The offset between the center lines of the polished end-face and the fiber core has a significant effect on coupling efficiency. The initial contact point and the contact force are two of the most important parameters that induce the offset. This study proposes an image assistant method to find the initial contact point and a mathematical model to estimate the contact force when fabricating the double-variable-curvature end-face of single mode glass fiber. The repeatability of finding the initial contact point via the vision assistant program is 0.3
A microlens improves the mode match between the laser source and single mode fiber by fabricating the tip of the single mode fiber as the microlens to allow for a direct coupling. The offset between the fiber center line and the microlens significantly affects the coupling efficiency. The coupling efficiency will drop 50% if the offset is more than 0.6
The broken edge of the optical fiber will affect the offset if there is an angle between the normal of the broken edge and the center line of the optical fiber. The offset occurs when the material removal rate changes at a different spinning angle while the optical fiber is spinning. Normally, the initial contact point between the optical fiber and the lapping film is manually judged, and when a high material removal rate occurs it causes an undercut, which leads to the offset. The control of the contact force between the optical fiber and the lapping film affects the offset and profile of the end-face of the optical fiber at the same time. To improve coupling efficiency, the lens radius of the curvature on the vertical axis should be near 3
In this study, a mathematical model via the vision assistant method is presented. The determination of the original contact point will avoid an undercut, and the control of the contact force will keep a better profile on the end-face of the optical fiber.
Normally, the initial contact point between the optical fiber and the lapping film is manually determined. The optical fiber is slowly moved down toward the lapping film, and the initial contact point is determined when the operator finds the optical fiber is touching the turning lapping film and some chips are observed. However, this method needs skillful operators and the repeatability is not easy to control.
Tseng et al. [
The force sensing mechanism [
In the present study, the vision recognition method was used to help find the initial contact point between the optical fiber and the lapping film. From Figure The edge of the lapping film is not easy to observe in the image. The lapping film may not be perfectly horizontal. A reflection image of the optical fiber is shown in the image.
Photo of optical fiber and image of optical fiber.
Finding the initial contact point between the fiber and the lapping film requires finding the lapping film and the end point of the edge of the optical fiber. Once this is done, the initial contact point and the distance between the optical fiber and the lapping film can be determined as shown in Figure
As shown in Figure
Edges of optical fiber and reflection image.
There are two methods for finding the line of the lapping film: the two-point method and the angular bisector method. Both methods are described below.
From Figure
Lines
From (
Since the lapping film plays the role of a mirror, the slope of the lapping film should be equal to half of the sum of the slopes of lines
From (
Once the location of the lapping film is found, it is important to note if the lapping film is horizontal enough. If the lapping film is not perpendicular to the vertical displacement axis,
A line drawn through the edge of optical fiber
The coordinates of the edge points,
The polishing mechanism of the glass was widely discussed [
Since the Preston equation is derived from plate glass polishing, (
Since
From (
Free body diagram of the polishing process.
As Figure
According to the coordinate transformation method, the relation of the contact point between the
From (
From the large deflection of cantilever beam theory [
Large deflection of cantilever beam under concentrated load.
The deflection of the cantilever beam can be calculated as follows:
The displacement of the contact point in the
From (
The third generation optical fiber polishing machine, developed by the authors, was used to evaluate the result of the original contact point, as shown in Figure
Photo of the 3rd generation optical fiber polishing machine.
Photo of the front panel of the vision assistant program.
A repeatability comparison between the two-point method and the angular bisector method was made. Table
Repeatability between the two-point and angular bisector methods.
Diameter of optical fiber |
Distance between optical fiber and lapping film |
Distance between fiber image and lapping film |
||
---|---|---|---|---|
Two-point method | Average | 164.70 | 31.14 | 29.78 |
Standard deviation | 1.59 | 2.21 | 3.40 | |
Variation ratio |
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|
|
|
|
||||
Angular bisector method | Average | 156.01 | 23.06 | 23.06 |
Standard deviation | 0.49 | 0.39 | 0.39 | |
Variation ratio |
|
|
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An experiment was conducted for comparing the difference between manual judging and the vision assistant program. First, the lapping film was stuck on the turntable, which was then turned. Then, an optical fiber with cladding and core only was prepared, and the prepared optical fiber was put into a spinning axis. Finally, the optical fiber was moved downward until it touched the turning lapping film, judged either manually or using the vision assistant program. As Figure
SEM photos of the end-face of the optical fiber.
Manual judging
Vision assistant program
Since the contact force was only up to several grams, a low-friction measuring stand was developed, as shown in Figure
Contact force measuring stand.
CAD model
Photo
In addition to the experiments, a DEFORM simulation and mathematical model were used to compare the results. The parameters were set to fit the conditions of the optical fiber polishing process. The length of the optical fiber was 1800
Solving (
Dimensionless positions of neutral point and contact point.
The comparison of the experiment, simulation, and mathematical model for the
Comparison of simulation and mathematical model.
The errors of contact force
Slopes and errors of contact force
Tilt angle (degree) | Slope (experiment) | Slope (DEFORM simulation) | Slope (mathematical model) | Errors (exp-math)/math |
---|---|---|---|---|
30 | 0.6511 | 0.6541 | 0.6181 | 5.3% |
45 | 1.0134 | 1.035 | 0.9469 | 7.0% |
60 | 2.1349 | 2.235 | 1.9586 | 9.0% |
As shown in Figure
To improve coupling efficiency, the lens curvature radius in the major axis, Rlx, was set as 30
Offset between grinding end-face and center line of fiber core at 45° tilt angle.
In this study, the image assistant method was successfully applied to find the initial contact point and to estimate the contact force when fabricating the elliptical end-face of glass fiber. A vision assistant program was built to find the initial contact point to avoid the undercut and to reduce the offset between the fiber core and the end-face. Further, a mathematical model was developed to describe the relationship between the contact force and the displacement of the lapping film and to assist in determining the feed amount of the lapping film. The main results can be summarized as follows. The vision assistant program showed that the repeatability of the distance between the optical fiber and the lapping film was 0.39 pixels, which corresponds to 0.3 According to the mathematical model, the relationship between the contact force and the displacement of the lapping film, The horizontal axis offsets between the fiber core and end-face were successfully controlled within 0.15 to 0.35
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Science Council, Taiwan, under Contracts NSC 102-2221-E-230-005.