared to the focusing intensity. One of the solutions^[16] is to increase the output power of the laser, which is also the reason why the wide-field illumination mode usually requires high incident power. The following problem is that Gaussian beams may overexpose the intensity of the central area, and the detection signal is not uniform. The application of flat-top beam illumination can effectively solve this problem, as it has a flatter horizontal profile and provides uniform spatial distribution^[17,18]. Due to these characteristics, a flat-top beam has been applied in the biomedical photonics microscopy imaging. The combination of flat-top illumination and wide-field fluorescence imaging can reduce the variation of fluorescence signal of measured objects and make the fluorescence signal generated by fluorescent beads and single molecules more uniform, which can effectively reduce photobleaching^[19,20]. Flat-top illumination can also be applied in superresolution single-molecule localization microscopy to improve the excitation efficiency of fluorophores and reduce the error of reconstructed images^[21]. Wide-field SHG imaging with a flat-top beam can illuminate the corners of the image, showcasing more imaging areas and expanding the field of view^[22].

In this paper, we collect SHG signals from rat muscle tissue using wide-field flat-top beam illumination and introduce a polarization orientation retraction algorithm, aiming to characterize the orientation of endogenously generated SHG structures on the basis of expanding the field of view. The acquisition of this information only requires 16 images with different incident and detecting polarization directions and is suitable for samples with cylindrically symmetric fiber structures.

The optical path diagram of polarization-sensitive wide-field SHG imaging experiment is shown in Fig. 1(A). The output energy of a near-infrared femtosecond collimated laser (FemtoNL®-920nm-1, Wuhan Yangtze Soton Laser, China) with 1 W power, 80 MHz repetition rate, and 920 nm wavelength is controlled by a half-wave plate and a polarization beam splitter [not shown in Fig. 1(A)]. Then, the output beam is expanded into a diameter (1/e²) of 10 mm through an afocal system consisting of two lenses, L1 and L2. This is done to meet the size requirements of the incident spot for the beam shaper (a|AiryShape, Asphericon, Germany). After passing through a half-wave plate (HWP@920 nm) again, the Gaussian beam passes through the beam shaper and the lens L3 with a focal length of 100 mm and forms a flat-top spot on the rear focal plane of the lens.

The working principle of the beam shaper^[23] is shown in Fig. 1(B). The beam shaper is a refractive aspherical structure, which has the advantage of simple structure and is suitable for a wide range of wavelengths. When the collimated Gaussian beam passes through the device, it is converted into a collimated Bessel-sinc-shaped profile. Then through Fourier transform of the intensity distribution by the focusing lens, a flat-top beam can be obtained at the back focal plane. The beam shaper and its rear-matched lens L3 adopt a cage structure to ensure that the laser is incident on the center of the device so as to obtain a better conversion effect from Gaussian beam to flat-top beam. When a Gaussian beam is required to illuminate the sample, it can be achieved by removing the beam shaper, which is a simple and convenient operation. The sample is placed at the focal plane of lens L3 to obtain wide-field flat-top or wide-field Gaussian beam illumination, and the signal generated after irradiating the sample is collected through an objective (Nikon Plan Fluor 40×, NA=0.75). The collected signals include a mixture of fundamental frequency laser and second harmonic. The combination of a short-pass filter (Chroma, ET555SPUV) and a bandpass filter (Chroma, CT460/10) can effectively filter out other signals and preserve the second-harmonic signal of the sample, which is transmitted through a tube lens to the scientific complementary metal-oxide semiconductor (sCMOS) camera (Marana, ANDOR) for recording. In the system structure diagram shown in Fig. 1(A), a half-wave plate at the fundamental wavelength and a polarizer placed behind the tube lens control the excitation polarization and determine the direction of detection polarization, respectively. Based on the control of the beam by these two devices and the principles discussed in the next part, Section 2.2, the measurement of the orientation angle of mouse muscle samples can be achieved.

When light propagates in a medium, polarization intensity will be generated due to the action of the photoelectric field. The polarization intensity includes linear polarization intensity and nonlinear polarization intensity. When the photoelectric field intensity is strong, the nonlinear polarization intensity should be considered. Polarization intensity P→ is usually a complex nonlinear function of electric field E→, which can be expressed as P→=χ(1)·E→+χ(2)·E→·E→+χ(3)·E→·E→·E→+….(1)

In the past, many scientific studies have shown that the local second-order nonlinear susceptibility tensor χ(2)(r) of myosin fibril and collagen fibers can be described as cylindrical symmetry (C∞). The general vector expression of second-order nonlinear polarization P→(2) under the assumption of cylindrical symmetry is^[24]P→(2)=as^(s^·E→)2+bs^(E→·E→)+cE→(s^·E→).(2)

Among them, s^ represents the unit vector along the axis of cylindrically symmetric fiber, and a, b, and c are the parameters related to the second-order nonlinear susceptibility tensor. Under the Kleinman symmetry assumption, there is a relationship b=c/2, which can be further derived as follows: P→(2)=as^(s^·E→)2+bs^(E→·E→)+2bE→(s^·E→).(3)

In the case of a given nonlinear polarization, the relationship between the second-harmonic intensity and the polarization direction is^[25]ISHG∝(P→(2)·s^)2+(P→(2)·(s^×k^))2.(4)

In this equation, k^ is the propagation direction of incident light. The above formula shows that the polarization dependence of the second-harmonic intensity signal is related to the orientation of myosin filament, but this biological information cannot be obtained directly from intensity measurement. Therefore, polarization measurement is required to obtain the orientation angle of myosin filament. From Eqs. (3) and (4), it can be concluded that I(ϕ,α)=U+Vcos(2α−2ϕ)+Wcos(4α−4ϕ),(5)where U, V, and W are functions related to a and b. To clarify the various angles more clearly, they are shown in Fig. 1(C). The incident laser propagates along the z-axis direction and, after passing through a half-wave plate, the angle between its polarization direction and the x axis is defined as α. The angle between the symmetry axis of myosin fibril and the x axis is defined as ϕ, which is the orientation angle for the target. For wide-field detection, a polarizer can be added in front of the camera to control the SHG polarization direction of the detection plane, and the angle between the transmission axis of the polarizer and the x axis is defined as ψ. By changing the polarization directions of incidence and detection separately, α=nπ4 (n=0, 1, 2, 3) and ψ=mπ4 (m=0, 1, 2, 3), the normalized relative field can be obtained as follows^[26]: Fmn=cos(mπ4)sin(nπ4+2ϕ)+12sin(mπ4)⁢[(1+ρ)−(1−ρ)cos(nπ2+2ϕ)],(6)where ρ=ba; thus, the intensity of detecting the second harmonic is determined, In(r)=12∑m=03|Fmn|2=U+Vcos(nπ4)+Wcos(nπ+4ϕ),(7)where U=14(I0+I1+I2+I3), V=±12ΔI312+ΔI022. Finally, we can calculate the orientation angle of the symmetrical axis, where ΔIab=Ia−Ib. The calculation is as follows: tan(2ϕ)=ΔI31ΔI02.(8)

First, we carry out simple simulation of a Gaussian beam, a super-Gaussian beam, and an ideal flat-top beam, respectively, to explain the reason why the flat-top beam can expand the wide-field SHG imaging field of view. The ideal flat-top beam intensity drops sharply from a uniform fixed value vertically to zero intensity, and its focal depth will be very short due to optical diffraction. The intensity of super-Gaussian beam continuously transits from a uniform fixed value to zero, with a certain circular edge, which can also be called a nearly flat-top beam, and the focus depth will increase. The beam we obtain in the later experiment is also this kind of flat-top beam.

As shown in Figs. 2(A)–2(C), the two-dimensional intensity distribution of three types of beams is simulated, respectively, and the corresponding intensity profile curves are obtained along the horizontal red dotted line, as shown in Fig. 2(D), which is more convenient and intuitive when comparing the variation trend of different beam intensities. Assuming that when the laser intensity is not less than a certain threshold, the sample can be excited to generate the second harmonic. Here, the intensity at the position marked with the horizontal black dotted line in Fig. 2(D) is set as the excitation threshold. The region located at and above this threshold line can generate the second harmonic, while the following part cannot. Therefore, it can be clearly seen on this threshold line that the normalized radius (abscissa range) of the ideal flat-top beam is greater than that of the Gaussian beam, while the super-Gaussian beam is slightly inferior to the ideal flat-top beam. The above comparison is also shown in the area selected by the black round dotted line box in the two-dimensional distribution of Figs. 2(A)–2(C). The area in which the flat-top beam can excite SHG signal is larger, allowing for an expanded field of view compared to the Gaussian beam. This is the reason why a flat-top beam can expand the field of view. It is worth noting that although the Gaussian beam can improve the signal intensity by increasing the total power of the whole, it also tends to cause overexposure in the central area. Essentially, the excess energy (shadow part) above the threshold of the Gaussian beam in Fig. 2(D) is flattened into a flat-top beam by the beam shaper to expand the effective illumination radius.

Next, we measured two types of beams on the focal plane of the L3 lens by experiment, as shown in Figs. 2(E) and 2(F) and obtained intensity profiles along the horizontal (black) and vertical (green) dotted lines, respectively. In Figs. 2(G) and 2(I), the intensity profiles of the Gaussian beam show a rapid downward trend from the center to both sides, which is the reason why the energy utilization of the beam is relatively low. The intensity profiles of the flat-top beam in Figs. 2(H) and 2(J) exhibit certain fluctuations, unlike the simulation results that maintain a constant value, but most values fall within the normalized range of 0.65–0.85. We also calculated the standard deviation of intensity profiles, as shown in Fig. 2(K), and the result of Gaussian beam illumination is σx=0.19, σy=0.2, while the result of the flat-top beam illumination is σx=0.07, σy=0.08, showing smaller fluctuation. Moreover, the overall intensity values are maintained within a wide range, ensuring an expansion of effective illumination radius.

According to the polarization measurement principle mentioned above, a 50 µm thick section of rat muscle tissue (legs of three-month-old mice) was illuminated by the Gaussian beam and flat-top beam, respectively. We tested the dependence of the intensity on the excitation polarization and found good agreement with the theoretical prediction, as shown in Fig. S1 (Supplementary Material). Wide-field SHG images were obtained with different incident and detected polarization directions, and the results are shown in Figs. 3(A) and 3(B). Sixteen intensity images were required for each illumination mode to calculate the orientation angle of the myosin filaments, where the incident polarization α angle and detected polarization ψ angle are selected as 0°, 45°, 90°, and 135°, respectively. The SHG signal in Fig. 3 exhibits multiple bright band shapes mainly because it originates from the myosin filaments located in the central part of the sarcomere, which are periodically arranged and distributed in space. This phenomenon and explanation have been reported and demonstrated in previous reports^[27].

It should be noted that the intensity of the SHG signal is dependent on the incident polarization direction and myosin filament orientation, as demonstrated by significant changes in response to alterations in the incident polarization angle shown in Fig. 3. Figure 3(B) is the imaging result of flat-top beam illumination. The signal intensity in the central area is lower than that of the Gaussian beam illumination, but more areas at the edges in Fig. 3(B) are illuminated, thus reducing laser damage and expanding the imaging field of view. The reason is that the energy flattening in the central area of flat-top beam increases the effective illumination radius, which is also explained in detail in the previous section.

Finally, we use images recorded above to calculate the orientation angle of myosin filaments under two types of beam illumination. Figures 4(A) and 4(B) show the superposition of the overall intensity U and orientation angle. Here, we select pixels with higher SHG intensity values to calculate the orientation angle, which can reduce errors caused by using low signal-to-noise ratio signals for calculation. It can be clearly seen that under the same laser power and camera exposure time conditions, flat-top beam illumination expands the imaging field of view. This allows for the muscle SHG signal to be obtained in more image areas, thus increasing the number of calculated orientation angle pixels and obtaining more myosin fibril symmetrical axis orientations.

Figures 4(C) and 4(D) show a magnified view selected by the dashed boxes in the Figs. 4(A) and 4(B), respectively. It is clear that most of the symmetrical axes exhibit strong regularity, pointing toward the perpendicular direction of the bright stripe structure, which is consistent with previous reports^[28]. Figures 4(E) and 4(F) show the statistical histograms of the symmetrical axis orientation ϕ calculated from the original data. In Fig. 4(E), the total number of ϕ by Gaussian beam illumination is 3872, while in Fig. 4(F), the total number of ϕ by flat-top beam illumination is 5161, which is greater than that of the former. Then Gaussian fitting is conducted on the data. The calculation result in Fig. 4(E) is ϕ¯=−0.237π, σ=0.13, R2≈0.86, and the result in Fig. 4(F) is ϕ¯=−0.241π, σ=0.14, R2≈0.93. σ is the standard deviation, and R2 is the square of the correlation coefficient. The results of both maintain good agreement, and the statistical average orientation of the symmetrical axes is consistent with the structure in Figs. 4(A) and 4(B). Furthermore, the second-harmonic signal generated by flat-top beam illumination yields a greater number of effective calculation values ϕ, better fitting results, and a stronger ability to analyze the orientation field of muscle fibers.

The measured total power reaching the surface of the sample is about 500 mW, and it takes about 0.04 s to acquire a 120×120 pixels image based on this incident power, which has a faster imaging speed than the scanning imaging method. In this experiment, in order to take into account that the SHG imaging comparison between the two kinds of beams is under the same experimental conditions, we chose the compromise laser output power to prevent the center intensity of the Gaussian beam illumination from overexposure, which would affect the experimental results. However, the flat-top beam illumination imaging was far from reaching the degree of overexposure. In the subsequent experiments, the SHG signal can be further enhanced by increasing the output power to reduce exposure time. Finally, we used two types of beam illumination combined with 16 images to obtain the orientation of the myosin fibril symmetry axis. The flat-top beam illumination expanded the imaging field of view, allowing for more data on orientation angles and a stronger ability to analyze fiber orientation field. Since our wide-field imaging speed is relatively fast and the sample does not need to be stained, imaging by its own endogenous signal will not invade or destroy the structure of the sample itself, and the impact on its light damage is minimal, which may be subsequently applied to the pathological analysis of skin pathology and liver fibrosis.