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Abstract
A new novel method, hyperspectral imaging (HSI), is presented in this work to measure the beam divergence angle and beam profile uniformity of supercontinuum lasers. The obtained results of divergence angles are consistent with theoretically calculated values. The uniformity of different-size projected Gaussian beams was measured through referencing the data sets provided by HSI camera under the wavelength variation. HSI, compared with traditional methods, is much faster and capable of providing critical reference to supercontinuum output parameters measurements and practical application in far-field situation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Supercontinuum (SC) has been greatly demanded by virtue of its crucial applications, inclusive of optical communications, optical frequency metrology, optical coherence tomography and spectroscopy [1–5], etc. Photonic crystal fiber (PCF) taking on various unique properties, such as high non-linearities and tailored dispersion features [6, 7], becomes a prominent choice of SC generation. Differing from those of conventional optical fiber, PCF has important features, especially in structure and light-guidance [8, 9]. The beam divergence angle demonstration of fiber is important among many parameters such as inclusive of numerical aperture, nonlinear coefficient. A novel method, hyperspectral imaging (HSI) [10], which accurately measures the divergence angle of home-made fiber laser with the pigtail as PCF, is demonstrated in this paper. The obtained result by utilizing this technology fits well with the simulated values, enabling its potential applications in other types of laser sources.
Similarly, for supercontinuum practical application, the far-field illumination of supercontinuum, which depends on the different divergence angles corresponding to diverse wavelengths, is of great significance in the field of biomedicine [11, 12], archaeology and art conservation [13, 14], active hyperspectral imaging [15, 16], etc., This is primarily because that the spectral components of diverse illuminated fields have considerable discrepancies as the inherent property of supercontinuum. The far-field beam profiles distribution and uniformity measurement were studied using HSI method that is essential for supercontinuum practical application.
2. Beam divergence angles measurement
The schematic image of experimental setups is presented in Fig. 1. The incident angle of supercontinuum laser source end-facet towards the diffuse reflection board is the right-angle (θa = 90°), keeping the accurate Gaussian fields distribution of the beam reaching the board. Such distribution would be recorded by camera. The fiber is fixed on the slide way frame for setting the distance between the fiber and board freely. In the meanwhile, the HSI camera is placed as close to the fiber’s output end as possible and the field view of the camera’s center height is set to the same level of the fiber output end face by the lifting plate. Accordingly, the y-axis beam intensity distribution reaching the board would be distorted to the least extent. Before the real beam measurement, we put calibration paper with grids on the board for length calibration measurement to subsequent image processing. The camera scanning speed, spectrum channels, spatial samples, and object distance in camera should be maintained as the same value, respectively. In the single test, camera exposure time is set, keeping the light intensity below the threshold value. The beam divergence situation is acquired through analyzing the y-axis beam profile intensity distribution.
More specifically, during the measurement, the HSI camera model was GaiaField-F-V10 (Zolix) with spectrum detection ranging from 400 nm-1000 nm, and the minimal spectral resolution reaches 0.55 nm. In the experiment, the spectrum channels are set as 520, while spatial samples as 696 for photographing conveniently (the max spectrum channel is 1040). The fiber end face is 15 cm away from the board with the fiber end face 22.5 cm in height. The integral time is 6 seconds and gain is 2 in the HSI camera setting. Meanwhile, these two parameters should be adjusted simultaneously to prevent the saturation of the camera by the maximum intensity in each wavelength of SC. The whole experiments were carried out in the darkroom to avoid the environmental disturbance. During the image processing, we averaged the superposition of three sets of photographs under the same condition. Using these methods, the image noise would be eliminated as possible.
In the measurement of beam divergence angle, the average pitch of holes is 3.35 µm and diameter of holes is 2.15 µm. The corresponding scanning electron microscope (SEM) image of the PCF is presented in Fig. 2(a). The output SC laser source power was adjusted to 2 W with output spectrum in Fig. 2(b).
Fig. 2 (a) SEM image of the PCF in the laser source and (b) the SC output spectrum when the output power is 2 W.
The output light intensity is defined as for each wavelength in supercontinuum as a Gaussian fundamental mode optical field radiates from the PCF. Given that light propagating in the PCF is symmetrical, one axis passing through the beam profile center can be selected to analyze the optical field distribution presented in Fig. 3. Each point’s decreases with the increase of distance between the center spot and the reference point. As indicated in the picture taken by camera, when optical field intensity of one wavelength decreases to of the max , which corresponds to the edge of the beam counting for the divergence angle, the following equation is acquired in Fig. 3 to evaluate the actual divergence angle in different wavelengths.
In the simulation part, the standard approximate expression for the Gaussian field of width for optical field intensity decreasing to is expressed aswhere represents the half angle of beam divergence [17].Fig. 3 Experimental measuring structure diagram. z: the distance between the fiber facet and diffuse reflection board. d: the distance between the center spot and the reference point when optical field intensity of one wavelength decreases to of the max . : divergence angle.
Introduce into upper equation is [18]
Simulations are performed by utilizing the commercial COMSOL Multiphysics software which is based on finite element method in calculation of the beam divergence angles in Eq. (3) for different wavelengths. The experimental results (dashed line in red) match well with simulation data (solid line in blue) in Fig. 4 through establishing PCF model and employing finite element method. The HSI method is faster and more convenient than traditional measurement methods of divergence angles, inclusive of far-field optical intensity measurement method [19], refracted near-field scanning method [20], etc. Moreover, the divergence angles of different wavelengths can be assessed under HSI camera’s limitation, for instance spectral range and threshold intensity of CCD.
Fig. 4 Theoretical results (solid line in blue) and experimental results (dashed line in red) of divergence angles in different wavelengths.
3. Beam profile uniformity analysis
The far-field beam profile of diverse wavelengths in SC is exhibited in the picture taken by the HSI camera. Figure 5(b) shows three pseudorandom color picture of the far-field beam profile with distance between the PCF facet and the diffuse reflection board fixed at 15 cm. Spot A (red dot), B (green dot), C (blue dot) are chosen in order as they move away from the center of the beam profile randomly. The 3D beam shape of light intensity in SC source of Fig. 5(b) at λ = 618.2 nm is showed in Fig. 6(a). In addition, the normalized spectral intensity of each spot is presented in Fig. 5(a). Similarly, the spectral intensity of all the points in the picture is incorporated to reach the total spectral intensity of the output light from the laser source, as the curve S (pink line) in Fig. 5(a). There is a distinct discrepancy between different spots’ spectral intensity distribution and the total spectral intensity. Accordingly, simple methods are inaccurate, e.g. spatial coupling by optic fiber patch cords connected to the spectrometer for spectrum measurement, given the measurement locations.
Fig. 5 (a) The normalized spectral intensity distribution of the whole beam profile in curve S (pink line) and spot A (red line), B (green line), C (blue line) and (b) each spots’ location in the photograph.
Fig. 6 (a) 3D beam shape of light intensity in SC source at λ = 618.2 nm and (b) the normalized beam intensity distribution at λ = 500.6 nm (black line), 618.2 nm (red line), 740.1 nm (blue line), 866.3 nm (green line) when the distance between fiber end face and board is 15 cm.
Furthermore, with the increase of the wavelength, the divergence angle also increases as described by the Eq. (2). At the same time, the relative intensity ratio of the beam’s center area decreases in Fig. 6(b) because of the Gaussian beam property of different wavelengths in y-axis. In that case, the relative intensity proportion of long wavelengths in total spectral intensity of light will rise from spot A to C as presented in Fig. 5(a).
In the practical application, the SC beam uniformity of different wavelength is critical for illumination because of the spectral component distinction of the different illuminated areas. Considering this aspect, the beam uniformity in different areas corresponding different angles from the laser source on the board is delved into. Due to the distortions of the graphs taken by the HSI camera, the image affine transformation is employed in the real imaging recovering process. The affine transformation from the distortional image to the original shape is conducted, basing on seeking the normal coordinates and the relationships of conversion. Then the image processing and setting the ideal field for uniformity calculation are employed to analyze beam uniformity. The light intensity distribution of each wavelength on the board is normalized first and the light intensity fluctuation variance in Eq. (4) is used to obtain uniformity result of each wavelength in the set area. The is the normalized average intensity of the entire required field in each wavelength on the board.
As showed in Fig. 7, different integrated square areas from (a) to (e) are selected with corresponding beam divergence full angle equal to 5 (black line), 7 (red line), 9 (blue line), 11 (green line), 13 (pink line) degrees. The internally tangent circle area of each square equals to the light emitting from the end cap to the board in set divergence angles. With the increase of wavelength, decreases slowly. In the meantime, the uniformity of each beam profile varies for the better as the Gaussian fundamental mode optical field distribution concentrates with the decrease of wavelengths. Similarly, while the divergence angle rises from 5 to 13 degrees, descends evidently because of the selective filed enlarging.
Fig. 7 The gray-scale map of the set field corresponding different divergence angles (5, 7, 9, 11, 13 degrees) on the board from (a)-(e) and respective uniformity in different wavelengths.
Beam profile uniformity is the inherent characteristic of SC brought by the Gaussian profile of one wavelength and the Gaussian profiles’ distinction of different wavelengths, which is a considerable factor in many practical applications of far-field situation. The HSI method would provide a new idea of measurement for beam profile uniformity in different wavelengths and regions. Meanwhile, this method will be beneficial for the measurement of the further research field of beam shaping for SC.
4. Conclusion
In conclusion, HSI method is utilized to measure the divergence angles of SC, which serves as a crucial parameter for SC property representation. This method is much faster and more convenient than conventional ones, providing a new approach to address the previous problem that the measurement of divergence angles is merely performed at some wavelengths. The experimental results match well with theoretical value by simulation and calculation. Moreover, the optical intensity distribution of SC far-field beam and uniformity for different wavelengths are investigated through anatomizing image that is critical for SC practical application. To the best of our knowledge, it is the first time that HSI experimental method was employed to discuss SC beam property of far-field characteristic.
Funding
National Natural Science Foundation of China (NSFC) (61235008, 61405254, 61435009); National High Technology Research and Development Program of China (2015AA021101).
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