High-quality laser beam diagnostics using modified coherent phase modulation imaging

Xiaoliang He; Hua Tao; Xingchen Pan; Cheng Liu; Jianqiang Zhu

doi:10.1364/OE.26.006239

1. Introduction

High power laser facilities are extensively applied for both scientific researches and industrial productions, and in most of applications, the quality of the focal spot including the size, the energy concentration, the shape and the smoothness are all important parameters to evaluate the performance of the whole laser facility. Many factors such as the static aberration and the thermal distortion of the optical elements, the misalignment of the system, the atmospheric turbulence and the non-linear effects all can deteriorate the laser beam quality and seriously twists the focal spot. Thus online laser beam diagnostics is very important for the high power laser facilities to run properly. The focal spot of high power laser beam can have the intensity higher than 10²⁰-10²¹ W/cm², and due to the limited dynamic range of the detector, it is difficult to directly record the focal spot by placing the detector exactly on the focal plane. An alternative approach for the focal spot diagnosis is to measure the complex amplitude of the laser beam including both its phase and modulus on the out-of-focus plane and then numerically propagate it to the focal plane. Since the laser beam to be measured is only a single laser pulse propagating in sealed tubes of high vacuum, interferometry based techniques [1,2] can't be applied to measure the complex amplitude of the laser because of their huge size and complex structure, though they always have quite high accuracy and spatial resolution. Shark- Hartman sensor [3,4] has small size, compact structure and low requirement on the stability of the working environment, thus it is the most commonly used device to measure the complex amplitude of the high power laser beam, however, since its spatial resolution is limited by the number of the microlens, the reached spatial resolution is only at the scale of several millimeters, which only provides the low frequency information of the laser beam, and the obtained focal spot by numerically propagating the measured complex amplitude to the focal plane can only describe the energy concentration of the focal spot, the details in the distribution of the focal spot are invisible. The ideal device for the high power laser beam diagnosis should have a resolution comparable to that of the interferometer as well as a compact structure comparable to that of Hartman-shark sensor, however, this kind of device is still not available by now. The recent development of coherent diffractive imaging (CDI) [5–8] provides alternative approach to circumvent the problem on the lack of ideal tools for the high power laser beam diagnosis.

CDI was developed for the imaging with short wavelengths including the x-ray and the high energy electron beam, where the high-quality lens is difficult to fabricate. Since it doesn't use any complex optics, CDI can reach the diffraction limited resolution in theory. On the other hand, since the optical setup is quite simple, CDI based imaging system has a structure much compacter than that of the Shark- Hartman sensor, and accordingly it has the potential to be an ideal diagnosis technique for the high power laser characterization. CDI was firstly used to measure the phase of the high power laser beams by Shinichi Matsuoka [9], in this measurement the intensity of the laser beam were recorded at two different planes along the optical axis, the complex amplitude of the laser beam is reconstructed using the standard G-S algorithm [10]. Bahk [11] used CDI to characterize the near-field of high energy laser beam by measuring the intensity of the laser beam at multiple focal spot planes inside the target chamber. CDI was also successfully applied to realize the focal-spot diagnostics (FSD) [12] for OMEGA EP laser facility, which is a petawatt-class high-energy laser system in University of Rochester. As most CDI techniques being used in the field of laser systems reported by now [9,11,12] adopt multiple plane recording scheme [13–15] to guarantee convergence. However, multiple plane recording scheme increases the requirement on the accuracy and stability of the experimental setup. More importantly, these methods might be quite complicated when measuring pulsed laser beam. However, since the performance of traditional CDI algorithm [16–20] with single-shot measurement including error-reduction (ER) algorithm [16–18], the hybrid input-output (HIO) algorithm [16–18] and the gradient-based algorithms [19,20] are not very satisfying in terms of the convergence speed, the reliability and the image quality, CDI was not widely applied for the laser beam diagnosis by now.

Coherent modulation imaging (CMI) [21–23] is a novel CDI method proposed by Prof. Rodenburg’s group in Sheffield University, which only needs single-shot measurement. The setup of CMI is quite compact that it employs a random phase mask to modulate the wave-front of the laser beam and a CCD to record the diffraction patterns formed. Since the structure of CMI based imaging system is much similar to that of Shark-Hartman sensor except that the micro-lens array is replaced by the random phase mask, and its resolution can be ten times higher that of Shark-Hartman sensor, it has been successfully demonstrated that CMI is a very promising technique for the high power laser beam diagnosis and focal spot characterization. After the first proof-of-principle experiment reported by Xiaoliang He [26] in 2015 on He-Ne laser beam, CMI has been successfully applied to monitor the near field and far field beam quality of the high power laser by Pan and Tao [27]. However, the quality of the reconstructed image especially the near field distribution of the laser beam is seriously degraded by the speckle noise, leading to poor signal-to-noise ratio (SNR). In this manuscript, we proposes adding a second CCD to record the intensity of the laser beam itself and using the recorded intensity as the second constraint in the reconstruction to improve the image quality of the recovered near field. Proof-of-principle experiments have been conducted with He-Ne laser to verify the feasibility of this proposed method. The manuscript is organized as follows: Section 2 describes the details of the proposed method and iterative process of the algorithm, Section3 shows the experimental results to demonstrate the feasibility of the method and Section 4 concludes.

2. Details of the method

As a CDI technique, CMI is also based on the principles of diffraction and convolution, and for practical experiments the light field transmitting the phase mask should be totally mixed together on the recording plane. Thus, the scattering capability of the phase mask should be strong enough, and it is always designed as a binary (0 and π) pure phase object. Since the highly random distribution of the phase mask remarkably reducing the ambiguity [24,25] existing in the traditional CDI, the complex amplitude of the laser beam incident on the random phase plate can be rapidly reconstructed iteratively with the known structure of the phase mask. In common CMI, there are two main reasons why the recovered light field of near field is degraded. Firstly, the high-angle diffracted light exiting the highly random phase mask are very weak in intensity which would not be recorded by the dynamic-range-limited CCD. Secondly, due to the grating effect of the phase mask, high-order diffractions fall beyond the area of the CCD chip, the beam information embed inside the high order diffractions is lost in the camera recording process. The information loss caused by these two reasons leads the poor quality of recovered near field. It is straightforward that the lost information can be compensated by recording the intensity of the laser beam without passing through the phase mask with another CCD. Since there is no information loss in the recorded intensity of the laser beam, the image quality of the near field is improved by the modified CMI.

The setup of common CMI is illustrated in Fig. 1(a). The wave-front to be measured is located at the near field plane in Fig. 1 and it propagates through a focusing lens, a random phase mask, finally the scattered intensity is collected by a CCD sensor placed several centimeters downstream of the phase mask. The collected intensity pattern is then used to reconstruct the wave-front by iterative phase retrieval algorithms. Figure 1(b) shows the setup of the modified method in this manuscript. Compared with the common CMI, the modified method utilizes a beam splitter downstream of the focusing lens and another CCD sensor C2 placed in the reflection path for collecting the intensity of the laser directly.

Fig. 1 Setup of (a) common CMI and (b) modified CMI. OL: objective lens, P: pinhole, L1: collimating lens, L2: focusing lens, BS: beam splitter, PM: phase mask, C1: CCD1, C2: CCD2.

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Assumed that the distribution of focus as $f_{n} (x, y)$ , $n$ denotes the iteration number. The algorithm of the modified CMI can be carried out as follows.

(1). The light field that incidents on the phase mask can be calculated by the Fresnel propagation. $p_{n} (x, y) = F_{p} [f_{n} (x, y), λ, d_{2}]$
where $λ$ is the wavelength and $d_{2}$ is the distance between the focus and the phase mask. $F_{p}$ represents the Fresnel transform, which is defined as
$F_{p} [f (x, y), λ, z] = \frac{e^{j k z}}{j λ z} \iint f (x, y) e^{[j k \frac{{(x_{0} - x)}^{2} + {(y_{0} - y)}^{2}}{2 z}]} d_{x} d_{y} .$
(2). Then the field is modulated by the phase mask and propagated to the plane of C1, the wave-front distribution at C1 plane can be obtained by $φ_{n} (x, y) = F_{p} [p_{n} (x, y) M (x, y), λ, (d_{3} - d_{2})] .$
where $M (x, y)$ is the complex distribution of the phase mask and $d_{3}$ is the distance between the focus and C1.
(3). The field at C1 plane is updated by replacing the modulus with the square root of the recorded $\sqrt{I_{C 1}}$ whilst preserving the phase $ψ_{n} (x, y) = \sqrt{I_{C 1}} φ_{n} (x, y) / | φ_{n} (x, y) | .$
(4). Back propagate the updated field from C1 plane to the phase mask $ϕ_{n} (x, y) = F_{p} [ψ_{n} (x, y), λ, - (d_{3} - d_{2})] .$
(5). The ptychography [28–31] update routine is used to remove the effect of the phase mask $p'_{n} (x, y) = p_{n} (x, y) + β \frac{M^{*} (x, y)}{{| M (x, y) |}_{\max}^{2}} [ϕ_{n} (x, y) - p_{n} (x, y) M (x, y)] .$
where $β$ is a constant to adjust the updating step length, in this manuscript, we set $β = 1$ .
(6). Propagate $p'_{n} (x, y)$ to the focus and use the 'virtual' spatial constraint $S (x, y)$ there. $S (x, y)$ is defined as circular function, the size of $S (x, y)$ is initialized with zero and gradually extended in the iterative process. $f'_{n} (x, y) = F_{p} [p'_{n} (x, y), λ, - d_{2}] \cdot S (x, y) .$
The above process is the same as the common CMI. In our modified method, another intensity $I_{C 2}$ recorded by the CCD sensor C2 is used as the intensity constraint in following processes.
(7). The field at C2 plane is propagated to the second CCD $τ_{n} (x, y) = F_{p} [f'_{n} (x, y), λ, d_{4}] .$
where $d_{4}$ is the distance between focus and C2, as shown in Fig. 1(b).
(8). For the consideration of splitting ratio of the splitter may not strictly 1:1, its effect is considered by enforcing the total energy of the recorded intensity by CCD2 equal to that of the established light field at the CCD2 plane in every iteration of the computation process. The modulus of $τ_{n} (x, y)$ is replaced with $\sqrt{I_{C 2} \cdot \sum_{x, y} {| τ_{n} (x, y) |}^{2} / \sum_{x, y} I_{C 2}}$ while the phase keeps unchanged, the newly updated field is propagated back to the focal plane ${\bar{f}}_{n} (x, y) = F_{p} [\sqrt{I_{C 2} \cdot \sum_{x, y} {| τ_{n} (x, y) |}^{2} / \sum_{x, y} I_{C 2}} \cdot τ_{n} (x, y) / | τ_{n} (x, y) |, λ, - d_{4}] .$
(9). The distribution of the focus is updated by the HIO algorithm $f_{n + 1} (x, y) = f_{n} (x, y) S (x, y) + δ (f_{n} (x, y) - {\bar{f}}_{n} (x, y)) S (x, y) .$
where $δ$ is a constant value. In this manuscript, we set $δ$ = 0.9.

The above steps goes on until the difference between the calculated intensities and the measured intensities in the CCD planes is sufficient small. After the final focus distribution is obtained, further propagation to the plane of near field gives the near field distribution of the laser beam. The flowchart in Fig. 2 shows the procedure of common CMI and modified CMI method, their difference is in the red rectangle with broken line.

Fig. 2 Flowchart of common CMI (without red dotted square) and modified CMI (with red dotted square).

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3. Experimental setup and results

In this section, the feasibility of the proposed method is verified experimentally. The experiments are carried out with the He-Ne laser beam.

3.1. Experimental setup

The experimental setup is shown in Fig. 1(b). A laser (HNL050RB, Thorlabs) beam of 5 mW is expanded into 25 mm in diameter, which is comparable to that of the real high power laser beam sampled from our SG II laser facility. The extended laser beam is focused by the lens L2 with a diameter of 40 mm and a focal length of 300 mm. The focused laser beam is split into two beams by the beam splitter. The beam splitter is placed upstream of the focus for the consideration of saving space between the focus and the phase mask to prevent the size of zero order scattered beam being larger than the CCD chip. The transmitted beam passes through a random binary phase mask (pixel size of 14.8 μm, 0 and π phase distribution) placed at d₂ = 31 mm downstream of the focus. The CCD C1 (Pike F421B, AVT) which consists 2048 × 2048 pixels with pixel pitch of 7.4 μm is placed at d₃ = 86 mm downstream of the focus to record the diffraction pattern. The reflected beam is recorded by the second CCD C2 (Pike F421B, AVT) placed at d₄ = 86 mm downstream of the focus. In experiment, the position of the second CCD relative to the first one should be known exactly and their positions are calibrated when there is no phase mask in the optical path. This is done by placing an object before the beam splitter and imaging it on each CCD simultaneously with a lens placed upstream the beam splitter. By adjusting the positions of these two CCDs, two identical images can be obtained and then the experiments can be carried with the calibrated system. To show the improvement in the spatial resolution clearly, a piece of slide with two characters “SG” is placed at d₁ = 1.1 m before L2 to simulate the near-field plane to observe in real high power laser facility.

3.2. Experimental results

Figure 4(e) shows the photo of the glass with two characters of 'SG'. Figure 3(a)-(b) show the diffraction patterns recorded by C1 and C2, respectively. Figure 4(a)-(b) are the reconstructed phase image and the intensity image with common CMI algorithm, respectively, and in the zoomed in intensity image we can clearly see serious speckle noise. Figure 4(c)-(d) show the reconstructed phase and intensity images with the modified CMI algorithm proposed in this manuscript, respectively. Both the common CMI and modified CMI reconstructions were finished with 250 iterations and the total calculation time was 12.3 seconds for common CMI and 17.6 seconds for modified CMI accelerated with a graphic processing unit (Tesla K40, NVIDIA). In the zoomed in intensity image we can clearly find that the speckle is distinctively reduced, and the fine fringes, which is the interference between the residual reflections from the two planes of the glass, are clearly visible. For comparison, the glass is directly imaged and its intensity is shown in Fig. 4(f). Correction coefficients CC1 and CC2 are calculated to demonstrate the SNR improvement quantitatively. CC1 represents the correction coefficient between reconstructed intensity by common CMI and the true intensity, the value of CC1 is 0.87 calculated between Fig. 4(b) and Fig. 4(f). CC2 represents the correction coefficient between reconstructed intensity by modified CMI and the true intensity, the value of CC2 is 0.98 calculated between Fig. 4(d) and Fig. 4(f). It can be concluded that the reconstruction quality is improved by the modified CMI.

Fig. 3 Recorded intensity pattern by (a) CCD C1 and (b) CCD C C2.

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Fig. 4 (a) Phase and (b) intensity obtained by common CMI. (c) Phase and (d) intensity obtained by modified CMI, (e) a photo of the slide taken by a cellphone and (f) intensity of directly imaged glass.

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Figure 5(a)-(b) show the reconstructed focal spot with the common CMI algorithm and that of the modified algorithm, we can find that there is almost no much difference between the low frequency components of Fig. 5(a) and that of Fig. 5(b), which are labeled with squares of broken line. However, the difference between their high frequency components (outside of the square) is quite visible. Figure 5(c) is the directly recorded focal spot by placing the CCD camera exactly on the focal plane, and in comparison it to Fig. 5(b), they are almost identical to each other.

Fig. 5 Reconstructed focal distribution by (a) common and (b) modified CMI, (c) the focal spot distribution directly recorded by CCD.

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To show the spatial resolution improvement quantitatively, the USAF resolution target is imaged with the same experimental setup, and the two recorded diffraction patterns are shown in Fig. 6(a) and Fig. 6(b), respectively.

Fig. 6 Recorded intensity pattern by (a) CCD C1 and (b) CCD C2.

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Figure 7(a)-(b) show the reconstructed intensity of the near field by common CMI and the modified CMI algorithms, respectively. And from their zoomed in images, we can find that, spatial resolution reached by the common CMI is about 176.78 μm (Group 1, Element 4) while the spatial resolution of the modified CMI method is about 55.68 μm (Group 3, Element 2). In other words, the spatial resolution can be improved by 3 times by simple using an additional CCD camera. For easy comparison, the image of the resolution target is directly imaged and its intensity is shown in Fig. 7(c). We can find that the resolution achieved by modified CMI is close to that of Fig. 7(c).

Fig. 7 Reconstructed intensity by (a) common CMI and (b) modified CMI. (c) Intensity of directly imaged USAF target. The bottom three images are enlarged images of the red squares in (a), (b) and (c).

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It is worthy to point out that, though the experiments are carried with continue He-Ne laser, which has good coherence, according to our previous research [27], this modified CMI method can be directly applied to measure pulsed high energy laser beam.

4. Conclusion

In this manuscript, a modified CMI method is proposed by adding a second CCD to record the intensity of the laser beam itself to improve the measurement accuracy of laser beam. Experiments have been conducted on He-Ne laser beam with a diameter of 2.5 cm. Compared with the common CMI method, the modified CMI can obtain a near field wavefront distribution with much less speckle noise and a higher resolution. Beam quality of near-field and focal-spot distribution are the utmost parameters in high power laser facilities. Shack–Hartmann sensor based wavefront diagnostics technologies have inherent limitations of low resolution, a method based on common CMI appears to be more flexibility and reliable but provides speckle noise in the near field. The modified CMI method overcomes the shortcomings of Shack-Hartmann and common CMI method and we believe that the proposed method will have potential applications in beam quality diagnosis in high power laser facilities.

Funding

National Natural Science Foundation of China (NSFC) (No. 61675215).

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High-quality laser beam diagnostics using modified coherent phase modulation imaging

Abstract

1. Introduction

2. Details of the method

3. Experimental setup and results

3.1. Experimental setup

3.2. Experimental results

4. Conclusion

Funding

References and links

Cited By

Figures (7)

Equations (10)

Optics Express