Fig. 1. Principle and schematic diagram of 2P-FOCUS. (A) Without correction, all pixels of the digital micromirror device (DMD) are turned on; the incident light is scattered and cannot form a tight focus. (B) The process of generating a correction mask involves three steps. (C) With correction, the binary correction mask is projected on the DMD, allowing only the beams that interfere constructively to pass through. The illumination power on the sample is maintained the same before and after correction by increasing the input power to the DMD to compensate for the power loss due to turning off some pixels. The correction results in a brighter focus compared to the case before correction. (D) Optical schematic diagram of 2P-FOCUS. Details are in Appendix A. (E) The lateral point-spread-function (PSF) before (left) and after (right) dispersion compensation, measured by a camera in reflection mode. (F) The lateral (left) and axial (right) PSF without scattering media, measured by the PMT in (D). (G) Intensity profile of the PSFs in (F). The lateral resolution is 1.7 μm and the axial resolution is 6.6 μm without scattering media.

Fig. 2. Focusing through bone with 2P-FOCUS. (A) Representative random patterns with a sparsity of 0.4 and a super-pixel radius of 8 pixels used in the experiment. (B) Fluorescence intensity corresponding to the 2500 patterns detected by the PMT in reflection mode. Random patterns contributing to the top 10% of fluorescence intensity are selected (above the red line). (C) The sum of the selected random binary patterns forms the grayscale correction mask. (D) The final correction mask is generated by binarizing the grayscale correction mask. (E) Photo of the bone sample and the fluorescence sample. (F), (G) Zoomed-in fluorescent image of the focus (F) before correction and (G) after correction taken with a camera in reflection mode. (H) Comparison of the intensity profile along the x-axis before (blue line) and after (red line) correction. (I) Fluorescence intensity before (blue dashed line) and after (blue solid line) correction, as well as the intensity ratio (red line), as functions of the laser power on the sample. (J) Fluorescence intensity before (blue) and after (red) correction as a function of the sparsity of random patterns with a super-pixel radius of 8 pixels. (K) Fluorescence intensity before (blue) and after (red) correction as a function of the size of super-pixels. Fluorescence intensity before correction is measured with random patterns in this plot. (L) Fluorescence intensity before (blue) and after (red) correction as a function of the number of measurements.

Fig. 3. Imaging fluorescence beads through a 200 μm thick bone beyond the memory effect range. (A) Schematic diagram of global correction. Global correction applies the same correction mask to all scanning locations during the imaging process. (B) Schematic diagram of subregion correction. Subregion correction applies a different correction mask for each subregion. The scanning mirror and the DMD are synchronized to project the corresponding mask at each scanning location. (C) Schematic diagram of the sample used in this experiment. A piece of chicken bone was adhered on top of red fluorescent beads in PDMS. (D) The 3×3 subregions and corresponding references. (E)–(H) Imaging fluorescent beads through highly scattering bone across a 230  μm×230  μm field-of-view. The laser power on the sample is 25 mW for all three cases. (E) The image taken without scattering correction. (F) The image taken under global correction. The reference object is indicated by the yellow arrow. The object outside the memory effect range is invisible (indicated by the red arrow). The peak intensity improved from 9 to 26 after global correction. (G) The image taken under subregion correction with the reference objects and correction masks in (D) and (I). With subregion correction, the previously invisible object in (F) becomes visible (pointed by the red arrow). The peak fluorescence intensity improved from 9 to 43 after subregion correction. (H) The intensity profile of the two clusters of beads indicated by arrows in (E)–(G). The distance between these two objects is 96 μm. The correction mask for imaging the left object cannot effectively correct scattering for imaging the right object, indicating the memory effect range of this region is smaller than 96 μm. (I)–(K) Zoomed-in views of the bead in the green box in (E)–(G) and their intensity profiles across the green line. (L) The correction masks for the nine subregions generated using the references pointed out in (D). (M) Images taken by applying each subregion mask as a global mask. These images clearly show different masks correct scattering differently even though they look similar to each other. The images are displayed under the same color bar for comparison.

Fig. 4. Imaging fluorescence-labeled neurons deep in the mouse brain ex vivo using 2P-FOCUS. (A) The volumetric view of parvalbumin (PV) interneurons expressing cell-fill tdTomato imaged by 2P-FOCUS. The image volume is 230  μm×230  μm×450  μm. (B) The top plane and (C) the bottom plane of the image stack. The image stack is shown in Visualization 1. (D) The correction mask for global correction at 250 μm depth, generated with the neuron pointed by the yellow arrow in (E). (E), (F) Images of the same region at 250 μm depth (E) before and (F) after global correction. Fluorescence intensity is improved by about 3-fold after correction. Note that these two figures are displayed with different color bars to visualize the dim objects before correction. The same figures displayed with the same color bar are shown in Fig. 8(D). Insert: zoomed-in view of the neurons pointed out by the blue and red arrows. Scale bar, 5 μm. (G) The four subregions. (H), (I) Images of the same region at 400 μm depth (H) before and (I) after subregion correction. Fluorescence intensity is improved by about 9.3-fold after correction. Insert: zoomed-in view of the neurons pointed out by the blue and red arrows. Scale bar, 5 μm. (J) The four subregion correction masks. (K) Comparison of the intensity profile of representative neurons [zoomed-in view in (E), (F)] at 250 μm depth before (blue) and after (red) correction. (L) Comparison of the intensity of representative neurons [zoomed-in view in (H), (I)] at 400 μm depth before (blue) and after correction (red).

Fig. 5. Imaging blood vessels with intravascular fluorophore injection deep in the mouse brain using 2P-FOCUS. (A) Volumetric view of cerebral blood vessels with intravascular FITC-dextran injection, imaged by 2P-FOCUS ex vivo. The image volume is 230  μm×230  μm×510  μm. (B) Maximum intensity projection (MIP) of the top 100 μm thick volume along the z axis. (C) MIP of the bottom 100 μm thick volume along the z axis. The image stack is shown in Visualization 2. (D), (E) Two-photon image of blood vessels at 300 μm depth (D) before and (E) after correction. The peak intensity is improved from 22 to 795, corresponding to 36.1-fold improvement. (F), (G) Two-photon image of blood vessels at 340 μm depth (F) before and (G) after correction. All pixels of the DMD are turned on when capturing (F). The peak fluorescence intensity is increased from 27 to 826, corresponding to 30.6-fold improvement. (H) Comparison of the fluorescence intensity profile before (yellow line) and after (red line) correction along the dashed line in (F), (G). The intensity profile of the case before correction is magnified by 10 times for display purposes. (I) The location of the four subregions on the image plane. (J) The correction masks used in the experiment when acquiring images (E) and (G).

Fig. 6. The influence of the binarization threshold on correction masks. (A), (B) Frequency analysis of 2500 random patterns with a super-pixel size of 8 pixels and a sparsity of 0.4. (A) The 2D frequency spectrum of a single random pattern from the set. (B) The average frequency spectrum along the x-axis across the 2500 random patterns. The red line represents the mean value, and the orange shading indicates the standard deviation. (C) Log-log plot of the fluorescence intensity before correction as a function of the laser power on the sample. The slope of the log-log plot is 1.75±0.58, indicating that the fluorescence intensity before correction increases quadratically with the illumination power. (D) The grayscale correction mask, the same as in Fig. 2(C). (E) The binary correction masks generated by applying different thresholds to (B). These masks are used to produce the data for “after correction” in Fig. 2(I).

Fig. 7. The influence of the sparsity of random patterns on correction masks. (A) Random patterns with varying sparsity levels. Sparsity refers to the percentage of pixels that are turned on out of the total number. When the sparsity is between 0.5 and 0.9, the random patterns act more like notch filters, determining which pixels should be turned off rather than on. (B) Histogram of all elements in the matrix I=PTP (left) and a zoomed-in view (right). The zoomed-in view highlights the values of the diagonal elements in matrix I, while the other bins represent the non-diagonal elements. The results indicate that the dot product of any two distinct vectors in matrix P is 0±0.02, and the dot product of a vector with itself is one. (C) Five correction masks used to generate the “after correction” data in Fig. 2(J). (D) Fluorescence intensity before (blue dashed line) and after (red line) correction as a function of random pattern sparsity. Data were collected by focusing a beam through another region of the bone. The results show that the fluorescence intensity decreases when the correction mask is generated with random patterns having a sparsity of 0.5 compared to those with a sparsity of 0.4. (E) Four correction masks used to generate the “after correction” data in (D) from random patterns with various sparsity levels.

Fig. 8. (A) Correction masks with varying degrees of smoothing (plots 1–5), as well as a low-NA mask (plot 6). These masks provide the same output power given the same input power to the DMD. (B) Imaging of a red fluorescent bead through a piece of chicken bone under the intensity modulation of the corresponding masks. The second row shows a zoomed-in view of the region highlighted by the yellow box in the first row. All images are displayed using the same color scale. The maximum intensity is 95, achieved with the fourth correction mask, while the peak intensity under the low-NA mask is 42. (C) Intensity profile of the cross-section along the green dashed line in (B). (D) Examining photobleaching due to correction processes. The peak intensity decreased from nine to eight when comparing the image taken before the process without correction and the image taken after the process without correction.

Fig. 9. Scattering correction for imaging PV neurons deep in the mouse brain. (A)–(C) Comparison of the images taken (A) before and (B) after global correction under the same color bar. The images are the same as in Figs. 4(E) and 4(F). The neuron used as a reference (pointed out by the arrows) becomes brighter rather than dimmer after correction. (C) The intensity profile of the reference neuron before and after correction. Background intensity is subtracted. The peak intensity of this neuron is improved by about 1.8-fold, which is not as much as the brightest neurons. (D)–(M) All correction performed for taking the 0–450 μm image stack in Fig. 4. The green arrows indicate the image is used to produce the corresponding mask. The black arrows point at images after correction. The yellow arrows in the images point to fluorescence objects used as references. Notice that (G), (J), and (M) are taken with last correction mask rather than blank screen on the DMD. (D)–(F) The first scattering correction is performed at 250 μm depth. (D) The image before correction, which is the same as Fig. 4(E). (E) A single correction mask is produced, which is the same as the bottom plot in Fig. 4(D). (F) The image after correction, which is the same as Fig. 4(F). (G)–(I) The second scattering correction is performed at 290 μm depth. (G) Image taken with the global correction mask in (E). The field-of-view is divided into three subregions. Notice that we used the background fluorescence as the reference in the third subregion to generate the correction mask. (H) Three correction masks corresponding to the three subregions. (I) Image after subregion correction. (J), (L) The third scattering correction is performed at 380 μm depth. (J) Image taken with the three correction masks in (H). Four neurons are identified as the references for four subregions. (K) Four correction masks (identical to Fig. 4(J)) corresponding to the four subregions. (L) Image after correction. (M) Image taken with the four correction masks (identical to Fig. 4(I)) in (K) at 400 μm depth.

Fig. 10. Subregion correction is performed at 390 μm depth. (A) Image taken with the four correction masks in Fig. 5, identifying six fractions of blood vessels as references for six subregions. (B) Six correction masks corresponding to the six subregions. (C) Image after correction. (D) The same as Fig. 5(E). (E), (G) Zoomed-in views of capillaries in the boxed regions in (D). (F), (H) Intensity profiles of the cross-sections of the capillaries in (E) and (G), marked by the dashed lines. Fine capillaries are resolvable after applying the correction masks.