1. Introduction

Optical scattering induced by microscopic inhomogeneity is a long-existing problem in optics. The capability of focusing light despite scattering holds promise for deep-tissue optical imaging, manipulation, and therapy. The wavefront shaping technique employs a spatial light modulator (SLM) to compensate for scattering-induced phase scrambling, making scattered light focusable [1–3]. Among existing techniques, optical phase conjugation (OPC) based wavefront shaping, which relies on the time-reversal symmetry of wave equations, is the most efficient one in finding the optimum wavefront to refocus scattered light [3,4]. Although efficient in handling millions of degrees of freedom, digital OPC (DOPC) based wavefront shaping generally suffers from degraded performance, mainly due to stringent requirements on system alignment. For such a wavefront shaping system, ideally, a precise mapping relationship between millions of pixels of the camera and the spatial light modulator (SLM) should be established [3]. Failure to comply with this rule makes wavefront modulation meaningless and even causes adverse effects on the intensity of the focus. This condition makes OPC-based wavefront shaping much less popular than other wavefront shaping schemes, such as feedback-based wavefront shaping [1] and transmission matrix based wavefront shaping [2]. Analog OPC with refractive crystals does not encounter this problem, but the low diffraction efficiency of the hologram and the lack of freedom to synthesize arbitrary wavefront make Analog OPC less attractive to biomedical applications [4–8].

Facing this hurdle, several research groups investigated alignment protocols for DOPC. In 2010, Cui et al. developed the first DOPC system by employing a sieve-like mask to serve as a referencing system during alignment [3]. Since the optical system was rather complicated and various types of optical aberrations remained uncompensated, the performance of the system is still limited. Quantitatively, the performance of DOPC can be evaluated by the fidelity of the focus, i.e., the peak-to-background ratio (PBR). This parameter is experimentally quantified by the ratio between the peak intensity of the focus formed by sending in the optimum incident wavefront and the ensemble-averaged intensity generated by a random incident wavefront. Theoretically, this parameter is statistically calculated as πN/4 with phase-only modulation, where N is the total number of independent degrees of freedom in the system. Due to the lack of a proper alignment protocol, for years, the PBRs achieved through DOPC were capped by several hundred, which are at least three orders of magnitude smaller than the theoretical value [3,9–14]. This condition indicates that only a small fraction of the pixels were matched properly while the rest did not contribute to turbidity suppression at all. In 2014, Jang et al. developed an auto-alignment protocol by computationally compensating for system misalignment through the angular spectrum method [15]. The peak intensity of the focus is used as the feedback signal when transversing misalignment parameters. With this protocol, PBRs up to tens or even hundreds of thousands can be achieved [15]. Alternatively, allowing the camera to directly image the surface of the SLM greatly simplified the pixel-matching process. Using this framework, the concept of adaptive optics was borrowed and small misalignments including tip and tilt, along with optical aberrations of the system, can be digitally compensated for using rectangular Zernike polynomials [16,17]. In addition, protocols using phase-conjugating crystals [18] and the transfer matrix method [19] were also demonstrated to improve the accuracy of pixel matching. With these protocols, the PBRs that approach the theoretical limit have been experimentally achieved through DOPC. It is worth noting that all alignment protocols were demonstrated using visible light so far.

To realize optical focusing inside scattering media, DOPC needs to be combined with appropriate guide stars [20]. Among various types of guide stars being demonstrated with DOPC [10,11,21–26], focused ultrasound is non-invasive and freely adjustable inside scattering media. This technique, termed term-reversed ultrasonically encoded (TRUE) focusing, was initially developed with photorefractive crystals [6] and later on demonstrated in a digital version [27,28]. Despite its high efficiency in fighting against dynamic scattering [8,29–32], one of the drawbacks of TRUE focusing is that the focal spot size is capped by the acoustic diffraction limit, which is much larger than a typical optical diffraction-limited focal spot. Through variance encoding, the TRUE focus could shrink to a single optical speckle, but this method requires time-consuming measurements and suffers from a heavy computational burden [33]. Alternatively, iterative TRUE (iTRUE) focusing is efficient in decreasing the focal spot size by continuously invoking acousto-optic interactions [34–36]. With only shot noise being considered, this iterative procedure, regardless of being implemented physically or computationally, can eventually lead to a single optical speckle within a finite number of iterations [37–39].

Unfortunately, however, alignment protocols for DOPC cannot be directly adapted for iTRUE. The main reason is iTRUE focusing naturally operates in a reflection mode. Moreover, it requires the SLM to modulate the incident wavefront and the camera to capture the backscattered wavefront simultaneously. That is to say, the camera cannot directly image the surface of the SLM, otherwise, the camera will be saturated by the reading beam. For the same reason, any part of the reading beam should not be leaked into the camera before interacting with scattering media. All these practical considerations make iTRUE focusing a challenge [34–36]. Moreover, most systems of iTRUE focusing reported so far were built with a 532-nm light source [31,34,35,40]. There is only one system developed at 778 nm (still visible), but it plays a trick to operate in a transmission mode to relieve the misalignment penalty [36]. Till now, no iTRUE focusing has been demonstrated using invisible light. Since many biomedical applications require to be operated at the near-infrared spectral range, developing an iTRUE focusing system using a near-infrared light source is highly desirable. To fill this blank, we describe an alignment protocol for iTRUE in this work, which integrates rough alignment with manual adjustment, fine-tuning with a high-precision motorized stage, and digital compensation through Zernike polynomials. This protocol overcomes certain limitations that exist in previous protocols for DOPC, leading to good pixel-matching conditions even with near-infrared light and achieving a high-fidelity focus with a PBR close to 70% of the theoretical limit. We further combined this system with focused ultrasound to demonstrate iTRUE focusing with near-infrared light. The evolution of the optical focus was manifested, revealing the transformation process from a large intensified spot to a tiny focal spot.

2. Principle of iTRUE focusing

A schematic illustration of the operational principle for iTRUE focusing is shown in Fig. 1. In the beginning, the phase map displayed by the SLM is set to all 0. The incident light with a frequency of f₀ is first reflected by the SLM and then enters the scattering medium. Deep inside the scattering medium, focused ultrasound with a frequency of f_US is triggered to locally modulate the scatterers within the range of the ultrasonic focus. Through acousto-optic effect, a portion of the light passing through the ultrasonic focus is ultrasonically encoded and frequency shifted. After being backscattered from the scattering medium, the scattered light is directed to the camera and subsequently measured through holographic approaches. Here, as a demonstration of the principle, we intentionally select to measure the wavefront of the ultrasonically encoded light with a frequency of f₀ + f_US by appropriately adjusting the frequency of the reference light. In practice, the ultrasonically encoded light with a frequency of f₀ - f_US can be targeted as well. Ideally, we would like to have the camera and the SLM positioned at the symmetric plane of the beam splitter and their pixels properly matched one by one. Based on the time-reversal symmetry of wave equations, loading the conjugate phase map of the measured ultrasonically encoded wavefront to the SLM allows the modulated wavefront to trace back to the position of the ultrasonic focus. In this condition, an optical focus is formed, despite scattering. Triggering the focused ultrasound again makes the acousto-optic interaction occur in a more confined region than the first time. By measuring the backscattered ultrasonically encoded light and loading its conjugate phase map to the SLM again, the newly achieved optical focus will have a smaller size than the previous one. As the iteration proceeds, the optical focus is expected to evolve from an acoustic diffraction-limited spot to an optical diffraction-limited one.

 

Fig. 1. Schematic illustration of the operational principle of iTRUE focusing. BS, beam splitter; sCMOS, scientific complementary metal oxide semiconductor camera; SLM, spatial light modulator; UT, ultrasonic transducer.

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3. Alignment protocol for digital optical phase conjugation using near-infrared light

The successful operation requires a good alignment protocol with precise one-to-one mapping between the pixels of the camera and the SLM. Empirically, as shown in Fig. 2(a), a small misalignment between these two planes in any one of six dimensions, i.e., (Δx, Δy, Δz, Δθ_x, Δθ_y, Δθ_z) can dramatically degrade the system performance. In the following, we will describe the alignment protocol that enables DOPC in more detail.

 

Fig. 2. Alignment protocol. (a) Six misalignment parameters persist: in-plane translation (Δx and Δy), in-plane rotation (Δθ_z), axial translation (Δz), and tip/tilt (Δθ_x and Δθ_y). BS, beam splitter; sCMOS, scientific complementary metal oxide semiconductor camera; SLM, spatial light modulator. (b) Workflow of the alignment protocol.

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The alignment protocol for DOPC using near-infrared light contains three steps, as shown in Fig. 2(b). Ultrasound is not needed during the alignment process. In the first step, the system is manually aligned with the assistance of a 4f system. This auxiliary system helps the camera to see the surface of the SLM under the illumination of near-infrared light, which is used only in this step and was blocked afterward. A checkerboard pattern is then displayed by the SLM for aligning (Δz, Δθ_z) first and then locating (Δx, Δy). After this step of rough alignment, a weak focus can be achieved through the scattering medium. Then, in the second step, by using the peak intensity of the focus as the feedback signal, we tune (Δθ_x, Δθ_y, Δθ_z) and (Δx, Δy, Δz) by traversing parameters accounting for different dimensions of misalignment using a six-axis motorized stage. The rule of thumb is to maximize the feedback signal, which is similar to the strategy used in Ref. [15]. One of the key advantages of using a motorized stage for physical compensation (this work) rather than employing a computational approach for digital compensation (Ref. [15]) is that the computational inaccuracy due to quantization errors can be minimized, leading to a more accurate alignment. After the step of fine-tuning, a bright focus can be obtained. In the third step, we further compensate for system misalignment that cannot be handled in the previous two steps, including optical aberrations induced by optical components and the curvature mismatch between the SLM and the camera. This step is essentially the same as that employed in Ref. [16,17], in which rectangular Zernike polynomials are loaded to the SLM in order. After these three steps, an optical focus with a PBR close to 70% of the theoretical limit can be obtained. This properly aligned system can then be combined with focused ultrasound for iTRUE focusing.

3.1 Step 1: rough alignment with manual adjustment

The experimental setup used for the step of rough alignment is depicted in Fig. 3. A homemade continuous-wave fiber laser, which operates at 1053 nm, was used as the light source in this study. The maximum output power of the laser is 6W. The output light was divided into three beams by using two pairs of half-wave plates (HWP1 and 3, OQQW-25.4-1053-2A, MFOPT) and polarizing beam splitters (PBS1 and 2, OQPBS-25.4-900-1300, MFOPT). Then, the polarization states of all beams in the system were adjusted to be horizontal. An acousto-optic modulator (AOM 1, 2, and 3, 402AF3, IntraAction) was also used to control the frequency of each beam. The step for rough alignment used only the reading beam, which was expanded to 1 inch through a pair of lenses (L1 and 2, OQLBV6-8, OQLBV25-250, MFOPT). A checkerboard phase pattern, which is interlaced with blocks of phase 0 and π, was loaded to the SLM (Pluto-2-NIR-149-D, Holoeye). Each block contains 128 × 128 pixels of the SLM. A mirror (M3) was inserted to transform the phase pattern into an amplitude one. The SLM was mounted on a high-precision motorized stage with six degrees of freedom. This stage was assembled by a 3-axis linear stage (SMPVM60-XYZF-P5, MFOPT) and a tip/tilt/rotation platform (M-37 and TRA12CC, Newport). Figure 4(a) shows the camera-captured image of the checkerboard pattern before rough alignment, which exhibits to be defocused and skewed. For visualization purposes, we added two-dimensional periodic white crosses through post-processing, which were expected to locate at the junctions of white and black blocks in the ideal case.

 

Fig. 3. Experimental setup used for the step of rough alignment. HWP, half-wave plate; PBS, polarizing beam splitter; AOM, acousto-optic modulator; BB, beam block; M, mirror; L, lens; BS, beam splitter; SLM, spatial light modulator; sCMOS, scientific complementary metal oxide semiconductor camera.

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Fig. 4. Rough alignment of the system using a checkerboard pattern. White crosses were digitally added for visualization purposes through post-processing, suggesting the ideal positions of the junctions of these blocks. (a) Camera-captured image before rough alignment. (b) Camera-captured image after rough alignment.

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Fig. 5. Experimental setup used for the step of fine-tuning. HWP, half-wave plate; PBS, polarizing beam splitter; AOM, acousto-optic modulator; BB, beam block; M, mirror; L, lens; BS, beam splitter; SLM, spatial light modulator; sCMOS, scientific complementary metal oxide semiconductor camera; SM, scattering medium; CMOS, complementary metal oxide semiconductor camera.

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To assist the camera to image the surface of the SLM, an auxiliary 4f system consisting of two lenses (L3 and 4, OQDLB25.4-150, MFOPT) and a mirror (M4) was introduced. Through the 4f system, the displayed pattern was first mapped to the mirror (M4) and then imaged to the sensor of a scientific CMOS (sCMOS) camera (Zyla 5.5, Andor). The parameter Δz was firstly optimized so that the camera can capture the sharp edge of the checkerboard. In practice, the positions of the stage, the mirror, and the sCMOS camera along the optical axis should be adjusted. Then, Δθ_z was also adjusted by manually rotating the stage until the SLM was horizontally positioned at the central view of the camera. After rough alignment, the captured checkerboard is shown in Fig. 4(b), leading to a sharp image.

The next task is to locate (Δx, Δy) so that the pixels of the SLM and the camera are one-to-one matched. Since the sizes of the pixels of these two devices are not the same (8 µm versus 6.5 µm), some previous systems adopted camera lenses to match their sizes [14,17,41–45]. Unfortunately, however, most of the camera lenses were designed for visible light, which did not function well for near-infrared light due to multiple reflections among optical lenses. As a result, our protocol directly constructs a matching table without the camera lens. This choice does not lose information because although the camera has a smaller pixel size, it has more than twice the pixel numbers of the SLM. In this condition, we selected four pixels of the SLM at the intersections of quarter lines, which are encircled using red in Fig. 4(b). Their coordinates on the camera sensor are treated as the benchmark, allowing the coordinates of the rest of the pixels to be estimated through linear interpolation and rounding to the nearest integers. For two million pixels, it was estimated that this interpolation method guaranteed more than 80% of pixels to be matched, while the rest of them were deviated by only one pixel in either the horizontal or the vertical direction due to quantization errors. This process is similar to the strategy reported in Ref. [17]. However, four corners in the image with apparent optical aberrations were chosen in that work, causing ambiguities in precisely determining the coordinates of benchmark pixels [17]. After this step, we estimated that the manual precisions in the step of rough alignment were 400 µm for Δz, 0.2° for Δθ_z, and 24 µm for (Δx, Δy), respectively, based on subsequent experimental results.

3.2 Step 2: fine-tuning with a high-precision motorized stage

Having roughly aligned the system, we then proceed to perform fine-tuning for system misalignment using motorized actuators. For translational dimensions, the precisions are 4 µm for (Δx, Δy) and 20 µm for Δz. For angular dimensions, the precisions are 0.0005° for (Δθ_x, Δθ_y) and 0.02° for Δθ_z. Figure 5 shows the experimental system used in this step, in which the 4f system and mirrors used in the previous step were blocked. In addition to the reading beam, the other two beams, namely a sample beam and a reference beam, were used with different functionalities. The sample beam interacted with the scattering medium in the transmission mode, while the reference beam served as a static and plane reference for wavefront determination. In particular, a small frequency difference of 10 Hz between the sample beam and the reference beam was introduced by the two AOMs, forming heterodyne holography. Since the phase difference evolves with time, we set the camera framerate to four times the beat frequency to effectively realize a four-step phase-shifting process. Having acquired the scattered wavefront on the camera sensor, a conjugate phase map was then displayed by the SLM. The reading beam acquired the phase map and focused light through the scattered medium. Before the step of fine-tuning, a weak focus could be achieved, with the assistance of a focusing lens (L8, OQDLB25.4-50, MFOPT), through six layers of scattering films (810-CQ33 tape, Scotch) on the sensor of a CMOS camera (MER-131-210U3M, Daheng Imaging) through DOPC. An optical thickness of about 25 was quantified for these combined scattering films.

Although relatively weak, the peak intensity of the focus could serve as a good feedback signal for the fine-tuning process. All six parameters (Δx, Δy, Δz, Δθ_x, Δθ_y, Δθ_z) were scanned and each parameter is updated to the optimum value after one-time scanning. We first fine-tuned the parameters (Δθ_x, Δθ_y) and Δθ_z, which are shown in Figs. 6(a) and (b), respectively. The scanning step size was set to 0.01° and 0.2°. Then, the parameters (Δx, Δy) and Δz were also examined, with a step size of 8 µm and 500 µm. The evolutions of the peak intensities are illustrated in Figs. 6(c) and (d), respectively. Then, we further fine-tuned these six parameters for the second round near the current optimum values with finer step sizes at 2 µm for (Δx, Δy), 10 µm for Δz, 0.0005° for (Δθ_x, Δθ_y), and 0.01° for Δθ_z, which are shown in Figs. 6(e), (f), (g), and (h), respectively. It should be noted that small intensity fluctuations in these figures are due to the instability of the system, which can be mitigated with averaging. After the step of fine-tuning, the SLM and the camera were physically aligned at the symmetric plane of the beam splitter, leading to a bright optical focus despite scattering.

 

Fig. 6. Evolution of the peak intensities during the step of fine-tuning with a high-precision motorized stage. The upper row shows the first scanning process with relatively large step sizes, while the bottom one shows the second round with relatively small step sizes. (a) and (e) for Δθ_x (red) and Δθ_y (blue). (b) and (f) for Δθ_z. (c) and (g) for Δx (red) and Δy (blue). (d) and (h) for Δz.

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3.3 Step 3: digital compensation through Zernike polynomials

The purpose of the previous two steps is to physically match the position of the camera and the SLM, which cannot handle optical aberrations caused by optical elements and curvature mismatch between the SLM and the camera. In this step, we follow the procedures developed in Ref. [16,17] to compensate for these effects. Again, by using the peak intensity as the feedback signal, different orders of rectangular Zernike polynomials, from low to high, are loaded to the SLM. The step size for scanning their coefficients is 0.02. Figure 7(a) illustrates the bar graph of the obtained coefficients during a typical experiment. As we can see from the figure, the 3^rd order, which represents the effect of defocusing, becomes the dominant one. This relatively large coefficient is due to the curvature mismatch between the SLM and the camera rather than defocusing, thus being much smaller than the one reported previously without using mechanical fine-tuning [17]. Moreover, thanks to the step of fine-tuning described above, the first two orders, which represent tip and tilt (dominant terms in Ref. [16,17]), are quite small in our case. As a result, the synthesized phase map that digitally compensates for the system is shown in Fig. 7(b). With this digital compensation, the PBR of the foci can further be enhanced.

 

Fig. 7. Digital compensation through Zernike polynomials. (a) A typical example of the distribution of the coefficients for each order. (b) The synthesized phase map used to compensate for optical aberrations and curvature mismatch.

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3.4 Result: optical focus achieved during each step

To have a better feeling regarding the effectiveness of the alignment protocol, we provide a typical example of camera-captured images obtained at each step in Fig. 8. A typical speckle pattern without modulating the incident wavefront is shown in Fig. 8(a), serving as the estimation of the intensity of the background. After rough alignment, the modulated wavefront can form an intensified spot with a slightly distorted shape, achieving a PBR of 2 × 10² (Fig. 8(b)). Then, after fine-tuning, a bright focus with a PBR around 6 × 10⁴ can be achieved (Fig. 8(c)). The shape of the focus becomes circular, indicating a much higher fidelity than before. Finally, after digital compensation, the PBR of the focus can further increase to 1.1 × 10⁵ (Fig. 8(d)). All intensities were normalized by the maximum value in Fig. 8(d). Because roughly 10 pixels were used to sample one speckle grain during experiments on average [15,16,22,27,41], the theoretical PBR is estimated as π/4 × 1920 × 1080/10 ≈ 1.6 × 10⁵. Thus, the achieved PBR is about 70% of the theoretical value. It is worth noting that the focus obtained after rough alignment (Fig. 8(b)) is larger than that obtained after fine-tuning (Fig. 8(c)). Such a phenomenon was also observed but not fully explained in the literature [15]. We believe that the origin of this phenomenon is associated with the spatial memory effect, as the scattering medium used for alignment purposes is geometrically thin.

 

Fig. 8. Evolution of the camera-captured images. (a) Speckle background without modulating the incident wavefront. (b) An intensified spot after rough alignment. (c) A bright focus after fine-tuning. (d) A bright focus after digital compensation. Scale bar: 50 µm.

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4. Demonstration of iTRUE focusing with near-infrared light

4.1 Experimental setup of iTRUE focusing

Having aligned the system, we proceed to demonstrate iTRUE focusing with near-infrared light. To perform iTRUE focusing, we blocked the sample beam to let the system operate in the reflection mode. The experiment setup is schematically shown in Fig. 9. The same scattering films were stacked and attached to the front surface of the water tank to induce optical scattering. The focused ultrasound was generated by an ultrasonic transducer with a central frequency of 5 MHz (5Z10SJ30DJ, SIUI). Thus, the frequency mismatch between the reading beam and the reference beam was set to 5 MHz through two AOMs. Similarly, an additional 10 Hz beat frequency was introduced to either the transducer or one of the AOMs to realize heterodyne holography. To aid the visualization of the iTRUE focus inside water, we placed a semi-transparent semi-reflective mirror (BSP) after the focus. This geometry allows the CMOS camera to image the iTRUE focus outside of the water tank through a single lens (L8, OQDLB25.4-50, MFOPT) [46].

 

Fig. 9. Experimental setup of the iTRUE focusing system. HWP, half-wave plate; PBS, polarizing beam splitter; AOM, acousto-optic modulator; BB, beam block; M, mirror; L, lens; BS, beam splitter; SLM, spatial light modulator; sCMOS, scientific complementary metal oxide semiconductor camera; SM, sample; CMOS, complementary metal oxide semiconductor camera; BSP, beam splitter (plate type); UT, ultrasonic transducer.

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4.2 Experimental results of iTRUE focusing

A typical experimental result of iTRUE focusing is shown in Fig. 10, which manifests the evolution of the focus during iterations. As a control, a camera-captured image of the speckles before shaping the incident wavefront is shown in Fig. 10(a). After triggering the ultrasound, a standard TRUE focus is achieved as shown in Fig. 10(b). Its size, defined as the full width at half maximum of the intensity envelope, is estimated to be 1 mm, which is roughly the same as the size of the acoustic focus (920 µm). It should be noted that since there are many speckles within the TRUE focus, when evaluating the PBR, the peak intensity is estimated as the average intensity within the focus. Using this definition, the PBR of the focus is about 8. After the 8^th iteration, the focus considerably decreased, as shown in Fig. 10(c). The size and PBR of this focus are quantified to be 280 µm and 40, respectively. After the 16^th iteration, as shown in Fig. 10(d), the optical focus only contains several optical speckles, exhibiting a size and a PBR of 160 µm and 70, respectively. Additional iterations did not further reduce the focal spot size, thus are not shown here. Nonetheless, the current size is about one-sixth of the original size determined by the acoustic diffraction limit. Before proceeding, we note that all intensities were normalized by the maximum value in Fig. 10(d). Correspondingly, evolutions of the one-dimensional intensity envelop of these optical foci are illustrated in Fig. 10(e), confirming the validity of iTRUE focusing in reducing the spot size. Moreover, the intensity of ultrasonically encoded light as a function of the number of iterations is also shown in Fig. 10(f). Here, the intensity of ultrasonically encoded light was estimated as the spatially ensemble-averaged amplitude of the beating signal from all camera pixels, which was extracted through heterodyne holography. The offset background, which was obtained similarly when the ultrasonic transducer was turned off, was subtracted. These observations are similar to the ones reported in Ref. [35,38].

 

Fig. 10. Experimental results of iTRUE focusing. (a) Image of speckles captured when the incident wavefront was not shaped. (b-d) Images of Foci after the 1^st, the 8^th, and the 16^th iterations. Scale bar: 1 mm. (e) Evolutions of the one-dimensional intensity envelope of the optical foci. (f) The intensity of ultrasonically encoded light as a function of the number of iterations.

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5. Discussion and conclusion

Although iTRUE focusing should end in one optical speckle theoretically [38], during experiments, we found that the resultant foci always contained considerable amount of optical speckles. Given 6 µm in size for speckles, the resultant iTRUE focus still contains roughly 1.6 × 10³ speckles. We speculate that several factors may contribute to this unsatisfactory observation. First, the wavelength of the ultrasound with a 5-MHz central frequency is way longer than the optical wavelength of the near-infrared light. Even though the size of optical speckles is slightly amplified when propagating inside clear water, we still encounter the condition to have a large number of optical speckles at the beginning of iterations, causing difficulties to converge. Employing an ultrasonic transducer with a higher central frequency, i.e., 50 MHz, might help by improving the initial condition. Second, without optimizing the hardware, each iteration currently takes about 1 second. For such a time scale, any environmental disturbance that causes instability of the system may vibrate the speckles in space, thus diminishing the efficiency of the iteration process. We anticipate that increasing the system response in the future can mitigate this affection.

In the alignment protocol, three steps are needed. Since near-infrared light was used in this work, we found that building the 4f system manually in the first step was the most challenging one. For skilled researchers, it generally takes a few hours in this step. All the rest procedures could be carried out digitally more or less, which is time efficient. For example, steps 2 and 3 usually take 10 minutes and 7 minutes, respectively, even scanned erotically with low efficiency. For a system with daily use, one only needs to execute the latter two steps before each experiment to slightly tune the misalignment parameters.

In summary, we developed an alignment protocol for iTRUE focusing system, which was shown to maintain high fidelity in wavefront shaping experiments. Using this aligned system, we demonstrated the first iTRUE focusing using near-infrared light, exhibiting its effectiveness in decreasing the focal spot size and increasing the peak intensity. We anticipate that the developed near-infrared iTRUE focusing system, along with the described alignment protocol, can bring great benefits to a variety of deep-tissue biomedical applications, including high-resolution optical imaging, manipulation, and therapy.