Continuous amplified digital optical phase conjugator for focusing through thick, heavy scattering medium

Yeh-Wei Yu; Ching-Cherng Sun; Xing-Chen Liu; Wei-Hsin Chen; Szu-Yu Chen; Yu-Heng Chen; Chih-Shun Ho; Che-Chu Lin; Tsung-Hsun Yang; Po-Kai Hsieh

doi:10.1364/OSAC.2.000703

1. Introduction

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 [12], 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 [39]. 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 [47].

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

(1)$${|{{R_{ref}} + O} |^2} = {|{{R_{ref}}} |^2} + {|O |^2} + {R_{ref}}^{\ast } \cdot O + {R_{ref}} \cdot {O^{\ast }}, $$

where O is the signal beam and R_ref is the reference beam. The tilting angle was 1.32˚, which made the first-order signal deviating from the DC peak but overlapping with a part of zero-order signal in the Fourier domain. The noise caused by the zero-order signal can be ignored if the PBR of the system was high enough. In order to produce a continuous phase conjugate signal, the reading beam was always turn on, even in the acquisition step. To obtain the input signals for the PSLM (HOLOEYE PLUTO; 1920×1080 pixels; 8-μm pixel size), a band-pass filter was applied to the Fourier spectrum of ${|{{R_{ref}} + O} |^2}$ to extract (R_ref · O*)_bp. An aperture Ap₁ was attached to the lens L₃ in order to block the zero-order reading light reflected by PSLM in the reconstruction step. Since the reading beam is independent of the reference beam in the CA-DOPC, simply applying (R_ref · O*)_bp to the PSLM and illuminating the reading beam, P, will lead to a phase error of (R_ref)_bp · P in the phase- conjugate wave. Therefore, the phase information between the reference beam and the reading beam has to be acquired. Figure 2 shows we use the Kitty SPPCM to generate an optical phase conjugate reading beam. By recording the interferogram formed by the reference beam and the optical phase conjugate reading beam,

(2)$${|{{R_{ref}} + {P^{\ast }}} |^2} = {|{{R_{ref}}} |^2} + {|P |^2} + {R_{ref}}^{\ast } \cdot {P^{\ast }} + {R_{ref}} \cdot P, $$

the information of (R_ref · P)_bp is obtained by applying a band-pass filter to the Fourier Spectrum of ${|{{R_{ref}} + {P^{\ast }}} |^2}$. Figure 1(b) shows only the reading beam was turn on and illuminated the PSLM in the reconstruction step. Taking the product of (R_ref · O*)_bp and the phase conjugate of (R_ref · P)_bp, the input signal for the PSLM can be obtained as

(3)$${S_{PSLM}} = [{{{({{R_{ref}} \cdot {O^{\ast }}} )}_{bp}}} ]\cdot {[{{{({{R_{ref}} \cdot P} )}_{bp}}} ]^\ast } = P_{bp}^\ast \cdot O_{bp}^\ast . $$

When applying S_PSLM to the PSLM, the phase-conjugate wave can be obtained by illuminating the reading light,

(4)$$P \cdot {S_{PSLM}} = ({P_{bp}^\ast \cdot P} )\cdot O_{bp}^\ast \approx O_{bp}^\ast . $$

Fig. 1. CA-DOPC system with temporal-continuous gain: (a) The acquisition step for collecting the wave-front passing through the Specimen; (b) The reconstruction step for producing phase conjugate signal. Obj: Objective lens; PH: Pin hole; L: Lens; CL: Cylindrical lens; M: Mirror; BS: Beam splitters; PBS: Polarization beam splitters; HWP: Half wave plates; PL: Linear polarizers; PSLM: Phase-only spatial light modulator; CMOS-IS: CMOS image sensor; BK: Block.

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Fig. 2. (a) Kitty SPPCM is used to generate an optical phase conjugate reading beam. (b) The interferogram formed by the reference beam and the optical phase conjugate reading beam is recorded by the CMOS-IS₁.

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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 [54], 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 (Φ_z) and out-of-plane rotation (Φ_x and Φ_y), can be accomplished. To benefit the alignment in axial shift (z) and out-of-plane rotation (Φ_x and Φ_y), 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° (Φ_x), 0.47° (Φ_y), and 0.01° (Φ_z).

Fig. 3. (a) Alignment of CA-DOPC system using Kitty SPPCM; (b) Kitty SPPCM; (c) SLM input signal of alignment marks; (d) Conjugate images of alignment marks readout by CMOS-IS₁. Obj: Objective lens; L: Lenses; M: Mirrors; CL: Cylindrical lens; BS: Beam splitters; PBS: Polarization beam splitters; HWP: Half wave plates; PSLM: Phase-only spatial light modulator; CMOS-IS: CMOS image sensor; BK: Block plate.

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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, S_PSLM, for the PSLM was calculated based on Eq. (3). The band-pass filter used for (R_ref · O*)_bp and (R_ref · 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 S_PSLM 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.

Fig. 4. The HDR image of the phase conjugate point for the chicken breast tissues with thickness (a) 0.5 mm, (b) 1 mm and (c) 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.

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The theoretical PBR of the DOPC system follows the framework of adaptive optics proposed by Vellekoop et al., it is expressed [57,58]

(5)$$PBR = \frac{\pi }{4}(N - 1) + 1, $$

because the size of CMOS-IS₁ is longer in the vertical direction, its vertical unit length in Fourier domain is shorter. When the radius of circular band pass filter in Fourier domain is set as 700 pixels, it leads to oval-shape speckles, and the area of each speckle is around 131.46µm², which is around the size of 2 SLM pixels. Since only 2 SLM pixels are used to sample one speckle grain, it contributes high PBR performance. [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. [54] 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].

(6)$$\phi = {\alpha _{specimen}}{\alpha _{Opt}}{\alpha _{Spectrum}}, $$

where

(7)$${\alpha _{specimen}} = \frac{{\int {{{|{{E_{{s_2}}}({{r_2}} )} |}^2}d{r_2}} }}{{\int {{{|{{E_{{s_1}}}({{r_1}} )} |}^2}d{r_1}} }}, $$

(8)$${\alpha _{Opt}} = \frac{{\int {{A_p}{{|{{E_{DOPC}}({{r_3}} )} |}^2}d{r_3}} }}{{\int {{{|{{E_{DOPC}}({{r_3}} )} |}^2}d{r_3}} }}, $$

and

(9)$${\alpha _{Spectrum}} = \frac{{\int {{A_{{p_f}}}{{|{{e_{{\mathop{\rm int}} }}(f )} |}^2}df} }}{{\int {{{|{{e_{{\mathop{\rm int}} }}(f )} |}^2}df} }}. $$

Here, α_specimen is the fidelity related to the specimen absorption, and α_Opt and α_spectrum are the fidelities related to the optical entrance pupil of the DOPC system and spectrum resolving capability, respectively. In addition, E_s1 is the electrical field of the signal beam before it passing through the specimen; E_s2 is the electrical field of the signal beam after it passing through the specimen; E_DOPC is the electrical field at the entrance pupil of the DOPC system; Ap is the optical entrance pupil of the DOPC system; e_int is the Fourier transform of the electrical field on the CMOS-IS₁; Ap_f is the spectrum entrance pupil of the DOPC system. It shows α_specimenα_Opt. equal to the ratio of DOPC-system collected power over the input signal power. And α_spectrum equals to the integrated energy insides the band-pass filter over the total energy in the Fourier spectrum. Accordingly, the measured fidelities are 2.9×10⁻⁴, 1.7×10⁻⁴, and 1.2×10⁻⁴, respectively. Figure 5 compares PBR with Fidelity, and it shows both curves are in the same trend with a constant PBR degradation. We believe it is caused by some system noises, ex., the noise induced by the reading beam in the acquisition step.

Fig. 5. PBR compared with Fidelity, it shows both curves are in the same trend with a constant PBR degradation.

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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 (P_S1) was 2.6 µW, 7.1µW, and 12.8 µW. When the light passing through the chicken tissue (P_S2), 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 (P_PC1) was 970 µW, 893 µW, and 861µW. After passing through the chicken breast tissue, the power of the phase conjugate signal (P_PC2) 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.

Table 1. Measured power in different positions

View Table

4. Conclusion

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.

Funding

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).

Acknowledgements

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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Specimen	Thickness of the chicken tissue	0.5 mm	1 mm	2 mm
Acquisition Step	Power of the signal before the chicken tissue and collected by the system (P_S1)	2.64µW	7.1µW	12.84µW
Acquisition Step	Power of the signal passing through the chicken tissue (P_S2)	101nW	154nW	200.2nW
Reconstruction Step	Power of the phase conjugate signal before the chicken tissue (P_PC1)	970µW	893µW	861µW
Reconstruction Step	Power of the phase conjugate signal passing through the chicken tissue (P_PC2)	438.8µW	312.6µW	39.5µW
System Gain	Reflection ratio (RR = P_PC1/P_S2)	19208	11597	8601
System Gain	Amplification ratio (AR = P_PC2/P_S1)	166.2	44	3.1

Continuous amplified digital optical phase conjugator for focusing through thick, heavy scattering medium

Abstract

1. Introduction

2. CA-DOP system

3. System performance and analysis

4. Conclusion

Funding

Acknowledgements

References

Cited By

Figures (5)

Tables (1)

Equations (9)

OSA Continuum