Digital optical phase conjugation (DOPC) is a well-known technique for generating a counter-propagating wavefront and reversing multiple scattering effects. Until now, implementations of DOPC are mostly based on a switching geometry. For some applications such as optical tweezers in turbid media, however, switching-based DOPC could fail to grab fast-moving particles. Besides, a DOPC modality with temporally-continuous gain is required. In this paper, a continuous amplified digital optical phase conjugator (CA-DOPC) is introduced to form a focusing point after passing through a heavily scattering medium. To achieve high-precision alignment between the CMOS image sensor and the spatial light modulator (SLM) in the CA-DOPC, an optical phase conjugator along with a specially designed alignment pattern was used. In this research, the CA-DOPC showed its ability to form a focus point in 2 -mm-thick chicken muscle tissue. In addition, a continuous gain of 166 and peak-to-background ratio (PBR) of 3×105 were observed in the case of 0.5-mm chicken muscle tissue.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Point focusing plays an important role in optical-imaging and optical-manipulation techniques, such as microscope and optical tweezers [1–6]. In the field of microscopy, optical phase conjugation (OPC) has shown excellent turbidity suppression capability in a variety of applications [7–11]. Various applications, including opposite virtual objective , harmonic generation imaging [13–16], fluorescence imaging [17–19], 4-Pi microscopy [20,21] and endoscopic imaging [22,23], have been proposed. Moreover, along with the demonstration of in vivo applications [24–26], OPC has emerged as the candidate of next-generation biomedical imaging technique. Instead of traditional OPC, digital optical phase conjugator (DOPC) has been proposed to provide higher light sensitivity, higher stability and wider wavelength fidelity [27–29]. It has shown its ability to produce point light sources inside specimens with the aid of ultrasound encoded images [30–35] or time differential images [36–38]. In the field of optical tweezers, OPC has been applied to perform multiple trapping by counter-propagating structured light . However, most DOPC techniques are based on a switching geometry and have to temporally switch between recording and reading modes [13,24,40–46]. During the period of the acquisition step, a spatial light modulator (SLM) switches to off state and create a half-period non-modulation window which is generally in an order of milliseconds to sub-ms. Due to this non-modulation window, Brownian motion of particles or in vivo dynamic activity could lead to unignorable noises or failure in particle trapping. Therefore, in order to continuously trap particles, a temporally-continuous gain is desired. Besides, continuous DOPC system was also desired and proposed to apply continuous scanning of time-reversed ultrasonically encoded optical focusing .
In this research, a continuous amplified DOPC (CA-DOPC) is proposed to provide temporally-continuous gain. Because the reading beam is separated from the reference beam in the CA-DOPC, the high-power reading beam can continuously illuminate the phase-only spatial light modulator (PSLM) to produce temporally-continuous gain. Based on a continuous refreshing mechanism, the CA-DOPC exists no non-modulation window so that the energy waste during this window and the possible failure in particle trapping can be avoided. However, CA-DOPC requires a reference beam separated from the reading beam, so typical alignment methods are no longer applicable [18,36,37,48–52]. Even the powerful iterative fine-tune alignment method can’t be applied to the CA-DOPC directly, because it needs an optical system to evaluate the phase difference between the reading beam and the reference beam [40,41].
To successfully generate the phase-conjugate wave, two significant steps have to be accomplished. One is the alignment between the PSLM and CMOS-IS, and the other is to record the interferogram formed by the reference beam and the conjugate reading beam. In this paper, we use a novel approach to achieve six-dimensional alignment by using a Kitty-type self-pumped phase-conjugate mirror (Kitty-SPPCM). With the Kitty-SPPCM’s capability of fast generating a conjugate wave with high sensitivity and phase fidelity [52,53], the alignment can be achieved with high precision. Besides, due to the phase-difference elimination and the SLM surface-undulation elimination aid by Kitty-SPPCM, the system peak to background ratio (PBR) approaches 38% of theoretical limit without iterative fine-tune process. With the aid of Kitty-SPPCM-based alignment, the CA-DOPC was constructed and applied to chicken muscle tissues with different thickness.
2. CA-DOP system
Figure 1 shows the system configuration of the CA-DOPC including the acquisition step and the reconstruction step. A 532-nm continuous-wave laser (Verdi-V5, Coherent Inc.) is used as the light source. Figure 1 (a) shows the acquisition step. The light originated from the light source was divided into a high-power beam and a low-power beam. The high-power beam includes reading and signal beam, whereas the low-power beam was reference beam. All three beams were TE polarization. The signal beam was focused by the objective lens Obj3 in front of the specimen. After passing through the specimen, the divergent signal beam was collected by the lens L3 and was directed to the CMOS-IS1 (CMOS image sensor of Canon 650D; 5184×3456 pixels; 4.3-μm pixel size). The off-axis interferogram of the signal beam and reference beam was captured by the CMOS-IS1, and is expressed as
The phase error between the reference beam and the reading beam as well as the phase error caused by SLM surface-undulation can thus be eliminated.
The Kitty-SPPCM-based optical phase conjugation is used to make alignment between the PSLM and CMOS-IS1. The system setup is shown in Fig. 3. Before the Kitty-SPPCM can be formed, a Cat-SPPCM has to be created in a photorefractive crystal , which is the BaTiO3 crystal in Fig. 3(a). The Cat-SPPCM is a self-induced phase conjugator based on two-wave mixing incorporated with crystal geometry. When a pumping beam was incident into BaTiO3 at an appropriate incident angle and position, a clear fanning loop was formed (Fig. 3(b)). Because two counter-propagation waves existed in the fanning loop, another incident wave (“Kitty” in Fig. 3(b)) passing through the loop would form two four-wave mixing regions and then be diffracted into a phase-conjugate wave. This is the mechanism of the Kitty-SPPCM. There are three advantages of using Kitty-SPPCM in the system alignment: (1) since the formation of the Kitty-SPPCM occurs at the same speed as recording an interference grating in BaTiO3, it can avoid the time delay for building the fanning loop in Cat-SPPCM; (2) the Kitty-SPPCM can achieve higher fidelity in phase reconstruction because it has larger acceptable numerical aperture than most of SPPCMs; (3) the adoption of Kitty-SPPCM makes the alignment free of lens distortion. As the alignment shown in Fig. 3(a), the mirror M4 direct a laser beam into the BaTiO3 crystal to form a Cat-SPPCM. Subsequently, the other laser beam was reflected by a polarized beam splitter (PBS) and expanded by Obj1, L7- L10 to form a convergent wave. This wave was then reflected by a beamsplitter (BS3) and impinge the PSLM. During the alignment, the PSLM transfered it function to amplitude modulation by changing the polarization of incident wave using the linear polarizer LP, and was given a specially designed pattern (Fig. 3(c)) and the light reflected by the PSLM will carry the information of this pattern. After reflected by the PSLM, the light being focused into the BaTiO3 crystal and the Kitty-SPPCM was then formed to generate a phase-conjugate wave. The phase-conjugate wave is reflected by the beamsplitter (BS2) and shined onto the CMOS-IS1. So that, an image of the designed pattern (Fig. 3(d)) can then be captured. By aligning the pattern given to the PSLM and captured by the CMOS-IS, six-axis geometrical alignment, including lateral shifts (x and y), axial shift (z), on-plane rotation (Φz) and out-of-plane rotation (Φx and Φy), can be accomplished. To benefit the alignment in axial shift (z) and out-of-plane rotation (Φx and Φy), the lenses L7- L10 were applied to produce a convergent wave with NA ∼ 0.035, it creates a vector magnification factor. Limiting by the panel size of PSLM (15.4 mm × 8.6 mm) and the pixel size of the CMOS-IS1 (4.3 μm), the accomplished shift tolerances were 4.3 μm (x), 4.3 μm (y), and 125 μm (z), and the rotation tolerances were 0.83° (Φx), 0.47° (Φy), and 0.01° (Φz).
3. System performance and analysis
To test the system’s performance of turbidity suppression and continuous amplification, chicken breast tissues with thickness 0.5 mm, 1 mm, and 2 mm were used as specimens. The mean free path for the chicken breast tissue has been widely studied and the published data is around 30 µm [18,55–56]. As shown in Fig. 1, the signal beam was focused to form a focusing point before the specimens. The divergent signal beam passed through the specimens and then was guided into the CMOS-IS. The measured irradiance of the reference beam was roughly the same as the signal beam in the CMOS-IS plane. Using the interference fringe captured by the CMOS-IS, the phase modulation image, SPSLM, for the PSLM was calculated based on Eq. (3). The band-pass filter used for (Rref · O*)bp and (Rref · P)bp was a circle with 700-pixels radius. Since the pixel sizes of the CMOS-IS and the PSLM are 4.3 μm and 8 μm, respectively, nearest-neighbor interpolation has to be applied to get the input signals for PSLM. By applying SPSLM to the PSLM and illuminating the reading beam on it, the conjugate signal beam was then generated. The conjugate signal beam inversely propagated back through the specimen and formed a focusing point after the specimens. We used BS3 to direct the conjugate signal to the imaging system consisting of the objective lens Obj3, a lens L5, and the CMOS-IS2 image sensor (iDS UI-3590CP; 4912×3684 pixels; 1.25-μm pixel size; gamma correction = 1.0). In order to calculate the PBR of the conjugate signal, we took high dynamic range (HDR) image of the conjugate focusing image by applying the ND filter (THORLABS NDC-100S-4) to control the exposure power of CMOS-IS2. And each HDR image is combined from 5 images with different exposure power. The calculated PBR for tissue thickness of 0.5 mm, 1 mm and 2 mm are 3×105, 1.6×105 and 0.6×105, respectively. The first row of Fig. 4(a)-(c) show the HDR image of the phase conjugate point for the chicken breast tissues with thickness 0.5 mm, 1 mm, and 2 mm, respectively. The second row and the third row show the light distribution along the red dash line and the green dash line, respectively. The measured full width of half maximum (FWHM) of the light distribution along the two axis are all below 5 µm. For the case of 0.5 mm and 1 mm, a tail of the conjugate point is observed. It is because the reading beam kept turn-on in the acquisition step to continuously produce DOPC focusing beam, and thus induces some system noise.9] The mode number N is estimated as the area of SLM divided by the area of the speckle, and is 1.01×106. When applying Eq. (5) to the proposed system, the theoretical PBR is 7.93×105. It shows the experimental PBR are 38%, 20%, and 7.5% of the theoretical limit for tissue thickness 0.5 mm, 1 mm, and 2 mm, respectively.
However, Eq. (5) can’t explain the PBR degradation along with the specimen-thickness increase. According to the experimental observation, the detected information of the DOPC system tends to be lost when the specimen getting thicker. Not only because of the specimen absorption, but also because of the larger channel number. The channel number is roughly equal to (2L)2/(λ/2)2, where L is the thickness of the sample and λ is the wavelength.  In the perspective of adaptive optics, larger channel number of the specimen just benefits the optimizing wave front. Because it enables the degree of freedom to control the wave-front passing through the specimen and to accumulating constructive interference. However, DOPC is intrinsically different. It is designed to fast duplicate a phase conjugate wave-front of the detected wave-front. If the channel number of the specimen is larger than the DOPC system, the DOPC system can’t resolve the extra information. The information loss leads to wave-front detection errors, and the duplication of error phase conjugated wave-front leads to PBR degradation. We can estimate the information loss by calculating the system fidelity (ϕ) [59,60].
Table 1 shows the measured power in different positions. The power of the signal before the chicken tissue was 13 µW, 35.5µW, and 64 µW for 0.5 mm, 1 mm and 2 mm chicken breast tissue, respectively. Since, only 20% of signal can be collected by the optical system. The power of the signal before the chicken tissue and collected by the system (PS1) was 2.6 µW, 7.1µW, and 12.8 µW. When the light passing through the chicken tissue (PS2), it became 101 nW, 154 nW, and 200nW. In the acquisition step, the light power of the reading beam illuminating the SLM was 80 mW. The power of the phase conjugate signal propagating to the front surface of the chicken breast tissue (PPC1) was 970 µW, 893 µW, and 861µW. After passing through the chicken breast tissue, the power of the phase conjugate signal (PPC2) was 438.8 μW, 312.6 μW and 39.5μW. Thus, the system reflection ratio was 19208, 11597 and 8601. As a result, we get the continuous amplification ratio 166.2, 44 and 3.1 for 0.5 mm, 1 mm and 2 mm chicken breast tissue, respectively.
The temporal-continuous amplified DOPC system owns a bright future in the field of optical tweezers, and it is successfully demonstrated in this paper. Because the reference beam must be separated from the reading beam, a new method for alignment between the PSLM and the CMOS-IS is proposed. The six-axis alignment for the DOPC system and phase difference elimination between the reference beam and the reading beam were realized using the Kitty-SPPCM. Through precise alignment of the DOPC system with the Kitty-SPPCM, a focus point passing through a 2-mm-thick chicken tissue slice was obtained using the DOPC system with continuous optical gain at a wavelength of 532 nm. Subsequently, we modified the light path to enlarge the power difference between the reference beam and the reading beam. Besides, the continuous gain of 166 44, and 3.1 and PBR of 3×105, 1.6×105 and 0.6×105, were observed in the case of 0.5-mm, 1-mm and 2-mm chicken tissue slice, respectively. The PBR degradation along chicken tissue thickness can’t be explained by the theoretical formula based on adaptive Optics. Therefore, we explain the PBR degradation using fidelity (ϕ) defined by Gu’s work. The experimental result shows the curves of PBR and Fidelity are in the same trend. It demonstrates the PBR degradation is caused by information lose.
Ministry of Science and Technology, Taiwan (MOST) (104-2221-E-008-073-MY3, 105-2218-E-035-009-MY3); Ministry of Education (MOE) (105G-903).
The authors acknowledge support by Ministry of Science and Technology of ROC with the grant number MOST 104-2221-E-008-073-MY3, MOST 105-2218-E-035-009-MY3, and by the National Central University’s “Plan to Develop First-class Universities and Top-level Research Centers” with the grant number 105G-903.
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